diff --git a/Mathlib/Algebra/BigOperators/Basic.lean b/Mathlib/Algebra/BigOperators/Basic.lean
index 452c55e29a58a..1bd95a0eef0ab 100644
--- a/Mathlib/Algebra/BigOperators/Basic.lean
+++ b/Mathlib/Algebra/BigOperators/Basic.lean
@@ -2111,8 +2111,7 @@ theorem finset_sum_eq_sup_iff_disjoint {β : Type _} {i : Finset β} {f : β →
     i.sum f = i.sup f ↔
       ∀ (x) (_ : x ∈ i) (y) (_ : y ∈ i), x ≠ y → Multiset.Disjoint (f x) (f y) := by
   induction' i using Finset.cons_induction_on with z i hz hr
-  ·
-    simp only [Finset.not_mem_empty, IsEmpty.forall_iff, imp_true_iff, Finset.sum_empty,
+  · simp only [Finset.not_mem_empty, IsEmpty.forall_iff, imp_true_iff, Finset.sum_empty,
       Finset.sup_empty, bot_eq_zero, eq_self_iff_true]
   · simp_rw [Finset.sum_cons hz, Finset.sup_cons, Finset.mem_cons, Multiset.sup_eq_union,
       forall_eq_or_imp, Ne.def, IsEmpty.forall_iff, true_and_iff,
diff --git a/Mathlib/Algebra/Category/MonCat/Adjunctions.lean b/Mathlib/Algebra/Category/MonCat/Adjunctions.lean
index 711926cff0cbf..b913ec0eb3fe8 100644
--- a/Mathlib/Algebra/Category/MonCat/Adjunctions.lean
+++ b/Mathlib/Algebra/Category/MonCat/Adjunctions.lean
@@ -62,8 +62,8 @@ def adjoinOneAdj : adjoinOne ⊣ forget₂ MonCat.{u} SemigroupCat.{u} :=
         simp only [Equiv.symm_symm, adjoinOne_map, coe_comp]
         simp_rw [WithOne.map]
         cases x
-        . rfl
-        . simp
+        · rfl
+        · simp
           rfl }
 #align adjoin_one_adj adjoinOneAdj
 #align adjoin_zero_adj adjoinZeroAdj
diff --git a/Mathlib/Algebra/Category/MonCat/Colimits.lean b/Mathlib/Algebra/Category/MonCat/Colimits.lean
index 3cd8eef8d7d62..f5669427b8414 100644
--- a/Mathlib/Algebra/Category/MonCat/Colimits.lean
+++ b/Mathlib/Algebra/Category/MonCat/Colimits.lean
@@ -227,17 +227,17 @@ def descFun (s : Cocone F) : ColimitType F → s.pt := by
   · intro x y r
     induction' r with _ _ _ _ h _ _ _ _ _ h₁ h₂ _ _ f x _ _ _ _ _ _ _ _ h _ _ _ _ h <;> try simp
     -- symm
-    . exact h.symm
+    · exact h.symm
     -- trans
-    . exact h₁.trans h₂
+    · exact h₁.trans h₂
     -- map
-    . exact s.w_apply f x
+    · exact s.w_apply f x
     -- mul_1
-    . rw [h]
+    · rw [h]
     -- mul_2
-    . rw [h]
+    · rw [h]
     -- mul_assoc
-    . rw [mul_assoc]
+    · rw [mul_assoc]
 set_option linter.uppercaseLean3 false in
 #align Mon.colimits.desc_fun MonCat.Colimits.descFun
 
@@ -261,12 +261,12 @@ def colimitIsColimit : IsColimit (colimitCocone F) where
     ext x
     induction' x using Quot.inductionOn with x
     induction' x with j x x y hx hy
-    . change _ = s.ι.app j _
+    · change _ = s.ι.app j _
       rw [← w j]
       rfl
-    . rw [quot_one, map_one]
+    · rw [quot_one, map_one]
       rfl
-    . rw [quot_mul, map_mul, hx, hy]
+    · rw [quot_mul, map_mul, hx, hy]
       dsimp [descMorphism, FunLike.coe, descFun]
       simp only [← quot_mul, descFunLift]
 set_option linter.uppercaseLean3 false in
diff --git a/Mathlib/Algebra/DirectLimit.lean b/Mathlib/Algebra/DirectLimit.lean
index 37c3a788bb219..1638a8b1b65c9 100644
--- a/Mathlib/Algebra/DirectLimit.lean
+++ b/Mathlib/Algebra/DirectLimit.lean
@@ -489,8 +489,7 @@ theorem of.zero_exact_aux2 {x : FreeCommRing (Σi, G i)} {s t} (hxs : IsSupporte
     f' j k hjk (lift (fun ix : s => f' ix.1.1 j (hj ix ix.2) ix.1.2) (restriction s x)) =
       lift (fun ix : t => f' ix.1.1 k (hk ix ix.2) ix.1.2) (restriction t x) := by
   refine' Subring.InClosure.recOn hxs _ _ _ _
-  ·
-    rw [(restriction _).map_one, (FreeCommRing.lift _).map_one, (f' j k hjk).map_one,
+  · rw [(restriction _).map_one, (FreeCommRing.lift _).map_one, (f' j k hjk).map_one,
       (restriction _).map_one, (FreeCommRing.lift _).map_one]
   · -- porting note: Lean 3 had `(FreeCommRing.lift _).map_neg` but I needed to replace it with
   -- `RingHom.map_neg` to get the rewrite to compile
diff --git a/Mathlib/Algebra/GCDMonoid/Finset.lean b/Mathlib/Algebra/GCDMonoid/Finset.lean
index e40b8ba2270ec..54c67e13a2f43 100644
--- a/Mathlib/Algebra/GCDMonoid/Finset.lean
+++ b/Mathlib/Algebra/GCDMonoid/Finset.lean
@@ -168,8 +168,7 @@ theorem dvd_gcd {a : α} : (∀ b ∈ s, a ∣ f b) → a ∣ s.gcd f :=
 theorem gcd_insert [DecidableEq β] {b : β} :
     (insert b s : Finset β).gcd f = GCDMonoid.gcd (f b) (s.gcd f) := by
   by_cases h : b ∈ s
-  ·
-    rw [insert_eq_of_mem h,
+  · rw [insert_eq_of_mem h,
       (gcd_eq_right_iff (f b) (s.gcd f) (Multiset.normalize_gcd (s.1.map f))).2 (gcd_dvd h)]
   apply fold_insert h
 #align finset.gcd_insert Finset.gcd_insert
diff --git a/Mathlib/Algebra/GroupPower/Order.lean b/Mathlib/Algebra/GroupPower/Order.lean
index 98219ab4e00c3..6a146e413cc15 100644
--- a/Mathlib/Algebra/GroupPower/Order.lean
+++ b/Mathlib/Algebra/GroupPower/Order.lean
@@ -403,10 +403,10 @@ theorem zero_pow_le_one : ∀ n : ℕ, (0 : R) ^ n ≤ 1
 theorem pow_add_pow_le (hx : 0 ≤ x) (hy : 0 ≤ y) (hn : n ≠ 0) : x ^ n + y ^ n ≤ (x + y) ^ n := by
   rcases Nat.exists_eq_succ_of_ne_zero hn with ⟨k, rfl⟩
   induction' k with k ih;
-  . have eqn : Nat.succ Nat.zero = 1 := rfl
+  · have eqn : Nat.succ Nat.zero = 1 := rfl
     rw [eqn]
     simp only [pow_one, le_refl]
-  . let n := k.succ
+  · let n := k.succ
     have h1 := add_nonneg (mul_nonneg hx (pow_nonneg hy n)) (mul_nonneg hy (pow_nonneg hx n))
     have h2 := add_nonneg hx hy
     calc
diff --git a/Mathlib/Algebra/Homology/Additive.lean b/Mathlib/Algebra/Homology/Additive.lean
index 07f2b6b4a0dee..67fcf47de0be1 100644
--- a/Mathlib/Algebra/Homology/Additive.lean
+++ b/Mathlib/Algebra/Homology/Additive.lean
@@ -359,12 +359,12 @@ def single₀MapHomologicalComplex (F : V ⥤ W) [F.Additive] :
               | _ + 1 => F.mapZeroObject.inv }
         hom_inv_id := by
           ext (_|_)
-          . simp
-          . exact IsZero.eq_of_src (IsZero.of_iso (isZero_zero _) F.mapZeroObject) _ _
+          · simp
+          · exact IsZero.eq_of_src (IsZero.of_iso (isZero_zero _) F.mapZeroObject) _ _
         inv_hom_id := by
           ext (_|_)
-          . simp
-          . exact IsZero.eq_of_src (isZero_zero _) _ _ })
+          · simp
+          · exact IsZero.eq_of_src (isZero_zero _) _ _ })
     fun f => by ext (_|_) <;> simp
 #align chain_complex.single₀_map_homological_complex ChainComplex.single₀MapHomologicalComplex
 
@@ -415,12 +415,12 @@ def single₀MapHomologicalComplex (F : V ⥤ W) [F.Additive] :
               | _ + 1 => F.mapZeroObject.inv }
         hom_inv_id := by
           ext (_|_)
-          . simp
-          . exact IsZero.eq_of_src (IsZero.of_iso (isZero_zero _) F.mapZeroObject) _ _
+          · simp
+          · exact IsZero.eq_of_src (IsZero.of_iso (isZero_zero _) F.mapZeroObject) _ _
         inv_hom_id := by
           ext (_|_)
-          . simp
-          . exact IsZero.eq_of_src (isZero_zero _) _ _ })
+          · simp
+          · exact IsZero.eq_of_src (isZero_zero _) _ _ })
     fun f => by ext (_|_) <;> simp
 #align cochain_complex.single₀_map_homological_complex CochainComplex.single₀MapHomologicalComplex
 
diff --git a/Mathlib/Algebra/Homology/HomologicalComplex.lean b/Mathlib/Algebra/Homology/HomologicalComplex.lean
index fa308422e79df..9e4c03777eb1a 100644
--- a/Mathlib/Algebra/Homology/HomologicalComplex.lean
+++ b/Mathlib/Algebra/Homology/HomologicalComplex.lean
@@ -75,7 +75,7 @@ theorem d_comp_d (C : HomologicalComplex V c) (i j k : ι) : C.d i j ≫ C.d j k
   by_cases hij : c.Rel i j
   · by_cases hjk : c.Rel j k
     · exact C.d_comp_d' i j k hij hjk
-    . rw [C.shape j k hjk, comp_zero]
+    · rw [C.shape j k hjk, comp_zero]
   · rw [C.shape i j hij, zero_comp]
 #align homological_complex.d_comp_d HomologicalComplex.d_comp_d
 
@@ -91,8 +91,8 @@ theorem ext {C₁ C₂ : HomologicalComplex V c} (h_X : C₁.X = C₂.X)
   simp only [mk.injEq, heq_eq_eq, true_and]
   ext i j
   by_cases hij: c.Rel i j
-  . simpa only [comp_id, id_comp, eqToHom_refl] using h_d i j hij
-  . rw [s₁ i j hij, s₂ i j hij]
+  · simpa only [comp_id, id_comp, eqToHom_refl] using h_d i j hij
+  · rw [s₁ i j hij, s₂ i j hij]
 #align homological_complex.ext HomologicalComplex.ext
 
 end HomologicalComplex
@@ -188,7 +188,7 @@ theorem Hom.comm {A B : HomologicalComplex V c} (f : A.Hom B) (i j : ι) :
     f.f i ≫ B.d i j = A.d i j ≫ f.f j := by
   by_cases hij : c.Rel i j
   · exact f.comm' i j hij
-  . rw [A.shape i j hij, B.shape i j hij, comp_zero, zero_comp]
+  · rw [A.shape i j hij, B.shape i j hij, comp_zero, zero_comp]
 #align homological_complex.hom.comm HomologicalComplex.Hom.comm
 
 instance (A B : HomologicalComplex V c) : Inhabited (Hom A B) :=
diff --git a/Mathlib/Algebra/Homology/Homotopy.lean b/Mathlib/Algebra/Homology/Homotopy.lean
index cb15060031e18..7f26205603302 100644
--- a/Mathlib/Algebra/Homology/Homotopy.lean
+++ b/Mathlib/Algebra/Homology/Homotopy.lean
@@ -122,7 +122,7 @@ theorem prevD_nat (C D : CochainComplex V ℕ) (i : ℕ) (f : ∀ i j, C.X i ⟶
   cases i
   · simp only [shape, CochainComplex.prev_nat_zero, ComplexShape.up_Rel, Nat.one_ne_zero,
       not_false_iff, comp_zero]
-  . congr <;> simp
+  · congr <;> simp
 #align prev_d_nat prevD_nat
 
 -- porting note: removed @[has_nonempty_instance]
@@ -555,16 +555,16 @@ def mkInductive : Homotopy e 0 where
     simp only [add_zero]
     refine' (mkInductiveAux₂ e zero comm_zero one comm_one succ i).2.2.trans _
     congr
-    . cases i
-      . dsimp [fromNext, mkInductiveAux₂]
+    · cases i
+      · dsimp [fromNext, mkInductiveAux₂]
         rw [dif_neg]
         simp only
-      . dsimp [fromNext]
+      · dsimp [fromNext]
         simp only [ChainComplex.next_nat_succ, dite_true]
         rw [mkInductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xNextIso]
         rw [Category.id_comp]
-    . dsimp [toPrev]
+    · dsimp [toPrev]
       erw [dif_pos, Category.comp_id]
       simp only [ChainComplex.prev]
 #align homotopy.mk_inductive Homotopy.mkInductive
@@ -680,16 +680,16 @@ def mkCoinductive : Homotopy e 0 where
     rw [add_comm]
     refine' (mkCoinductiveAux₂ e zero comm_zero one comm_one succ i).2.2.trans _
     congr
-    . cases i
-      . dsimp [toPrev, mkCoinductiveAux₂]
+    · cases i
+      · dsimp [toPrev, mkCoinductiveAux₂]
         rw [dif_neg]
         simp only
-      . dsimp [toPrev]
+      · dsimp [toPrev]
         simp only [CochainComplex.prev_nat_succ, dite_true]
         rw [mkCoinductiveAux₃ e zero comm_zero one comm_one succ]
         dsimp [xPrevIso]
         rw [Category.comp_id]
-    . dsimp [fromNext]
+    · dsimp [fromNext]
       erw [dif_pos, Category.id_comp]
       simp only [CochainComplex.next]
 #align homotopy.mk_coinductive Homotopy.mkCoinductive
diff --git a/Mathlib/Algebra/Homology/Single.lean b/Mathlib/Algebra/Homology/Single.lean
index db67869d17ac9..e91d23221f774 100644
--- a/Mathlib/Algebra/Homology/Single.lean
+++ b/Mathlib/Algebra/Homology/Single.lean
@@ -136,12 +136,12 @@ def single₀ : V ⥤ ChainComplex V ℕ where
         | n + 1 => 0 }
   map_id X := by
     ext (_|_)
-    . rfl
-    . simp
+    · rfl
+    · simp
   map_comp f g := by
     ext (_|_)
-    . rfl
-    . simp
+    · rfl
+    · simp
 #align chain_complex.single₀ ChainComplex.single₀
 
 @[simp]
@@ -239,10 +239,10 @@ def toSingle₀Equiv (C : ChainComplex V ℕ) (X : V) :
         | n + 1 => 0
       comm' := fun i j h => by
         rcases i with (_|_|i) <;> cases j <;> simp only [single₀_obj_X_d, comp_zero]
-        . rw [C.shape, zero_comp]
+        · rw [C.shape, zero_comp]
           simp
-        . exact f.2.symm
-        . rw [C.shape, zero_comp]
+        · exact f.2.symm
+        · rw [C.shape, zero_comp]
           exact i.succ_succ_ne_one.symm }
   left_inv f := by
     ext i
@@ -297,9 +297,9 @@ def single₀IsoSingle : single₀ V ≅ single V _ 0 :=
         hom_inv_id := to_single₀_ext _ _ (by simp)
         inv_hom_id := by
           ext (_|_)
-          . dsimp
+          · dsimp
             simp
-          . dsimp
+          · dsimp
             rw [Category.comp_id] })
     fun f => by ext (_|_) <;> aesop_cat
 #align chain_complex.single₀_iso_single ChainComplex.single₀IsoSingle
@@ -333,12 +333,12 @@ def single₀ : V ⥤ CochainComplex V ℕ where
         | n + 1 => 0 }
   map_id X := by
     ext (_|_)
-    . rfl
-    . simp
+    · rfl
+    · simp
   map_comp f g := by
     ext (_|_)
-    . rfl
-    . simp
+    · rfl
+    · simp
 #align cochain_complex.single₀ CochainComplex.single₀
 
 @[simp]
@@ -436,10 +436,10 @@ def fromSingle₀Equiv (C : CochainComplex V ℕ) (X : V) :
       comm' := fun i j h => by
         rcases f with ⟨f, hf⟩
         rcases j with (_|_|j) <;> cases i <;> simp only [single₀_obj_X_d, zero_comp]
-        . rw [C.shape, comp_zero]
+        · rw [C.shape, comp_zero]
           simp
-        . exact hf
-        . rw [C.shape, comp_zero]
+        · exact hf
+        · rw [C.shape, comp_zero]
           simp
           exact j.succ_succ_ne_one.symm }
   left_inv f := by
@@ -470,9 +470,9 @@ def single₀IsoSingle : single₀ V ≅ single V _ 0 :=
       hom_inv_id := from_single₀_ext _ _ (by simp)
       inv_hom_id := by
         ext (_|_)
-        . dsimp
+        · dsimp
           simp
-        . dsimp
+        · dsimp
           rw [Category.id_comp]
           rfl }
 #align cochain_complex.single₀_iso_single CochainComplex.single₀IsoSingle
diff --git a/Mathlib/Algebra/IndicatorFunction.lean b/Mathlib/Algebra/IndicatorFunction.lean
index 741628e7e1e98..42f5647fa786b 100644
--- a/Mathlib/Algebra/IndicatorFunction.lean
+++ b/Mathlib/Algebra/IndicatorFunction.lean
@@ -464,11 +464,9 @@ theorem mulIndicator_mul_compl_eq_piecewise [DecidablePred (· ∈ s)] (f g : α
     s.mulIndicator f * sᶜ.mulIndicator g = s.piecewise f g := by
   ext x
   by_cases h : x ∈ s
-  ·
-    rw [piecewise_eq_of_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_mem h,
+  · rw [piecewise_eq_of_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_mem h,
       Set.mulIndicator_of_not_mem (Set.not_mem_compl_iff.2 h), mul_one]
-  ·
-    rw [piecewise_eq_of_not_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_not_mem h,
+  · rw [piecewise_eq_of_not_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_not_mem h,
       Set.mulIndicator_of_mem (Set.mem_compl h), one_mul]
 #align set.mul_indicator_mul_compl_eq_piecewise Set.mulIndicator_mul_compl_eq_piecewise
 #align set.indicator_add_compl_eq_piecewise Set.indicator_add_compl_eq_piecewise
diff --git a/Mathlib/Algebra/Module/LinearMap.lean b/Mathlib/Algebra/Module/LinearMap.lean
index 3e05f3933bf1a..d968392ee17e9 100644
--- a/Mathlib/Algebra/Module/LinearMap.lean
+++ b/Mathlib/Algebra/Module/LinearMap.lean
@@ -373,8 +373,7 @@ theorem _root_.preimage_smul_setₛₗ [SemilinearMapClass F σ M M₃] {c : R}
   apply Set.Subset.antisymm
   · rintro x ⟨y, ys, hy⟩
     refine' ⟨(hc.unit.inv : R) • x, _, _⟩
-    ·
-      simp only [← hy, smul_smul, Set.mem_preimage, Units.inv_eq_val_inv, map_smulₛₗ h, ← map_mul,
+    · simp only [← hy, smul_smul, Set.mem_preimage, Units.inv_eq_val_inv, map_smulₛₗ h, ← map_mul,
         IsUnit.val_inv_mul, one_smul, map_one, ys]
     · simp only [smul_smul, IsUnit.mul_val_inv, one_smul, Units.inv_eq_val_inv]
   · rintro x ⟨y, hy, rfl⟩
diff --git a/Mathlib/Algebra/Order/Field/Basic.lean b/Mathlib/Algebra/Order/Field/Basic.lean
index 43627a128a539..bf975009fc558 100644
--- a/Mathlib/Algebra/Order/Field/Basic.lean
+++ b/Mathlib/Algebra/Order/Field/Basic.lean
@@ -237,8 +237,8 @@ theorem div_le_of_nonneg_of_le_mul (hb : 0 ≤ b) (hc : 0 ≤ c) (h : a ≤ c *
 /-- One direction of `div_le_iff` where `c` is allowed to be `0` (but `b` must be nonnegative) -/
 lemma mul_le_of_nonneg_of_le_div (hb : 0 ≤ b) (hc : 0 ≤ c) (h : a ≤ b / c) : a * c ≤ b := by
   obtain rfl | hc := hc.eq_or_lt
-  . simpa using hb
-  . rwa [le_div_iff hc] at h
+  · simpa using hb
+  · rwa [le_div_iff hc] at h
 #align mul_le_of_nonneg_of_le_div mul_le_of_nonneg_of_le_div
 
 theorem div_le_one_of_le (h : a ≤ b) (hb : 0 ≤ b) : a / b ≤ 1 :=
diff --git a/Mathlib/AlgebraicGeometry/AffineScheme.lean b/Mathlib/AlgebraicGeometry/AffineScheme.lean
index a9abf46e8ff60..5a8b6b4954355 100644
--- a/Mathlib/AlgebraicGeometry/AffineScheme.lean
+++ b/Mathlib/AlgebraicGeometry/AffineScheme.lean
@@ -273,7 +273,7 @@ theorem isAffineOpen_iff_of_isOpenImmersion {X Y : Scheme} (f : X ⟶ Y) [H : Is
     dsimp [Opens.inclusion]
     rw [ContinuousMap.coe_mk, ContinuousMap.coe_mk, Subtype.range_coe, Subtype.range_coe]
     rfl
-  . infer_instance
+  · infer_instance
 #align algebraic_geometry.is_affine_open_iff_of_is_open_immersion AlgebraicGeometry.isAffineOpen_iff_of_isOpenImmersion
 
 instance Scheme.quasi_compact_of_affine (X : Scheme) [IsAffine X] : CompactSpace X :=
@@ -349,7 +349,7 @@ theorem IsAffineOpen.basicOpenIsAffine {X : Scheme} {U : Opens X} (hU : IsAffine
     Scheme.Spec.map
       (CommRingCat.ofHom (algebraMap ((X.presheaf.obj <| op U)) (Localization.Away f))).op ≫
     hU.fromSpec
-  . exact PresheafedSpace.IsOpenImmersion.comp (hf := inferInstance) (hg := inferInstance)
+  · exact PresheafedSpace.IsOpenImmersion.comp (hf := inferInstance) (hg := inferInstance)
   convert
     rangeIsAffineOpenOfOpenImmersion
       (Scheme.Spec.map
@@ -406,7 +406,7 @@ theorem Scheme.map_PrimeSpectrum_basicOpen_of_affine (X : Scheme) [IsAffine X]
       ((Scheme.Spec.obj (op (Scheme.Γ.obj (op X)))).basicOpen
         ((inv (X.isoSpec.hom.1.c.app (op ((Opens.map (inv X.isoSpec.hom).val.base).obj ⊤))))
           ((X.presheaf.map (eqToHom <| by congr)) f)))
-  . congr
+  · congr
     · rw [← IsIso.inv_eq_inv, IsIso.inv_inv, IsIso.Iso.inv_inv, NatIso.app_hom]
       -- Porting note : added this `change` to prevent timeout
       change SpecΓIdentity.hom.app (X.presheaf.obj <| op ⊤) = _
diff --git a/Mathlib/AlgebraicGeometry/Limits.lean b/Mathlib/AlgebraicGeometry/Limits.lean
index 2329c2d84f1df..d9137b19f0659 100644
--- a/Mathlib/AlgebraicGeometry/Limits.lean
+++ b/Mathlib/AlgebraicGeometry/Limits.lean
@@ -106,7 +106,7 @@ instance (priority := 100) isIso_of_isEmpty {X Y : Scheme} (f : X ⟶ Y) [IsEmpt
     IsIso f := by
   haveI : IsEmpty X.carrier := ⟨fun x => isEmptyElim (show Y.carrier from f.1.base x)⟩
   have : Epi f.1.base
-  . rw [TopCat.epi_iff_surjective]; rintro (x : Y.carrier)
+  · rw [TopCat.epi_iff_surjective]; rintro (x : Y.carrier)
     exact isEmptyElim x
   apply IsOpenImmersion.to_iso
 #align algebraic_geometry.is_iso_of_is_empty AlgebraicGeometry.isIso_of_isEmpty
diff --git a/Mathlib/AlgebraicGeometry/LocallyRingedSpace/HasColimits.lean b/Mathlib/AlgebraicGeometry/LocallyRingedSpace/HasColimits.lean
index 6065e86cd9721..f7f820c4c5d91 100644
--- a/Mathlib/AlgebraicGeometry/LocallyRingedSpace/HasColimits.lean
+++ b/Mathlib/AlgebraicGeometry/LocallyRingedSpace/HasColimits.lean
@@ -299,7 +299,7 @@ noncomputable def coequalizerCoforkIsColimit : IsColimit (coequalizerCofork f g)
     set h := _
     change IsLocalRingHom h
     suffices : IsLocalRingHom ((PresheafedSpace.stalkMap (coequalizerCofork f g).π.1 _).comp h)
-    . apply isLocalRingHom_of_comp _ (PresheafedSpace.stalkMap (coequalizerCofork f g).π.1 _)
+    · apply isLocalRingHom_of_comp _ (PresheafedSpace.stalkMap (coequalizerCofork f g).π.1 _)
     change IsLocalRingHom (_ ≫ PresheafedSpace.stalkMap (coequalizerCofork f g).π.val y)
     erw [← PresheafedSpace.stalkMap.comp]
     apply isLocalRingHom_stalkMap_congr _ _ (coequalizer.π_desc s.π.1 e).symm y
@@ -331,7 +331,7 @@ noncomputable instance preservesCoequalizer :
     -- of colimit is provided later
     suffices : PreservesColimit (parallelPair (F.map WalkingParallelPairHom.left)
       (F.map WalkingParallelPairHom.right)) forgetToSheafedSpace
-    . apply preservesColimitOfIsoDiagram _ (diagramIsoParallelPair F).symm
+    · apply preservesColimitOfIsoDiagram _ (diagramIsoParallelPair F).symm
     apply preservesColimitOfPreservesColimitCocone (coequalizerCoforkIsColimit _ _)
     apply (isColimitMapCoconeCoforkEquiv _ _).symm _
     dsimp only [forgetToSheafedSpace]
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
index 3b5d952873043..9ac40cbcc776e 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/Basic.lean
@@ -324,8 +324,8 @@ theorem AffineTargetMorphismProperty.IsLocal.affine_openCover_iff {P : AffineTar
     targetAffineLocally P f ↔ ∀ i, @P _ _ (pullback.snd : pullback f (𝒰.map i) ⟶ _) (h𝒰 i) := by
   refine' ⟨fun H => let h := ((hP.affine_openCover_TFAE f).out 0 2).mp H; _,
     fun H => let h := ((hP.affine_openCover_TFAE f).out 1 0).mp; _⟩
-  . exact fun i => h 𝒰 i
-  . exact h ⟨𝒰, inferInstance, H⟩
+  · exact fun i => h 𝒰 i
+  · exact h ⟨𝒰, inferInstance, H⟩
 #align algebraic_geometry.affine_target_morphism_property.is_local.affine_open_cover_iff AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.affine_openCover_iff
 
 theorem AffineTargetMorphismProperty.IsLocal.affine_target_iff {P : AffineTargetMorphismProperty}
@@ -440,8 +440,8 @@ theorem PropertyIsLocalAtTarget.openCover_iff {P : MorphismProperty Scheme}
   -- Porting note : couldn't get the term mode proof work
   refine ⟨fun H => let h := ((hP.openCover_TFAE f).out 0 2).mp H; fun i => ?_,
     fun H => let h := ((hP.openCover_TFAE f).out 1 0).mp; ?_⟩
-  . exact h 𝒰 i
-  . exact h ⟨𝒰, H⟩
+  · exact h 𝒰 i
+  · exact h ⟨𝒰, H⟩
 #align algebraic_geometry.property_is_local_at_target.open_cover_iff AlgebraicGeometry.PropertyIsLocalAtTarget.openCover_iff
 
 namespace AffineTargetMorphismProperty
@@ -563,8 +563,8 @@ theorem AffineTargetMorphismProperty.diagonalOfTargetAffineLocally
   -- Porting note : added this instance
   haveI hg₁ : IsOpenImmersion g₁ := by
     apply (config := { allowSynthFailures := true }) Scheme.pullback_map_isOpenImmersion
-    . exact PresheafedSpace.IsOpenImmersion.comp (hf := hf₁) _
-    . exact PresheafedSpace.IsOpenImmersion.comp (hf := hf₂) _
+    · exact PresheafedSpace.IsOpenImmersion.comp (hf := hf₁) _
+    · exact PresheafedSpace.IsOpenImmersion.comp (hf := hf₂) _
   specialize H g₁
   rw [← affine_cancel_left_isIso hP.1 (pullbackDiagonalMapIso f _ f₁ f₂).hom]
   convert H
diff --git a/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean b/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
index 42a4cca290829..5395baf925ff8 100644
--- a/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
+++ b/Mathlib/AlgebraicGeometry/Morphisms/QuasiCompact.lean
@@ -326,7 +326,7 @@ theorem exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isCompact (X : Scheme
     convert congr_arg (X.presheaf.map (homOfLE _).op) H
     · simp only [← comp_apply, ← Functor.map_comp]
       rfl
-    . rw [map_zero]
+    · rw [map_zero]
       simp only [Scheme.basicOpen_res, ge_iff_le, inf_le_right]
   choose n hn using H'
   haveI := hs.to_subtype
diff --git a/Mathlib/AlgebraicGeometry/OpenImmersion/Basic.lean b/Mathlib/AlgebraicGeometry/OpenImmersion/Basic.lean
index 0efbc34a31429..c6c624cf32ba4 100644
--- a/Mathlib/AlgebraicGeometry/OpenImmersion/Basic.lean
+++ b/Mathlib/AlgebraicGeometry/OpenImmersion/Basic.lean
@@ -117,7 +117,7 @@ noncomputable def isoRestrict : X ≅ Y.restrict H.base_open :=
   PresheafedSpace.isoOfComponents (Iso.refl _) <| by
     symm
     fapply NatIso.ofComponents
-    . intro U
+    · intro U
       refine' asIso (f.c.app (op (H.openFunctor.obj (unop U)))) ≪≫ X.presheaf.mapIso (eqToIso _)
       · induction U using Opposite.rec' with | h U => ?_
         cases U
@@ -299,7 +299,7 @@ instance ofRestrict {X : TopCat} (Y : PresheafedSpace C) {f : X ⟶ Y.carrier}
       apply Subsingleton.helim
       rw [this]
       rfl
-    . infer_instance
+    · infer_instance
 #align algebraic_geometry.PresheafedSpace.is_open_immersion.of_restrict AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict
 
 @[elementwise, simp]
@@ -317,7 +317,7 @@ theorem to_iso (f : X ⟶ Y) [h : IsOpenImmersion f] [h' : Epi f.base] : IsIso f
   -- Porting Note : was `apply (config := { instances := False }) ...`
   -- See https://github.com/leanprover/lean4/issues/2273
   have : ∀ (U : (Opens Y)ᵒᵖ), IsIso (f.c.app U)
-  . intro U
+  · intro U
     have : U = op (h.openFunctor.obj ((Opens.map f.base).obj (unop U))) := by
       induction U using Opposite.rec' with | h U => ?_
       cases U
@@ -531,7 +531,7 @@ instance forgetPreservesLimitsOfLeft : PreservesLimit (cospan f g) (forget C) :=
       apply (IsLimit.postcomposeHomEquiv (diagramIsoCospan _) _).toFun
       refine' (IsLimit.equivIsoLimit _).toFun (limit.isLimit (cospan f.base g.base))
       fapply Cones.ext
-      . exact Iso.refl _
+      · exact Iso.refl _
       change ∀ j, _ = 𝟙 _ ≫ _ ≫ _
       simp_rw [Category.id_comp]
       rintro (_ | _ | _) <;> symm
@@ -728,7 +728,7 @@ instance forgetMapIsOpenImmersion : PresheafedSpace.IsOpenImmersion ((forget).ma
 
 instance hasLimit_cospan_forget_of_left : HasLimit (cospan f g ⋙ forget) := by
   have : HasLimit (cospan ((cospan f g ⋙ forget).map Hom.inl) ((cospan f g ⋙ forget).map Hom.inr))
-  . change HasLimit (cospan ((forget).map f) ((forget).map g))
+  · change HasLimit (cospan ((forget).map f) ((forget).map g))
     infer_instance
   apply hasLimitOfIso (diagramIsoCospan _).symm
 #align algebraic_geometry.SheafedSpace.is_open_immersion.has_limit_cospan_forget_of_left AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_left
@@ -740,7 +740,7 @@ instance hasLimit_cospan_forget_of_left' :
 
 instance hasLimit_cospan_forget_of_right : HasLimit (cospan g f ⋙ forget) := by
   have : HasLimit (cospan ((cospan g f ⋙ forget).map Hom.inl) ((cospan g f ⋙ forget).map Hom.inr))
-  . change HasLimit (cospan ((forget).map g) ((forget).map f))
+  · change HasLimit (cospan ((forget).map g) ((forget).map f))
     infer_instance
   apply hasLimitOfIso (diagramIsoCospan _).symm
 #align algebraic_geometry.SheafedSpace.is_open_immersion.has_limit_cospan_forget_of_right AlgebraicGeometry.SheafedSpace.IsOpenImmersion.hasLimit_cospan_forget_of_right
@@ -772,7 +772,7 @@ instance sheafedSpaceForgetPreservesOfLeft : PreservesLimit (cospan f g) (Sheafe
       have : PreservesLimit
         (cospan ((cospan f g ⋙ forget).map Hom.inl)
           ((cospan f g ⋙ forget).map Hom.inr)) (PresheafedSpace.forget C)
-      . dsimp
+      · dsimp
         infer_instance
       apply preservesLimitOfIsoDiagram _ (diagramIsoCospan _).symm
 #align algebraic_geometry.SheafedSpace.is_open_immersion.SheafedSpace_forget_preserves_of_left AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sheafedSpaceForgetPreservesOfLeft
@@ -1013,7 +1013,7 @@ def pullbackConeOfLeftIsLimit : IsLimit (pullbackConeOfLeft f g) :=
       rw [PresheafedSpace.stalkMap.comp, ← IsIso.eq_inv_comp] at this
       rw [this]
       infer_instance
-    . intro m _ h₂
+    · intro m _ h₂
       rw [← cancel_mono (pullbackConeOfLeft f g).snd]
       exact h₂.trans <| LocallyRingedSpace.Hom.ext _ _
         (PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftLift_snd f.1 g.1 <|
@@ -1084,10 +1084,10 @@ instance forgetToTopPreservesPullbackOfLeft :
         WalkingCospan.Hom.inl)
       ((cospan f g ⋙ forgetToSheafedSpace ⋙ SheafedSpace.forgetToPresheafedSpace).map
         WalkingCospan.Hom.inr)) (PresheafedSpace.forget CommRingCat)
-  . dsimp; infer_instance
+  · dsimp; infer_instance
   have : PreservesLimit (cospan f g ⋙ forgetToSheafedSpace ⋙ SheafedSpace.forgetToPresheafedSpace)
     (PresheafedSpace.forget CommRingCat)
-  . apply preservesLimitOfIsoDiagram _ (diagramIsoCospan _).symm
+  · apply preservesLimitOfIsoDiagram _ (diagramIsoCospan _).symm
   apply Limits.compPreservesLimit
 #align algebraic_geometry.LocallyRingedSpace.is_open_immersion.forget_to_Top_preserves_pullback_of_left AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.forgetToTopPreservesPullbackOfLeft
 
diff --git a/Mathlib/AlgebraicGeometry/OpenImmersion/Scheme.lean b/Mathlib/AlgebraicGeometry/OpenImmersion/Scheme.lean
index 1e50056d38cb1..b920cac10acf1 100644
--- a/Mathlib/AlgebraicGeometry/OpenImmersion/Scheme.lean
+++ b/Mathlib/AlgebraicGeometry/OpenImmersion/Scheme.lean
@@ -58,7 +58,7 @@ protected def scheme (X : LocallyRingedSpace)
     skip
     apply PresheafedSpace.IsOpenImmersion.isoOfRangeEq (PresheafedSpace.ofRestrict _ _) f.1
     · exact Subtype.range_coe_subtype
-    . exact Opens.openEmbedding _ -- Porting note : was `infer_instance`
+    · exact Opens.openEmbedding _ -- Porting note : was `infer_instance`
 #align algebraic_geometry.LocallyRingedSpace.IsOpenImmersion.Scheme AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.scheme
 
 end LocallyRingedSpace.IsOpenImmersion
@@ -215,8 +215,8 @@ instance basic_open_isOpenImmersion {R : CommRingCat} (f : R) :
     AlgebraicGeometry.IsOpenImmersion
       (Scheme.Spec.map (CommRingCat.ofHom (algebraMap R (Localization.Away f))).op) := by
   apply SheafedSpace.IsOpenImmersion.of_stalk_iso (H := ?_)
-  . exact (PrimeSpectrum.localization_away_openEmbedding (Localization.Away f) f : _)
-  . intro x
+  · exact (PrimeSpectrum.localization_away_openEmbedding (Localization.Away f) f : _)
+  · intro x
     exact Spec_map_localization_isIso R (Submonoid.powers f) x
 #align algebraic_geometry.Scheme.basic_open_IsOpenImmersion AlgebraicGeometry.Scheme.basic_open_isOpenImmersion
 
@@ -538,7 +538,7 @@ instance forgetToTopPreservesOfLeft : PreservesLimit (cospan f g) Scheme.forgetT
   delta Scheme.forgetToTop
   apply @Limits.compPreservesLimit (K := cospan f g) (F := forget)
     (G := LocallyRingedSpace.forgetToTop) ?_ ?_
-  . infer_instance
+  · infer_instance
   apply @preservesLimitOfIsoDiagram (F := _) _ _ _ _ _ _ (diagramIsoCospan.{u} _).symm ?_
   dsimp [LocallyRingedSpace.forgetToTop]
   infer_instance
@@ -1030,7 +1030,7 @@ theorem morphismRestrict_c_app {X Y : Scheme} (f : X ⟶ Y) (U : Opens Y) (V : O
     ext1; exact Set.preimage_image_eq _ Subtype.coe_injective
   have : _ ≫ X.presheaf.map _ = _ :=
     (((f ∣_ U).1.c.naturality (eqToHom e).op).symm.trans ?_).trans this
-  . rw [← IsIso.eq_comp_inv, ← Functor.map_inv, Category.assoc] at this
+  · rw [← IsIso.eq_comp_inv, ← Functor.map_inv, Category.assoc] at this
     rw [this]
     congr 1
     erw [← X.presheaf.map_comp, ← X.presheaf.map_comp]
@@ -1092,10 +1092,10 @@ def morphismRestrictRestrict {X Y : Scheme} (f : X ⟶ Y) (U : Opens Y) (V : Ope
         ((Category.comp_id _).trans (Category.id_comp _).symm) (by aesop_cat) ≫
       (pullbackRightPullbackFstIso _ _ _).hom ≫ (pullbackSymmetry _ _).hom
   have i3 : IsIso h
-  . repeat
+  · repeat
       apply (config := { allowSynthFailures := true }) IsIso.comp_isIso
   have : (f ∣_ U ∣_ V) ≫ (Iso.refl _).hom = (asIso h).hom ≫ pullback.snd (f := f) (g := g)
-  . simp only [Category.comp_id, pullbackRightPullbackFstIso_hom_fst, Iso.refl_hom,
+  · simp only [Category.comp_id, pullbackRightPullbackFstIso_hom_fst, Iso.refl_hom,
       Category.assoc, pullbackSymmetry_hom_comp_snd, asIso_hom, pullback.lift_fst,
       pullbackSymmetry_hom_comp_fst]
     rfl
@@ -1152,7 +1152,7 @@ def morphismRestrictStalkMap {X Y : Scheme} (f : X ⟶ Y) (U : Opens Y) (x) :
     erw [PresheafedSpace.stalkMap_germ _ (U.openEmbedding.isOpenMap.functor.obj V)
       ⟨x.1, ⟨⟨f.1.base x.1, x.2⟩, _, rfl⟩⟩]
     swap
-    . rw [morphismRestrict_val_base] at hxV
+    · rw [morphismRestrict_val_base] at hxV
       exact hxV
     erw [PresheafedSpace.restrictStalkIso_hom_eq_germ]
     rw [morphismRestrict_c_app, Category.assoc, TopCat.Presheaf.germ_res]
diff --git a/Mathlib/AlgebraicGeometry/PresheafedSpace.lean b/Mathlib/AlgebraicGeometry/PresheafedSpace.lean
index fa2f0039bedd6..e3a3f797873c5 100644
--- a/Mathlib/AlgebraicGeometry/PresheafedSpace.lean
+++ b/Mathlib/AlgebraicGeometry/PresheafedSpace.lean
@@ -178,7 +178,7 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
   id_comp _ := by
     dsimp
     ext
-    . dsimp
+    · dsimp
       simp only [map_id, whiskerRight_id', assoc]
       erw [comp_id, comp_id]
     · dsimp
@@ -392,7 +392,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     simp only [PresheafedSpace.comp_base, PresheafedSpace.ofRestrict_base] at this
     rw [cancel_mono] at this
     exact this
-  . ext V
+  · ext V
     have hV : (Opens.map (X.ofRestrict hf).base).obj (hf.isOpenMap.functor.obj V) = V := by
       ext1
       exact Set.preimage_image_eq _ hf.inj
diff --git a/Mathlib/AlgebraicGeometry/Pullbacks.lean b/Mathlib/AlgebraicGeometry/Pullbacks.lean
index 07be759c433d2..65e16d38c87e3 100644
--- a/Mathlib/AlgebraicGeometry/Pullbacks.lean
+++ b/Mathlib/AlgebraicGeometry/Pullbacks.lean
@@ -675,7 +675,7 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
     rfl
   · simp only [Category.comp_id, Category.id_comp]
   -- Porting note : this `IsIso` instance was `inferInstance`
-  . apply IsIso.comp_isIso
+  · apply IsIso.comp_isIso
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base' AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'
 
 /-- Given an open cover `{ Zᵢ }` of `Z`, then `X ×[Z] Y` is covered by `Xᵢ ×[Zᵢ] Yᵢ`, where
@@ -695,7 +695,7 @@ def openCoverOfBase (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover
   -- Porting note : deviated from original proof a bit so that it won't timeout.
   rw [Iso.refl_hom, Category.id_comp, openCoverOfBase'_map]
   apply pullback.hom_ext <;> dsimp <;>
-  . simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.assoc,
+  · simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.assoc,
       limit.lift_π_assoc, cospan_left, Category.comp_id, limit.isoLimitCone_inv_π,
       limit.isoLimitCone_inv_π_assoc, pullbackSymmetry_hom_comp_fst_assoc,
       pullbackSymmetry_hom_comp_snd_assoc]
diff --git a/Mathlib/AlgebraicGeometry/RingedSpace.lean b/Mathlib/AlgebraicGeometry/RingedSpace.lean
index 79d204ecca2ce..7fb952e86cce0 100644
--- a/Mathlib/AlgebraicGeometry/RingedSpace.lean
+++ b/Mathlib/AlgebraicGeometry/RingedSpace.lean
@@ -69,7 +69,7 @@ theorem isUnit_res_of_isUnit_germ (U : Opens X) (f : X.presheaf.obj (op U)) (x :
   -- desired form
   replace heq : (X.presheaf.germ ⟨x.val, hxW⟩) ((X.presheaf.map (U.infLELeft V).op) f *
     (X.presheaf.map (U.infLERight V).op) g) = (X.presheaf.germ ⟨x.val, hxW⟩) 1
-  . dsimp [germ]
+  · dsimp [germ]
     erw [map_mul, map_one, show X.presheaf.germ ⟨x, hxW⟩ ((X.presheaf.map (U.infLELeft V).op) f) =
       X.presheaf.germ x f from X.presheaf.germ_res_apply (Opens.infLELeft U V) ⟨x.1, hxW⟩ f,
       show X.presheaf.germ ⟨x, hxW⟩ (X.presheaf.map (U.infLERight V).op g) =
@@ -89,7 +89,7 @@ theorem isUnit_of_isUnit_germ (U : Opens X) (f : X.presheaf.obj (op U))
   -- We pick a cover of `U` by open sets `V x`, such that `f` is a unit on each `V x`.
   choose V iVU m h_unit using fun x : U => X.isUnit_res_of_isUnit_germ U f x (h x)
   have hcover : U ≤ iSup V
-  . intro x hxU
+  · intro x hxU
     -- Porting note : in Lean3 `rw` is sufficient
     erw [Opens.mem_iSup]
     exact ⟨⟨x, hxU⟩, m ⟨x, hxU⟩⟩
diff --git a/Mathlib/AlgebraicGeometry/Scheme.lean b/Mathlib/AlgebraicGeometry/Scheme.lean
index fbf9064cafeb0..5604a12d905a7 100644
--- a/Mathlib/AlgebraicGeometry/Scheme.lean
+++ b/Mathlib/AlgebraicGeometry/Scheme.lean
@@ -302,9 +302,9 @@ theorem mem_basicOpen (x : U) : ↑x ∈ X.basicOpen f ↔ IsUnit (X.presheaf.ge
 theorem mem_basicOpen_top' {U : Opens X} (f : X.presheaf.obj (op U)) (x : X.carrier) :
     x ∈ X.basicOpen f ↔ ∃ (m : x ∈ U), IsUnit (X.presheaf.germ (⟨x, m⟩ : U) f) := by
   fconstructor
-  . rintro ⟨y, hy1, rfl⟩
+  · rintro ⟨y, hy1, rfl⟩
     exact ⟨y.2, hy1⟩
-  . rintro ⟨m, hm⟩
+  · rintro ⟨m, hm⟩
     exact ⟨⟨x, m⟩, hm, rfl⟩
 
 @[simp]
diff --git a/Mathlib/AlgebraicGeometry/Spec.lean b/Mathlib/AlgebraicGeometry/Spec.lean
index 3cd4e6c573db2..ecd551980707c 100644
--- a/Mathlib/AlgebraicGeometry/Spec.lean
+++ b/Mathlib/AlgebraicGeometry/Spec.lean
@@ -420,7 +420,7 @@ theorem isLocalizedModule_toPushforwardStalkAlgHom_aux (y) :
           ⟨p, hpr⟩ _).trans e
   set s' := (Spec.topMap (algebraMap R S) _* (structureSheaf S).1).map (homOfLE hrU).op s with h
   replace e : ((Spec.topMap (algebraMap R S) _* (structureSheaf S).val).germ ⟨p, hpr⟩) s' = y
-  . rw [h]; exact e
+  · rw [h]; exact e
   clear_value s'; clear! U
   obtain ⟨⟨s, ⟨_, n, rfl⟩⟩, hsn⟩ :=
     @IsLocalization.surj _ _ _ _ _ _
diff --git a/Mathlib/AlgebraicGeometry/StructureSheaf.lean b/Mathlib/AlgebraicGeometry/StructureSheaf.lean
index 2868b3eb814e2..8048924b3ca59 100644
--- a/Mathlib/AlgebraicGeometry/StructureSheaf.lean
+++ b/Mathlib/AlgebraicGeometry/StructureSheaf.lean
@@ -854,7 +854,7 @@ theorem toBasicOpen_surjective (f : R) : Function.Surjective (toBasicOpen R f) :
   rw [← SetLike.coe_subset_coe, Opens.coe_iSup] at ht_cover
   replace ht_cover : (PrimeSpectrum.basicOpen f : Set <| PrimeSpectrum R) ⊆
     ⋃ (i : ι) (x : i ∈ t), (PrimeSpectrum.basicOpen (h i) : Set _)
-  . convert ht_cover using 2
+  · convert ht_cover using 2
     exact funext fun j => by rw [Opens.coe_iSup]
   -- Next we show that some power of `f` is a linear combination of the `h i`
   obtain ⟨n, hn⟩ : f ∈ (Ideal.span (h '' ↑t)).radical := by
@@ -862,9 +862,9 @@ theorem toBasicOpen_surjective (f : R) : Function.Surjective (toBasicOpen R f) :
     -- Porting note : simp with `PrimeSpectrum.basicOpen_eq_zeroLocus_compl` does not work
     replace ht_cover : (PrimeSpectrum.zeroLocus {f})ᶜ ⊆
       ⋃ (i : ι) (x : i ∈ t), (PrimeSpectrum.zeroLocus {h i})ᶜ
-    . convert ht_cover
-      . rw [PrimeSpectrum.basicOpen_eq_zeroLocus_compl]
-      . simp only [Opens.iSup_mk, Opens.carrier_eq_coe, PrimeSpectrum.basicOpen_eq_zeroLocus_compl]
+    · convert ht_cover
+      · rw [PrimeSpectrum.basicOpen_eq_zeroLocus_compl]
+      · simp only [Opens.iSup_mk, Opens.carrier_eq_coe, PrimeSpectrum.basicOpen_eq_zeroLocus_compl]
     rw [Set.compl_subset_comm] at ht_cover
     -- Why doesn't `simp_rw` do this?
     simp_rw [Set.compl_iUnion, compl_compl, ← PrimeSpectrum.zeroLocus_iUnion,
diff --git a/Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean b/Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean
index 45b06f4ba9a3b..0e16638251b37 100644
--- a/Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean
+++ b/Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean
@@ -98,9 +98,9 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     dsimp
     simp only [zsmul_comp, comp_zsmul, smul_smul, ← neg_smul]
     congr 1
-    . simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
+    · simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
       apply mul_comm
-    . rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
+    · rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
       simpa using hij
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
@@ -112,11 +112,11 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
     refine' ⟨(j'.pred _, Fin.castSucc i'), _, _⟩
-    . rintro rfl
+    · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
-    . simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
+    · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
         Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
-    . simp only [Fin.castLT_castSucc, Fin.succ_pred]
+    · simp only [Fin.castLT_castSucc, Fin.succ_pred]
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!
@@ -264,7 +264,7 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
   simp only [AlternatingFaceMapComplex.objD, comp_sum]
   rw [Fin.sum_univ_succ, Fintype.sum_eq_zero]
   swap
-  . intro j
+  · intro j
     rw [NormalizedMooreComplex.objX, comp_zsmul,
       ← factorThru_arrow _ _ (finset_inf_arrow_factors Finset.univ _ _ (Finset.mem_univ j)),
       Category.assoc, kernelSubobject_arrow_comp, comp_zero, smul_zero]
diff --git a/Mathlib/AlgebraicTopology/CechNerve.lean b/Mathlib/AlgebraicTopology/CechNerve.lean
index 525db5815b113..b2975f9fe50ce 100644
--- a/Mathlib/AlgebraicTopology/CechNerve.lean
+++ b/Mathlib/AlgebraicTopology/CechNerve.lean
@@ -138,10 +138,10 @@ def equivalenceLeftToRight (X : SimplicialObject.Augmented C) (F : Arrow C)
         intro x y f
         dsimp
         ext
-        . dsimp
+        · dsimp
           simp only [WidePullback.lift_π, Category.assoc, ← X.left.map_comp_assoc]
           rfl
-        . dsimp
+        · dsimp
           simp }
   right := G.right
 #align category_theory.simplicial_object.equivalence_left_to_right CategoryTheory.SimplicialObject.equivalenceLeftToRight
@@ -173,11 +173,11 @@ def cechNerveEquiv (X : SimplicialObject.Augmented C) (F : Arrow C) :
     dsimp
     ext x : 2
     · refine' WidePullback.hom_ext _ _ _ (fun j => _) _
-      . dsimp
+      · dsimp
         simp
         rfl
-      . simpa using congr_app A.w.symm x
-    . rfl
+      · simpa using congr_app A.w.symm x
+    · rfl
 #align category_theory.simplicial_object.cech_nerve_equiv CategoryTheory.SimplicialObject.cechNerveEquiv
 
 /-- The augmented Čech nerve construction is right adjoint to the `toArrow` functor. -/
@@ -314,14 +314,14 @@ def cechConerveEquiv (F : Arrow C) (X : CosimplicialObject.Augmented C) :
     intro A
     dsimp
     ext x : 2
-    . rfl
-    . refine' WidePushout.hom_ext _ _ _ (fun j => _) _
-      . dsimp
+    · rfl
+    · refine' WidePushout.hom_ext _ _ _ (fun j => _) _
+      · dsimp
         simp only [Category.assoc, ← NatTrans.naturality A.right, Arrow.augmentedCechConerve_right,
           SimplexCategory.len_mk, Arrow.cechConerve_map, colimit.ι_desc,
           WidePushoutShape.mkCocone_ι_app, colimit.ι_desc_assoc]
         rfl
-      . dsimp
+      · dsimp
         rw [colimit.ι_desc]
         exact congr_app A.w x
   right_inv := by
diff --git a/Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean b/Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean
index c5e8499498cae..e42a52cac3e78 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean
@@ -75,7 +75,7 @@ theorem decomposition_Q (n q : ℕ) :
         simp only [Fin.val_mk, (HigherFacesVanish.of_P q n).comp_Hσ_eq hnaq',
           q'.rev_eq hnaq', neg_neg]
         rfl
-      . ext ⟨i, hi⟩
+      · ext ⟨i, hi⟩
         simp only [Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
           forall_true_left, Finset.mem_filter, lt_self_iff_false, or_true, and_self, not_true,
           Finset.mem_erase, ne_eq, Fin.mk.injEq, true_and]
@@ -121,7 +121,7 @@ theorem id_φ : (id X n).φ = 𝟙 _ := by
   simp only [← P_add_Q_f (n + 1) (n + 1), φ]
   congr 1
   · simp only [id, PInfty_f, P_f_idem]
-  . exact Eq.trans (by congr ; simp) (decomposition_Q n (n + 1)).symm
+  · exact Eq.trans (by congr ; simp) (decomposition_Q n (n + 1)).symm
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ
 
 variable {X n}
diff --git a/Mathlib/AlgebraicTopology/DoldKan/Faces.lean b/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
index 1e3e038b23136..8d3b81c70a451 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/Faces.lean
@@ -94,21 +94,21 @@ theorem comp_Hσ_eq {Y : C} {n a q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFac
   swap
   · rintro ⟨k, hk⟩
     rw [assoc, X.δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
-    . simp only [Fin.lt_iff_val_lt_val]
+    · simp only [Fin.lt_iff_val_lt_val]
       dsimp [Fin.natAdd, Fin.cast]
       linarith
-    . intro h
+    · intro h
       rw [Fin.pred_eq_iff_eq_succ, Fin.ext_iff] at h
       dsimp [Fin.cast] at h
       linarith
-    . dsimp [Fin.cast, Fin.pred]
+    · dsimp [Fin.cast, Fin.pred]
       rw [Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
       linarith
   simp only [assoc]
   conv_lhs =>
     congr
-    . rw [Fin.sum_univ_castSucc]
-    . rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc]
   dsimp [Fin.cast, Fin.castLE, Fin.castLT]
   /- the purpose of the following `simplif` is to create three subgoals in order
       to finish the proof -/
@@ -159,13 +159,13 @@ theorem comp_Hσ_eq_zero {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : Higher
     · intro j
       dsimp [Fin.cast, Fin.castLE, Fin.castLT]
       rw [comp_zsmul, comp_zsmul, δ_comp_σ_of_gt', v.comp_δ_eq_zero_assoc, zero_comp, zsmul_zero]
-      . simp only [Fin.lt_iff_val_lt_val]
+      · simp only [Fin.lt_iff_val_lt_val]
         dsimp [Fin.succ]
         linarith
-      . intro h
+      · intro h
         simp only [Fin.pred, Fin.ext_iff, Nat.pred_eq_sub_one, Nat.succ_add_sub_one, Fin.val_zero,
           add_eq_zero, false_and] at h
-      . simp only [Fin.pred, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
+      · simp only [Fin.pred, Nat.pred_eq_sub_one, Nat.succ_add_sub_one]
         linarith
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_Hσ_eq_zero AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero
diff --git a/Mathlib/AlgebraicTopology/DoldKan/HomotopyEquivalence.lean b/Mathlib/AlgebraicTopology/DoldKan/HomotopyEquivalence.lean
index 6b7f764f33d1a..b36555aa7d399 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/HomotopyEquivalence.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/HomotopyEquivalence.lean
@@ -71,7 +71,7 @@ def homotopyPInftyToId : Homotopy (PInfty : K[X] ⟶ _) (𝟙 _) where
   zero i j hij := Homotopy.zero _ i j hij
   comm n := by
     rcases n with _|n
-    . simpa only [Homotopy.dNext_zero_chainComplex, Homotopy.prevD_chainComplex,
+    · simpa only [Homotopy.dNext_zero_chainComplex, Homotopy.prevD_chainComplex,
         PInfty_f, Nat.zero_eq, P_f_0_eq, zero_add] using (homotopyPToId X 2).comm 0
     · -- Porting note: this branch had been:
       -- simpa only [Homotopy.dNext_succ_chainComplex, Homotopy.prevD_chainComplex,
diff --git a/Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean b/Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean
index d750ba10006ed..65c41cad5ede4 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean
@@ -67,7 +67,7 @@ theorem PInfty_comp_map_mono_eq_zero (X : SimplicialObject C) {n : ℕ} {Δ' : S
         dsimp at h'
         linarith
     by_cases hj₁ : j₁ = 0
-    . subst hj₁
+    · subst hj₁
       rw [assoc, ← SimplexCategory.δ_comp_δ'' (Fin.zero_le _)]
       simp only [op_comp, X.map_comp, assoc, PInfty_f]
       erw [(HigherFacesVanish.of_P _ _).comp_δ_eq_zero_assoc _ j₂.succ_ne_zero, zero_comp]
diff --git a/Mathlib/AlgebraicTopology/DoldKan/NReflectsIso.lean b/Mathlib/AlgebraicTopology/DoldKan/NReflectsIso.lean
index ba9be12b5dee3..b9c69b49e2369 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/NReflectsIso.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/NReflectsIso.lean
@@ -76,7 +76,7 @@ theorem compatibility_N₂_N₁_karoubi :
     · ext n
       · dsimp
         simp only [karoubi_PInfty_f, comp_id, PInfty_f_naturality, id_comp, eqToHom_refl]
-      . rfl
+      · rfl
     · rintro _ n (rfl : n + 1 = _)
       ext
       have h := (AlternatingFaceMapComplex.map P.p).comm (n + 1) n
diff --git a/Mathlib/AlgebraicTopology/DoldKan/Projections.lean b/Mathlib/AlgebraicTopology/DoldKan/Projections.lean
index 2cbe83468235f..d63e2fdcbbc9b 100644
--- a/Mathlib/AlgebraicTopology/DoldKan/Projections.lean
+++ b/Mathlib/AlgebraicTopology/DoldKan/Projections.lean
@@ -129,7 +129,7 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
       comp_id, ← assoc, hq v.of_succ, add_right_eq_self]
     by_cases hqn : n < q
     · exact v.of_succ.comp_Hσ_eq_zero hqn
-    . obtain ⟨a, ha⟩ := Nat.le.dest (not_lt.mp hqn)
+    · obtain ⟨a, ha⟩ := Nat.le.dest (not_lt.mp hqn)
       have hnaq : n = a + q := by linarith
       simp only [v.of_succ.comp_Hσ_eq hnaq, neg_eq_zero, ← assoc]
       have eq := v ⟨a, by linarith⟩ (by
diff --git a/Mathlib/AlgebraicTopology/ExtraDegeneracy.lean b/Mathlib/AlgebraicTopology/ExtraDegeneracy.lean
index c068e12a9ea02..63b5a8becf3da 100644
--- a/Mathlib/AlgebraicTopology/ExtraDegeneracy.lean
+++ b/Mathlib/AlgebraicTopology/ExtraDegeneracy.lean
@@ -218,9 +218,9 @@ protected noncomputable def extraDegeneracy (Δ : SimplexCategory) :
     ext j : 2
     dsimp [SimplicialObject.δ, SimplexCategory.δ, SSet.standardSimplex]
     by_cases j = 0
-    . subst h
+    · subst h
       simp only [Fin.succ_succAbove_zero, shiftFun_0]
-    . obtain ⟨_, rfl⟩ := Fin.eq_succ_of_ne_zero h
+    · obtain ⟨_, rfl⟩ := Fin.eq_succ_of_ne_zero h
       simp only [Fin.succ_succAbove_succ, shiftFun_succ, Function.comp_apply]
   s_comp_σ n i := by
     ext1 φ
@@ -399,7 +399,7 @@ noncomputable def homotopyEquiv {C : Type _} [Category C] [Preadditive C] [HasZe
         · simp only [eq_self_iff_true]
       comm := fun i => by
         rcases i with _|i
-        . rw [Homotopy.prevD_chainComplex, Homotopy.dNext_zero_chainComplex, zero_add]
+        · rw [Homotopy.prevD_chainComplex, Homotopy.dNext_zero_chainComplex, zero_add]
           dsimp [ChainComplex.fromSingle₀Equiv, ChainComplex.toSingle₀Equiv]
           simp only [comp_id, ite_true, zero_add, ComplexShape.down_Rel, not_true,
             AlternatingFaceMapComplex.obj_d_eq, Preadditive.neg_comp]
diff --git a/Mathlib/AlgebraicTopology/MooreComplex.lean b/Mathlib/AlgebraicTopology/MooreComplex.lean
index dc568a1d77e92..c7d6f016d1137 100644
--- a/Mathlib/AlgebraicTopology/MooreComplex.lean
+++ b/Mathlib/AlgebraicTopology/MooreComplex.lean
@@ -95,11 +95,11 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
   -- It's a pity we need to do a case split here;
     -- after the first erw the proofs are almost identical
   rcases n with _ | n <;> dsimp [objD]
-  . erw [Subobject.factorThru_arrow_assoc, Category.assoc,
+  · erw [Subobject.factorThru_arrow_assoc, Category.assoc,
       ← X.δ_comp_δ_assoc (Fin.zero_le (0 : Fin 2)),
       ← factorThru_arrow _ _ (finset_inf_arrow_factors Finset.univ _ (0 : Fin 2) (by simp)),
       Category.assoc, kernelSubobject_arrow_comp_assoc, zero_comp, comp_zero]
-  . erw [factorThru_right, factorThru_eq_zero, factorThru_arrow_assoc, Category.assoc,
+  · erw [factorThru_right, factorThru_eq_zero, factorThru_arrow_assoc, Category.assoc,
       ← X.δ_comp_δ (Fin.zero_le (0 : Fin (n + 3))),
       ← factorThru_arrow _ _ (finset_inf_arrow_factors Finset.univ _ (0 : Fin (n + 3)) (by simp)),
       Category.assoc, kernelSubobject_arrow_comp_assoc, zero_comp, comp_zero]
diff --git a/Mathlib/AlgebraicTopology/SimplexCategory.lean b/Mathlib/AlgebraicTopology/SimplexCategory.lean
index 66cdc8c7bdea8..f027fe1200ba9 100644
--- a/Mathlib/AlgebraicTopology/SimplexCategory.lean
+++ b/Mathlib/AlgebraicTopology/SimplexCategory.lean
@@ -408,9 +408,9 @@ instance : EssSurj skeletalFunctor.{v} where
           rw [← hf.le_iff_le]
           show f (f.symm i) ≤ f (f.symm j)
           simpa only [OrderIso.apply_symm_apply]
-        . ext1 ⟨i⟩
+        · ext1 ⟨i⟩
           exact congr_arg ULift.up (f.symm_apply_apply i)
-        . ext1 i
+        · ext1 i
           exact f.apply_symm_apply i⟩⟩
 
 noncomputable instance isEquivalence : IsEquivalence skeletalFunctor.{v} :=
@@ -525,7 +525,7 @@ instance {n : ℕ} {i : Fin (n + 1)} : Epi (σ i) := by
   intro b
   simp only [σ, mkHom, Hom.toOrderHom_mk, OrderHom.coe_fun_mk]
   by_cases b ≤ i
-  . use b
+  · use b
     rw [Fin.predAbove_below i b (by simpa only [Fin.coe_eq_castSucc] using h)]
     simp only [len_mk, Fin.coe_eq_castSucc, Fin.castPred_castSucc]
   · use b.succ
diff --git a/Mathlib/AlgebraicTopology/TopologicalSimplex.lean b/Mathlib/AlgebraicTopology/TopologicalSimplex.lean
index 1f775f3b88841..acb9a82a3ec08 100644
--- a/Mathlib/AlgebraicTopology/TopologicalSimplex.lean
+++ b/Mathlib/AlgebraicTopology/TopologicalSimplex.lean
@@ -60,7 +60,7 @@ def toTopMap {x y : SimplexCategory} (f : x ⟶ y) : x.toTopObj → y.toTopObj :
     dsimp [toTopObj] at hg
     convert hg
     · simp [Finset.eq_univ_iff_forall]
-    . intro i _ j _ h
+    · intro i _ j _ h
       rw [Function.onFun, disjoint_iff_inf_le]
       intro e he
       simp only [Finset.bot_eq_empty, Finset.not_mem_empty]
@@ -107,10 +107,10 @@ def toTop : SimplexCategory ⥤ TopCat where
     rw [CategoryTheory.comp_apply, ContinuousMap.coe_mk, ContinuousMap.coe_mk, ContinuousMap.coe_mk]
     simp only [coe_toTopMap]
     erw [← Finset.sum_biUnion]
-    . apply Finset.sum_congr
-      . exact Finset.ext (fun j => ⟨fun hj => by simpa using hj, fun hj => by simpa using hj⟩)
-      . tauto
-    . intro j _ k _ h
+    · apply Finset.sum_congr
+      · exact Finset.ext (fun j => ⟨fun hj => by simpa using hj, fun hj => by simpa using hj⟩)
+      · tauto
+    · intro j _ k _ h
       rw [Function.onFun, disjoint_iff_inf_le]
       intro e he
       simp only [Finset.bot_eq_empty, Finset.not_mem_empty]
diff --git a/Mathlib/Analysis/Convex/Segment.lean b/Mathlib/Analysis/Convex/Segment.lean
index f39c97a087895..72290e5fdfe7f 100644
--- a/Mathlib/Analysis/Convex/Segment.lean
+++ b/Mathlib/Analysis/Convex/Segment.lean
@@ -495,8 +495,7 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] := by
   rw [← sub_pos] at h
   refine' ⟨(y - z) / (y - x), (z - x) / (y - x), div_nonneg hyz h.le, div_nonneg hxz h.le, _, _⟩
   · rw [← add_div, sub_add_sub_cancel, div_self h.ne']
-  ·
-    rw [smul_eq_mul, smul_eq_mul, ← mul_div_right_comm, ← mul_div_right_comm, ← add_div,
+  · rw [smul_eq_mul, smul_eq_mul, ← mul_div_right_comm, ← mul_div_right_comm, ← add_div,
       div_eq_iff h.ne', add_comm, sub_mul, sub_mul, mul_comm x, sub_add_sub_cancel, mul_sub]
 #align Icc_subset_segment Icc_subset_segment
 
diff --git a/Mathlib/Analysis/Convex/StoneSeparation.lean b/Mathlib/Analysis/Convex/StoneSeparation.lean
index c6bbcd0dad29c..25c40d9221305 100644
--- a/Mathlib/Analysis/Convex/StoneSeparation.lean
+++ b/Mathlib/Analysis/Convex/StoneSeparation.lean
@@ -65,7 +65,7 @@ theorem not_disjoint_segment_convexHull_triple {p q u v x y z : E} (hz : z ∈ s
       · exact mul_nonneg hau hav
     have hw : ∑ i, w i = az * av + bz * au := by
       trans az * av * bu + (bz * au * bv + au * av)
-      . simp [Fin.sum_univ_succ, Fin.sum_univ_zero]
+      · simp [Fin.sum_univ_succ, Fin.sum_univ_zero]
       rw [← one_mul (au * av), ← habz, add_mul, ← add_assoc, add_add_add_comm, mul_assoc, ← mul_add,
         mul_assoc, ← mul_add, mul_comm av, ← add_mul, ← mul_add, add_comm bu, add_comm bv, habu,
         habv, one_mul, mul_one]
diff --git a/Mathlib/Analysis/LocallyConvex/Basic.lean b/Mathlib/Analysis/LocallyConvex/Basic.lean
index 6298fec0749a8..a23d470d8f6df 100644
--- a/Mathlib/Analysis/LocallyConvex/Basic.lean
+++ b/Mathlib/Analysis/LocallyConvex/Basic.lean
@@ -100,8 +100,7 @@ theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
     induction' t using Finset.induction_on with i t _ht hi
-    ·
-      simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
+    · simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
         IsEmpty.forall_iff, imp_true_iff]
     rw [Finset.set_biUnion_insert, absorbs_union, hi]
     constructor <;> intro h
diff --git a/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean b/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
index 35e3a22942899..dbf3b9d70df72 100644
--- a/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
+++ b/Mathlib/Analysis/LocallyConvex/WithSeminorms.lean
@@ -692,9 +692,9 @@ lemma bound_of_continuous_normedSpace (q : Seminorm 𝕜 F)
   have : 0 < ‖c‖ / ε := by positivity
   refine ⟨‖c‖ / ε, this, fun x ↦ ?_⟩
   by_cases hx : ‖x‖ = 0
-  . rw [hx, mul_zero]
+  · rw [hx, mul_zero]
     exact le_of_eq (map_eq_zero_of_norm_zero q hq hx)
-  . refine (normSeminorm 𝕜 F).bound_of_shell q ε_pos hc (fun x hle hlt ↦ ?_) hx
+  · refine (normSeminorm 𝕜 F).bound_of_shell q ε_pos hc (fun x hle hlt ↦ ?_) hx
     refine (le_of_lt <| show q x < _ from hε hlt).trans ?_
     rwa [← div_le_iff' this, one_div_div]
 
diff --git a/Mathlib/Analysis/Normed/Ring/Seminorm.lean b/Mathlib/Analysis/Normed/Ring/Seminorm.lean
index c2ebae282008a..08c0fb1116121 100644
--- a/Mathlib/Analysis/Normed/Ring/Seminorm.lean
+++ b/Mathlib/Analysis/Normed/Ring/Seminorm.lean
@@ -129,8 +129,7 @@ instance [DecidableEq R] : One (RingSeminorm R) :=
   ⟨{ (1 : AddGroupSeminorm R) with
       mul_le' := fun x y => by
         by_cases h : x * y = 0
-        ·
-          refine' (if_pos h).trans_le (mul_nonneg _ _) <;>
+        · refine' (if_pos h).trans_le (mul_nonneg _ _) <;>
             · change _ ≤ ite _ _ _
               split_ifs
               exacts [le_rfl, zero_le_one]
diff --git a/Mathlib/Analysis/NormedSpace/lpSpace.lean b/Mathlib/Analysis/NormedSpace/lpSpace.lean
index fe3361d3ccf97..a775b21e424d4 100644
--- a/Mathlib/Analysis/NormedSpace/lpSpace.lean
+++ b/Mathlib/Analysis/NormedSpace/lpSpace.lean
@@ -1236,8 +1236,8 @@ lemma LipschitzWith.uniformly_bounded [PseudoMetricSpace α] (g : α → ι →
     _ ≤ |g a i - g a₀ i| + |g a₀ i| := abs_add _ _
     _ ≤ ↑K * dist a a₀ + M := by
         gcongr
-        . exact lipschitzWith_iff_dist_le_mul.1 (hg i) a a₀
-        . exact hM ⟨i, rfl⟩
+        · exact lipschitzWith_iff_dist_le_mul.1 (hg i) a a₀
+        · exact hM ⟨i, rfl⟩
 
 theorem LipschitzOnWith.coordinate [PseudoMetricSpace α] (f : α → ℓ^∞(ι)) (s : Set α) (K : ℝ≥0) :
     LipschitzOnWith K f s ↔ ∀ i : ι, LipschitzOnWith K (fun a : α ↦ f a i) s := by
diff --git a/Mathlib/Analysis/Seminorm.lean b/Mathlib/Analysis/Seminorm.lean
index a2b3edfb3f9dd..69149ddc26f4b 100644
--- a/Mathlib/Analysis/Seminorm.lean
+++ b/Mathlib/Analysis/Seminorm.lean
@@ -408,8 +408,8 @@ theorem exists_apply_eq_finset_sup (p : ι → Seminorm 𝕜 E) {s : Finset ι}
 theorem zero_or_exists_apply_eq_finset_sup (p : ι → Seminorm 𝕜 E) (s : Finset ι) (x : E) :
     s.sup p x = 0 ∨ ∃ i ∈ s, s.sup p x = p i x := by
   rcases Finset.eq_empty_or_nonempty s with (rfl|hs)
-  . left; rfl
-  . right; exact exists_apply_eq_finset_sup p hs x
+  · left; rfl
+  · right; exact exists_apply_eq_finset_sup p hs x
 
 theorem finset_sup_smul (p : ι → Seminorm 𝕜 E) (s : Finset ι) (C : ℝ≥0) :
     s.sup (C • p) = C • s.sup p := by
@@ -1226,17 +1226,17 @@ lemma rescale_to_shell_zpow (p : Seminorm 𝕜 E) {c : 𝕜} (hc : 1 < ‖c‖)
   have cpos : 0 < ‖c‖ := lt_trans (zero_lt_one : (0 :ℝ) < 1) hc
   have cnpos : 0 < ‖c^(n+1)‖ := by rw [norm_zpow]; exact lt_trans xεpos hn.2
   refine ⟨-(n+1), ?_, ?_, ?_, ?_⟩
-  . show c ^ (-(n + 1)) ≠ 0; exact zpow_ne_zero _ (norm_pos_iff.1 cpos)
-  . show p ((c ^ (-(n + 1))) • x) < ε
+  · show c ^ (-(n + 1)) ≠ 0; exact zpow_ne_zero _ (norm_pos_iff.1 cpos)
+  · show p ((c ^ (-(n + 1))) • x) < ε
     rw [map_smul_eq_mul, zpow_neg, norm_inv, ← div_eq_inv_mul, div_lt_iff cnpos, mul_comm,
         norm_zpow]
     exact (div_lt_iff εpos).1 (hn.2)
-  . show ε / ‖c‖ ≤ p (c ^ (-(n + 1)) • x)
+  · show ε / ‖c‖ ≤ p (c ^ (-(n + 1)) • x)
     rw [zpow_neg, div_le_iff cpos, map_smul_eq_mul, norm_inv, norm_zpow, zpow_add₀ (ne_of_gt cpos),
         zpow_one, mul_inv_rev, mul_comm, ← mul_assoc, ← mul_assoc, mul_inv_cancel (ne_of_gt cpos),
         one_mul, ← div_eq_inv_mul, le_div_iff (zpow_pos_of_pos cpos _), mul_comm]
     exact (le_div_iff εpos).1 hn.1
-  . show ‖(c ^ (-(n + 1)))‖⁻¹ ≤ ε⁻¹ * ‖c‖ * p x
+  · show ‖(c ^ (-(n + 1)))‖⁻¹ ≤ ε⁻¹ * ‖c‖ * p x
     have : ε⁻¹ * ‖c‖ * p x = ε⁻¹ * p x * ‖c‖ := by ring
     rw [zpow_neg, norm_inv, inv_inv, norm_zpow, zpow_add₀ (ne_of_gt cpos), zpow_one, this,
         ← div_eq_inv_mul]
diff --git a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
index 1814b8a618f4d..fb33c0fd4293b 100644
--- a/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
+++ b/Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
@@ -73,8 +73,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem abs_eq_one_iff (z : ℂ) : abs z = 1 ↔ ∃ θ : ℝ, exp (θ * I) = z := by
   refine' ⟨fun hz => ⟨arg z, _⟩, _⟩
-  ·
-    calc
+  · calc
       exp (arg z * I) = abs z * exp (arg z * I) := by rw [hz, ofReal_one, one_mul]
       _ = z := abs_mul_exp_arg_mul_I z
 
@@ -385,8 +384,7 @@ theorem arg_neg_eq_arg_add_pi_of_im_neg {x : ℂ} (hi : x.im < 0) : arg (-x) = a
 theorem arg_neg_eq_arg_sub_pi_iff {x : ℂ} :
     arg (-x) = arg x - π ↔ 0 < x.im ∨ x.im = 0 ∧ x.re < 0 := by
   rcases lt_trichotomy x.im 0 with (hi | hi | hi)
-  ·
-    simp [hi, hi.ne, hi.not_lt, arg_neg_eq_arg_add_pi_of_im_neg, sub_eq_add_neg, ←
+  · simp [hi, hi.ne, hi.not_lt, arg_neg_eq_arg_add_pi_of_im_neg, sub_eq_add_neg, ←
       add_eq_zero_iff_eq_neg, Real.pi_ne_zero]
   · rw [(ext rfl hi : x = x.re)]
     rcases lt_trichotomy x.re 0 with (hr | hr | hr)
@@ -409,8 +407,7 @@ theorem arg_neg_eq_arg_add_pi_iff {x : ℂ} :
     · simp [hr, hi, Real.pi_ne_zero.symm]
     · rw [arg_ofReal_of_nonneg hr.le, ← ofReal_neg, arg_ofReal_of_neg (Left.neg_neg_iff.2 hr)]
       simp [hr]
-  ·
-    simp [hi, hi.ne.symm, hi.not_lt, arg_neg_eq_arg_sub_pi_of_im_pos, sub_eq_add_neg, ←
+  · simp [hi, hi.ne.symm, hi.not_lt, arg_neg_eq_arg_sub_pi_of_im_pos, sub_eq_add_neg, ←
       add_eq_zero_iff_neg_eq, Real.pi_ne_zero]
 #align complex.arg_neg_eq_arg_add_pi_iff Complex.arg_neg_eq_arg_add_pi_iff
 
diff --git a/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean b/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
index cb091e3d8c29d..d3ca012fd82c8 100644
--- a/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
+++ b/Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean
@@ -216,8 +216,8 @@ def Adjunction.restrictFullyFaithful (iC : C ⥤ C') (iD : D ⥤ D') {L' : C' 
       homEquiv_naturality_right := fun {X Y' Y} f g => by
         apply iC.map_injective
         suffices : R'.map (iD.map g) ≫ comm2.hom.app Y = comm2.hom.app Y' ≫ iC.map (R.map g)
-        . simp [Trans.trans, this]
-        . apply comm2.hom.naturality g }
+        · simp [Trans.trans, this]
+        · apply comm2.hom.naturality g }
 #align category_theory.adjunction.restrict_fully_faithful CategoryTheory.Adjunction.restrictFullyFaithful
 
 end CategoryTheory
diff --git a/Mathlib/CategoryTheory/Category/Cat/Limit.lean b/Mathlib/CategoryTheory/Category/Cat/Limit.lean
index 81340e40df1bf..8cccb2361ce88 100644
--- a/Mathlib/CategoryTheory/Category/Cat/Limit.lean
+++ b/Mathlib/CategoryTheory/Category/Cat/Limit.lean
@@ -145,11 +145,11 @@ def limitConeIsLimit (F : J ⥤ Cat.{v, v}) : IsLimit (limitCone F) where
   uniq s m w := by
     symm
     refine' CategoryTheory.Functor.ext _ _
-    . intro X
+    · intro X
       apply Types.limit_ext.{v, v}
       intro j
       simp [Types.Limit.lift_π_apply', ← w j]
-    . intro X Y f
+    · intro X Y f
       dsimp
       simp [fun j => Functor.congr_hom (w j).symm f]
 set_option linter.uppercaseLean3 false in
diff --git a/Mathlib/CategoryTheory/Category/PartialFun.lean b/Mathlib/CategoryTheory/Category/PartialFun.lean
index 1dad8bc69c50b..004bec6ea7e57 100644
--- a/Mathlib/CategoryTheory/Category/PartialFun.lean
+++ b/Mathlib/CategoryTheory/Category/PartialFun.lean
@@ -108,9 +108,9 @@ def pointedToPartialFun : Pointed.{u} ⥤ PartialFun where
     apply PFun.ext _
     rintro ⟨a, ha⟩ ⟨c, hc⟩
     constructor
-    . rintro ⟨h₁, h₂⟩
+    · rintro ⟨h₁, h₂⟩
       exact ⟨⟨fun h₀ => h₁ ((congr_arg g.toFun h₀).trans g.map_point), h₁⟩, h₂⟩
-    . rintro ⟨_, _, _⟩
+    · rintro ⟨_, _, _⟩
       exact ⟨_, rfl⟩
 #align Pointed_to_PartialFun pointedToPartialFun
 
@@ -152,12 +152,12 @@ noncomputable def partialFunEquivPointed : PartialFun.{u} ≌ Pointed :=
           refine' (Part.mem_bind_iff.trans _).trans PFun.mem_toSubtype_iff.symm
           obtain ⟨b | b, hb⟩ := b
           · exact (hb rfl).elim
-          . dsimp [Part.toOption]
+          · dsimp [Part.toOption]
             simp_rw [Part.mem_some_iff, Subtype.mk_eq_mk]
             constructor
-            . rintro ⟨_, ⟨h₁, h₂⟩, h₃⟩
+            · rintro ⟨_, ⟨h₁, h₂⟩, h₃⟩
               rw [h₃, ← h₂, dif_pos h₁]
-            . intro h
+            · intro h
               split_ifs at h with ha
               rw [some_inj] at h
               refine' ⟨b, ⟨ha, h.symm⟩, rfl⟩)
@@ -173,9 +173,9 @@ noncomputable def partialFunEquivPointed : PartialFun.{u} ≌ Pointed :=
         right_inv := fun a => by
           dsimp
           split_ifs with h
-          . rw [h]
+          · rw [h]
             rfl
-          . rfl} rfl)
+          · rfl} rfl)
       fun {X Y} f =>
       Pointed.Hom.ext _ _ <|
         funext fun a =>
@@ -187,8 +187,8 @@ noncomputable def partialFunEquivPointed : PartialFun.{u} ≌ Pointed :=
             -- conflicting `Decidable` instances
             rw [Option.elim'_eq_elim, @Part.elim_toOption _ _ _ (Classical.propDecidable _)]
             split_ifs with h
-            . rfl
-            . exact Eq.symm (of_not_not h)))
+            · rfl
+            · exact Eq.symm (of_not_not h)))
 #align PartialFun_equiv_Pointed partialFunEquivPointed
 
 /-- Forgetting that maps are total and making them total again by adding a point is the same as just
diff --git a/Mathlib/CategoryTheory/Category/Pointed.lean b/Mathlib/CategoryTheory/Category/Pointed.lean
index ce72c2f7be2ed..005ad1cf7109f 100644
--- a/Mathlib/CategoryTheory/Category/Pointed.lean
+++ b/Mathlib/CategoryTheory/Category/Pointed.lean
@@ -144,8 +144,8 @@ def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
             apply Pointed.Hom.ext
             funext x
             cases x
-            . exact f.map_point.symm
-            . rfl
+            · exact f.map_point.symm
+            · rfl
           right_inv := fun f => funext fun _ => rfl }
       homEquiv_naturality_left_symm := fun f g => by
         apply Pointed.Hom.ext
diff --git a/Mathlib/CategoryTheory/Extensive.lean b/Mathlib/CategoryTheory/Extensive.lean
index 571041ccc90eb..f57052ff5b31c 100644
--- a/Mathlib/CategoryTheory/Extensive.lean
+++ b/Mathlib/CategoryTheory/Extensive.lean
@@ -442,8 +442,8 @@ noncomputable def finitaryExtensiveTopCatAux (Z : TopCat.{u})
     ext ⟨⟨x, ⟨⟩⟩, (hx : f x = Sum.inl PUnit.unit)⟩
     change dite _ _ _ = _
     split_ifs with h
-    . rfl
-    . cases (h hx) -- Porting note : in Lean3 it is `rfl`
+    · rfl
+    · cases (h hx) -- Porting note : in Lean3 it is `rfl`
   · intro s
     ext ⟨⟨x, ⟨⟩⟩, hx⟩
     change dite _ _ _ = _
diff --git a/Mathlib/CategoryTheory/Filtered.lean b/Mathlib/CategoryTheory/Filtered.lean
index 02e51be43296a..035724588ed9d 100644
--- a/Mathlib/CategoryTheory/Filtered.lean
+++ b/Mathlib/CategoryTheory/Filtered.lean
@@ -240,8 +240,8 @@ variable [IsFiltered C]
 theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (X ⟶ S) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  . exact ⟨Classical.choice IsFiltered.Nonempty, by intro; simp⟩
-  . obtain ⟨S', w'⟩ := h
+  · exact ⟨Classical.choice IsFiltered.Nonempty, by intro; simp⟩
+  · obtain ⟨S', w'⟩ := h
     use max X S'
     rintro Y mY
     obtain rfl | h := eq_or_ne Y X
@@ -278,9 +278,9 @@ theorem sup_exists :
       · rw [@w' _ _ mX mY f']
         simp only [Finset.mem_insert, PSigma.mk.injEq, heq_eq_eq, true_and] at mf'
         rcases mf' with mf' | mf'
-        . exfalso
+        · exfalso
           exact hf mf'.symm
-        . exact mf'
+        · exact mf'
     · rw [@w' _ _ mX' mY' f' _]
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h
@@ -684,8 +684,8 @@ variable [IsCofiltered C]
 theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (S ⟶ X) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  . exact ⟨Classical.choice IsCofiltered.Nonempty, by intro; simp⟩
-  . obtain ⟨S', w'⟩ := h
+  · exact ⟨Classical.choice IsCofiltered.Nonempty, by intro; simp⟩
+  · obtain ⟨S', w'⟩ := h
     use min X S'
     rintro Y mY
     obtain rfl | h := eq_or_ne Y X
@@ -722,9 +722,9 @@ theorem inf_exists :
       · rw [@w' _ _ mX mY f']
         simp only [Finset.mem_insert, PSigma.mk.injEq, heq_eq_eq, true_and] at mf'
         rcases mf' with mf' | mf'
-        . exfalso
+        · exfalso
           exact hf mf'.symm
-        . exact mf'
+        · exact mf'
     · rw [@w' _ _ mX' mY' f' _]
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h
diff --git a/Mathlib/CategoryTheory/Functor/LeftDerived.lean b/Mathlib/CategoryTheory/Functor/LeftDerived.lean
index 36bc6ffd516d8..0ee9051b0c217 100644
--- a/Mathlib/CategoryTheory/Functor/LeftDerived.lean
+++ b/Mathlib/CategoryTheory/Functor/LeftDerived.lean
@@ -123,8 +123,8 @@ theorem Functor.leftDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y : C
   apply HomotopyCategory.eq_of_homotopy
   apply Functor.mapHomotopy
   apply ProjectiveResolution.liftHomotopy f
-  . simp
-  . simp [w]
+  · simp
+  · simp [w]
 #align category_theory.functor.left_derived_map_eq CategoryTheory.Functor.leftDerived_map_eq
 
 /-- The natural transformation between left-derived functors induced by a natural transformation. -/
diff --git a/Mathlib/CategoryTheory/Idempotents/Biproducts.lean b/Mathlib/CategoryTheory/Idempotents/Biproducts.lean
index f32dfe4853f5a..f5b43a7263222 100644
--- a/Mathlib/CategoryTheory/Idempotents/Biproducts.lean
+++ b/Mathlib/CategoryTheory/Idempotents/Biproducts.lean
@@ -64,10 +64,10 @@ def bicone [HasFiniteBiproducts C] {J : Type} [Finite J] (F : J → Karoubi C) :
       comm := by simp only [biproduct.ι_map, assoc, idem_assoc] }
   ι_π j j' := by
     split_ifs with h
-    . subst h
+    · subst h
       simp only [biproduct.ι_map, biproduct.bicone_π, biproduct.map_π, eqToHom_refl,
         id_eq, hom_ext_iff, comp_f, assoc, bicone_ι_π_self_assoc, idem]
-    . dsimp
+    · dsimp
       simp only [hom_ext_iff, biproduct.ι_map, biproduct.map_π, comp_f, assoc, ne_eq,
         biproduct.ι_π_ne_assoc  _ h, comp_zero, zero_comp]
 #align category_theory.idempotents.karoubi.biproducts.bicone CategoryTheory.Idempotents.Karoubi.Biproducts.bicone
@@ -84,10 +84,10 @@ theorem karoubi_hasFiniteBiproducts [HasFiniteBiproducts C] : HasFiniteBiproduct
             biproduct.bicone_π, biproduct.map_π, Biproducts.bicone_ι_f, biproduct.ι_map, assoc,
             idem_assoc, id_eq, Biproducts.bicone_pt_p, comp_sum]
           rw [Finset.sum_eq_single j]
-          . simp only [bicone_ι_π_self_assoc]
-          . intro b _ hb
+          · simp only [bicone_ι_π_self_assoc]
+          · intro b _ hb
             simp only [biproduct.ι_π_ne_assoc _ hb.symm, zero_comp]
-          . intro hj
+          · intro hj
             simp only [Finset.mem_univ, not_true] at hj } }
 #align category_theory.idempotents.karoubi.karoubi_has_finite_biproducts CategoryTheory.Idempotents.Karoubi.karoubi_hasFiniteBiproducts
 
@@ -132,13 +132,13 @@ def decomposition (P : Karoubi C) : P ⊞ P.complement ≅ (toKaroubi _).obj P.X
   inv := biprod.lift P.decompId_p P.complement.decompId_p
   hom_inv_id := by
     apply biprod.hom_ext'
-    . rw [biprod.inl_desc_assoc, comp_id, biprod.lift_eq, comp_add, ← decompId_assoc,
+    · rw [biprod.inl_desc_assoc, comp_id, biprod.lift_eq, comp_add, ← decompId_assoc,
         add_right_eq_self, ← assoc]
       refine' (_ =≫ _).trans zero_comp
       ext
       simp only [comp_f, toKaroubi_obj_X, decompId_i_f, decompId_p_f,
         complement_p, comp_sub, comp_id, idem, sub_self, instAddCommGroupHom_zero]
-    . rw [biprod.inr_desc_assoc, comp_id, biprod.lift_eq, comp_add, ← decompId_assoc,
+    · rw [biprod.inr_desc_assoc, comp_id, biprod.lift_eq, comp_add, ← decompId_assoc,
         add_left_eq_self, ← assoc]
       refine' (_ =≫ _).trans zero_comp
       ext
diff --git a/Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean b/Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean
index 64a7aa516ed38..02abed2353210 100644
--- a/Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean
+++ b/Mathlib/CategoryTheory/Idempotents/FunctorCategories.lean
@@ -82,11 +82,11 @@ instance functor_category_isIdempotentComplete [IsIdempotentComplete C] :
       naturality := fun j j' φ => equalizer.hom_ext (by simp) }
   use Y, i, e
   constructor
-  . ext j
+  · ext j
     apply equalizer.hom_ext
     dsimp
     rw [assoc, equalizer.lift_ι, ← equalizer.condition, id_comp, comp_id]
-  . ext j
+  · ext j
     simp
 namespace KaroubiFunctorCategoryEmbedding
 
diff --git a/Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean b/Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean
index fdf61ecbc1233..d455feb607472 100644
--- a/Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean
+++ b/Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean
@@ -121,8 +121,8 @@ theorem functorExtension₁_comp_whiskeringLeft_toKaroubi :
     refine' Functor.ext _ _
     · intro X
       ext
-      . simp
-      . simp
+      · simp
+      · simp
     · aesop_cat
   · intro F G φ
     aesop_cat
@@ -194,8 +194,8 @@ theorem functorExtension₁_comp (F : C ⥤ Karoubi D) (G : D ⥤ Karoubi E) :
     (functorExtension₁ C E).obj (F ⋙ (functorExtension₁ D E).obj G) =
       (functorExtension₁ C D).obj F ⋙ (functorExtension₁ D E).obj G := by
   refine' Functor.ext _ _
-  . aesop_cat
-  . intro X Y f
+  · aesop_cat
+  · intro X Y f
     ext
     simp only [eqToHom_refl, id_comp, comp_id]
     rfl
diff --git a/Mathlib/CategoryTheory/Limits/Bicones.lean b/Mathlib/CategoryTheory/Limits/Bicones.lean
index 9dcac4ffe1068..21650e207bbfd 100644
--- a/Mathlib/CategoryTheory/Limits/Bicones.lean
+++ b/Mathlib/CategoryTheory/Limits/Bicones.lean
@@ -84,13 +84,13 @@ instance biconeCategoryStruct : CategoryStruct (Bicone J)
   id j := Bicone.casesOn j BiconeHom.left_id BiconeHom.right_id fun k => BiconeHom.diagram (𝟙 k)
   comp f g := by
     rcases f with (_ | _ | _ | _ | f)
-    . exact g
-    . exact g
-    . cases g
+    · exact g
+    · exact g
+    · cases g
       apply BiconeHom.left
-    . cases g
+    · cases g
       apply BiconeHom.right
-    . rcases g with (_|_|_|_|g)
+    · rcases g with (_|_|_|_|g)
       exact BiconeHom.diagram (f ≫ g)
 #align category_theory.bicone_category_struct CategoryTheory.biconeCategoryStruct
 
@@ -115,51 +115,51 @@ def biconeMk {C : Type u₁} [Category.{v₁} C] {F : J ⥤ C} (c₁ c₂ : Cone
   obj X := Bicone.casesOn X c₁.pt c₂.pt fun j => F.obj j
   map f := by
     rcases f with (_|_|_|_|f)
-    . exact 𝟙 _
-    . exact 𝟙 _
-    . exact c₁.π.app _
-    . exact c₂.π.app _
-    . exact F.map f
+    · exact 𝟙 _
+    · exact 𝟙 _
+    · exact c₁.π.app _
+    · exact c₂.π.app _
+    · exact F.map f
   map_id X := by cases X <;> simp
   map_comp f g := by
     rcases f with (_|_|_|_|_)
-    . exact (Category.id_comp _).symm
-    . exact (Category.id_comp _).symm
-    . cases g
+    · exact (Category.id_comp _).symm
+    · exact (Category.id_comp _).symm
+    · cases g
       exact (Category.id_comp _).symm.trans (c₁.π.naturality _)
-    . cases g
+    · cases g
       exact (Category.id_comp _).symm.trans (c₂.π.naturality _)
-    . cases g
+    · cases g
       apply F.map_comp
 #align category_theory.bicone_mk CategoryTheory.biconeMk
 
 instance finBiconeHom [FinCategory J] (j k : Bicone J) : Fintype (j ⟶ k) := by
   cases j <;> cases k
-  . exact
+  · exact
       { elems := {BiconeHom.left_id}
         complete := fun f => by cases f; simp }
-  . exact
+  · exact
     { elems := ∅
       complete := fun f => by cases f }
-  . exact
+  · exact
     { elems := {BiconeHom.left _}
       complete := fun f => by cases f; simp }
-  . exact
+  · exact
     { elems := ∅
       complete := fun f => by cases f }
-  . exact
+  · exact
       { elems := {BiconeHom.right_id}
         complete := fun f => by cases f; simp }
-  . exact
+  · exact
     { elems := {BiconeHom.right _}
       complete := fun f => by cases f; simp }
-  . exact
+  · exact
     { elems := ∅
       complete := fun f => by cases f }
-  . exact
+  · exact
     { elems := ∅
       complete := fun f => by cases f }
-  . exact
+  · exact
     { elems := Finset.image BiconeHom.diagram Fintype.elems
       complete := fun f => by
         rcases f with (_|_|_|_|f)
diff --git a/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean b/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
index 95b5222e8b8b1..dc9ff416ffff3 100644
--- a/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
+++ b/Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean
@@ -70,9 +70,9 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
         apply colimit.hom_ext
         rintro ⟨⟨j, hj⟩⟩
         convert h j using 1
-        . simp [← colimit.w (liftToFinset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
+        · simp [← colimit.w (liftToFinset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
           rfl
-        . aesop_cat }
+        · aesop_cat }
 #align category_theory.limits.coproducts_from_finite_filtered.lift_to_finset_colimit_cocone CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone
 
 end CoproductsFromFiniteFiltered
diff --git a/Mathlib/CategoryTheory/Limits/Opposites.lean b/Mathlib/CategoryTheory/Limits/Opposites.lean
index df22af11c7248..3c899b2925ba9 100644
--- a/Mathlib/CategoryTheory/Limits/Opposites.lean
+++ b/Mathlib/CategoryTheory/Limits/Opposites.lean
@@ -575,10 +575,10 @@ in the opposite category is a limit cone. -/
 def isColimitEquivIsLimitOp {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z} (c : PushoutCocone f g) :
     IsColimit c ≃ IsLimit c.op := by
   apply equivOfSubsingletonOfSubsingleton
-  . intro h
+  · intro h
     exact (IsLimit.postcomposeHomEquiv _ _).invFun
       ((IsLimit.whiskerEquivalenceEquiv walkingSpanOpEquiv.symm).toFun (isLimitCoconeOp _ h))
-  . intro h
+  · intro h
     exact (IsColimit.equivIsoColimit c.opUnop).toFun
       (isColimitConeUnop _ ((IsLimit.postcomposeHomEquiv _ _).invFun
         ((IsLimit.whiskerEquivalenceEquiv _).toFun h)))
@@ -589,10 +589,10 @@ in `C` is a limit cone. -/
 def isColimitEquivIsLimitUnop {X Y Z : Cᵒᵖ} {f : X ⟶ Y} {g : X ⟶ Z} (c : PushoutCocone f g) :
     IsColimit c ≃ IsLimit c.unop := by
   apply equivOfSubsingletonOfSubsingleton
-  . intro h
+  · intro h
     exact isLimitCoconeUnop _ ((IsColimit.precomposeHomEquiv _ _).invFun
       ((IsColimit.whiskerEquivalenceEquiv _).toFun h))
-  . intro h
+  · intro h
     exact (IsColimit.equivIsoColimit c.unopOp).toFun
       ((IsColimit.precomposeHomEquiv _ _).invFun
       ((IsColimit.whiskerEquivalenceEquiv walkingCospanOpEquiv.symm).toFun (isColimitConeOp _ h)))
diff --git a/Mathlib/CategoryTheory/Limits/Over.lean b/Mathlib/CategoryTheory/Limits/Over.lean
index 6bc01bc7ee9d5..3b6ccfee388b8 100644
--- a/Mathlib/CategoryTheory/Limits/Over.lean
+++ b/Mathlib/CategoryTheory/Limits/Over.lean
@@ -107,9 +107,9 @@ def mapPullbackAdj {A B : C} (f : A ⟶ B) : Over.map f ⊣ pullback f :=
             -- TODO: It would be nice to replace the next two lines with just `ext`.
             apply OverMorphism.ext
             apply pullback.hom_ext
-            . dsimp
+            · dsimp
               simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app]
-            . dsimp
+            · dsimp
               simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, ← Over.w Y ]
               rfl } }
 #align category_theory.over.map_pullback_adj CategoryTheory.Over.mapPullbackAdj
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean b/Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean
index fc382fc00acd6..8f92067da33e8 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean
@@ -1005,7 +1005,7 @@ theorem Functor.map_isPullback [PreservesLimit (cospan h i) F] (s : IsPullback f
         (isLimitOfPreserves F s.isLimit))
   · rfl
   · simp
-  . simp
+  · simp
 #align category_theory.functor.map_is_pullback CategoryTheory.Functor.map_isPullback
 
 theorem Functor.map_isPushout [PreservesColimit (span f g) F] (s : IsPushout f g h i) :
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean b/Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean
index 3eaf2748de519..54cdc99fb1e3b 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean
@@ -137,16 +137,16 @@ def pullbackDiagonalMapIso :
   hom :=
     pullback.lift (pullback.snd ≫ pullback.fst) (pullback.snd ≫ pullback.snd) (by
       ext
-      . simp [Category.assoc, pullback_diagonal_map_snd_fst_fst, pullback_diagonal_map_snd_snd_fst]
-      . simp [Category.assoc, pullback.condition, pullback.condition_assoc])
+      · simp [Category.assoc, pullback_diagonal_map_snd_fst_fst, pullback_diagonal_map_snd_snd_fst]
+      · simp [Category.assoc, pullback.condition, pullback.condition_assoc])
   inv :=
     pullback.lift (pullback.fst ≫ i₁ ≫ pullback.fst)
       (pullback.map _ _ _ _ (𝟙 _) (𝟙 _) pullback.snd (Category.id_comp _).symm
         (Category.id_comp _).symm) (by
         ext
-        . simp only [Category.assoc, diagonal_fst, Category.comp_id, limit.lift_π,
+        · simp only [Category.assoc, diagonal_fst, Category.comp_id, limit.lift_π,
             PullbackCone.mk_pt, PullbackCone.mk_π_app, limit.lift_π_assoc, cospan_left]
-        . simp only [condition_assoc, Category.assoc, diagonal_snd, Category.comp_id,
+        · simp only [condition_assoc, Category.assoc, diagonal_snd, Category.comp_id,
             limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app,
             limit.lift_π_assoc, cospan_right])
 #align category_theory.limits.pullback_diagonal_map_iso CategoryTheory.Limits.pullbackDiagonalMapIso
@@ -227,16 +227,16 @@ def pullbackDiagonalMapIdIso :
       pullback f g := by
   refine' _ ≪≫
     pullbackDiagonalMapIso i (𝟙 _) (f ≫ inv pullback.fst) (g ≫ inv pullback.fst) ≪≫ _
-  . refine' @asIso _ _ _ _ (pullback.map _ _ _ _ (𝟙 T) ((pullback.congrHom _ _).hom) (𝟙 _) _ _) ?_
-    . rw [← Category.comp_id pullback.snd, ← condition, Category.assoc, IsIso.inv_hom_id_assoc]
-    . rw [← Category.comp_id pullback.snd, ← condition, Category.assoc, IsIso.inv_hom_id_assoc]
+  · refine' @asIso _ _ _ _ (pullback.map _ _ _ _ (𝟙 T) ((pullback.congrHom _ _).hom) (𝟙 _) _ _) ?_
+    · rw [← Category.comp_id pullback.snd, ← condition, Category.assoc, IsIso.inv_hom_id_assoc]
+    · rw [← Category.comp_id pullback.snd, ← condition, Category.assoc, IsIso.inv_hom_id_assoc]
     · rw [Category.comp_id, Category.id_comp]
-    . ext <;> simp
-    . infer_instance
-  . refine' @asIso _ _ _ _ (pullback.map _ _ _ _ (𝟙 _) (𝟙 _) pullback.fst _ _) ?_
-    . rw [Category.assoc, IsIso.inv_hom_id, Category.comp_id, Category.id_comp]
-    . rw [Category.assoc, IsIso.inv_hom_id, Category.comp_id, Category.id_comp]
-    . infer_instance
+    · ext <;> simp
+    · infer_instance
+  · refine' @asIso _ _ _ _ (pullback.map _ _ _ _ (𝟙 _) (𝟙 _) pullback.fst _ _) ?_
+    · rw [Category.assoc, IsIso.inv_hom_id, Category.comp_id, Category.id_comp]
+    · rw [Category.assoc, IsIso.inv_hom_id, Category.comp_id, Category.id_comp]
+    · infer_instance
 #align category_theory.limits.pullback_diagonal_map_id_iso CategoryTheory.Limits.pullbackDiagonalMapIdIso
 
 @[reassoc (attr := simp)]
@@ -407,24 +407,24 @@ def pullbackFstFstIso {X Y S X' Y' S' : C} (f : X ⟶ S) (g : Y ⟶ S) (f' : X'
     -- We could use `ext` here to immediately descend to the leaf goals,
     -- but it only obscures the structure.
     apply pullback.hom_ext
-    . apply pullback.hom_ext
-      . apply pullback.hom_ext
-        . simp only [Category.assoc, lift_fst, lift_fst_assoc, Category.id_comp]
+    · apply pullback.hom_ext
+      · apply pullback.hom_ext
+        · simp only [Category.assoc, lift_fst, lift_fst_assoc, Category.id_comp]
           rw [condition]
-        . simp [Category.assoc, lift_snd]
+        · simp [Category.assoc, lift_snd]
           rw [condition_assoc, condition]
-      . simp only [Category.assoc, lift_fst_assoc, lift_snd, lift_fst, Category.id_comp]
-    . apply pullback.hom_ext
-      . apply pullback.hom_ext
-        . simp only [Category.assoc, lift_snd_assoc, lift_fst_assoc, lift_fst, Category.id_comp]
+      · simp only [Category.assoc, lift_fst_assoc, lift_snd, lift_fst, Category.id_comp]
+    · apply pullback.hom_ext
+      · apply pullback.hom_ext
+        · simp only [Category.assoc, lift_snd_assoc, lift_fst_assoc, lift_fst, Category.id_comp]
           rw [← condition_assoc, condition]
-        . simp only [Category.assoc, lift_snd, lift_fst_assoc, lift_snd_assoc, Category.id_comp]
+        · simp only [Category.assoc, lift_snd, lift_fst_assoc, lift_snd_assoc, Category.id_comp]
           rw [condition]
-      . simp only [Category.assoc, lift_snd_assoc, lift_snd, Category.id_comp]
+      · simp only [Category.assoc, lift_snd_assoc, lift_snd, Category.id_comp]
   inv_hom_id := by
     apply pullback.hom_ext
-    . simp only [Category.assoc, lift_fst, lift_fst_assoc, lift_snd, Category.id_comp]
-    . simp only [Category.assoc, lift_snd, lift_snd_assoc, Category.id_comp]
+    · simp only [Category.assoc, lift_fst, lift_fst_assoc, lift_snd, Category.id_comp]
+    · simp only [Category.assoc, lift_snd, lift_snd_assoc, Category.id_comp]
 #align category_theory.limits.pullback_fst_fst_iso CategoryTheory.Limits.pullbackFstFstIso
 
 theorem pullback_map_eq_pullbackFstFstIso_inv {X Y S X' Y' S' : C} (f : X ⟶ S) (g : Y ⟶ S)
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean b/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
index bf441f4868eac..2b0998311f908 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
@@ -122,9 +122,9 @@ theorem cancel_right {f₁ : X ⟶ Y} {f₂ : Y ⟶ Z} (comm : a ≫ f₁ = b 
           big_k.isLimit.fac _ WalkingCospan.right, fun m₁ m₂ => _⟩
         apply big_k.isLimit.hom_ext
         refine' (PullbackCone.mk a b _ : PullbackCone (f₁ ≫ f₂) _).equalizer_ext _ _
-        . apply reassoc_of% comm
-        . apply m₁.trans (big_k.isLimit.fac s' WalkingCospan.left).symm
-        . apply m₂.trans (big_k.isLimit.fac s' WalkingCospan.right).symm⟩ }
+        · apply reassoc_of% comm
+        · apply m₁.trans (big_k.isLimit.fac s' WalkingCospan.left).symm
+        · apply m₂.trans (big_k.isLimit.fac s' WalkingCospan.right).symm⟩ }
 #align category_theory.is_kernel_pair.cancel_right CategoryTheory.IsKernelPair.cancel_right
 
 /-- If `(a,b)` is a kernel pair for `f₁ ≫ f₂` and `f₂` is mono, then `(a,b)` is a kernel pair for
@@ -147,11 +147,11 @@ theorem comp_of_mono {f₁ : X ⟶ Y} {f₂ : Y ⟶ Z} [Mono f₂] (small_k : Is
       refine' PullbackCone.isLimitAux _
         (fun s => small_k.lift s.fst s.snd (by rw [← cancel_mono f₂, assoc, s.condition, assoc]))
         (by simp) (by simp) _
-      . intro s m hm
+      · intro s m hm
         apply small_k.isLimit.hom_ext
         apply PullbackCone.equalizer_ext small_k.cone _ _
-        . exact (hm WalkingCospan.left).trans (by simp)
-        . exact (hm WalkingCospan.right).trans (by simp)⟩ }
+        · exact (hm WalkingCospan.left).trans (by simp)
+        · exact (hm WalkingCospan.right).trans (by simp)⟩ }
 #align category_theory.is_kernel_pair.comp_of_mono CategoryTheory.IsKernelPair.comp_of_mono
 
 /--
@@ -166,8 +166,8 @@ def toCoequalizer (k : IsKernelPair f a b) [r : RegularEpi f] : IsColimit (Cofor
     (fun s => Cofork.IsColimit.desc r.isColimit s.π
       (by rw [← ht, assoc, s.condition, reassoc_of% kt]))
     (fun s => _) (fun s m w => _)
-  . apply Cofork.IsColimit.π_desc' r.isColimit
-  . apply Cofork.IsColimit.hom_ext r.isColimit
+  · apply Cofork.IsColimit.π_desc' r.isColimit
+  · apply Cofork.IsColimit.hom_ext r.isColimit
     exact w.trans (Cofork.IsColimit.π_desc' r.isColimit _ _).symm
 #align category_theory.is_kernel_pair.to_coequalizer CategoryTheory.IsKernelPair.toCoequalizer
 
@@ -182,17 +182,17 @@ protected theorem pullback {X Y Z A : C} {g : Y ⟶ Z} {a₁ a₂ : A ⟶ Y} (h
     (fun s => pullback.lift (s.fst ≫ pullback.fst)
       (h.lift (s.fst ≫ pullback.snd) (s.snd ≫ pullback.snd) _ ) _) (fun s => _) (fun s => _)
         (fun s m hm => _)⟩⟩
-  . simp_rw [Category.assoc, ← pullback.condition, ← Category.assoc, s.condition]
-  . simp only [assoc, lift_fst_assoc, pullback.condition]
-  . ext <;> simp
-  . ext
-    . simp [s.condition]
-    . simp
-  . apply pullback.hom_ext
-    . simpa using hm WalkingCospan.left =≫ pullback.fst
-    . apply PullbackCone.IsLimit.hom_ext h.isLimit
-      . simpa using hm WalkingCospan.left =≫ pullback.snd
-      . simpa using hm WalkingCospan.right =≫ pullback.snd
+  · simp_rw [Category.assoc, ← pullback.condition, ← Category.assoc, s.condition]
+  · simp only [assoc, lift_fst_assoc, pullback.condition]
+  · ext <;> simp
+  · ext
+    · simp [s.condition]
+    · simp
+  · apply pullback.hom_ext
+    · simpa using hm WalkingCospan.left =≫ pullback.fst
+    · apply PullbackCone.IsLimit.hom_ext h.isLimit
+      · simpa using hm WalkingCospan.left =≫ pullback.snd
+      · simpa using hm WalkingCospan.right =≫ pullback.snd
 #align category_theory.is_kernel_pair.pullback CategoryTheory.IsKernelPair.pullback
 
 theorem mono_of_isIso_fst (h : IsKernelPair f a b) [IsIso a] : Mono f := by
diff --git a/Mathlib/CategoryTheory/Limits/Shapes/Types.lean b/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
index 1c37a43ab374c..faf16c4a3eb23 100644
--- a/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
+++ b/Mathlib/CategoryTheory/Limits/Shapes/Types.lean
@@ -221,8 +221,8 @@ noncomputable def binaryProductIsoProd : binaryProductFunctor ≅ (prod.functor
   refine' NatIso.ofComponents (fun X => _) (fun _ => _)
   · refine' NatIso.ofComponents (fun Y => _) (fun _ => _)
     · exact ((limit.isLimit _).conePointUniqueUpToIso (binaryProductLimit X Y)).symm
-    . apply Limits.prod.hom_ext <;> simp <;> rfl
-  . ext : 2
+    · apply Limits.prod.hom_ext <;> simp <;> rfl
+  · ext : 2
     apply Limits.prod.hom_ext <;> simp <;> rfl
 #align category_theory.limits.types.binary_product_iso_prod CategoryTheory.Limits.Types.binaryProductIsoProd
 
@@ -416,9 +416,9 @@ noncomputable def typeEqualizerOfUnique (t : ∀ y : Y, g y = h y → ∃! x : X
     refine' ⟨fun i => _, _, _⟩
     · apply Classical.choose (t (s.ι i) _)
       apply congr_fun s.condition i
-    . funext i
+    · funext i
       exact (Classical.choose_spec (t (s.ι i) (congr_fun s.condition i))).1
-    . intro m hm
+    · intro m hm
       funext i
       exact (Classical.choose_spec (t (s.ι i) (congr_fun s.condition i))).2 _ (congr_fun hm i)
 #align category_theory.limits.types.type_equalizer_of_unique CategoryTheory.Limits.Types.typeEqualizerOfUnique
diff --git a/Mathlib/CategoryTheory/Limits/Types.lean b/Mathlib/CategoryTheory/Limits/Types.lean
index 6586665df3b95..2ae9171b2ecf5 100644
--- a/Mathlib/CategoryTheory/Limits/Types.lean
+++ b/Mathlib/CategoryTheory/Limits/Types.lean
@@ -427,8 +427,8 @@ theorem rel_of_quot_rel (x y : Σ j, F.obj j) :
 theorem eqvGen_quot_rel_of_rel (x y : Σ j, F.obj j) :
     FilteredColimit.Rel.{v, u} F x y → EqvGen (Quot.Rel.{v, u} F) x y := fun ⟨k, f, g, h⟩ => by
   refine' EqvGen.trans _ ⟨k, F.map f x.2⟩ _ _ _
-  . exact (EqvGen.rel _ _ ⟨f, rfl⟩)
-  . exact (EqvGen.symm _ _ (EqvGen.rel _ _ ⟨g, h⟩))
+  · exact (EqvGen.rel _ _ ⟨f, rfl⟩)
+  · exact (EqvGen.symm _ _ (EqvGen.rel _ _ ⟨g, h⟩))
 #align category_theory.limits.types.filtered_colimit.eqv_gen_quot_rel_of_rel CategoryTheory.Limits.Types.FilteredColimit.eqvGen_quot_rel_of_rel
 
 --attribute [local elab_without_expected_type] nat_trans.app
@@ -457,12 +457,12 @@ noncomputable def isColimitOf (t : Cocone F) (hsurj : ∀ x : t.pt, ∃ i xi, x
       rw [← colimit.w F f, ← colimit.w F g]
       change colimit.ι F k (F.map f xi) = colimit.ι F k (F.map g xj)
       rw [h']
-    . show Function.Surjective _
+    · show Function.Surjective _
       intro x
       rcases hsurj x with ⟨i, xi, rfl⟩
       use colimit.ι F i xi
       apply Colimit.ι_desc_apply.{v, u}
-  . intro j
+  · intro j
     apply colimit.ι_desc
 #align category_theory.limits.types.filtered_colimit.is_colimit_of CategoryTheory.Limits.Types.FilteredColimit.isColimitOf
 
diff --git a/Mathlib/CategoryTheory/Localization/Construction.lean b/Mathlib/CategoryTheory/Localization/Construction.lean
index 15b75de5cc6e5..f3aee6a582af2 100644
--- a/Mathlib/CategoryTheory/Localization/Construction.lean
+++ b/Mathlib/CategoryTheory/Localization/Construction.lean
@@ -158,8 +158,8 @@ def liftToPathCategory : Paths (LocQuiver W) ⥤ D :=
       map := by
         intros X Y
         rintro (f | ⟨g, hg⟩)
-        . exact G.map f
-        . haveI := hG g hg
+        · exact G.map f
+        · haveI := hG g hg
           exact inv (G.map g) }
 #align category_theory.localization.construction.lift_to_path_category CategoryTheory.Localization.Construction.liftToPathCategory
 
@@ -171,8 +171,8 @@ def lift : W.Localization ⥤ D :=
       rintro ⟨X⟩ ⟨Y⟩ f₁ f₂ r
       --Porting note: rest of proof was `rcases r with ⟨⟩; tidy`
       rcases r with (_|_|⟨f,hf⟩|⟨f,hf⟩)
-      . aesop_cat
-      . aesop_cat
+      · aesop_cat
+      · aesop_cat
       all_goals
         dsimp
         haveI := hG f hf
@@ -237,7 +237,7 @@ theorem morphismProperty_is_top (P : MorphismProperty W.Localization)
   funext X Y f
   ext
   constructor
-  . intro
+  · intro
     apply MorphismProperty.top_apply
   · intro
     let G : _ ⥤ W.Localization := Quotient.functor _
@@ -249,12 +249,12 @@ theorem morphismProperty_is_top (P : MorphismProperty W.Localization)
     intros X₁ X₂ p
     induction' p with X₂ X₃ p g hp
     · simpa only [Functor.map_id] using hP₁ (𝟙 X₁.obj)
-    . let p' : X₁ ⟶X₂ := p
+    · let p' : X₁ ⟶X₂ := p
       rw [show p'.cons g = p' ≫ Quiver.Hom.toPath g by rfl, G.map_comp]
       refine' hP₃ _ _ hp _
       rcases g with (g | ⟨g, hg⟩)
-      . apply hP₁
-      . apply hP₂
+      · apply hP₁
+      · apply hP₂
 #align category_theory.localization.construction.morphism_property_is_top CategoryTheory.Localization.Construction.morphismProperty_is_top
 
 /-- A `MorphismProperty` in `W.Localization` is satisfied by all
diff --git a/Mathlib/CategoryTheory/Localization/Predicate.lean b/Mathlib/CategoryTheory/Localization/Predicate.lean
index db062c6663b88..63147fad1e7f8 100644
--- a/Mathlib/CategoryTheory/Localization/Predicate.lean
+++ b/Mathlib/CategoryTheory/Localization/Predicate.lean
@@ -236,7 +236,7 @@ instance : IsEquivalence (whiskeringLeftFunctor L W E) := by
         dsimp [Construction.whiskeringLeftEquivalence, equivalenceFromModel, whiskerLeft]
         erw [NatTrans.comp_app, NatTrans.comp_app, eqToHom_app, eqToHom_app, eqToHom_refl,
           eqToHom_refl, comp_id, id_comp]
-        . rfl
+        · rfl
         all_goals
           change (W.Q ⋙ Localization.Construction.lift L (inverts L W)) ⋙ _ = L ⋙ _
           rw [Construction.fac]
diff --git a/Mathlib/CategoryTheory/Monoidal/Free/Basic.lean b/Mathlib/CategoryTheory/Monoidal/Free/Basic.lean
index 29c5186eb87f4..12c765c4085d8 100644
--- a/Mathlib/CategoryTheory/Monoidal/Free/Basic.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Free/Basic.lean
@@ -324,12 +324,12 @@ def project : MonoidalFunctor (F C) D where
   μ X Y := 𝟙 _
   μ_natural := @fun _ _ _ _ f g => by
     induction' f using Quotient.recOn
-    . induction' g using Quotient.recOn
-      . dsimp
+    · induction' g using Quotient.recOn
+      · dsimp
         simp
         rfl
-      . rfl
-    . rfl
+      · rfl
+    · rfl
 #align category_theory.free_monoidal_category.project CategoryTheory.FreeMonoidalCategory.project
 
 end Functor
diff --git a/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean b/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
index b0d158add5de1..492a3e635b3aa 100644
--- a/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean
@@ -245,8 +245,8 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
       rintro X Y f
       induction' f using Quotient.recOn with f ; swap ; rfl
       induction' f with _ X₁ X₂ X₃ _ _ _ _ _ _ _ _ _ _ _ _ h₁ h₂ X₁ X₂ Y₁ Y₂ f g h₁ h₂
-      . simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
-      . ext n
+      · simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
+      · ext n
         dsimp
         rw [mk_α_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
@@ -258,41 +258,41 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           pentagon_inv_assoc (inclusionObj n.as) X₁ X₂ X₃,
           tensor_inv_hom_id_assoc, tensor_id, Category.id_comp, Iso.inv_hom_id,
           Category.comp_id]
-      . ext n
+      · ext n
         dsimp
         rw [mk_α_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [Category.assoc, comp_tensor_id, tensor_id, Category.comp_id,
           pentagon_inv_assoc, ← associator_inv_naturality_assoc]
         rfl
-      . ext n
+      · ext n
         dsimp [Functor.comp]
         rw [mk_l_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [triangle_assoc_comp_right_assoc, Category.assoc, Category.comp_id]
         rfl
-      . ext n
+      · ext n
         dsimp [Functor.comp]
         rw [mk_l_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [triangle_assoc_comp_left_inv_assoc, inv_hom_id_tensor_assoc, tensor_id,
           Category.id_comp, Category.comp_id]
         rfl
-      . ext n
+      · ext n
         dsimp
         rw [mk_ρ_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [← (Iso.inv_comp_eq _).2 (rightUnitor_tensor _ _), Category.assoc,
           ← rightUnitor_naturality, Category.comp_id]; rfl
-      . ext n
+      · ext n
         dsimp
         rw [mk_ρ_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [← (Iso.eq_comp_inv _).1 (rightUnitor_tensor_inv _ _), rightUnitor_conjugation,
           Category.assoc, Iso.hom_inv_id_assoc, Iso.inv_hom_id_assoc, Iso.inv_hom_id,
           Discrete.functor, Category.comp_id, Function.comp]
-      . rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
-      . ext ⟨n⟩
+      · rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
+      · ext ⟨n⟩
         replace h₁ := NatTrans.congr_app h₁ ⟨n⟩
         replace h₂ := NatTrans.congr_app h₂ ((Discrete.functor (normalizeObj X₁)).obj ⟨n⟩)
         have h₃ := (normalizeIsoAux _ Y₂).hom.naturality ((normalizeMapAux f).app ⟨n⟩)
diff --git a/Mathlib/CategoryTheory/Monoidal/Transport.lean b/Mathlib/CategoryTheory/Monoidal/Transport.lean
index d661f304c2847..58f7064c31978 100644
--- a/Mathlib/CategoryTheory/Monoidal/Transport.lean
+++ b/Mathlib/CategoryTheory/Monoidal/Transport.lean
@@ -135,8 +135,8 @@ def transport (e : C ≌ D) : MonoidalCategory.{v₂} D where
     slice_lhs 1 2 => rw [tensor_id_comp_id_tensor]
     conv_rhs =>
       congr
-      . skip
-      . rw [← id_tensor_comp_tensor_id, id_tensor_comp]
+      · skip
+      · rw [← id_tensor_comp_tensor_id, id_tensor_comp]
     simp only [Category.assoc]
     slice_rhs 1 2 =>
       rw [← id_tensor_comp, Iso.hom_inv_id_app]
diff --git a/Mathlib/CategoryTheory/Preadditive/Injective.lean b/Mathlib/CategoryTheory/Preadditive/Injective.lean
index 14032b3f61a5e..9856287861e66 100644
--- a/Mathlib/CategoryTheory/Preadditive/Injective.lean
+++ b/Mathlib/CategoryTheory/Preadditive/Injective.lean
@@ -365,12 +365,10 @@ def injectivePresentationOfMapInjectivePresentation (X : C)
 theorem enoughInjectives_iff (F : C ≌ D) : EnoughInjectives C ↔ EnoughInjectives D := by
   constructor
   all_goals intro H; constructor; intro X; constructor
-  ·
-    exact
+  · exact
       F.symm.injectivePresentationOfMapInjectivePresentation _
         (Nonempty.some (H.presentation (F.inverse.obj X)))
-  ·
-    exact
+  · exact
       F.injectivePresentationOfMapInjectivePresentation X
         (Nonempty.some (H.presentation (F.functor.obj X)))
 #align category_theory.equivalence.enough_injectives_iff CategoryTheory.Equivalence.enoughInjectives_iff
diff --git a/Mathlib/CategoryTheory/Preadditive/Mat.lean b/Mathlib/CategoryTheory/Preadditive/Mat.lean
index 6a510e61cd5a8..2874bec3079df 100644
--- a/Mathlib/CategoryTheory/Preadditive/Mat.lean
+++ b/Mathlib/CategoryTheory/Preadditive/Mat.lean
@@ -221,9 +221,9 @@ instance hasFiniteBiproducts : HasFiniteBiproducts (Mat_ C)
               split_ifs with h h'
               · substs h h'
                 simp only [CategoryTheory.eqToHom_refl, CategoryTheory.Mat_.id_apply_self]
-              . subst h
+              · subst h
                 rw [eqToHom_refl, id_apply_of_ne _ _ _ h']
-              . rfl }
+              · rfl }
           (by
             dsimp
             ext1 ⟨i, j⟩
@@ -231,30 +231,30 @@ instance hasFiniteBiproducts : HasFiniteBiproducts (Mat_ C)
             rw [Finset.sum_apply, Finset.sum_apply]
             dsimp
             rw [Finset.sum_eq_single i] ; rotate_left
-            . intro b _ hb
+            · intro b _ hb
               apply Finset.sum_eq_zero
               intro x _
               rw [dif_neg hb.symm, zero_comp]
-            . intro hi
+            · intro hi
               simp at hi
             rw [Finset.sum_eq_single j] ; rotate_left
-            . intro b _ hb
+            · intro b _ hb
               rw [dif_pos rfl, dif_neg, zero_comp]
               simp only
               tauto
-            . intro hj
+            · intro hj
               simp at hj
             simp only [eqToHom_refl, dite_eq_ite, ite_true, Category.id_comp, ne_eq,
               Sigma.mk.inj_iff, not_and, id_def]
             by_cases i' = i
-            . subst h
+            · subst h
               rw [dif_pos rfl]
               simp only [heq_eq_eq, true_and]
               by_cases j' = j
-              . subst h
+              · subst h
                 simp
-              . rw [dif_neg h, dif_neg (Ne.symm h)]
-            . rw [dif_neg h, dif_neg]
+              · rw [dif_neg h, dif_neg (Ne.symm h)]
+            · rw [dif_neg h, dif_neg]
               tauto ) }
 set_option linter.uppercaseLean3 false in
 #align category_theory.Mat_.has_finite_biproducts CategoryTheory.Mat_.hasFiniteBiproducts
@@ -343,11 +343,11 @@ def isoBiproductEmbedding (M : Mat_ C) : M ≅ ⨁ fun i => (embedding C).obj (M
     funext i j
     dsimp [id_def]
     rw [Finset.sum_apply, Finset.sum_apply, Finset.sum_eq_single i] ; rotate_left
-    . intro b _ hb
+    · intro b _ hb
       dsimp
       simp only [Finset.sum_const, Finset.card_singleton, one_smul]
       rw [dif_neg hb.symm, zero_comp]
-    . intro h
+    · intro h
       simp at h
     simp
   inv_hom_id := by
@@ -361,9 +361,9 @@ def isoBiproductEmbedding (M : Mat_ C) : M ≅ ⨁ fun i => (embedding C).obj (M
     simp only [embedding, comp_apply, comp_dite, dite_comp, comp_zero, zero_comp,
       Finset.sum_dite_eq', Finset.mem_univ, ite_true, eqToHom_refl, Category.comp_id]
     split_ifs with h
-    . subst h
+    · subst h
       simp
-    . rfl
+    · rfl
 set_option linter.uppercaseLean3 false in
 #align category_theory.Mat_.iso_biproduct_embedding CategoryTheory.Mat_.isoBiproductEmbedding
 
@@ -442,8 +442,8 @@ def lift (F : C ⥤ D) [Functor.Additive F] : Mat_ C ⥤ D where
     dsimp
     ext i j
     by_cases h : j = i
-    . subst h; simp
-    . simp [h]
+    · subst h; simp
+    · simp [h]
 set_option linter.uppercaseLean3 false in
 #align category_theory.Mat_.lift CategoryTheory.Mat_.lift
 
diff --git a/Mathlib/CategoryTheory/Preadditive/Schur.lean b/Mathlib/CategoryTheory/Preadditive/Schur.lean
index f263165613f6e..43af2b3517189 100644
--- a/Mathlib/CategoryTheory/Preadditive/Schur.lean
+++ b/Mathlib/CategoryTheory/Preadditive/Schur.lean
@@ -206,7 +206,7 @@ theorem finrank_hom_simple_simple_eq_zero_iff (X Y : C) [FiniteDimensional 𝕜
   refine' ⟨fun h => by rw [h]; simp, fun h => _⟩
   have := finrank_hom_simple_simple_le_one 𝕜 X Y
   interval_cases finrank 𝕜 (X ⟶ Y)
-  . rfl
+  · rfl
   · exact False.elim (h rfl)
 #align category_theory.finrank_hom_simple_simple_eq_zero_iff CategoryTheory.finrank_hom_simple_simple_eq_zero_iff
 
diff --git a/Mathlib/CategoryTheory/Sites/LeftExact.lean b/Mathlib/CategoryTheory/Sites/LeftExact.lean
index c369a03d12180..c5205ff5dfd0d 100644
--- a/Mathlib/CategoryTheory/Sites/LeftExact.lean
+++ b/Mathlib/CategoryTheory/Sites/LeftExact.lean
@@ -188,7 +188,7 @@ instance preservesLimitsOfShape_plusFunctor
   refine' ⟨fun S => liftToPlusObjLimitObj.{w, v, u} F X.unop S, _, _⟩
   · intro S k
     apply liftToPlusObjLimitObj_fac
-  . intro S m hm
+  · intro S m hm
     dsimp [liftToPlusObjLimitObj]
     simp_rw [← Category.assoc, Iso.eq_comp_inv, ← Iso.comp_inv_eq]
     refine' limit.hom_ext (fun k => _)
diff --git a/Mathlib/CategoryTheory/Sites/Plus.lean b/Mathlib/CategoryTheory/Sites/Plus.lean
index 952af4f5ec66d..0139e868070f0 100644
--- a/Mathlib/CategoryTheory/Sites/Plus.lean
+++ b/Mathlib/CategoryTheory/Sites/Plus.lean
@@ -265,12 +265,12 @@ theorem plusMap_toPlus : J.plusMap (J.toPlus P) = J.toPlus (J.plusObj P) := by
   convert (Multiequalizer.condition (S.unop.index P)
       ⟨_, _, _, II.f, 𝟙 _, I.f, II.f ≫ I.f, I.hf,
         Sieve.downward_closed _ I.hf _, by simp⟩) using 1
-  . dsimp [diagram]
+  · dsimp [diagram]
     cases I
     simp only [Category.assoc, limit.lift_π, Multifork.ofι_pt, Multifork.ofι_π_app,
       Cover.Arrow.map_Y, Cover.Arrow.map_f]
     rfl
-  . erw [Multiequalizer.lift_ι]
+  · erw [Multiequalizer.lift_ι]
     dsimp [Cover.index]
     simp only [Functor.map_id, Category.comp_id]
     rfl
diff --git a/Mathlib/CategoryTheory/Sites/SheafOfTypes.lean b/Mathlib/CategoryTheory/Sites/SheafOfTypes.lean
index 789fdc93bbf73..f3bc5dd3cfc18 100644
--- a/Mathlib/CategoryTheory/Sites/SheafOfTypes.lean
+++ b/Mathlib/CategoryTheory/Sites/SheafOfTypes.lean
@@ -975,11 +975,11 @@ theorem compatible_iff (x : FirstObj P S) :
     ((firstObjEqFamily P S).hom x).Compatible ↔ firstMap P S x = secondMap P S x := by
   rw [Presieve.compatible_iff_sieveCompatible]
   constructor
-  . intro t
+  · intro t
     apply SecondObj.ext
     intros Y Z g f hf
     simpa [firstMap, secondMap] using t _ g hf
-  . intro t Y Z f g hf
+  · intro t Y Z f g hf
     rw [Types.limit_ext_iff'] at t
     simpa [firstMap, secondMap] using t ⟨⟨Y, Z, g, f, hf⟩⟩
 #align category_theory.equalizer.sieve.compatible_iff CategoryTheory.Equalizer.Sieve.compatible_iff
@@ -998,7 +998,7 @@ theorem equalizer_sheaf_condition :
   rw [← Iso.toEquiv_symm_fun]
   rw [Equiv.eq_symm_apply]
   constructor
-  . intro q
+  · intro q
     funext Y f hf
     simpa [firstObjEqFamily, forkMap] using q _ _
   · intro q Y f hf
@@ -1056,7 +1056,7 @@ theorem compatible_iff (x : FirstObj P R) :
     ((firstObjEqFamily P R).hom x).Compatible ↔ firstMap P R x = secondMap P R x := by
   rw [Presieve.pullbackCompatible_iff]
   constructor
-  . intro t
+  · intro t
     apply Limits.Types.limit_ext.{max u₁ v₁, u₁}
     rintro ⟨⟨Y, f, hf⟩, Z, g, hg⟩
     simpa [firstMap, secondMap] using t hf hg
diff --git a/Mathlib/CategoryTheory/Sites/Sieves.lean b/Mathlib/CategoryTheory/Sites/Sieves.lean
index db5c779db6bd9..80de35eea001f 100644
--- a/Mathlib/CategoryTheory/Sites/Sieves.lean
+++ b/Mathlib/CategoryTheory/Sites/Sieves.lean
@@ -339,8 +339,8 @@ instance : CompleteLattice (Sieve X)
   le_sup_right _ _ _ _ := Or.inr
   sup_le _ _ _ h₁ h₂ _ f := by--ℰ S hS Y f := by
     rintro (hf | hf)
-    . exact h₁ _ hf
-    . exact h₂ _ hf
+    · exact h₁ _ hf
+    · exact h₂ _ hf
   inf_le_left _ _ _ _ := And.left
   inf_le_right _ _ _ _ := And.right
   le_inf _ _ _ p q _ _ z := ⟨p _ z, q _ z⟩
diff --git a/Mathlib/CategoryTheory/Subobject/Basic.lean b/Mathlib/CategoryTheory/Subobject/Basic.lean
index 0369aa8204f1f..e63f0e8fb0827 100644
--- a/Mathlib/CategoryTheory/Subobject/Basic.lean
+++ b/Mathlib/CategoryTheory/Subobject/Basic.lean
@@ -610,14 +610,14 @@ def mapIsoToOrderIso (e : X ≅ Y) : Subobject X ≃o Subobject Y where
   map_rel_iff' {A B} := by
     dsimp
     constructor
-    . intro h
+    · intro h
       apply_fun (map e.inv).obj at h
-      . simpa only [← map_comp, e.hom_inv_id, map_id] using h
-      . apply Functor.monotone
-    . intro h
+      · simpa only [← map_comp, e.hom_inv_id, map_id] using h
+      · apply Functor.monotone
+    · intro h
       apply_fun (map e.hom).obj at h
-      . exact h
-      . apply Functor.monotone
+      · exact h
+      · apply Functor.monotone
 #align category_theory.subobject.map_iso_to_order_iso CategoryTheory.Subobject.mapIsoToOrderIso
 
 @[simp]
diff --git a/Mathlib/CategoryTheory/Subobject/Comma.lean b/Mathlib/CategoryTheory/Subobject/Comma.lean
index a5b0a031dceec..f12668118f9e4 100644
--- a/Mathlib/CategoryTheory/Subobject/Comma.lean
+++ b/Mathlib/CategoryTheory/Subobject/Comma.lean
@@ -112,8 +112,8 @@ def subobjectEquiv [HasLimits C] [PreservesLimits T] (A : StructuredArrow S T) :
     refine' ⟨fun h => Subobject.mk_le_mk_of_comm _ _, fun h => _⟩
     · exact homMk (Subobject.ofMkLEMk _ _ h)
         ((cancel_mono (T.map g.right)).1 (by simp [← T.map_comp]))
-    . aesop_cat
-    . refine' Subobject.mk_le_mk_of_comm (Subobject.ofMkLEMk _ _ h).right _
+    · aesop_cat
+    · refine' Subobject.mk_le_mk_of_comm (Subobject.ofMkLEMk _ _ h).right _
       exact congr_arg CommaMorphism.right (Subobject.ofMkLEMk_comp h)
 #align category_theory.structured_arrow.subobject_equiv CategoryTheory.StructuredArrow.subobjectEquiv
 
@@ -224,7 +224,7 @@ def quotientEquiv [HasColimits C] [PreservesColimits S] (A : CostructuredArrow S
       dsimp
       simp only [← S.map_comp_assoc, unop_left_comp_ofMkLEMk_unop, unop_op, CommaMorphism.w,
         Functor.const_obj_obj, right_eq_id, Functor.const_obj_map, Category.comp_id]
-    . apply Quiver.Hom.unop_inj
+    · apply Quiver.Hom.unop_inj
       ext
       exact unop_left_comp_ofMkLEMk_unop _
     · refine' Subobject.mk_le_mk_of_comm (Subobject.ofMkLEMk _ _ h).unop.left.op _
diff --git a/Mathlib/CategoryTheory/Subobject/Lattice.lean b/Mathlib/CategoryTheory/Subobject/Lattice.lean
index a2a639e219fc9..25d6b377d1e68 100644
--- a/Mathlib/CategoryTheory/Subobject/Lattice.lean
+++ b/Mathlib/CategoryTheory/Subobject/Lattice.lean
@@ -205,7 +205,7 @@ def supLe {A : C} (f g h : MonoOver A) : (f ⟶ h) → (g ⟶ h) → ((sup.obj f
   intro k₁ k₂
   refine' homMk _ _
   apply image.lift ⟨_, h.arrow, coprod.desc k₁.left k₂.left, _⟩
-  . ext
+  · ext
     · simp [w k₁]
     · simp [w k₂]
   · apply image.lift_fac
@@ -438,8 +438,8 @@ theorem finset_inf_factors {I : Type _} {A B : C} {s : Finset I} {P : I → Subo
     (s.inf P).Factors f ↔ ∀ i ∈ s, (P i).Factors f := by
   classical
   induction' s using Finset.induction_on with _ _ _ ih
-  . simp [top_factors]
-  . simp [ih]
+  · simp [top_factors]
+  · simp [ih]
 #align category_theory.subobject.finset_inf_factors CategoryTheory.Subobject.finset_inf_factors
 
 -- `i` is explicit here because often we'd like to defer a proof of `m`
@@ -448,8 +448,8 @@ theorem finset_inf_arrow_factors {I : Type _} {B : C} (s : Finset I) (P : I →
   classical
   revert i m
   induction' s using Finset.induction_on with _ _ _ ih
-  . rintro _ ⟨⟩
-  . intro _ m
+  · rintro _ ⟨⟩
+  · intro _ m
     rw [Finset.inf_insert]
     simp only [Finset.mem_insert] at m
     rcases m with (rfl | m)
@@ -475,8 +475,8 @@ theorem inf_eq_map_pullback {A : C} (f₁ : MonoOver A) (f₂ : Subobject A) :
 theorem prod_eq_inf {A : C} {f₁ f₂ : Subobject A} [HasBinaryProduct f₁ f₂] :
     (f₁ ⨯ f₂) = f₁ ⊓ f₂ := by
   apply le_antisymm
-  . refine' le_inf _ _ _ (Limits.prod.fst.le) (Limits.prod.snd.le)
-  . apply leOfHom
+  · refine' le_inf _ _ _ (Limits.prod.fst.le) (Limits.prod.snd.le)
+  · apply leOfHom
     exact prod.lift (inf_le_left _ _).hom (inf_le_right _ _).hom
 #align category_theory.subobject.prod_eq_inf CategoryTheory.Subobject.prod_eq_inf
 
@@ -639,7 +639,7 @@ def sInf {A : C} (s : Set (Subobject A)) : Subobject A :=
 
 theorem sInf_le {A : C} (s : Set (Subobject A)) (f) (hf : f ∈ s) : sInf s ≤ f := by
   fapply le_of_comm
-  . exact (underlyingIso _).hom ≫
+  · exact (underlyingIso _).hom ≫
       Limits.limit.π (wideCospan s)
         (some ⟨equivShrink (Subobject A) f,
           Set.mem_image_of_mem (equivShrink (Subobject A)) hf⟩) ≫
@@ -703,7 +703,7 @@ theorem symm_apply_mem_iff_mem_image {α β : Type _} (e : α ≃ β) (s : Set 
 theorem sSup_le {A : C} (s : Set (Subobject A)) (f : Subobject A) (k : ∀ g ∈ s, g ≤ f) :
     sSup s ≤ f := by
   fapply le_of_comm
-  . refine'(underlyingIso _).hom ≫ image.lift ⟨_, f.arrow, _, _⟩
+  · refine'(underlyingIso _).hom ≫ image.lift ⟨_, f.arrow, _, _⟩
     · refine' Sigma.desc _
       rintro ⟨g, m⟩
       refine' underlying.map (homOfLE (k _ _))
@@ -711,7 +711,7 @@ theorem sSup_le {A : C} (s : Set (Subobject A)) (f : Subobject A) (k : ∀ g ∈
     · ext
       dsimp [smallCoproductDesc]
       simp
-  . dsimp [sSup]
+  · dsimp [sSup]
     rw [assoc, image.lift_fac, underlyingIso_hom_comp_eq_mk]
 #align category_theory.subobject.Sup_le CategoryTheory.Subobject.sSup_le
 
@@ -763,10 +763,10 @@ def subobjectOrderIso {X : C} (Y : Subobject X) : Subobject (Y : C) ≃o Set.Iic
   map_rel_iff' {W Z} := by
     dsimp
     constructor
-    . intro h
+    · intro h
       exact le_of_comm (((underlyingIso _).inv ≫ ofLE _ _ (Subtype.mk_le_mk.mp h) ≫
         (underlyingIso _).hom)) (by aesop_cat)
-    . intro h
+    · intro h
       exact Subtype.mk_le_mk.mpr (le_of_comm
         ((underlyingIso _).hom ≫ ofLE _ _ h ≫ (underlyingIso _).inv) (by simp))
 #align category_theory.subobject.subobject_order_iso CategoryTheory.Subobject.subobjectOrderIso
diff --git a/Mathlib/CategoryTheory/WithTerminal.lean b/Mathlib/CategoryTheory/WithTerminal.lean
index 6a3a7964ba394..8a3ee6e524f18 100644
--- a/Mathlib/CategoryTheory/WithTerminal.lean
+++ b/Mathlib/CategoryTheory/WithTerminal.lean
@@ -102,9 +102,9 @@ instance : Category.{v} (WithTerminal C) where
     -- so the `false_of_from_star` destruct rule below can be used here.
     -- That works, but causes mysterious failures of `aesop_cat` in `map`.
     cases a <;> cases b <;> cases c <;> cases d <;> try aesop_cat
-    . exact (h : PEmpty).elim
-    . exact (g : PEmpty).elim
-    . exact (h : PEmpty).elim
+    · exact (h : PEmpty).elim
+    · exact (g : PEmpty).elim
+    · exact (h : PEmpty).elim
 
 /-- Helper function for typechecking. -/
 def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f
@@ -289,9 +289,9 @@ instance : Category.{v} (WithInitial C) where
     -- Porting note: it would be nice to automate this away as well.
     -- See the note on `Category (WithTerminal C)`
     cases a <;> cases b <;> cases c <;> cases d <;> try aesop_cat
-    . exact (g : PEmpty).elim
-    . exact (f : PEmpty).elim
-    . exact (f : PEmpty).elim
+    · exact (g : PEmpty).elim
+    · exact (f : PEmpty).elim
+    · exact (f : PEmpty).elim
 
 /-- Helper function for typechecking. -/
 def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f
diff --git a/Mathlib/Combinatorics/Composition.lean b/Mathlib/Combinatorics/Composition.lean
index 02854d5eadbb2..37358f35c1ea9 100644
--- a/Mathlib/Combinatorics/Composition.lean
+++ b/Mathlib/Combinatorics/Composition.lean
@@ -677,8 +677,8 @@ theorem splitWrtCompositionAux_cons (l : List α) (n ns) :
 theorem length_splitWrtCompositionAux (l : List α) (ns) :
     length (l.splitWrtCompositionAux ns) = ns.length := by
     induction ns generalizing l
-    . simp [splitWrtCompositionAux, *]
-    . simp [*]
+    · simp [splitWrtCompositionAux, *]
+    · simp [*]
 #align list.length_split_wrt_composition_aux List.length_splitWrtCompositionAux
 
 /-- When one splits a list along a composition `c`, the number of sublists thus created is
@@ -693,12 +693,12 @@ theorem length_splitWrtComposition (l : List α) (c : Composition n) :
 theorem map_length_splitWrtCompositionAux {ns : List ℕ} :
     ∀ {l : List α}, ns.sum ≤ l.length → map length (l.splitWrtCompositionAux ns) = ns := by
   induction' ns with n ns IH <;> intro l h <;> simp at h
-  . simp
+  · simp
   have := le_trans (Nat.le_add_right _ _) h
   simp only [splitWrtCompositionAux_cons, this] ; dsimp
   rw [length_take, IH] <;> simp [length_drop]
-  . assumption
-  . exact le_tsub_of_add_le_left h
+  · assumption
+  · exact le_tsub_of_add_le_left h
 #align list.map_length_split_wrt_composition_aux List.map_length_splitWrtCompositionAux
 
 /-- When one splits a list along a composition `c`, the lengths of the sublists thus created are
@@ -730,9 +730,9 @@ theorem nthLe_splitWrtCompositionAux (l : List α) (ns : List ℕ) {i : ℕ} (hi
   induction' ns with n ns IH generalizing l i
   · cases hi
   cases' i with i
-  . rw [Nat.add_zero, List.take_zero, sum_nil, nthLe_zero]; dsimp
+  · rw [Nat.add_zero, List.take_zero, sum_nil, nthLe_zero]; dsimp
     simp only [splitWrtCompositionAux_cons, head!, sum, foldl, zero_add]
-  . simp only [splitWrtCompositionAux_cons, take, sum_cons,
+  · simp only [splitWrtCompositionAux_cons, take, sum_cons,
       Nat.add_eq, add_zero, gt_iff_lt, nthLe_cons, IH]; dsimp
     rw [Nat.succ_sub_succ_eq_sub, ←Nat.succ_eq_add_one,tsub_zero]
     simp only [← drop_take, drop_drop]
@@ -763,7 +763,7 @@ theorem join_splitWrtCompositionAux {ns : List ℕ} :
   simp only [splitWrtCompositionAux_cons] ; dsimp
   rw [IH]
   · simp
-  . rw [length_drop, ← h, add_tsub_cancel_left]
+  · rw [length_drop, ← h, add_tsub_cancel_left]
 #align list.join_split_wrt_composition_aux List.join_splitWrtCompositionAux
 
 /-- If one splits a list along a composition, and then joins the sublists, one gets back the
@@ -855,9 +855,9 @@ def compositionAsSetEquiv (n : ℕ) : CompositionAsSet n ≃ Finset (Fin (n - 1)
     constructor
     · intro h
       cases' h with n h
-      . rw [add_comm] at this
+      · rw [add_comm] at this
         contradiction
-      . cases' h with w h; cases' h with h₁ h₂
+      · cases' h with w h; cases' h with h₁ h₂
         rw [←Fin.ext_iff] at h₂
         rwa [h₂]
     · intro h
diff --git a/Mathlib/Combinatorics/Derangements/Basic.lean b/Mathlib/Combinatorics/Derangements/Basic.lean
index 28f94562fc4fc..b8d41fcc9c952 100644
--- a/Mathlib/Combinatorics/Derangements/Basic.lean
+++ b/Mathlib/Combinatorics/Derangements/Basic.lean
@@ -91,10 +91,10 @@ def atMostOneFixedPointEquivSum_derangements [DecidableEq α] (a : α) :
           { f : Perm α // fixedPoints f ⊆ {a} ∧ a ∉ fixedPoints f } := by
       -- porting note: `subtypeSubtypeEquivSubtypeInter` no longer works with placeholder `_`s.
       refine' Equiv.sumCongr _ _
-      . exact subtypeSubtypeEquivSubtypeInter
+      · exact subtypeSubtypeEquivSubtypeInter
           (fun x : Perm α => fixedPoints x ⊆ {a})
           (a ∈ fixedPoints ·)
-      . exact subtypeSubtypeEquivSubtypeInter
+      · exact subtypeSubtypeEquivSubtypeInter
           (fun x : Perm α => fixedPoints x ⊆ {a})
           (¬a ∈ fixedPoints ·)
     _ ≃ Sum { f : Perm α // fixedPoints f = {a} } { f : Perm α // fixedPoints f = ∅ } := by
diff --git a/Mathlib/Combinatorics/Young/SemistandardTableau.lean b/Mathlib/Combinatorics/Young/SemistandardTableau.lean
index 291830f8984f7..0e0bf9a1b0429 100644
--- a/Mathlib/Combinatorics/Young/SemistandardTableau.lean
+++ b/Mathlib/Combinatorics/Young/SemistandardTableau.lean
@@ -128,15 +128,15 @@ theorem zeros {μ : YoungDiagram} (T : Ssyt μ) {i j : ℕ} (not_cell : (i, j) 
 theorem row_weak_of_le {μ : YoungDiagram} (T : Ssyt μ) {i j1 j2 : ℕ} (hj : j1 ≤ j2)
     (cell : (i, j2) ∈ μ) : T i j1 ≤ T i j2 := by
   cases' eq_or_lt_of_le hj with h h
-  . rw [h]
-  . exact T.row_weak h cell
+  · rw [h]
+  · exact T.row_weak h cell
 #align ssyt.row_weak_of_le Ssyt.row_weak_of_le
 
 theorem col_weak {μ : YoungDiagram} (T : Ssyt μ) {i1 i2 j : ℕ} (hi : i1 ≤ i2) (cell : (i2, j) ∈ μ) :
     T i1 j ≤ T i2 j := by
   cases' eq_or_lt_of_le hi with h h
-  . rw [h]
-  . exact le_of_lt (T.col_strict h cell)
+  · rw [h]
+  · exact le_of_lt (T.col_strict h cell)
 #align ssyt.col_weak Ssyt.col_weak
 
 /-- The "highest weight" SSYT of a given shape has all i's in row i, for each i. -/
diff --git a/Mathlib/Control/EquivFunctor/Instances.lean b/Mathlib/Control/EquivFunctor/Instances.lean
index 6089fcb8c453f..9223a742c4ca6 100644
--- a/Mathlib/Control/EquivFunctor/Instances.lean
+++ b/Mathlib/Control/EquivFunctor/Instances.lean
@@ -39,9 +39,9 @@ instance EquivFunctorFinset : EquivFunctor Finset where
   map_refl' α := by ext; simp
   map_trans' k h := by
     ext _ a; simp; constructor <;> intro h'
-    . let ⟨a, ha₁, ha₂⟩ := h'
+    · let ⟨a, ha₁, ha₂⟩ := h'
       rw [← ha₂]; simp; apply ha₁
-    . exists (Equiv.symm k) ((Equiv.symm h) a)
+    · exists (Equiv.symm k) ((Equiv.symm h) a)
       simp [h']
 #align equiv_functor_finset EquivFunctorFinset
 
diff --git a/Mathlib/Control/Fold.lean b/Mathlib/Control/Fold.lean
index ea5994ceb241c..a95516f3dc50e 100644
--- a/Mathlib/Control/Fold.lean
+++ b/Mathlib/Control/Fold.lean
@@ -398,8 +398,8 @@ theorem length_toList {xs : t α} : length xs = List.length (toList xs) := by
   rw [← Nat.add_zero ys.length]
   generalize 0 = n
   induction' ys with _ _ ih generalizing n
-  . simp
-  . simp_arith [ih]
+  · simp
+  · simp_arith [ih]
 #align traversable.length_to_list Traversable.length_toList
 
 variable {m : Type u → Type u} [Monad m] [LawfulMonad m]
diff --git a/Mathlib/Data/Complex/Exponential.lean b/Mathlib/Data/Complex/Exponential.lean
index 9f45645695ddd..3666cecbfb67d 100644
--- a/Mathlib/Data/Complex/Exponential.lean
+++ b/Mathlib/Data/Complex/Exponential.lean
@@ -556,8 +556,8 @@ theorem exp_sub : exp (x - y) = exp x / exp y := by
 
 theorem exp_int_mul (z : ℂ) (n : ℤ) : Complex.exp (n * z) = Complex.exp z ^ n := by
   cases n
-  . simp [exp_nat_mul]
-  . simp [exp_add, add_mul, pow_add, exp_neg, exp_nat_mul]
+  · simp [exp_nat_mul]
+  · simp [exp_add, add_mul, pow_add, exp_neg, exp_nat_mul]
 #align complex.exp_int_mul Complex.exp_int_mul
 
 @[simp]
diff --git a/Mathlib/Data/ENat/Basic.lean b/Mathlib/Data/ENat/Basic.lean
index 1cfb472ae5db4..e8b8cc914316e 100644
--- a/Mathlib/Data/ENat/Basic.lean
+++ b/Mathlib/Data/ENat/Basic.lean
@@ -210,8 +210,8 @@ theorem nat_induction {P : ℕ∞ → Prop} (a : ℕ∞) (h0 : P 0) (hsuc : ∀
     (htop : (∀ n : ℕ, P n) → P ⊤) : P a := by
   have A : ∀ n : ℕ, P n := fun n => Nat.recOn n h0 hsuc
   cases a
-  . exact htop A
-  . exact A _
+  · exact htop A
+  · exact A _
 #align enat.nat_induction ENat.nat_induction
 
 end ENat
diff --git a/Mathlib/Data/Fin/Basic.lean b/Mathlib/Data/Fin/Basic.lean
index a2b92498ec4a8..1d34958229382 100644
--- a/Mathlib/Data/Fin/Basic.lean
+++ b/Mathlib/Data/Fin/Basic.lean
@@ -255,14 +255,14 @@ theorem forall_iff {p : Fin n → Prop} : (∀ i, p i) ↔ ∀ i h, p ⟨i, h⟩
 lemma ite_val {n : ℕ} {c : Prop} [Decidable c] {x : c → Fin n} (y : ¬c → Fin n) :
     (if h : c then x h else y h).val = if h : c then (x h).val else (y h).val := by
   by_cases c
-  . simp only [dif_pos h]
-  . simp only [dif_neg h]
+  · simp only [dif_pos h]
+  · simp only [dif_neg h]
 
 lemma dite_val {n : ℕ} {c : Prop} [Decidable c] {x y : Fin n} :
     (if c then x else y).val = if c then x.val else y.val := by
   by_cases c
-  . simp only [if_pos h]
-  . simp only [if_neg h]
+  · simp only [if_pos h]
+  · simp only [if_neg h]
 
 end coe
 
diff --git a/Mathlib/Data/Finset/NoncommProd.lean b/Mathlib/Data/Finset/NoncommProd.lean
index 99b53e76123dc..952549cc6e706 100644
--- a/Mathlib/Data/Finset/NoncommProd.lean
+++ b/Mathlib/Data/Finset/NoncommProd.lean
@@ -422,15 +422,15 @@ theorem noncommProd_mul_single [Fintype ι] [DecidableEq ι] (x : ∀ i, M i) :
   ext i
   apply (univ.noncommProd_map (fun i => MonoidHom.single M i (x i)) _ (Pi.evalMonoidHom M i)).trans
   refine' (noncommProd_congr (insert_erase (mem_univ i)).symm _ _).trans _
-  . intro i _ j _ _
+  · intro i _ j _ _
     exact Pi.mulSingle_apply_commute x i j
-  . intro j
+  · intro j
     exact Pi.mulSingle j (x j) i
-  . intro j _; dsimp
-  . rw [noncommProd_insert_of_not_mem _ _ _ _ (not_mem_erase _ _),
+  · intro j _; dsimp
+  · rw [noncommProd_insert_of_not_mem _ _ _ _ (not_mem_erase _ _),
       noncommProd_eq_pow_card (univ.erase i), one_pow, mul_one]
     simp
-    . intro j hj
+    · intro j hj
       simp at hj
       simp [Pi.mulSingle, Function.update]
       intro h
diff --git a/Mathlib/Data/Finset/Powerset.lean b/Mathlib/Data/Finset/Powerset.lean
index d66c51edd418f..82e5953bf9f18 100644
--- a/Mathlib/Data/Finset/Powerset.lean
+++ b/Mathlib/Data/Finset/Powerset.lean
@@ -336,7 +336,7 @@ theorem powersetLen_map {β : Type _} (f : α ↪ β) (n : ℕ) (s : Finset α)
   ext <| fun t => by
     simp only [card_map, mem_powersetLen, le_eq_subset, gt_iff_lt, mem_map, mapEmbedding_apply]
     constructor
-    . classical
+    · classical
       intro h
       have : map f (filter (fun x => (f x ∈ t)) s) = t := by
         ext x
@@ -345,7 +345,7 @@ theorem powersetLen_map {β : Type _} (f : α ↪ β) (n : ℕ) (s : Finset α)
           fun hx => let ⟨y, hy⟩ := mem_map.1 (h.1 hx); ⟨y, ⟨hy.1, hy.2 ▸ hx⟩, hy.2⟩⟩
       refine' ⟨_, _, this⟩
       rw [← card_map f, this, h.2]; simp
-    . rintro ⟨a, ⟨has, rfl⟩, rfl⟩
+    · rintro ⟨a, ⟨has, rfl⟩, rfl⟩
       dsimp [RelEmbedding.coe_toEmbedding]
       --Porting note: Why is `rw` required here and not `simp`?
       rw [mapEmbedding_apply]
diff --git a/Mathlib/Data/Finset/Prod.lean b/Mathlib/Data/Finset/Prod.lean
index 8d78923bbb1c7..d29d7607d213f 100644
--- a/Mathlib/Data/Finset/Prod.lean
+++ b/Mathlib/Data/Finset/Prod.lean
@@ -170,8 +170,8 @@ theorem filter_product_card (s : Finset α) (t : Finset β) (p : α → Prop) (q
       ext ⟨a, b⟩
       simp only [filter_union_right, mem_filter, mem_product]
       constructor <;> intro h <;> use h.1
-      . simp only [h.2, Function.comp_apply, Decidable.em, and_self]
-      . revert h
+      · simp only [h.2, Function.comp_apply, Decidable.em, and_self]
+      · revert h
         simp only [Function.comp_apply, and_imp]
         rintro _ _ (_|_) <;> simp [*]
     · apply Finset.disjoint_filter_filter'
diff --git a/Mathlib/Data/Finset/Sigma.lean b/Mathlib/Data/Finset/Sigma.lean
index 310eaa4c3b1ca..323a0c6db09ed 100644
--- a/Mathlib/Data/Finset/Sigma.lean
+++ b/Mathlib/Data/Finset/Sigma.lean
@@ -175,8 +175,8 @@ theorem sigmaLift_nonempty :
 theorem sigmaLift_eq_empty : sigmaLift f a b = ∅ ↔ ∀ h : a.1 = b.1, f (h ▸ a.2) b.2 = ∅ := by
   simp_rw [sigmaLift]
   split_ifs with h
-  . simp [h, forall_prop_of_true h]
-  . simp [h, forall_prop_of_false h]
+  · simp [h, forall_prop_of_true h]
+  · simp [h, forall_prop_of_false h]
 #align finset.sigma_lift_eq_empty Finset.sigmaLift_eq_empty
 
 theorem sigmaLift_mono (h : ∀ ⦃i⦄ ⦃a : α i⦄ ⦃b : β i⦄, f a b ⊆ g a b) (a : Σi, α i) (b : Σi, β i) :
diff --git a/Mathlib/Data/Finsupp/AList.lean b/Mathlib/Data/Finsupp/AList.lean
index 13dd756859d9e..58c8dfc8c31d5 100644
--- a/Mathlib/Data/Finsupp/AList.lean
+++ b/Mathlib/Data/Finsupp/AList.lean
@@ -88,8 +88,8 @@ theorem lookupFinsupp_support [DecidableEq α] [DecidableEq M] (l : AList fun _x
     l.lookupFinsupp.support = (l.1.filter fun x => Sigma.snd x ≠ 0).keys.toFinset := by
     -- porting note: was `convert rfl`
      simp only [lookupFinsupp, ne_eq, Finsupp.coe_mk]; congr
-     . apply Subsingleton.elim
-     . funext ; congr
+     · apply Subsingleton.elim
+     · funext ; congr
 #align alist.lookup_finsupp_support AList.lookupFinsupp_support
 
 theorem lookupFinsupp_eq_iff_of_ne_zero [DecidableEq α] {l : AList fun _x : α => M} {a : α} {x : M}
diff --git a/Mathlib/Data/Finsupp/Basic.lean b/Mathlib/Data/Finsupp/Basic.lean
index 78d4c82147995..99dbd049eff7e 100644
--- a/Mathlib/Data/Finsupp/Basic.lean
+++ b/Mathlib/Data/Finsupp/Basic.lean
@@ -662,8 +662,7 @@ theorem mapDomain_injOn (S : Set α) {f : α → β} (hf : Set.InjOn f S) :
   ext a
   classical
     by_cases h : a ∈ v₁.support ∪ v₂.support
-    ·
-      rw [← mapDomain_apply' S _ hv₁ hf _, ← mapDomain_apply' S _ hv₂ hf _, eq] <;>
+    · rw [← mapDomain_apply' S _ hv₁ hf _, ← mapDomain_apply' S _ hv₂ hf _, eq] <;>
         · apply Set.union_subset hv₁ hv₂
           exact_mod_cast h
     · simp only [not_or, mem_union, not_not, mem_support_iff] at h
@@ -1224,8 +1223,7 @@ theorem sum_curry_index (f : α × β →₀ M) (g : α → β → M → N) (hg
     (f.curry.sum fun a f => f.sum (g a)) = f.sum fun p c => g p.1 p.2 c := by
   rw [Finsupp.curry]
   trans
-  ·
-    exact
+  · exact
       sum_sum_index (fun a => sum_zero_index) fun a b₀ b₁ =>
         sum_add_index' (fun a => hg₀ _ _) fun c d₀ d₁ => hg₁ _ _ _ _
   congr ; funext p c
diff --git a/Mathlib/Data/Int/Bitwise.lean b/Mathlib/Data/Int/Bitwise.lean
index 798bbf8a1a1fe..2bc3495029519 100644
--- a/Mathlib/Data/Int/Bitwise.lean
+++ b/Mathlib/Data/Int/Bitwise.lean
@@ -225,15 +225,15 @@ theorem bitwise_or : bitwise or = lor := by
   cases' m with m m <;> cases' n with n n <;> try {rfl}
     <;> simp only [bitwise, natBitwise, Bool.not_false, Bool.or_true, cond_true, lor, Nat.ldiff',
       negSucc.injEq, Bool.true_or, Nat.land']
-  . rw [Nat.bitwise'_swap, Function.swap]
+  · rw [Nat.bitwise'_swap, Function.swap]
     congr
     funext x y
     cases x <;> cases y <;> rfl
     rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
 #align int.bitwise_or Int.bitwise_or
@@ -245,12 +245,12 @@ theorem bitwise_and : bitwise and = land := by
     <;> simp only [bitwise, natBitwise, Bool.not_false, Bool.or_true,
       cond_false, cond_true, lor, Nat.ldiff', Bool.and_true, negSucc.injEq,
       Bool.and_false, Nat.land']
-  . rw [Nat.bitwise'_swap, Function.swap]
+  · rw [Nat.bitwise'_swap, Function.swap]
     congr
     funext x y
     cases x <;> cases y <;> rfl
     rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
 #align int.bitwise_and Int.bitwise_and
@@ -262,13 +262,13 @@ theorem bitwise_diff : (bitwise fun a b => a && not b) = ldiff' := by
     <;> simp only [bitwise, natBitwise, Bool.not_false, Bool.or_true,
       cond_false, cond_true, lor, Nat.ldiff', Bool.and_true, negSucc.injEq,
       Bool.and_false, Nat.land', Bool.not_true, ldiff', Nat.lor']
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
-  . rw [Nat.bitwise'_swap, Function.swap]
+  · rw [Nat.bitwise'_swap, Function.swap]
     congr
     funext x y
     cases x <;> cases y <;> rfl
@@ -282,13 +282,13 @@ theorem bitwise_xor : bitwise xor = lxor' := by
     <;> simp only [bitwise, natBitwise, Bool.not_false, Bool.or_true,
       cond_false, cond_true, lor, Nat.ldiff', Bool.and_true, negSucc.injEq, Bool.false_xor,
       Bool.true_xor, Bool.and_false, Nat.land', Bool.not_true, ldiff', Nat.lor', lxor', Nat.lxor']
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
-  . congr
+  · congr
     funext x y
     cases x <;> cases y <;> rfl
 #align int.bitwise_xor Int.bitwise_xor
@@ -299,10 +299,10 @@ theorem bitwise_bit (f : Bool → Bool → Bool) (a m b n) :
   cases' m with m m <;> cases' n with n n <;>
   simp only [bitwise, ofNat_eq_coe, bit_coe_nat, natBitwise, Bool.not_false, Bool.not_eq_false',
     bit_negSucc]
-  . by_cases h : f false false <;> simp [h]
-  . by_cases h : f false true <;> simp [h]
-  . by_cases h : f true false <;> simp [h]
-  . by_cases h : f true true <;> simp [h]
+  · by_cases h : f false false <;> simp [h]
+  · by_cases h : f false true <;> simp [h]
+  · by_cases h : f true false <;> simp [h]
+  · by_cases h : f true true <;> simp [h]
 #align int.bitwise_bit Int.bitwise_bit
 
 @[simp]
@@ -335,10 +335,10 @@ theorem lnot_bit (b) : ∀ n, lnot (bit b n) = bit (not b) (lnot n)
 theorem testBit_bitwise (f : Bool → Bool → Bool) (m n k) :
     testBit (bitwise f m n) k = f (testBit m k) (testBit n k) := by
   cases m <;> cases n <;> simp only [testBit, bitwise, natBitwise]
-  . by_cases h : f false false <;> simp [h]
-  . by_cases h : f false true <;> simp [h]
-  . by_cases h : f true false <;> simp [h]
-  . by_cases h : f true true <;> simp [h]
+  · by_cases h : f false false <;> simp [h]
+  · by_cases h : f false true <;> simp [h]
+  · by_cases h : f true false <;> simp [h]
+  · by_cases h : f true true <;> simp [h]
 #align int.test_bit_bitwise Int.testBit_bitwise
 
 @[simp]
diff --git a/Mathlib/Data/Int/Range.lean b/Mathlib/Data/Int/Range.lean
index b005fd5f886ff..3749379154638 100644
--- a/Mathlib/Data/Int/Range.lean
+++ b/Mathlib/Data/Int/Range.lean
@@ -51,9 +51,9 @@ instance decidableLELE (P : Int → Prop) [DecidablePred P] (m n : ℤ) :
   -- `Decidable (∀ (r : ℤ), r ∈ range m (n + 1) → P r)`
     apply decidable_of_iff (∀ r ∈ range m (n + 1), P r)
     apply Iff.intro <;> intros h _ _
-    . intro _; apply h
+    · intro _; apply h
       simp_all only [mem_range_iff, and_imp, lt_add_one_iff]
-    . simp_all only [mem_range_iff, and_imp, lt_add_one_iff]
+    · simp_all only [mem_range_iff, and_imp, lt_add_one_iff]
 #align int.decidable_le_le Int.decidableLELE
 
 instance decidableLTLT (P : Int → Prop) [DecidablePred P] (m n : ℤ) :
diff --git a/Mathlib/Data/List/AList.lean b/Mathlib/Data/List/AList.lean
index 4fe605ff511d7..8976437d96dc1 100644
--- a/Mathlib/Data/List/AList.lean
+++ b/Mathlib/Data/List/AList.lean
@@ -506,7 +506,7 @@ theorem union_comm_of_disjoint {s₁ s₂ : AList β} (h : Disjoint s₁ s₂) :
     (by
       intros ; simp
       constructor <;> intro h'
-      . cases' h' with h' h'
+      · cases' h' with h' h'
         · right
           refine' ⟨_, h'⟩
           apply h
@@ -514,7 +514,7 @@ theorem union_comm_of_disjoint {s₁ s₂ : AList β} (h : Disjoint s₁ s₂) :
           exact rfl
         · left
           rw [h'.2]
-      . cases' h' with h' h'
+      · cases' h' with h' h'
         · right
           refine' ⟨_, h'⟩
           intro h''
diff --git a/Mathlib/Data/List/Basic.lean b/Mathlib/Data/List/Basic.lean
index 3679a3382698e..574edb4d7f7c1 100644
--- a/Mathlib/Data/List/Basic.lean
+++ b/Mathlib/Data/List/Basic.lean
@@ -3181,8 +3181,8 @@ theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : 
   induction' l with hd tl hl generalizing n
   · simp
   · cases' n with n
-    . simp
-    . simp [hl]
+    · simp
+    · simp [hl]
 #align list.nth_pmap List.get?_pmap
 
 theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) {n : ℕ}
@@ -3543,8 +3543,8 @@ theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
 theorem mem_filter_of_mem {a : α} : ∀ {l}, a ∈ l → p a → a ∈ filter p l
   | x :: l, h, h1 => by
     rcases mem_cons.1 h with rfl | h
-    . simp [filter, h1]
-    . rw [filter]
+    · simp [filter, h1]
+    · rw [filter]
       cases p x <;> simp [mem_filter_of_mem h h1]
 #align list.mem_filter_of_mem List.mem_filter_of_mem
 
diff --git a/Mathlib/Data/List/Chain.lean b/Mathlib/Data/List/Chain.lean
index 89eeb1bf4fd65..2b771ff9e4546 100644
--- a/Mathlib/Data/List/Chain.lean
+++ b/Mathlib/Data/List/Chain.lean
@@ -155,7 +155,7 @@ theorem chain_iff_get {R} : ∀ {a : α} {l : List α}, Chain R a l ↔
       intro i w
       cases' i with i
       · apply h0
-      . exact h i (lt_pred_iff.2 <| by simpa using w)
+      · exact h i (lt_pred_iff.2 <| by simpa using w)
     rintro ⟨h0, h⟩; constructor
     · apply h0
       simp
diff --git a/Mathlib/Data/List/Cycle.lean b/Mathlib/Data/List/Cycle.lean
index 8982cc877279f..03a7e8647ad5f 100644
--- a/Mathlib/Data/List/Cycle.lean
+++ b/Mathlib/Data/List/Cycle.lean
@@ -73,8 +73,8 @@ theorem nextOr_eq_nextOr_of_mem_of_ne (xs : List α) (x d d' : α) (x_mem : x 
   by_cases h : x = y
   · rw [h, nextOr_self_cons_cons, nextOr_self_cons_cons]
   · rw [nextOr, nextOr, IH]
-    . simpa [h] using x_mem
-    . simpa using x_ne
+    · simpa [h] using x_mem
+    · simpa using x_ne
 #align list.next_or_eq_next_or_of_mem_of_ne List.nextOr_eq_nextOr_of_mem_of_ne
 
 theorem mem_of_nextOr_ne {xs : List α} {x d : α} (h : nextOr xs x d ≠ d) : x ∈ xs := by
@@ -285,24 +285,24 @@ theorem next_get : ∀ (l : List α) (_h : Nodup l) (i : Fin l.length),
     · subst hi'
       rw [next_getLast_cons]
       · simp [hi', get]
-      . rw [get_cons_succ]; exact get_mem _ _ _
-      . exact hx'
-      . simp [getLast_eq_get]
-      . exact hn.of_cons
-    . rw [next_ne_head_ne_getLast _ _ _ _ _ hx']
+      · rw [get_cons_succ]; exact get_mem _ _ _
+      · exact hx'
+      · simp [getLast_eq_get]
+      · exact hn.of_cons
+    · rw [next_ne_head_ne_getLast _ _ _ _ _ hx']
       simp only [get_cons_succ]
       rw [next_get (y::l), ← get_cons_succ (a := x)]
       congr
       dsimp
       rw [Nat.mod_eq_of_lt (Nat.succ_lt_succ_iff.2 hi'),
         Nat.mod_eq_of_lt (Nat.succ_lt_succ_iff.2 (Nat.succ_lt_succ_iff.2 hi'))]
-      . simp [Nat.mod_eq_of_lt (Nat.succ_lt_succ_iff.2 hi'), Nat.succ_eq_add_one, hi']
-      . exact hn.of_cons
-      . rw [getLast_eq_get]
+      · simp [Nat.mod_eq_of_lt (Nat.succ_lt_succ_iff.2 hi'), Nat.succ_eq_add_one, hi']
+      · exact hn.of_cons
+      · rw [getLast_eq_get]
         intro h
         have := nodup_iff_injective_get.1 hn h
         simp at this; simp [this] at hi'
-      . rw [get_cons_succ]; exact get_mem _ _ _
+      · rw [get_cons_succ]; exact get_mem _ _ _
 
 set_option linter.deprecated false in
 @[deprecated next_get]
@@ -414,7 +414,7 @@ theorem prev_reverse_eq_next (l : List α) (h : Nodup l) (x : α) (hx : x ∈ l)
     rw [← nthLe_reverse]
     · simp [tsub_tsub_cancel_of_le (Nat.le_pred_of_lt hk)]
     · simpa using (Nat.sub_le _ _).trans_lt (tsub_lt_self lpos Nat.succ_pos')
-    . simpa
+    · simpa
 #align list.prev_reverse_eq_next List.prev_reverse_eq_next
 
 theorem next_reverse_eq_prev (l : List α) (h : Nodup l) (x : α) (hx : x ∈ l) :
diff --git a/Mathlib/Data/List/Forall2.lean b/Mathlib/Data/List/Forall2.lean
index 0f5984fbc2316..ffc709bb81fb9 100644
--- a/Mathlib/Data/List/Forall2.lean
+++ b/Mathlib/Data/List/Forall2.lean
@@ -202,8 +202,8 @@ theorem forall₂_iff_zip {l₁ l₂} :
     · cases length_eq_zero.1 h₁.symm
       constructor
     · cases' l₂ with b l₂
-      . simp at h₁
-      . simp only [length_cons, succ.injEq] at h₁
+      · simp at h₁
+      · simp only [length_cons, succ.injEq] at h₁
         exact Forall₂.cons (h₂ <| by simp [zip])
           (IH h₁ <| fun h => h₂ <| by
             simp only [zip, zipWith, find?, mem_cons, Prod.mk.injEq]; right
diff --git a/Mathlib/Data/List/MinMax.lean b/Mathlib/Data/List/MinMax.lean
index b79eeeb8e521c..01a0e76761e92 100644
--- a/Mathlib/Data/List/MinMax.lean
+++ b/Mathlib/Data/List/MinMax.lean
@@ -217,11 +217,11 @@ theorem index_of_argmax :
     obtain ha | ha := ha <;> split_ifs at hm <;> injection hm with hm <;> subst hm
     · cases not_le_of_lt ‹_› ‹_›
     · rw [if_pos rfl]
-    . rw [if_neg, if_neg]
+    · rw [if_neg, if_neg]
       exact Nat.succ_le_succ (index_of_argmax h (by assumption) ham)
       · exact ne_of_apply_ne f (lt_of_lt_of_le ‹_› ‹_›).ne'
       · exact ne_of_apply_ne _ ‹f hd < f _›.ne'
-    . rw [if_pos rfl]
+    · rw [if_pos rfl]
       exact Nat.zero_le _
 #align list.index_of_argmax List.index_of_argmax
 
diff --git a/Mathlib/Data/List/Nodup.lean b/Mathlib/Data/List/Nodup.lean
index 9f079a586a4a0..9626437f5d5fa 100644
--- a/Mathlib/Data/List/Nodup.lean
+++ b/Mathlib/Data/List/Nodup.lean
@@ -99,9 +99,9 @@ theorem nodup_iff_injective_get {l : List α} :
     ⟨fun h i j hg => by
       cases' i with i hi; cases' j with j hj
       rcases lt_trichotomy i j with (hij | rfl | hji)
-      . exact (h ⟨i, hi⟩ ⟨j, hj⟩ hij hg).elim
-      . rfl
-      . exact (h ⟨j, hj⟩ ⟨i, hi⟩ hji hg.symm).elim,
+      · exact (h ⟨i, hi⟩ ⟨j, hj⟩ hij hg).elim
+      · rfl
+      · exact (h ⟨j, hj⟩ ⟨i, hi⟩ hji hg.symm).elim,
       fun hinj i j hij h => Nat.ne_of_lt hij (Fin.veq_of_eq (hinj h))⟩
 
 set_option linter.deprecated false in
@@ -128,10 +128,10 @@ theorem nodup_iff_get?_ne_get? {l : List α} :
     l.Nodup ↔ ∀ i j : ℕ, i < j → j < l.length → l.get? i ≠ l.get? j := by
   rw [Nodup, pairwise_iff_get]
   constructor
-  . intro h i j hij hj
+  · intro h i j hij hj
     rw [get?_eq_get (lt_trans hij hj), get?_eq_get hj, Ne.def, Option.some_inj]
     exact h _ _ hij
-  . intro h i j hij
+  · intro h i j hij
     rw [Ne.def, ← Option.some_inj, ← get?_eq_get, ← get?_eq_get]
     exact h i j hij j.2
 #align list.nodup_iff_nth_ne_nth List.nodup_iff_get?_ne_get?
diff --git a/Mathlib/Data/List/OfFn.lean b/Mathlib/Data/List/OfFn.lean
index 4f9e8937161bd..3721ec96d8ef0 100644
--- a/Mathlib/Data/List/OfFn.lean
+++ b/Mathlib/Data/List/OfFn.lean
@@ -63,7 +63,7 @@ theorem get?_ofFn {n} (f : Fin n → α) (i) : get? (ofFn f) i = ofFnNthVal f i
   if h : i < (ofFn f).length
   then by
     rw [get?_eq_get h, get_ofFn]
-    . simp at h; simp [ofFnNthVal, h]
+    · simp at h; simp [ofFnNthVal, h]
   else by
     rw [ofFnNthVal, dif_neg] <;>
     simpa using h
@@ -117,8 +117,8 @@ theorem ofFn_zero (f : Fin 0 → α) : ofFn f = [] :=
 theorem ofFn_succ {n} (f : Fin (succ n) → α) : ofFn f = f 0 :: ofFn fun i => f i.succ :=
   ext_get (by simp) (fun i hi₁ hi₂ => by
     cases i
-    . simp
-    . simp)
+    · simp
+    · simp)
 #align list.of_fn_succ List.ofFn_succ
 
 theorem ofFn_succ' {n} (f : Fin (succ n) → α) :
diff --git a/Mathlib/Data/List/Pairwise.lean b/Mathlib/Data/List/Pairwise.lean
index 733e5d16411fd..4f22a04850068 100644
--- a/Mathlib/Data/List/Pairwise.lean
+++ b/Mathlib/Data/List/Pairwise.lean
@@ -143,9 +143,9 @@ theorem Pairwise.forall_of_forall (H : Symmetric R) (H₁ : ∀ x ∈ l, R x x)
 theorem Pairwise.forall (hR : Symmetric R) (hl : l.Pairwise R) :
     ∀ ⦃a⦄, a ∈ l → ∀ ⦃b⦄, b ∈ l → a ≠ b → R a b := by
   apply Pairwise.forall_of_forall
-  . exact fun a b h hne => hR (h hne.symm)
-  . exact fun _ _ hx => (hx rfl).elim
-  . exact hl.imp (@fun a b h _ => by exact h)
+  · exact fun a b h hne => hR (h hne.symm)
+  · exact fun _ _ hx => (hx rfl).elim
+  · exact hl.imp (@fun a b h _ => by exact h)
 #align list.pairwise.forall List.Pairwise.forall
 
 theorem Pairwise.set_pairwise (hl : Pairwise R l) (hr : Symmetric R) : { x | x ∈ l }.Pairwise R :=
@@ -329,7 +329,7 @@ theorem pairwise_iff_get : ∀ {l : List α}, Pairwise R l ↔
       have := H ⟨0, show 0 < (a::l).length from Nat.succ_pos _⟩ ⟨n.succ, Nat.succ_lt_succ n.2⟩
         (Nat.succ_pos n)
       simpa
-    . simpa using H i.succ j.succ (show i.1.succ < j.1.succ from Nat.succ_lt_succ hij)
+    · simpa using H i.succ j.succ (show i.1.succ < j.1.succ from Nat.succ_lt_succ hij)
 
 set_option linter.deprecated false in
 @[deprecated pairwise_iff_get]
diff --git a/Mathlib/Data/List/Perm.lean b/Mathlib/Data/List/Perm.lean
index d39613c28293d..03e9ef36f25b1 100644
--- a/Mathlib/Data/List/Perm.lean
+++ b/Mathlib/Data/List/Perm.lean
@@ -567,10 +567,10 @@ theorem Perm.prod_eq' [M : Monoid α] {l₁ l₂ : List α} (h : l₁ ~ l₂) (h
     l₁.prod = l₂.prod := by
   refine h.foldl_eq' ?_ _
   apply Pairwise.forall_of_forall
-  . intro x y h z
+  · intro x y h z
     exact (h z).symm
-  . intros; rfl
-  . apply hc.imp
+  · intros; rfl
+  · apply hc.imp
     intro a b h z
     rw [mul_assoc z, mul_assoc z, h]
 #align list.perm.prod_eq' List.Perm.prod_eq'
@@ -1190,8 +1190,8 @@ theorem Perm.dropSlice_inter {α} [DecidableEq α] {xs ys : List α} (n m : ℕ)
   have : n ≤ n + m := Nat.le_add_right _ _
   have h₂ := h.nodup_iff.2 h'
   apply Perm.trans _ (Perm.inter_append _).symm
-  . exact Perm.append (Perm.take_inter _ h h') (Perm.drop_inter _ h h')
-  . exact disjoint_take_drop h₂ this
+  · exact Perm.append (Perm.take_inter _ h h') (Perm.drop_inter _ h h')
+  · exact disjoint_take_drop h₂ this
 #align list.perm.slice_inter List.Perm.dropSlice_inter
 
 -- enumerating permutations
@@ -1426,11 +1426,9 @@ theorem nodup_permutations'Aux_iff {s : List α} {x : α} : Nodup (permutations'
     rw [length_insertNth _ _ hk.le, length_insertNth _ _ (Nat.succ_le_of_lt hk)]
   refine' ext_nthLe hl fun n hn hn' => _
   rcases lt_trichotomy n k with (H | rfl | H)
-  ·
-    rw [nthLe_insertNth_of_lt _ _ _ _ H (H.trans hk),
+  · rw [nthLe_insertNth_of_lt _ _ _ _ H (H.trans hk),
       nthLe_insertNth_of_lt _ _ _ _ (H.trans (Nat.lt_succ_self _))]
-  ·
-    rw [nthLe_insertNth_self _ _ _ hk.le, nthLe_insertNth_of_lt _ _ _ _ (Nat.lt_succ_self _) hk,
+  · rw [nthLe_insertNth_self _ _ _ hk.le, nthLe_insertNth_of_lt _ _ _ _ (Nat.lt_succ_self _) hk,
       hk']
   · rcases(Nat.succ_le_of_lt H).eq_or_lt with (rfl | H')
     · rw [nthLe_insertNth_self _ _ _ (Nat.succ_le_of_lt hk)]
diff --git a/Mathlib/Data/List/Permutation.lean b/Mathlib/Data/List/Permutation.lean
index 3cf0366061dcf..5e136e61e4afd 100644
--- a/Mathlib/Data/List/Permutation.lean
+++ b/Mathlib/Data/List/Permutation.lean
@@ -93,12 +93,12 @@ theorem map_permutationsAux2' {α β α' β'} (g : α → α') (g' : β → β')
     map g' (permutationsAux2 t ts r ys f).2 =
       (permutationsAux2 (g t) (map g ts) (map g' r) (map g ys) f').2 := by
   induction' ys with ys_hd _ ys_ih generalizing f f'
-  . simp
-  . simp only [map, permutationsAux2_snd_cons, cons_append, cons.injEq]
+  · simp
+  · simp only [map, permutationsAux2_snd_cons, cons_append, cons.injEq]
     rw [ys_ih, permutationsAux2_fst]
     refine' ⟨_, rfl⟩
-    . simp only [← map_cons, ← map_append]; apply H
-    . intro a; apply H
+    · simp only [← map_cons, ← map_append]; apply H
+    · intro a; apply H
 #align list.map_permutations_aux2' List.map_permutationsAux2'
 
 /-- The `f` argument to `permutationsAux2` when `r = []` can be eliminated. -/
diff --git a/Mathlib/Data/List/Sigma.lean b/Mathlib/Data/List/Sigma.lean
index 0c9ac517b3e27..5c893bd68ce8e 100644
--- a/Mathlib/Data/List/Sigma.lean
+++ b/Mathlib/Data/List/Sigma.lean
@@ -285,8 +285,8 @@ theorem head?_lookupAll (a : α) : ∀ l : List (Sigma β), head? (lookupAll a l
   | [] => by simp
   | ⟨a', b⟩ :: l => by
     by_cases h : a = a'
-    . subst h; simp
-    . rw [lookupAll_cons_ne, dlookup_cons_ne, head?_lookupAll a l] <;> assumption
+    · subst h; simp
+    · rw [lookupAll_cons_ne, dlookup_cons_ne, head?_lookupAll a l] <;> assumption
 #align list.head_lookup_all List.head?_lookupAll
 
 theorem mem_lookupAll {a : α} {b : β a} :
@@ -296,7 +296,7 @@ theorem mem_lookupAll {a : α} {b : β a} :
     by_cases h : a = a'
     · subst h
       simp [*, mem_lookupAll]
-    . simp [*, mem_lookupAll]
+    · simp [*, mem_lookupAll]
 #align list.mem_lookup_all List.mem_lookupAll
 
 theorem lookupAll_sublist (a : α) : ∀ l : List (Sigma β), (lookupAll a l).map (Sigma.mk a) <+ l
@@ -348,7 +348,7 @@ theorem kreplace_of_forall_not (a : α) (b : β a) {l : List (Sigma β)}
     rintro ⟨a', b'⟩ h; dsimp; split_ifs
     · subst a'
       exact H _ h
-    . rfl
+    · rfl
 #align list.kreplace_of_forall_not List.kreplace_of_forall_not
 
 theorem kreplace_self {a : α} {b : β a} {l : List (Sigma β)} (nd : NodupKeys l)
diff --git a/Mathlib/Data/List/Sublists.lean b/Mathlib/Data/List/Sublists.lean
index 725523c93acc0..0efea1358b023 100644
--- a/Mathlib/Data/List/Sublists.lean
+++ b/Mathlib/Data/List/Sublists.lean
@@ -65,8 +65,8 @@ theorem sublists'_eq_sublists'Aux (l : List α) :
   simp only [sublists', sublists'Aux_eq_array_foldl]
   dsimp only
   rw [← List.foldr_hom Array.toList]
-  . rfl
-  . intros _ _; congr <;> simp
+  · rfl
+  · intros _ _; congr <;> simp
 
 theorem sublists'Aux_eq_map (a : α) (r₁ : List (List α)) : ∀ (r₂ : List (List α)),
     sublists'Aux a r₁ r₂ = r₂ ++ map (cons a) r₁ :=
@@ -143,8 +143,8 @@ theorem sublists_eq_sublistsAux (l : List α) :
     sublists l = l.foldr sublistsAux [[]] := by
   simp only [sublists, sublistsAux_eq_array_foldl, Array.foldr_eq_foldr_data]
   rw [← foldr_hom Array.toList]
-  . rfl
-  . intros _ _; congr <;> simp
+  · rfl
+  · intros _ _; congr <;> simp
 
 #noalign list.sublists_aux₁_eq_sublists_aux
 #noalign list.sublists_aux_cons_eq_sublists_aux₁
@@ -160,8 +160,8 @@ theorem sublists_append (l₁ l₂ : List α) :
     sublists (l₁ ++ l₂) = (sublists l₂) >>= (fun x => (sublists l₁).map (. ++ x)) := by
   simp only [sublists_eq_sublistsAux, foldr_append, sublistsAux_eq_bind]
   induction l₁
-  . case nil => simp
-  . case cons a l₁ ih =>
+  · case nil => simp
+  · case cons a l₁ ih =>
       rw [foldr_cons, ih]
       simp [List.bind, join_join, Function.comp]
 #align list.sublists_append List.sublists_append
@@ -430,10 +430,10 @@ theorem sublists_cons_perm_append (a : α) (l : List α) :
 theorem revzip_sublists (l : List α) : ∀ l₁ l₂, (l₁, l₂) ∈ revzip l.sublists → l₁ ++ l₂ ~ l := by
   rw [revzip]
   induction' l using List.reverseRecOn with l' a ih
-  . intro l₁ l₂ h
+  · intro l₁ l₂ h
     simp at h
     simp [h]
-  . intro l₁ l₂ h
+  · intro l₁ l₂ h
     rw [sublists_concat, reverse_append, zip_append, ← map_reverse, zip_map_right,
       zip_map_left] at * <;> [skip; simp]
     simp only [Prod.mk.inj_iff, mem_map, mem_append, Prod.map_mk, Prod.exists] at h
diff --git a/Mathlib/Data/MvPolynomial/Rename.lean b/Mathlib/Data/MvPolynomial/Rename.lean
index 204d0bdd03bfe..68263de8a2a4d 100644
--- a/Mathlib/Data/MvPolynomial/Rename.lean
+++ b/Mathlib/Data/MvPolynomial/Rename.lean
@@ -236,8 +236,7 @@ theorem exists_finset_rename (p : MvPolynomial σ R) :
     exact ⟨∅, C r, by rw [rename_C]⟩
   · rintro p q ⟨s, p, rfl⟩ ⟨t, q, rfl⟩
     refine' ⟨s ∪ t, ⟨_, _⟩⟩
-    ·
-      refine' rename (Subtype.map id _) p + rename (Subtype.map id _) q <;>
+    · refine' rename (Subtype.map id _) p + rename (Subtype.map id _) q <;>
         simp (config := { contextual := true }) only [id.def, true_or_iff, or_true_iff,
           Finset.mem_union, forall_true_iff]
     · simp only [rename_rename, AlgHom.map_add]
diff --git a/Mathlib/Data/Nat/Choose/Basic.lean b/Mathlib/Data/Nat/Choose/Basic.lean
index 63c13f390773a..a04380cc012b9 100644
--- a/Mathlib/Data/Nat/Choose/Basic.lean
+++ b/Mathlib/Data/Nat/Choose/Basic.lean
@@ -100,7 +100,7 @@ theorem triangle_succ (n : ℕ) : (n + 1) * (n + 1 - 1) / 2 = n * (n - 1) / 2 +
 /-- `choose n 2` is the `n`-th triangle number. -/
 theorem choose_two_right (n : ℕ) : choose n 2 = n * (n - 1) / 2 := by
   induction' n with n ih
-  . simp
+  · simp
   · rw [triangle_succ n, choose, ih]
     simp [add_comm]
 #align nat.choose_two_right Nat.choose_two_right
@@ -187,7 +187,7 @@ theorem factorial_mul_factorial_dvd_factorial {n k : ℕ} (hk : k ≤ n) : k ! *
 
 theorem factorial_mul_factorial_dvd_factorial_add (i j : ℕ) : i ! * j ! ∣ (i + j)! := by
   suffices : i ! * (i + j - i) ! ∣ (i + j)!
-  . rwa [add_tsub_cancel_left i j] at this
+  · rwa [add_tsub_cancel_left i j] at this
   exact factorial_mul_factorial_dvd_factorial (Nat.le_add_right _ _)
 #align nat.factorial_mul_factorial_dvd_factorial_add Nat.factorial_mul_factorial_dvd_factorial_add
 
@@ -199,7 +199,7 @@ theorem choose_symm {n k : ℕ} (hk : k ≤ n) : choose n (n - k) = choose n k :
 
 theorem choose_symm_of_eq_add {n a b : ℕ} (h : n = a + b) : Nat.choose n a = Nat.choose n b := by
   suffices : choose n (n - b) = choose n b
-  . rw [h, add_tsub_cancel_right] at this; rwa [h]
+  · rw [h, add_tsub_cancel_right] at this; rwa [h]
   exact choose_symm (h ▸ le_add_left _ _)
 #align nat.choose_symm_of_eq_add Nat.choose_symm_of_eq_add
 
diff --git a/Mathlib/Data/Nat/Digits.lean b/Mathlib/Data/Nat/Digits.lean
index 388f9d501c161..2865b9f78c32b 100644
--- a/Mathlib/Data/Nat/Digits.lean
+++ b/Mathlib/Data/Nat/Digits.lean
@@ -310,7 +310,7 @@ theorem digits_eq_cons_digits_div {b n : ℕ} (h : 1 < b) (w : n ≠ 0) :
   · norm_num at h
   rcases n with (_ | n)
   · norm_num at w
-  . simp only [digits_add_two_add_one, ne_eq]
+  · simp only [digits_add_two_add_one, ne_eq]
 #align nat.digits_eq_cons_digits_div Nat.digits_eq_cons_digits_div
 
 theorem digits_getLast {b : ℕ} (m : ℕ) (h : 1 < b) (p q) :
@@ -381,8 +381,8 @@ theorem digits_lt_base' {b m : ℕ} : ∀ {d}, d ∈ digits (b + 2) m → d < b
   -- Porting note: Previous code (single line) contained linarith.
   -- . exact IH _ (Nat.div_lt_self (Nat.succ_pos _) (by linarith)) hd
   · apply IH ((n + 1) / (b + 2))
-    . apply Nat.div_lt_self <;> simp
-    . assumption
+    · apply Nat.div_lt_self <;> simp
+    · assumption
 #align nat.digits_lt_base' Nat.digits_lt_base'
 
 /-- The digits in the base b expansion of n are all less than b, if b ≥ 2 -/
diff --git a/Mathlib/Data/Nat/ModEq.lean b/Mathlib/Data/Nat/ModEq.lean
index 5e8a057f944d6..137c354d51688 100644
--- a/Mathlib/Data/Nat/ModEq.lean
+++ b/Mathlib/Data/Nat/ModEq.lean
@@ -293,8 +293,7 @@ lemma cancel_left_div_gcd (hm : 0 < m) (h : c * a ≡ c * b [MOD m]) :  a ≡ b
     rw [mul_sub]
     exact modEq_iff_dvd.mp h
   show Int.gcd (m / d) (c / d) = 1
-  ·
-    simp only [← Int.coe_nat_div, Int.coe_nat_gcd (m / d) (c / d), gcd_div hmd hcd,
+  · simp only [← Int.coe_nat_div, Int.coe_nat_gcd (m / d) (c / d), gcd_div hmd hcd,
       Nat.div_self (gcd_pos_of_pos_left c hm)]
 #align nat.modeq.cancel_left_div_gcd Nat.ModEq.cancel_left_div_gcd
 
diff --git a/Mathlib/Data/Ordmap/Ordnode.lean b/Mathlib/Data/Ordmap/Ordnode.lean
index 7a22c17beb925..fd1929c2caefd 100644
--- a/Mathlib/Data/Ordmap/Ordnode.lean
+++ b/Mathlib/Data/Ordmap/Ordnode.lean
@@ -208,8 +208,7 @@ def balanceL (l : Ordnode α) (x : α) (r : Ordnode α) : Ordnode α := by
         · exact node 3 (ι lx) lrx ι x
       · cases' id lr with lrs lrl lrx lrr
         · exact node 3 ll lx ι x
-        ·
-          exact
+        · exact
             if lrs < ratio * lls then node (ls + 1) ll lx (node (lrs + 1) lr x nil)
             else
               node (ls + 1) (node (lls + size lrl + 1) ll lx lrl) lrx
@@ -245,8 +244,7 @@ def balanceR (l : Ordnode α) (x : α) (r : Ordnode α) : Ordnode α := by
         · exact node 3 (ι x) rlx ι rx
       · cases' id rl with rls rll rlx rlr
         · exact node 3 (ι x) rx rr
-        ·
-          exact
+        · exact
             if rls < ratio * rrs then node (rs + 1) (node (rls + 1) nil x rl) rx rr
             else
               node (rs + 1) (node (size rll + 1) nil x rll) rlx
diff --git a/Mathlib/Data/PEquiv.lean b/Mathlib/Data/PEquiv.lean
index d4434d980303e..80070ce44ebc7 100644
--- a/Mathlib/Data/PEquiv.lean
+++ b/Mathlib/Data/PEquiv.lean
@@ -335,12 +335,12 @@ def single (a : α) (b : β) :
   inv x y := by
     dsimp only
     split_ifs with h1 h2
-    . simp [*]
-    . simp only [mem_def, some.injEq, iff_false] at *
+    · simp [*]
+    · simp only [mem_def, some.injEq, iff_false] at *
       exact Ne.symm h2
-    . simp only [mem_def, some.injEq, false_iff] at *
+    · simp only [mem_def, some.injEq, false_iff] at *
       exact Ne.symm h1
-    . simp
+    · simp
 #align pequiv.single PEquiv.single
 
 theorem mem_single (a : α) (b : β) : b ∈ single a b a :=
diff --git a/Mathlib/Data/PFunctor/Multivariate/Basic.lean b/Mathlib/Data/PFunctor/Multivariate/Basic.lean
index 7e64e04d16d62..43023fc6d8f83 100644
--- a/Mathlib/Data/PFunctor/Multivariate/Basic.lean
+++ b/Mathlib/Data/PFunctor/Multivariate/Basic.lean
@@ -174,7 +174,7 @@ theorem liftP_iff' {α : TypeVec n} (p : ∀ ⦃i⦄, α i → Prop) (a : P.A) (
   simp only [liftP_iff, Sigma.mk.inj_iff]; constructor
   · rintro ⟨_, _, ⟨⟩, _⟩
     assumption
-  . intro
+  · intro
     repeat' first |constructor|assumption
 #align mvpfunctor.liftp_iff' MvPFunctor.liftP_iff'
 
diff --git a/Mathlib/Data/PNat/Xgcd.lean b/Mathlib/Data/PNat/Xgcd.lean
index cf403fb3157cf..d5ac7bacc354d 100644
--- a/Mathlib/Data/PNat/Xgcd.lean
+++ b/Mathlib/Data/PNat/Xgcd.lean
@@ -155,8 +155,8 @@ theorem isSpecial_iff : u.IsSpecial ↔ u.IsSpecial' := by
   let ⟨wp, x, y, zp, ap, bp⟩ := u
   constructor <;> intro h <;> simp [w, z, succPNat] at * <;>
     simp only [← coe_inj, mul_coe, mk_coe] at *
-  . simp_all [← h, Nat.mul, Nat.succ_eq_add_one]; ring
-  . simp [Nat.succ_eq_add_one, Nat.mul_add, Nat.add_mul, ← Nat.add_assoc] at h; rw [← h]; ring
+  · simp_all [← h, Nat.mul, Nat.succ_eq_add_one]; ring
+  · simp [Nat.succ_eq_add_one, Nat.mul_add, Nat.add_mul, ← Nat.add_assoc] at h; rw [← h]; ring
   -- Porting note: Old code has been removed as it was much more longer.
 #align pnat.xgcd_type.is_special_iff PNat.XgcdType.isSpecial_iff
 
diff --git a/Mathlib/Data/Part.lean b/Mathlib/Data/Part.lean
index 7f2edcdc55c9c..fd64cdf7acf08 100644
--- a/Mathlib/Data/Part.lean
+++ b/Mathlib/Data/Part.lean
@@ -343,8 +343,8 @@ theorem ofOption_dom {α} : ∀ o : Option α, (ofOption o).Dom ↔ o.isSome
 theorem ofOption_eq_get {α} (o : Option α) : ofOption o = ⟨_, @Option.get _ o⟩ :=
   Part.ext' (ofOption_dom o) fun h₁ h₂ => by
     cases o
-    . simp at h₂
-    . rfl
+    · simp at h₂
+    · rfl
 #align part.of_option_eq_get Part.ofOption_eq_get
 
 instance : Coe (Option α) (Part α) :=
diff --git a/Mathlib/Data/Polynomial/RingDivision.lean b/Mathlib/Data/Polynomial/RingDivision.lean
index 015ee21974f67..49bac25287fa8 100644
--- a/Mathlib/Data/Polynomial/RingDivision.lean
+++ b/Mathlib/Data/Polynomial/RingDivision.lean
@@ -286,8 +286,7 @@ theorem irreducible_of_monic (hp : p.Monic) (hp1 : p ≠ 1) :
           (isUnit_of_mul_eq_one g _)⟩⟩
   · rwa [Monic, leadingCoeff_mul, leadingCoeff_C, ← leadingCoeff_mul, mul_comm, ← hfg, ← Monic]
   · rwa [Monic, leadingCoeff_mul, leadingCoeff_C, ← leadingCoeff_mul, ← hfg, ← Monic]
-  ·
-    rw [mul_mul_mul_comm, ← C_mul, ← leadingCoeff_mul, ← hfg, hp.leadingCoeff, C_1, mul_one,
+  · rw [mul_mul_mul_comm, ← C_mul, ← leadingCoeff_mul, ← hfg, hp.leadingCoeff, C_1, mul_one,
       mul_comm, ← hfg]
 #align polynomial.irreducible_of_monic Polynomial.irreducible_of_monic
 
@@ -734,8 +733,7 @@ theorem roots_pow (p : R[X]) (n : ℕ) : (p ^ n).roots = n • p.roots := by
   · rw [pow_zero, roots_one, Nat.zero_eq, zero_smul, empty_eq_zero]
   · rcases eq_or_ne p 0 with (rfl | hp)
     · rw [zero_pow n.succ_pos, roots_zero, smul_zero]
-    ·
-      rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
+    · rw [pow_succ', roots_mul (mul_ne_zero (pow_ne_zero _ hp) hp), ihn, Nat.succ_eq_add_one,
         add_smul, one_smul]
 #align polynomial.roots_pow Polynomial.roots_pow
 
@@ -897,8 +895,7 @@ theorem comp_eq_zero_iff : p.comp q = 0 ↔ p = 0 ∨ p.eval (q.coeff 0) = 0 ∧
       exact Or.inl (key.trans h)
     · rw [key, comp_C, C_eq_zero] at h
       exact Or.inr ⟨h, key⟩
-  ·
-    exact fun h =>
+  · exact fun h =>
       Or.rec (fun h => by rw [h, zero_comp]) (fun h => by rw [h.2, comp_C, h.1, C_0]) h
 #align polynomial.comp_eq_zero_iff Polynomial.comp_eq_zero_iff
 
diff --git a/Mathlib/Data/Rat/Floor.lean b/Mathlib/Data/Rat/Floor.lean
index 04af58e1d2f69..35e1d2d42e70d 100644
--- a/Mathlib/Data/Rat/Floor.lean
+++ b/Mathlib/Data/Rat/Floor.lean
@@ -36,8 +36,8 @@ variable {α : Type _} [LinearOrderedField α] [FloorRing α]
 protected theorem floor_def' (a : ℚ) : a.floor = a.num / a.den := by
   rw [Rat.floor]
   split
-  . next h => simp [h]
-  . next => rfl
+  · next h => simp [h]
+  · next => rfl
 
 protected theorem le_floor {z : ℤ} : ∀ {r : ℚ}, z ≤ Rat.floor r ↔ (z : ℚ) ≤ r
   | ⟨n, d, h, c⟩ => by
diff --git a/Mathlib/Data/Seq/Computation.lean b/Mathlib/Data/Seq/Computation.lean
index c72e51785363e..43bf76562f02e 100644
--- a/Mathlib/Data/Seq/Computation.lean
+++ b/Mathlib/Data/Seq/Computation.lean
@@ -58,8 +58,8 @@ instance : CoeTC α (Computation α) :=
 def think (c : Computation α) : Computation α :=
   ⟨Stream'.cons none c.1, fun n a h => by
     cases' n with n
-    . contradiction
-    . exact c.2 h⟩
+    · contradiction
+    · exact c.2 h⟩
 #align computation.think Computation.think
 
 /-- `thinkN c n` is the computation that delays for `n` ticks and then performs
@@ -304,8 +304,8 @@ theorem eq_of_bisim (bisim : IsBisimulation R) {s₁ s₂} (r : s₁ ~ s₂) : s
       have h := bisim r; revert r h
       apply recOn s _ _ <;> intro r' <;> apply recOn s' _ _ <;> intro a' r h
       · constructor <;> dsimp at h
-        . rw [h]
-        . rw [h] at r
+        · rw [h]
+        · rw [h] at r
           rw [tail_pure, tail_pure,h]
           assumption
       · rw [destruct_pure, destruct_think] at h
@@ -653,7 +653,7 @@ def map (f : α → β) : Computation α → Computation β
     ⟨s.map fun o => Option.casesOn o none (some ∘ f), fun n b => by
       dsimp [Stream'.map, Stream'.nth]
       induction' e : s n with a <;> intro h
-      . contradiction
+      · contradiction
       · rw [al e]; exact h⟩
 #align computation.map Computation.map
 
@@ -761,13 +761,13 @@ theorem bind_pure (f : α → β) (s) : bind s (pure ∘ f) = map f s := by
 @[simp]
 theorem bind_pure' (s : Computation α) : bind s pure = s := by
   apply eq_of_bisim fun c₁ c₂ => c₁ = c₂ ∨ ∃ s, c₁ = bind s (pure) ∧ c₂ = s
-  . intro c₁ c₂ h
+  · intro c₁ c₂ h
     exact
       match c₁, c₂, h with
       | _, c₂, Or.inl (Eq.refl _) => by cases' destruct c₂ with b cb <;> simp
       | _, _, Or.inr ⟨s, rfl, rfl⟩ => by
         apply recOn s <;> intro s <;> simp
-  . exact Or.inr ⟨s, rfl, rfl⟩
+  · exact Or.inr ⟨s, rfl, rfl⟩
 #align computation.bind_ret' Computation.bind_pure'
 
 @[simp]
diff --git a/Mathlib/Data/Seq/Seq.lean b/Mathlib/Data/Seq/Seq.lean
index 9d81450dd176d..e8c0024852a15 100644
--- a/Mathlib/Data/Seq/Seq.lean
+++ b/Mathlib/Data/Seq/Seq.lean
@@ -394,8 +394,8 @@ theorem eq_of_bisim (bisim : IsBisimulation R) {s₁ s₂} (r : s₁ ~ s₂) : s
       apply recOn s _ _ <;> apply recOn s' _ _
       · intro r _
         constructor
-        . rfl
-        . assumption
+        · rfl
+        · assumption
       · intro x s _ this
         rw [destruct_nil, destruct_cons] at this
         exact False.elim this
@@ -528,7 +528,7 @@ def map (f : α → β) : Seq α → Seq β
       induction' e : s n with e <;> intro
       · rw [al e]
         assumption
-      . contradiction⟩
+      · contradiction⟩
 #align stream.seq.map Stream'.Seq.map
 
 /-- Flatten a sequence of sequences. (It is required that the
@@ -862,8 +862,8 @@ theorem exists_of_mem_map {f} {b : β} : ∀ {s : Seq α}, b ∈ map f s → ∃
   | ⟨g, al⟩ =>
     let ⟨o, om, oe⟩ := @Stream'.exists_of_mem_map _ _ (Option.map f) (some b) g h
     cases' o with a
-    . injection oe
-    . injection oe with h' ; exact ⟨a, om, h'⟩
+    · injection oe
+    · injection oe with h' ; exact ⟨a, om, h'⟩
 #align stream.seq.exists_of_mem_map Stream'.Seq.exists_of_mem_map
 
 theorem of_mem_append {s₁ s₂ : Seq α} {a : α} (h : a ∈ append s₁ s₂) : a ∈ s₁ ∨ a ∈ s₂ := by
diff --git a/Mathlib/Data/Set/Basic.lean b/Mathlib/Data/Set/Basic.lean
index 908470e20d926..d8b3d033ec5aa 100644
--- a/Mathlib/Data/Set/Basic.lean
+++ b/Mathlib/Data/Set/Basic.lean
@@ -2188,8 +2188,8 @@ theorem powerset_singleton (x : α) : 𝒫({x} : Set α) = {∅, {x}} := by
 theorem mem_dite (p : Prop) [Decidable p] (s : p → Set α) (t : ¬ p → Set α) (x : α) :
     (x ∈ if h : p then s h else t h) ↔ (∀ h : p, x ∈ s h) ∧ ∀ h : ¬p, x ∈ t h := by
   split_ifs with hp
-  . exact ⟨fun hx => ⟨fun _ => hx, fun hnp => (hnp hp).elim⟩, fun hx => hx.1 hp⟩
-  . exact ⟨fun hx => ⟨fun h => (hp h).elim, fun _ => hx⟩, fun hx => hx.2 hp⟩
+  · exact ⟨fun hx => ⟨fun _ => hx, fun hnp => (hnp hp).elim⟩, fun hx => hx.1 hp⟩
+  · exact ⟨fun hx => ⟨fun h => (hp h).elim, fun _ => hx⟩, fun hx => hx.2 hp⟩
 
 --Porting note: Old proof was `split_ifs; simp [h]`
 theorem mem_dite_univ_right (p : Prop) [Decidable p] (t : p → Set α) (x : α) :
diff --git a/Mathlib/Data/Set/Image.lean b/Mathlib/Data/Set/Image.lean
index a5e6514abb914..db23b74022a07 100644
--- a/Mathlib/Data/Set/Image.lean
+++ b/Mathlib/Data/Set/Image.lean
@@ -1014,11 +1014,11 @@ theorem range_subtype_map {p : α → Prop} {q : β → Prop} (f : α → β) (h
   ext ⟨x, hx⟩
   rw [mem_preimage, mem_range, mem_image, Subtype.exists, Subtype.coe_mk]
   apply Iff.intro
-  . rintro ⟨a, b, hab⟩
+  · rintro ⟨a, b, hab⟩
     rw [Subtype.map, Subtype.mk.injEq] at hab
     use a
     trivial
-  . rintro ⟨a, b, hab⟩
+  · rintro ⟨a, b, hab⟩
     use a
     use b
     rw [Subtype.map, Subtype.mk.injEq]
@@ -1135,12 +1135,12 @@ theorem range_inclusion (h : s ⊆ t) : range (inclusion h) = { x : t | (x : α)
   ext ⟨x, hx⟩
   -- Porting note: `simp [inclusion]` doesn't solve goal
   apply Iff.intro
-  . rw [mem_range]
+  · rw [mem_range]
     rintro ⟨a, ha⟩
     rw [inclusion, Subtype.mk.injEq] at ha
     rw [mem_setOf, Subtype.coe_mk, ← ha]
     exact Subtype.coe_prop _
-  . rw [mem_setOf, Subtype.coe_mk, mem_range]
+  · rw [mem_setOf, Subtype.coe_mk, mem_range]
     intro hx'
     use ⟨x, hx'⟩
     trivial
diff --git a/Mathlib/Data/Set/Opposite.lean b/Mathlib/Data/Set/Opposite.lean
index 84619f0bb57f8..6296f90eae227 100644
--- a/Mathlib/Data/Set/Opposite.lean
+++ b/Mathlib/Data/Set/Opposite.lean
@@ -80,32 +80,32 @@ def opEquiv : Set α ≃ Set αᵒᵖ :=
 theorem singleton_op (x : α) : ({x} : Set α).op = {op x} := by
   ext
   constructor
-  . apply unop_injective
-  . apply op_injective
+  · apply unop_injective
+  · apply op_injective
 #align set.singleton_op Set.singleton_op
 
 @[simp]
 theorem singleton_unop (x : αᵒᵖ) : ({x} : Set αᵒᵖ).unop = {unop x} := by
   ext
   constructor
-  . apply op_injective
-  . apply unop_injective
+  · apply op_injective
+  · apply unop_injective
 #align set.singleton_unop Set.singleton_unop
 
 @[simp 1100]
 theorem singleton_op_unop (x : α) : ({op x} : Set αᵒᵖ).unop = {x} := by
   ext
   constructor
-  . apply op_injective
-  . apply unop_injective
+  · apply op_injective
+  · apply unop_injective
 #align set.singleton_op_unop Set.singleton_op_unop
 
 @[simp 1100]
 theorem singleton_unop_op (x : αᵒᵖ) : ({unop x} : Set α).op = {x} := by
   ext
   constructor
-  . apply unop_injective
-  . apply op_injective
+  · apply unop_injective
+  · apply op_injective
 #align set.singleton_unop_op Set.singleton_unop_op
 
 end Set
diff --git a/Mathlib/Data/TypeVec.lean b/Mathlib/Data/TypeVec.lean
index 1c67cbe77d0f4..c4f6738d49c48 100644
--- a/Mathlib/Data/TypeVec.lean
+++ b/Mathlib/Data/TypeVec.lean
@@ -175,8 +175,8 @@ theorem eq_of_drop_last_eq {α β : TypeVec (n + 1)} {f g : α ⟹ β} (h₀ : d
   -- porting note: FIXME: congr_fun h₀ <;> ext1 ⟨⟩ <;> apply_assumption
   refine funext (fun x => ?_)
   cases x
-  . apply h₁
-  . apply congr_fun h₀
+  · apply h₁
+  · apply congr_fun h₀
 #align typevec.eq_of_drop_last_eq TypeVec.eq_of_drop_last_eq
 
 @[simp]
@@ -675,9 +675,9 @@ theorem append_prod_appendFun {n} {α α' β β' : TypeVec.{u} n} {φ φ' ψ ψ'
     ((f₀ ⊗' g₀) ::: (_root_.Prod.map f₁ g₁)) = ((f₀ ::: f₁) ⊗' (g₀ ::: g₁)) := by
   ext i a
   cases i
-  . cases a
+  · cases a
     rfl
-  . rfl
+  · rfl
 #align typevec.append_prod_append_fun TypeVec.append_prod_appendFun
 
 end Liftp'
@@ -782,8 +782,8 @@ theorem prod_map_id {α β : TypeVec n} : (@TypeVec.id _ α ⊗' @TypeVec.id _ 
 theorem subtypeVal_diagSub {α : TypeVec n} : subtypeVal (repeatEq α) ⊚ diagSub = prod.diag := by
   ext i x
   induction' i with _ _ _ i_ih
-  . simp [comp, diagSub, subtypeVal, prod.diag]
-  . simp [prod.diag]
+  · simp [comp, diagSub, subtypeVal, prod.diag]
+  · simp [prod.diag]
     simp [comp, diagSub, subtypeVal, prod.diag] at *
     apply @i_ih (drop _)
 #align typevec.subtype_val_diag_sub TypeVec.subtypeVal_diagSub
diff --git a/Mathlib/Data/Vector/Basic.lean b/Mathlib/Data/Vector/Basic.lean
index 26b1593be0fcf..8806d69a8321e 100644
--- a/Mathlib/Data/Vector/Basic.lean
+++ b/Mathlib/Data/Vector/Basic.lean
@@ -581,14 +581,14 @@ theorem removeNth_insertNth' {v : Vector α (n + 1)} :
     · rcases Nat.exists_eq_succ_of_ne_zero
         (Nat.pos_iff_ne_zero.1 (lt_of_le_of_lt (Nat.zero_le _) hij)) with ⟨j, rfl⟩
       rw [← List.insertNth_removeNth_of_ge]
-      . simp; rfl
-      . simpa
-      . simpa [Nat.lt_succ_iff] using hij
+      · simp; rfl
+      · simpa
+      · simpa [Nat.lt_succ_iff] using hij
     · dsimp
       rw [← List.insertNth_removeNth_of_le i j _ _ _]
-      . rfl
-      . simpa
-      . simpa [not_lt] using hij
+      · rfl
+      · simpa
+      · simpa [not_lt] using hij
 #align vector.remove_nth_insert_nth' Vector.removeNth_insertNth'
 
 theorem insertNth_comm (a b : α) (i j : Fin (n + 1)) (h : i ≤ j) :
@@ -631,8 +631,8 @@ theorem get_set_of_ne {v : Vector α n} {i j : Fin n} (h : i ≠ j) (a : α) :
   cases v; cases i; cases j
   simp [Vector.set, Vector.get_eq_get, List.get_set_of_ne (Fin.vne_of_ne h)]
   rw [List.get_set_of_ne]
-  . rfl
-  . simpa using h
+  · rfl
+  · simpa using h
 #align vector.nth_update_nth_of_ne Vector.get_set_of_ne
 
 theorem get_set_eq_if {v : Vector α n} {i j : Fin n} (a : α) :
@@ -713,8 +713,8 @@ protected theorem comp_traverse (f : β → F γ) (g : α → G β) (x : Vector
       Comp.mk (Vector.traverse f <$> Vector.traverse g x) := by
   induction' x using Vector.inductionOn with n x xs ih
   simp! [cast, *, functor_norm]
-  . rfl
-  . rw [Vector.traverse_def, ih]
+  · rfl
+  · rw [Vector.traverse_def, ih]
     simp [functor_norm, (. ∘ .)]
 #align vector.comp_traverse Vector.comp_traverse
 
@@ -728,8 +728,8 @@ variable (η : ApplicativeTransformation F G)
 protected theorem naturality {α β : Type _} (f : α → F β) (x : Vector α n) :
     η (x.traverse f) = x.traverse (@η _ ∘ f) := by
   induction' x using Vector.inductionOn with n x xs ih
-  . simp! [functor_norm, cast, η.preserves_pure]
-  . rw [Vector.traverse_def, Vector.traverse_def, ← ih, η.preserves_seq, η.preserves_map]
+  · simp! [functor_norm, cast, η.preserves_pure]
+  · rw [Vector.traverse_def, Vector.traverse_def, ← ih, η.preserves_seq, η.preserves_map]
     rfl
 #align vector.naturality Vector.naturality
 
@@ -807,8 +807,8 @@ theorem get_map₂ (v₁ : Vector α n) (v₂ : Vector β n) (f : α → β →
   case cons x xs y ys ih =>
     rw [map₂_cons]
     cases i using Fin.cases
-    . simp only [get_zero, head_cons]
-    . simp only [get_cons_succ, ih]
+    · simp only [get_zero, head_cons]
+    · simp only [get_cons_succ, ih]
 
 
 
diff --git a/Mathlib/Data/Vector/Snoc.lean b/Mathlib/Data/Vector/Snoc.lean
index e4af114c0d6be..39cd695bad044 100644
--- a/Mathlib/Data/Vector/Snoc.lean
+++ b/Mathlib/Data/Vector/Snoc.lean
@@ -141,8 +141,8 @@ theorem mapAccumr_snoc :
       let r := mapAccumr f xs q.1
       (r.1, r.2.snoc q.2) := by
   induction xs using Vector.inductionOn
-  . rfl
-  . simp[*]
+  · rfl
+  · simp[*]
 
 variable (ys : Vector β n)
 
diff --git a/Mathlib/Data/ZMod/Basic.lean b/Mathlib/Data/ZMod/Basic.lean
index e1a564628991b..6eeb68c1dce0a 100644
--- a/Mathlib/Data/ZMod/Basic.lean
+++ b/Mathlib/Data/ZMod/Basic.lean
@@ -161,8 +161,8 @@ instance (priority := 900) (n : ℕ) : CoeTC (ZMod n) R :=
 theorem cast_zero : ((0 : ZMod n) : R) = 0 := by
   delta ZMod.cast
   cases n
-  . exact Int.cast_zero
-  . simp
+  · exact Int.cast_zero
+  · simp
 #align zmod.cast_zero ZMod.cast_zero
 
 theorem cast_eq_val [NeZero n] (a : ZMod n) : (a : R) = a.val := by
@@ -176,15 +176,15 @@ variable {S : Type _} [AddGroupWithOne S]
 @[simp]
 theorem _root_.Prod.fst_zmod_cast (a : ZMod n) : (a : R × S).fst = a := by
   cases n
-  . rfl
-  . simp [ZMod.cast]
+  · rfl
+  · simp [ZMod.cast]
 #align prod.fst_zmod_cast Prod.fst_zmod_cast
 
 @[simp]
 theorem _root_.Prod.snd_zmod_cast (a : ZMod n) : (a : R × S).snd = a := by
   cases n
-  . rfl
-  . simp [ZMod.cast]
+  · rfl
+  · simp [ZMod.cast]
 #align prod.snd_zmod_cast Prod.snd_zmod_cast
 
 end
@@ -750,14 +750,14 @@ def chineseRemainder {m n : ℕ} (h : m.coprime n) : ZMod (m * n) ≃+* ZMod m 
   have inv : Function.LeftInverse inv_fun to_fun ∧ Function.RightInverse inv_fun to_fun :=
     if hmn0 : m * n = 0 then by
       rcases h.eq_of_mul_eq_zero hmn0 with (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩)
-      . constructor
-        . intro x; rfl
-        . rintro ⟨x, y⟩
+      · constructor
+        · intro x; rfl
+        · rintro ⟨x, y⟩
           fin_cases y
           simp [castHom, Prod.ext_iff]
-      . constructor
-        . intro x; rfl
-        . rintro ⟨x, y⟩
+      · constructor
+        · intro x; rfl
+        · rintro ⟨x, y⟩
           fin_cases x
           simp [castHom, Prod.ext_iff]
     else by
@@ -1162,8 +1162,8 @@ instance subsingleton_ringEquiv [Semiring R] : Subsingleton (ZMod n ≃+* R) :=
 @[simp]
 theorem ringHom_map_cast [Ring R] (f : R →+* ZMod n) (k : ZMod n) : f k = k := by
   cases n
-  . dsimp [ZMod, ZMod.cast] at f k ⊢; simp
-  . dsimp [ZMod, ZMod.cast] at f k ⊢
+  · dsimp [ZMod, ZMod.cast] at f k ⊢; simp
+  · dsimp [ZMod, ZMod.cast] at f k ⊢
     erw [map_natCast, Fin.cast_val_eq_self]
 #align zmod.ring_hom_map_cast ZMod.ringHom_map_cast
 
diff --git a/Mathlib/FieldTheory/Normal.lean b/Mathlib/FieldTheory/Normal.lean
index 144aab95b4e51..daf45d3754534 100644
--- a/Mathlib/FieldTheory/Normal.lean
+++ b/Mathlib/FieldTheory/Normal.lean
@@ -521,7 +521,7 @@ theorem restrictScalars_eq_iSup_adjoin [h : Normal F L] :
     apply PowerBasis.lift_gen
     change aeval y (minpoly F (AdjoinSimple.gen F x)) = 0
     suffices : minpoly F (AdjoinSimple.gen F x) = minpoly F x
-    . exact this ▸ aeval_eq_zero_of_mem_rootSet (Multiset.mem_toFinset.mpr hy)
+    · exact this ▸ aeval_eq_zero_of_mem_rootSet (Multiset.mem_toFinset.mpr hy)
     exact minpoly_gen ((isIntegral_algebraMap_iff (algebraMap K L).injective).mp
       (h.isIntegral (algebraMap K L x)))
 
diff --git a/Mathlib/FieldTheory/RatFunc.lean b/Mathlib/FieldTheory/RatFunc.lean
index 4bb8995af21ad..6009bdc0dc1d3 100644
--- a/Mathlib/FieldTheory/RatFunc.lean
+++ b/Mathlib/FieldTheory/RatFunc.lean
@@ -253,8 +253,7 @@ theorem liftOn_mk {P : Sort v} (p q : K[X]) (f : ∀ _p _q : K[X], P) (f0 : ∀
   · subst hq
     simp only [mk_zero, f0, ← Localization.mk_zero 1, Localization.liftOn_mk,
       liftOn_ofFractionRing_mk, Submonoid.coe_one]
-  ·
-    simp only [mk_eq_localization_mk _ hq, Localization.liftOn_mk, liftOn_ofFractionRing_mk]
+  · simp only [mk_eq_localization_mk _ hq, Localization.liftOn_mk, liftOn_ofFractionRing_mk]
 #align ratfunc.lift_on_mk RatFunc.liftOn_mk
 
 /-- Non-dependent recursion principle for `RatFunc K`: if `f p q : P` for all `p q`,
diff --git a/Mathlib/Geometry/Manifold/VectorBundle/Basic.lean b/Mathlib/Geometry/Manifold/VectorBundle/Basic.lean
index e6c5beaf93043..74a1619da6c60 100644
--- a/Mathlib/Geometry/Manifold/VectorBundle/Basic.lean
+++ b/Mathlib/Geometry/Manifold/VectorBundle/Basic.lean
@@ -422,7 +422,7 @@ theorem Trivialization.contMDiffOn_symm_trans :
   rintro ⟨b, x⟩ hb
   refine Prod.ext ?_ rfl
   · have : (e.toLocalHomeomorph.symm (b, x)).1 ∈ e'.baseSet
-    . simp_all only [Trivialization.mem_target, mfld_simps]
+    · simp_all only [Trivialization.mem_target, mfld_simps]
     exact (e'.coe_fst' this).trans (e.proj_symm_apply hb.1)
 
 variable {IB e e'}
diff --git a/Mathlib/GroupTheory/Congruence.lean b/Mathlib/GroupTheory/Congruence.lean
index 7ca24681e3e00..d8d17c9fdacb1 100644
--- a/Mathlib/GroupTheory/Congruence.lean
+++ b/Mathlib/GroupTheory/Congruence.lean
@@ -512,11 +512,11 @@ theorem conGen_eq (r : M → M → Prop) : conGen r = sInf { s : Con M | ∀ x y
     (le_sInf (fun s hs x y (hxy : (conGen r).r x y) =>
       show s.r x y by
         apply ConGen.Rel.recOn (motive := fun x y _ => s.r x y) hxy
-        . exact fun x y h => hs x y h
-        . exact s.refl'
-        . exact fun _ => s.symm'
-        . exact fun _ _ => s.trans'
-        . exact fun _ _ => s.mul))
+        · exact fun x y h => hs x y h
+        · exact s.refl'
+        · exact fun _ => s.symm'
+        · exact fun _ _ => s.trans'
+        · exact fun _ _ => s.mul))
     (sInf_le ConGen.Rel.of)
 #align con.con_gen_eq Con.conGen_eq
 #align add_con.add_con_gen_eq AddCon.addConGen_eq
@@ -716,10 +716,10 @@ def correspondence : { d // c ≤ d } ≃o Con c.Quotient
           Con.induction_on₂ x y fun w z h => ⟨w, z, rfl, rfl, h⟩⟩
   map_rel_iff' := @fun s t => by
     constructor
-    . intros h x y hs
+    · intros h x y hs
       rcases h ⟨x, y, rfl, rfl, hs⟩ with ⟨a, b, hx, hy, ht⟩
       exact t.1.trans (t.1.symm <| t.2 <| eq_rel.1 hx) (t.1.trans ht (t.2 <| eq_rel.1 hy))
-    . intros h _ _ hs
+    · intros h _ _ hs
       rcases hs with ⟨a, b, hx, hy, Hs⟩
       exact ⟨a, b, hx, hy, h Hs⟩
 #align con.correspondence Con.correspondence
@@ -1305,10 +1305,10 @@ def liftOnUnits (u : Units c.Quotient) (f : ∀ x y : M, c (x * y) 1 → c (y *
       (fun x y x' y' hx hy => _) u.3 u.4
   refine' Function.hfunext _ _
   rw [c.eq.2 hx, c.eq.2 hy]
-  . rintro Hxy Hxy' -
+  · rintro Hxy Hxy' -
     refine' Function.hfunext _ _
     · rw [c.eq.2 hx, c.eq.2 hy]
-    . rintro Hyx Hyx' -
+    · rintro Hyx Hyx' -
       exact heq_of_eq (Hf _ _ _ _ _ _ _ _ hx hy)
 #align con.lift_on_units Con.liftOnUnits
 #align add_con.lift_on_add_units AddCon.liftOnAddUnits
diff --git a/Mathlib/GroupTheory/FreeProduct.lean b/Mathlib/GroupTheory/FreeProduct.lean
index d143cad46390b..63f282ae051e1 100644
--- a/Mathlib/GroupTheory/FreeProduct.lean
+++ b/Mathlib/GroupTheory/FreeProduct.lean
@@ -428,8 +428,8 @@ theorem of_smul_def (i) (w : Word M) (m : M i) :
 theorem cons_eq_smul {i} {m : M i} {ls h1 h2} :
     Word.mk (⟨i, m⟩::ls) h1 h2 = of m • mkAux ls h1 h2 := by
   rw [cons_eq_rcons, of_smul_def, equivPair_eq_of_fstIdx_ne _]
-  . simp
-  . rw [fstIdx_ne_iff]
+  · simp
+  · rw [fstIdx_ne_iff]
     exact (List.chain'_cons'.1 h2).1
 #align free_product.word.cons_eq_smul FreeProduct.Word.cons_eq_smul
 
@@ -950,10 +950,10 @@ theorem _root_.FreeGroup.injective_lift_of_ping_pong : Function.Injective (FreeG
         _ ⊆ X i := by
           clear hnne0 hlt
           refine Int.le_induction (P := fun n => a i ^ n • (Y i)ᶜ ⊆ X i) ?_ ?_ n h1n
-          . dsimp
+          · dsimp
             rw [zpow_one]
             exact hX i
-          . dsimp
+          · dsimp
             intro n _hle hi
             calc
               a i ^ (n + 1) • (Y i)ᶜ = (a i ^ n * a i) • (Y i)ᶜ := by rw [zpow_add, zpow_one]
diff --git a/Mathlib/GroupTheory/Nilpotent.lean b/Mathlib/GroupTheory/Nilpotent.lean
index d2861cb83ad02..d7affaa034c3f 100644
--- a/Mathlib/GroupTheory/Nilpotent.lean
+++ b/Mathlib/GroupTheory/Nilpotent.lean
@@ -712,8 +712,7 @@ theorem lowerCentralSeries_prod (n : ℕ) :
     lowerCentralSeries (G₁ × G₂) n = (lowerCentralSeries G₁ n).prod (lowerCentralSeries G₂ n) := by
   induction' n with n ih
   · simp
-  ·
-    calc
+  · calc
       lowerCentralSeries (G₁ × G₂) n.succ = ⁅lowerCentralSeries (G₁ × G₂) n, ⊤⁆ := rfl
       _ = ⁅(lowerCentralSeries G₁ n).prod (lowerCentralSeries G₂ n), ⊤⁆ := by rw [ih]
       _ = ⁅(lowerCentralSeries G₁ n).prod (lowerCentralSeries G₂ n), (⊤ : Subgroup G₁).prod ⊤⁆ :=
@@ -755,8 +754,7 @@ theorem lowerCentralSeries_pi_le (n : ℕ) :
   let pi := fun f : ∀ i, Subgroup (Gs i) => Subgroup.pi Set.univ f
   induction' n with n ih
   · simp [pi_top]
-  ·
-    calc
+  · calc
       lowerCentralSeries (∀ i, Gs i) n.succ = ⁅lowerCentralSeries (∀ i, Gs i) n, ⊤⁆ := rfl
       _ ≤ ⁅pi fun i => lowerCentralSeries (Gs i) n, ⊤⁆ := (commutator_mono ih (le_refl _))
       _ = ⁅pi fun i => lowerCentralSeries (Gs i) n, pi fun i => ⊤⁆ := by simp [pi_top]
@@ -790,8 +788,7 @@ theorem lowerCentralSeries_pi_of_finite [Finite η] (n : ℕ) :
   let pi := fun f : ∀ i, Subgroup (Gs i) => Subgroup.pi Set.univ f
   induction' n with n ih
   · simp [pi_top]
-  ·
-    calc
+  · calc
       lowerCentralSeries (∀ i, Gs i) n.succ = ⁅lowerCentralSeries (∀ i, Gs i) n, ⊤⁆ := rfl
       _ = ⁅pi fun i => lowerCentralSeries (Gs i) n, ⊤⁆ := by rw [ih]
       _ = ⁅pi fun i => lowerCentralSeries (Gs i) n, pi fun i => ⊤⁆ := by simp [pi_top]
diff --git a/Mathlib/GroupTheory/Perm/Cycle/Basic.lean b/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
index e8d8b12923b4f..fa378b342fa14 100644
--- a/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
+++ b/Mathlib/GroupTheory/Perm/Cycle/Basic.lean
@@ -1713,8 +1713,7 @@ theorem isConj_of_support_equiv
   by_cases hx : x ∈ σ.support
   · rw [Equiv.extendSubtype_apply_of_mem, Equiv.extendSubtype_apply_of_mem]
     · exact hf x (Finset.mem_coe.2 hx)
-  ·
-    rwa [Classical.not_not.1 ((not_congr mem_support).1 (Equiv.extendSubtype_not_mem f _ _)),
+  · rwa [Classical.not_not.1 ((not_congr mem_support).1 (Equiv.extendSubtype_not_mem f _ _)),
       Classical.not_not.1 ((not_congr mem_support).mp hx)]
 #align equiv.perm.is_conj_of_support_equiv Equiv.Perm.isConj_of_support_equiv
 
diff --git a/Mathlib/GroupTheory/Perm/List.lean b/Mathlib/GroupTheory/Perm/List.lean
index 4f4c89f836373..d41beb9d97d8b 100644
--- a/Mathlib/GroupTheory/Perm/List.lean
+++ b/Mathlib/GroupTheory/Perm/List.lean
@@ -95,9 +95,9 @@ theorem formPerm_apply_mem_of_mem (x : α) (l : List α) (h : x ∈ l) : formPer
   · by_cases hx : x ∈ z :: l
     · rw [formPerm_cons_cons, mul_apply, swap_apply_def]
       split_ifs
-      . simp [IH _ _ hx]
-      . simp
-      . simpa [*] using IH _ _ hx
+      · simp [IH _ _ hx]
+      · simp
+      · simpa [*] using IH _ _ hx
     · replace h : x = y := Or.resolve_right (mem_cons.1 h) hx
       simp [formPerm_apply_of_not_mem _ _ hx, ← h]
 #align list.form_perm_apply_mem_of_mem List.formPerm_apply_mem_of_mem
@@ -116,7 +116,7 @@ theorem mem_of_formPerm_apply_mem (x : α) (l : List α) (h : l.formPerm x ∈ l
         List.mem_cons, swap_apply_def, ite_eq_left_iff] at h
       simp only [List.mem_cons]
       rcases h with h | h | h <;> split_ifs at h with h1 <;> try { aesop }
-      . simp [h1, imp_false] at h
+      · simp [h1, imp_false] at h
         simp [h]
 #align list.mem_of_form_perm_apply_mem List.mem_of_formPerm_apply_mem
 
@@ -221,7 +221,7 @@ theorem formPerm_apply_lt (xs : List α) (h : Nodup xs) (n : ℕ) (hn : n + 1 <
       simp only [swap_apply_eq_iff, coe_mul, formPerm_cons_cons, Function.comp]
       simp only [nthLe, get_cons_succ] at *
       rw [← IH, swap_apply_of_ne_of_ne] <;>
-      . intro hx
+      · intro hx
         rw [← hx, IH] at h
         simp [get_mem] at h
 #align list.form_perm_apply_lt List.formPerm_apply_lt
@@ -304,7 +304,7 @@ theorem formPerm_reverse (l : List α) (h : Nodup l) : formPerm l.reverse = (for
   -- We only have to check for `x ∈ l` that `formPerm l (formPerm l.reverse x)`
   rw [mul_apply, one_apply]
   cases' Classical.em (x ∈ l) with hx hx
-  . obtain ⟨k, hk, rfl⟩ := nthLe_of_mem ((mem_reverse _ _).mpr hx)
+  · obtain ⟨k, hk, rfl⟩ := nthLe_of_mem ((mem_reverse _ _).mpr hx)
     have h1 : l.length - 1 - k < l.length := by
       rw [Nat.sub_sub, add_comm]
       exact Nat.sub_lt_self (Nat.succ_pos _) (Nat.succ_le_of_lt (by simpa using hk))
@@ -317,10 +317,10 @@ theorem formPerm_reverse (l : List α) (h : Nodup l) : formPerm l.reverse = (for
     congr
     rw [length_reverse] at *
     cases' lt_or_eq_of_le (Nat.succ_le_of_lt hk) with h h
-    . rw [Nat.mod_eq_of_lt h, ← Nat.sub_add_comm, Nat.succ_sub_succ_eq_sub,
+    · rw [Nat.mod_eq_of_lt h, ← Nat.sub_add_comm, Nat.succ_sub_succ_eq_sub,
         Nat.mod_eq_of_lt h1]
       exact (Nat.le_sub_iff_add_le (length_pos_of_mem hx)).2 (Nat.succ_le_of_lt h)
-    . rw [← h]; simp
+    · rw [← h]; simp
   · rw [formPerm_apply_of_not_mem x l.reverse, formPerm_apply_of_not_mem _ _ hx]
     simpa using hx
 #align list.form_perm_reverse List.formPerm_reverse
@@ -389,8 +389,7 @@ theorem formPerm_apply_mem_eq_self_iff (hl : Nodup l) (x : α) (hx : x ∈ l) :
   · rw [hn] at hk
     cases' (Nat.le_of_lt_succ hk).eq_or_lt with hk' hk'
     · simp [← hk', Nat.succ_le_succ_iff, eq_comm]
-    ·
-      simpa [Nat.mod_eq_of_lt (Nat.succ_lt_succ hk'), Nat.succ_lt_succ_iff] using
+    · simpa [Nat.mod_eq_of_lt (Nat.succ_lt_succ hk'), Nat.succ_lt_succ_iff] using
         k.zero_le.trans_lt hk'
 #align list.form_perm_apply_mem_eq_self_iff List.formPerm_apply_mem_eq_self_iff
 
diff --git a/Mathlib/GroupTheory/Perm/Sign.lean b/Mathlib/GroupTheory/Perm/Sign.lean
index 2fed0f3b84cb8..bbe12adac0db9 100644
--- a/Mathlib/GroupTheory/Perm/Sign.lean
+++ b/Mathlib/GroupTheory/Perm/Sign.lean
@@ -50,9 +50,9 @@ def modSwap [DecidableEq α] (i j : α) : Setoid (Perm α) :=
     fun {σ τ υ} hστ hτυ => by
     cases' hστ with hστ hστ <;> cases' hτυ with hτυ hτυ <;> try rw [hστ, hτυ, swap_mul_self_mul] <;>
     simp [hστ, hτυ] -- porting note: should close goals, but doesn't
-    . simp [hστ, hτυ]
-    . simp [hστ, hτυ]
-    . simp [hστ, hτυ]⟩
+    · simp [hστ, hτυ]
+    · simp [hστ, hτυ]
+    · simp [hστ, hτυ]⟩
 #align equiv.perm.mod_swap Equiv.Perm.modSwap
 
 noncomputable instance {α : Type _} [Fintype α] [DecidableEq α] (i j : α) :
@@ -184,8 +184,7 @@ theorem Disjoint.extendDomain {α : Type _} {p : β → Prop} [DecidablePred p]
     {σ τ : Perm α} (h : Disjoint σ τ) : Disjoint (σ.extendDomain f) (τ.extendDomain f) := by
   intro b
   by_cases pb : p b
-  ·
-    refine' (h (f.symm ⟨b, pb⟩)).imp _ _ <;>
+  · refine' (h (f.symm ⟨b, pb⟩)).imp _ _ <;>
       · intro h
         rw [extendDomain_apply_subtype _ _ pb, h, apply_symm_apply, Subtype.coe_mk]
   · left
@@ -339,8 +338,8 @@ theorem signBijAux_inj {n : ℕ} {f : Perm (Fin n)} :
     have : ¬b₁ < b₂ := hb.le.not_lt
     split_ifs at h <;>
     simp_all [(Equiv.injective f).eq_iff, eq_self_iff_true, and_self_iff, heq_iff_eq]
-    . exact absurd this (not_le.mpr ha)
-    . exact absurd this (not_le.mpr ha)
+    · exact absurd this (not_le.mpr ha)
+    · exact absurd this (not_le.mpr ha)
 #align equiv.perm.sign_bij_aux_inj Equiv.Perm.signBijAux_inj
 
 theorem signBijAux_surj {n : ℕ} {f : Perm (Fin n)} :
@@ -377,18 +376,18 @@ theorem signAux_inv {n : ℕ} (f : Perm (Fin n)) : signAux f⁻¹ = signAux f :=
         simp_all [signBijAux, dif_pos h, if_neg h.not_le, apply_inv_self, apply_inv_self,
           if_neg (mem_finPairsLT.1 hab).not_le]
         split_ifs with h₁
-        . dsimp [finPairsLT] at hab
+        · dsimp [finPairsLT] at hab
           simp at hab
           exact absurd h₁ (not_le_of_gt hab)
-        . rfl
+        · rfl
       else by
         simp_all [signBijAux, if_pos (le_of_not_gt h), dif_neg h, apply_inv_self, apply_inv_self,
           if_pos (mem_finPairsLT.1 hab).le]
         split_ifs with h₁ h₂ h₃
-        . rfl
-        . exact absurd h (not_le_of_gt h₁)
-        . rfl
-        . dsimp at *
+        · rfl
+        · exact absurd h (not_le_of_gt h₁)
+        · rfl
+        · dsimp at *
           dsimp [finPairsLT] at hab
           simp at *
           exact absurd h₃ (asymm_of LT.lt hab))
@@ -410,8 +409,8 @@ theorem signAux_mul {n : ℕ} (f g : Perm (Fin n)) : signAux (f * g) = signAux f
   · rw [dif_pos h]
     simp only [not_le_of_gt hab, mul_one, mul_ite, mul_neg, Perm.inv_apply_self, if_false]
     split_ifs with h₁ h₂ h₃ <;> dsimp at *
-    . exact absurd hab (not_lt_of_ge h₂)
-    . exact absurd hab (not_lt_of_ge h₃)
+    · exact absurd hab (not_lt_of_ge h₂)
+    · exact absurd hab (not_lt_of_ge h₃)
   · rw [dif_neg h, inv_apply_self, inv_apply_self, if_pos hab.le]
     by_cases h₁ : f (g b) ≤ f (g a)
     · have : f (g b) ≠ f (g a) := by
diff --git a/Mathlib/GroupTheory/Perm/Support.lean b/Mathlib/GroupTheory/Perm/Support.lean
index 1231fc5864727..ad497c6727537 100644
--- a/Mathlib/GroupTheory/Perm/Support.lean
+++ b/Mathlib/GroupTheory/Perm/Support.lean
@@ -518,8 +518,7 @@ theorem eq_on_support_mem_disjoint {l : List (Perm α)} (h : f ∈ l) (hl : l.Pa
     rw [List.pairwise_cons] at hl
     rw [List.mem_cons] at h
     rcases h with (rfl | h)
-    ·
-      rw [List.prod_cons, mul_apply,
+    · rw [List.prod_cons, mul_apply,
         not_mem_support.mp ((disjoint_prod_right tl hl.left).mem_imp hx)]
     · rw [List.prod_cons, mul_apply, ← IH h hl.right _ hx, eq_comm, ← not_mem_support]
       refine' (hl.left _ h).symm.mem_imp _
diff --git a/Mathlib/GroupTheory/SpecificGroups/Cyclic.lean b/Mathlib/GroupTheory/SpecificGroups/Cyclic.lean
index 13919064d6099..30f9babbedc0a 100644
--- a/Mathlib/GroupTheory/SpecificGroups/Cyclic.lean
+++ b/Mathlib/GroupTheory/SpecificGroups/Cyclic.lean
@@ -199,7 +199,7 @@ instance Subgroup.isCyclic {α : Type u} [Group α] [IsCyclic α] (H : Subgroup
             cases' k with k k
             · rw [Int.ofNat_eq_coe, Int.natAbs_cast k, ← zpow_ofNat, ←Int.ofNat_eq_coe, hk]
               exact hx₁
-            . rw [Int.natAbs_negSucc, ← Subgroup.inv_mem_iff H]; simp_all⟩
+            · rw [Int.natAbs_negSucc, ← Subgroup.inv_mem_iff H]; simp_all⟩
     ⟨⟨⟨g ^ Nat.find hex, (Nat.find_spec hex).2⟩, fun ⟨x, hx⟩ =>
         let ⟨k, hk⟩ := hg x
         have hk : g ^ k = x := hk
diff --git a/Mathlib/GroupTheory/Torsion.lean b/Mathlib/GroupTheory/Torsion.lean
index 4b63e8191af23..49a729a7d3eef 100644
--- a/Mathlib/GroupTheory/Torsion.lean
+++ b/Mathlib/GroupTheory/Torsion.lean
@@ -251,8 +251,7 @@ theorem primaryComponent.disjoint {p' : ℕ} [hp' : Fact p'.Prime] (hne : p ≠
   Submonoid.disjoint_def.mpr <| by
     rintro g ⟨_ | n, hn⟩ ⟨n', hn'⟩
     · rwa [pow_zero, orderOf_eq_one_iff] at hn
-    ·
-      exact
+    · exact
         absurd (eq_of_prime_pow_eq hp.out.prime hp'.out.prime n.succ_pos (hn.symm.trans hn')) hne
 #align comm_monoid.primary_component.disjoint CommMonoid.primaryComponent.disjoint
 #align add_comm_monoid.primary_component.disjoint AddCommMonoid.primaryComponent.disjoint
diff --git a/Mathlib/Init/Data/List/Instances.lean b/Mathlib/Init/Data/List/Instances.lean
index 999d90487ca79..2327600de9786 100644
--- a/Mathlib/Init/Data/List/Instances.lean
+++ b/Mathlib/Init/Data/List/Instances.lean
@@ -24,8 +24,8 @@ instance decidableBex : ∀ (l : List α), Decidable (∃ x ∈ l, p x)
       | isFalse h₂ => isFalse <| by
         intro h; cases' h with y h; cases' h with hm hp;
         cases' mem_cons.1 hm with h h
-        . rw [h] at hp; contradiction
-        . exact absurd ⟨y, h, hp⟩ h₂
+        · rw [h] at hp; contradiction
+        · exact absurd ⟨y, h, hp⟩ h₂
 #align list.decidable_bex List.decidableBex
 
 instance decidableBall (l : List α) : Decidable (∀ x ∈ l, p x) :=
diff --git a/Mathlib/LinearAlgebra/Dual.lean b/Mathlib/LinearAlgebra/Dual.lean
index c3f4c6df09a15..1fc13b1654007 100644
--- a/Mathlib/LinearAlgebra/Dual.lean
+++ b/Mathlib/LinearAlgebra/Dual.lean
@@ -1624,8 +1624,8 @@ isomorphism `R ⊗ R ≃ R`.
 noncomputable def dualDistribEquivOfBasis (b : Basis ι R M) (c : Basis κ R N) :
     Dual R M ⊗[R] Dual R N ≃ₗ[R] Dual R (M ⊗[R] N) := by
   refine' LinearEquiv.ofLinear (dualDistrib R M N) (dualDistribInvOfBasis b c) _ _
-  . exact dualDistrib_dualDistribInvOfBasis_left_inverse _ _
-  . exact dualDistrib_dualDistribInvOfBasis_right_inverse _ _
+  · exact dualDistrib_dualDistribInvOfBasis_left_inverse _ _
+  · exact dualDistrib_dualDistribInvOfBasis_right_inverse _ _
 #align tensor_product.dual_distrib_equiv_of_basis TensorProduct.dualDistribEquivOfBasis
 
 variable (R M N)
diff --git a/Mathlib/LinearAlgebra/Matrix/Adjugate.lean b/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
index c8c913e67f105..d035d3fd903a1 100644
--- a/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Adjugate.lean
@@ -348,8 +348,7 @@ theorem adjugate_diagonal (v : n → α) :
   ext i j
   simp only [adjugate_def, cramer_apply, diagonal_transpose, of_apply]
   obtain rfl | hij := eq_or_ne i j
-  ·
-    rw [diagonal_apply_eq, diagonal_updateColumn_single, det_diagonal,
+  · rw [diagonal_apply_eq, diagonal_updateColumn_single, det_diagonal,
       prod_update_of_mem (Finset.mem_univ _), sdiff_singleton_eq_erase, one_mul]
   · rw [diagonal_apply_ne _ hij]
     refine' det_eq_zero_of_row_eq_zero j fun k => _
diff --git a/Mathlib/LinearAlgebra/Matrix/Determinant.lean b/Mathlib/LinearAlgebra/Matrix/Determinant.lean
index 15d69608cd330..7888e3ebc1a48 100644
--- a/Mathlib/LinearAlgebra/Matrix/Determinant.lean
+++ b/Mathlib/LinearAlgebra/Matrix/Determinant.lean
@@ -716,8 +716,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   rw [Matrix.det_apply, Finset.univ_perm_fin_succ, ← Finset.univ_product_univ]
   simp only [Finset.sum_map, Equiv.toEmbedding_apply, Finset.sum_product, Matrix.submatrix]
   refine' Finset.sum_congr rfl fun i _ => Fin.cases _ (fun i => _) i
-  ·
-    simp only [Fin.prod_univ_succ, Matrix.det_apply, Finset.mul_sum,
+  · simp only [Fin.prod_univ_succ, Matrix.det_apply, Finset.mul_sum,
       Equiv.Perm.decomposeFin_symm_apply_zero, Fin.val_zero, one_mul,
       Equiv.Perm.decomposeFin.symm_sign, Equiv.swap_self, if_true, id.def, eq_self_iff_true,
       Equiv.Perm.decomposeFin_symm_apply_succ, Fin.succAbove_zero, Equiv.coe_refl, pow_zero,
diff --git a/Mathlib/LinearAlgebra/PiTensorProduct.lean b/Mathlib/LinearAlgebra/PiTensorProduct.lean
index d8b5699de80c1..df6ae79d669bd 100644
--- a/Mathlib/LinearAlgebra/PiTensorProduct.lean
+++ b/Mathlib/LinearAlgebra/PiTensorProduct.lean
@@ -533,7 +533,7 @@ def isEmptyEquiv [IsEmpty ι] : (⨂[R] _ : ι, M) ≃ₗ[R] R where
         smul_eq_mul, mul_one]
       congr
       aesop
-    . simp only
+    · simp only
       intro x y hx hy
       rw [map_add, add_smul, hx, hy]
   right_inv t := by simp
diff --git a/Mathlib/Logic/Equiv/Defs.lean b/Mathlib/Logic/Equiv/Defs.lean
index ec42614a8b39e..7a53f0012af5a 100644
--- a/Mathlib/Logic/Equiv/Defs.lean
+++ b/Mathlib/Logic/Equiv/Defs.lean
@@ -870,7 +870,7 @@ protected theorem exists_unique_congr_left {p : β → Prop} (f : α ≃ β) :
 protected theorem forall_congr {p : α → Prop} {q : β → Prop} (f : α ≃ β)
     (h : ∀ {x}, p x ↔ q (f x)) : (∀ x, p x) ↔ (∀ y, q y) := by
   constructor <;> intro h₂ x
-  . rw [← f.right_inv x]; apply h.mp; apply h₂
+  · rw [← f.right_inv x]; apply h.mp; apply h₂
   · apply h.mpr; apply h₂
 #align equiv.forall_congr Equiv.forall_congr
 
diff --git a/Mathlib/Logic/Equiv/Set.lean b/Mathlib/Logic/Equiv/Set.lean
index ac8618976f170..290984b3e4e07 100644
--- a/Mathlib/Logic/Equiv/Set.lean
+++ b/Mathlib/Logic/Equiv/Set.lean
@@ -668,8 +668,8 @@ theorem preimage_piEquivPiSubtypeProd_symm_pi {α : Type _} {β : α → Type _}
   -- Porting note: Two lines below were `by_cases hi <;> simp [hi]`
   -- This regression is https://github.com/leanprover/lean4/issues/1926
   by_cases hi : p i
-  . simp [forall_prop_of_true hi, forall_prop_of_false (not_not.2 hi), hi]
-  . simp [forall_prop_of_false hi, hi, forall_prop_of_true hi]
+  · simp [forall_prop_of_true hi, forall_prop_of_false (not_not.2 hi), hi]
+  · simp [forall_prop_of_false hi, hi, forall_prop_of_true hi]
 #align equiv.preimage_pi_equiv_pi_subtype_prod_symm_pi Equiv.preimage_piEquivPiSubtypeProd_symm_pi
 
 -- See also `Equiv.sigmaFiberEquiv`.
diff --git a/Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean b/Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean
index cb65880031bbe..c32aeb3f62670 100644
--- a/Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean
+++ b/Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean
@@ -111,8 +111,7 @@ theorem aemeasurable_of_tendsto_metrizable_ae {ι} {μ : Measure α} {f : ι →
     · simp_rw [aeSeq.mk_eq_fun_of_mem_aeSeqSet h'f hx]
       exact @aeSeq.fun_prop_of_mem_aeSeqSet _ α β _ _ _ _ _ h'f x hx
     · exact tendsto_const_nhds
-  ·
-    exact
+  · exact
       (ite_ae_eq_of_measure_compl_zero g (fun x => (⟨f (v 0) x⟩ : Nonempty β).some) (aeSeqSet h'f p)
           (aeSeq.measure_compl_aeSeqSet_eq_zero h'f hp)).symm
 #align ae_measurable_of_tendsto_metrizable_ae aemeasurable_of_tendsto_metrizable_ae
diff --git a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
index 0ee41a10e2927..47f0a91305590 100644
--- a/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
+++ b/Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
@@ -865,8 +865,7 @@ theorem _root_.MeasurableEmbedding.stronglyMeasurable_extend {f : α → β} {g
   · rcases hx with ⟨y, rfl⟩
     simpa only [SimpleFunc.extend_apply, hg.injective, Injective.extend_apply] using
       hf.tendsto_approx y
-  ·
-    simpa only [hx, SimpleFunc.extend_apply', not_false_iff, extend_apply'] using
+  · simpa only [hx, SimpleFunc.extend_apply', not_false_iff, extend_apply'] using
       hg'.tendsto_approx x
 #align measurable_embedding.strongly_measurable_extend MeasurableEmbedding.stronglyMeasurable_extend
 
diff --git a/Mathlib/MeasureTheory/Integral/Layercake.lean b/Mathlib/MeasureTheory/Integral/Layercake.lean
index 38cc5f41fd196..82a8ff8e063f7 100644
--- a/Mathlib/MeasureTheory/Integral/Layercake.lean
+++ b/Mathlib/MeasureTheory/Integral/Layercake.lean
@@ -111,14 +111,12 @@ theorem lintegral_comp_eq_lintegral_meas_le_mul_of_measurable (μ : Measure α)
           (Ici s).indicator (fun _ : ℝ => (1 : ℝ≥0∞)) (f x) := by
       funext a
       by_cases s ∈ Ioc (0 : ℝ) (f a)
-      ·
-        simp only [h, show s ∈ Ioi (0 : ℝ) from h.1, show f a ∈ Ici s from h.2, indicator_of_mem,
+      · simp only [h, show s ∈ Ioi (0 : ℝ) from h.1, show f a ∈ Ici s from h.2, indicator_of_mem,
           mul_one]
       · have h_copy := h
         simp only [mem_Ioc, not_and, not_le] at h
         by_cases h' : 0 < s
-        ·
-          simp only [h_copy, h h', indicator_of_not_mem, not_false_iff, mem_Ici, not_le,
+        · simp only [h_copy, h h', indicator_of_not_mem, not_false_iff, mem_Ici, not_le,
             MulZeroClass.mul_zero]
         · have : s ∉ Ioi (0 : ℝ) := h'
           simp only [this, h', indicator_of_not_mem, not_false_iff, MulZeroClass.mul_zero,
diff --git a/Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean b/Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean
index 279961053511f..56ffad3c2b059 100644
--- a/Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean
+++ b/Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean
@@ -252,8 +252,7 @@ theorem exists_lt_lowerSemicontinuous_lintegral_ge_of_aemeasurable [SigmaFinite
     · have : f x = fmeas.mk f x := by rw [Set.compl_subset_comm] at hs ; exact hs h
       rw [this]
       exact (f_lt_g0 x).trans_le le_self_add
-  ·
-    calc
+  · calc
       ∫⁻ x, g0 x + g1 x ∂μ = (∫⁻ x, g0 x ∂μ) + ∫⁻ x, g1 x ∂μ :=
         lintegral_add_left g0_cont.measurable _
       _ ≤ (∫⁻ x, f x ∂μ) + ε / 2 + (0 + ε / 2) := by
@@ -301,8 +300,7 @@ theorem exists_lt_lowerSemicontinuous_integral_gt_nnreal [SigmaFinite μ] (f : 
     simp only [hasFiniteIntegral_iff_norm, Real.norm_eq_abs, abs_of_nonneg ENNReal.toReal_nonneg]
     convert gint_ne.lt_top using 1
   · rw [integral_eq_lintegral_of_nonneg_ae, integral_eq_lintegral_of_nonneg_ae]
-    ·
-      calc
+    · calc
         ENNReal.toReal (∫⁻ a : α, ENNReal.ofReal (g a).toReal ∂μ) =
             ENNReal.toReal (∫⁻ a : α, g a ∂μ) :=
           by congr 1
diff --git a/Mathlib/MeasureTheory/MeasurableSpace.lean b/Mathlib/MeasureTheory/MeasurableSpace.lean
index 9c60120ca0c8e..7eb6baa3b0d53 100644
--- a/Mathlib/MeasureTheory/MeasurableSpace.lean
+++ b/Mathlib/MeasureTheory/MeasurableSpace.lean
@@ -1677,7 +1677,7 @@ theorem measurable_injection_nat_bool_of_countablyGenerated [MeasurableSpace α]
   obtain ⟨e, he⟩ := Set.Countable.exists_eq_range (bct.insert ∅) (insert_nonempty _ _)
   rw [← generateFrom_insert_empty, he] at hb
   refine' ⟨fun x n => x ∈ e n, _, _⟩
-  . rw [measurable_pi_iff]
+  · rw [measurable_pi_iff]
     intro n
     apply measurable_to_bool
     simp only [preimage, mem_singleton_iff, Bool.decide_iff]
diff --git a/Mathlib/MeasureTheory/Measure/NullMeasurable.lean b/Mathlib/MeasureTheory/Measure/NullMeasurable.lean
index 677af520601b8..f209d34353109 100644
--- a/Mathlib/MeasureTheory/Measure/NullMeasurable.lean
+++ b/Mathlib/MeasureTheory/Measure/NullMeasurable.lean
@@ -314,8 +314,7 @@ theorem measure_inter_add_diff₀ (s : Set α) (ht : NullMeasurableSet t μ) :
             (@disjoint_inf_sdiff _ s' t _).aedisjoint).symm
       _ = μ s' := (congr_arg μ (inter_union_diff _ _))
       _ = μ s := hs'
-  ·
-    calc
+  · calc
       μ s = μ (s ∩ t ∪ s \ t) := by rw [inter_union_diff]
       _ ≤ μ (s ∩ t) + μ (s \ t) := measure_union_le _ _
 
diff --git a/Mathlib/MeasureTheory/Measure/OuterMeasure.lean b/Mathlib/MeasureTheory/Measure/OuterMeasure.lean
index 3c9df9e2c1a18..4262c00c670f8 100644
--- a/Mathlib/MeasureTheory/Measure/OuterMeasure.lean
+++ b/Mathlib/MeasureTheory/Measure/OuterMeasure.lean
@@ -742,8 +742,7 @@ theorem ofFunction_union_of_top_of_nonempty_inter {s t : Set α}
   refine' le_antisymm (OuterMeasure.union _ _ _) (le_iInf fun f => le_iInf fun hf => _)
   set μ := OuterMeasure.ofFunction m m_empty
   rcases Classical.em (∃ i, (s ∩ f i).Nonempty ∧ (t ∩ f i).Nonempty) with (⟨i, hs, ht⟩ | he)
-  ·
-    calc
+  · calc
       μ s + μ t ≤ ∞ := le_top
       _ = m (f i) := (h (f i) hs ht).symm
       _ ≤ ∑' i, m (f i) := ENNReal.le_tsum i
@@ -1007,8 +1006,8 @@ theorem isCaratheodory_iUnion_nat {s : ℕ → Set α} (h : ∀ i, IsCaratheodor
       intro t
       have hp : m (t ∩ ⋃ i, s i) ≤ ⨆ n, m (t ∩ ⋃ i < n, s i) := by
         convert m.iUnion fun i => t ∩ s i using 1
-        . simp [inter_iUnion]
-        . simp [ENNReal.tsum_eq_iSup_nat, isCaratheodory_sum m h hd]
+        · simp [inter_iUnion]
+        · simp [ENNReal.tsum_eq_iSup_nat, isCaratheodory_sum m h hd]
       refine' le_trans (add_le_add_right hp _) _
       rw [ENNReal.iSup_add]
       refine'
@@ -1417,8 +1416,7 @@ theorem extend_iUnion {β} [Countable β] {f : β → Set α} (hd : Pairwise (Di
     (hm : ∀ i, P (f i)) : extend m (⋃ i, f i) = ∑' i, extend m (f i) := by
   cases nonempty_encodable β
   rw [← Encodable.iUnion_decode₂, ← tsum_iUnion_decode₂]
-  ·
-    exact
+  · exact
       extend_iUnion_nat PU (fun n => Encodable.iUnion_decode₂_cases P0 hm)
         (mU _ (Encodable.iUnion_decode₂_disjoint_on hd))
   · exact extend_empty P0 m0
diff --git a/Mathlib/ModelTheory/Semantics.lean b/Mathlib/ModelTheory/Semantics.lean
index c9710fd6a1646..e7aeb68672b1c 100644
--- a/Mathlib/ModelTheory/Semantics.lean
+++ b/Mathlib/ModelTheory/Semantics.lean
@@ -185,8 +185,8 @@ theorem realize_varsToConstants [L[[α]].Structure M] [(lhomWithConstants L α).
   induction' t with ab n f ts ih
   · cases' ab with a b
     --Porting note: both cases were `simp [Language.con]`
-    . simp [Language.con, realize, constantMap, funMap_eq_coe_constants]
-    . simp [realize, constantMap]
+    · simp [Language.con, realize, constantMap, funMap_eq_coe_constants]
+    · simp [realize, constantMap]
   · simp only [realize, constantsOn, mk₂_Functions, ih]
     --Porting note: below lemma does not work with simp for some reason
     rw [withConstants_funMap_sum_inl]
@@ -335,8 +335,7 @@ theorem realize_foldr_sup (l : List (L.BoundedFormula α n)) (v : α → M) (xs
     (l.foldr (· ⊔ ·) ⊥).Realize v xs ↔ ∃ φ ∈ l, BoundedFormula.Realize φ v xs := by
   induction' l with φ l ih
   · simp
-  ·
-    simp_rw [List.foldr_cons, realize_sup, ih, exists_prop, List.mem_cons, or_and_right, exists_or,
+  · simp_rw [List.foldr_cons, realize_sup, ih, exists_prop, List.mem_cons, or_and_right, exists_or,
       exists_eq_left]
 #align first_order.language.bounded_formula.realize_foldr_sup FirstOrder.Language.BoundedFormula.realize_foldr_sup
 
@@ -557,9 +556,9 @@ theorem realize_toPrenexImp {φ ψ : L.BoundedFormula α n} (hφ : IsPrenex φ)
 theorem realize_toPrenex (φ : L.BoundedFormula α n) {v : α → M} :
     ∀ {xs : Fin n → M}, φ.toPrenex.Realize v xs ↔ φ.Realize v xs := by
   induction' φ with _ _ _ _ _ _ _ _ _ f1 f2 h1 h2 _ _ h
-  . exact Iff.rfl
-  . exact Iff.rfl
-  . exact Iff.rfl
+  · exact Iff.rfl
+  · exact Iff.rfl
+  · exact Iff.rfl
   · intros
     rw [toPrenex, realize_toPrenexImp f1.toPrenex_isPrenex f2.toPrenex_isPrenex, realize_imp,
       realize_imp, h1, h2]
@@ -741,8 +740,8 @@ theorem realize_equivSentence_symm_con [L[[α]].Structure M]
   refine' _root_.trans _ BoundedFormula.realize_constantsVarsEquiv
   rw [iff_iff_eq]
   congr with (_ | a)
-  . simp
-  . cases a
+  · simp
+  · cases a
 #align first_order.language.formula.realize_equiv_sentence_symm_con FirstOrder.Language.Formula.realize_equivSentence_symm_con
 
 @[simp]
@@ -919,8 +918,7 @@ theorem realize_toFormula (φ : L.BoundedFormula α n) (v : Sum α (Fin n) → M
   · rfl
   · simp [BoundedFormula.Realize]
   · simp [BoundedFormula.Realize]
-  ·
-    rw [toFormula, Formula.Realize, realize_imp, ← Formula.Realize, ih1, ← Formula.Realize, ih2,
+  · rw [toFormula, Formula.Realize, realize_imp, ← Formula.Realize, ih1, ← Formula.Realize, ih2,
       realize_imp]
   · rw [toFormula, Formula.Realize, realize_all, realize_all]
     refine' forall_congr' fun a => _
diff --git a/Mathlib/NumberTheory/ArithmeticFunction.lean b/Mathlib/NumberTheory/ArithmeticFunction.lean
index 4713bdafeb660..bf9ae5ef7f34d 100644
--- a/Mathlib/NumberTheory/ArithmeticFunction.lean
+++ b/Mathlib/NumberTheory/ArithmeticFunction.lean
@@ -567,8 +567,8 @@ theorem ppow_succ {f : ArithmeticFunction R} {k : ℕ} : f.ppow (k + 1) = f.pmul
   ext x
   simp_rw [ppow_apply (Nat.succ_pos k), pow_succ] -- porting note: was `rw [..., pow_succ]`
   induction k <;> simp
-  . exact pow_one _       -- porting note: added
-  . exact pow_succ'' _ _  -- porting note: added
+  · exact pow_one _       -- porting note: added
+  · exact pow_succ'' _ _  -- porting note: added
 #align nat.arithmetic_function.ppow_succ Nat.ArithmeticFunction.ppow_succ
 
 theorem ppow_succ' {f : ArithmeticFunction R} {k : ℕ} {kpos : 0 < k} :
@@ -666,22 +666,19 @@ theorem mul [CommSemiring R] {f g : ArithmeticFunction R} (hf : f.IsMultiplicati
           rw [← hcd.1.1, h.1, Nat.gcd_mul_left,
             cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one, mul_one]
       · trans Nat.gcd (a1 * a2) (a2 * b2)
-        ·
-          rw [mul_comm, Nat.gcd_mul_left, cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one,
+        · rw [mul_comm, Nat.gcd_mul_left, cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one,
             mul_one]
         · rw [← hcd.1.1, ← hcd.2.1] at cop
           rw [← hcd.1.1, h.2, mul_comm, Nat.gcd_mul_left,
             cop.coprime_mul_right.coprime_mul_left_right.gcd_eq_one, mul_one]
       · trans Nat.gcd (b1 * b2) (a1 * b1)
-        ·
-          rw [mul_comm, Nat.gcd_mul_right,
+        · rw [mul_comm, Nat.gcd_mul_right,
             cop.coprime_mul_right.coprime_mul_left_right.symm.gcd_eq_one, one_mul]
         · rw [← hcd.1.1, ← hcd.2.1] at cop
           rw [← hcd.2.1, h.1, mul_comm c1 d1, Nat.gcd_mul_left,
             cop.coprime_mul_right.coprime_mul_left_right.symm.gcd_eq_one, mul_one]
       · trans Nat.gcd (b1 * b2) (a2 * b2)
-        ·
-          rw [Nat.gcd_mul_right, cop.coprime_mul_left.coprime_mul_right_right.symm.gcd_eq_one,
+        · rw [Nat.gcd_mul_right, cop.coprime_mul_left.coprime_mul_right_right.symm.gcd_eq_one,
             one_mul]
         · rw [← hcd.1.1, ← hcd.2.1] at cop
           rw [← hcd.2.1, h.2, Nat.gcd_mul_right,
diff --git a/Mathlib/NumberTheory/BernoulliPolynomials.lean b/Mathlib/NumberTheory/BernoulliPolynomials.lean
index c968632b151ac..f89c4ae4d91cb 100644
--- a/Mathlib/NumberTheory/BernoulliPolynomials.lean
+++ b/Mathlib/NumberTheory/BernoulliPolynomials.lean
@@ -131,11 +131,11 @@ nonrec theorem sum_bernoulli (n : ℕ) :
   simp_rw [smul_monomial, mul_comm (_root_.bernoulli _) _, smul_eq_mul, ← mul_assoc]
   conv_lhs =>
     apply_congr
-    . skip
-    . conv =>
+    · skip
+    · conv =>
       apply_congr
-      . skip
-      . rw [← Nat.cast_mul, choose_mul ((le_tsub_iff_left <| mem_range_le (by assumption)).1 <|
+      · skip
+      · rw [← Nat.cast_mul, choose_mul ((le_tsub_iff_left <| mem_range_le (by assumption)).1 <|
             mem_range_le (by assumption)) (le.intro rfl),
           Nat.cast_mul, add_tsub_cancel_left, mul_assoc, mul_comm, ← smul_eq_mul, ←
           smul_monomial]
@@ -203,17 +203,17 @@ theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
     bernoulli_eq_sub_sum, eval_sub, eval_finset_sum]
   conv_lhs =>
     congr
-    . skip
-    . apply_congr
-      . skip
-      . rw [eval_smul, hd _ (mem_range.1 (by assumption))]
+    · skip
+    · apply_congr
+      · skip
+      · rw [eval_smul, hd _ (mem_range.1 (by assumption))]
   rw [eval_sub, eval_finset_sum]
   simp_rw [eval_smul, smul_add]
   rw [sum_add_distrib, sub_add, sub_eq_sub_iff_sub_eq_sub, _root_.add_sub_sub_cancel]
   conv_rhs =>
     congr
-    . skip
-    . congr
+    · skip
+    · congr
       rw [succ_eq_add_one, ← choose_succ_self_right d]
   rw [Nat.cast_succ, ← smul_eq_mul, ← sum_range_succ _ d, eval_monomial_one_add_sub]
   simp_rw [smul_eq_mul]
diff --git a/Mathlib/NumberTheory/Bertrand.lean b/Mathlib/NumberTheory/Bertrand.lean
index 3932002cf1b77..42d801e69053b 100644
--- a/Mathlib/NumberTheory/Bertrand.lean
+++ b/Mathlib/NumberTheory/Bertrand.lean
@@ -77,7 +77,7 @@ theorem real_main_inequality {x : ℝ} (n_large : (512 : ℝ) ≤ x) :
       (Set.Ioi_subset_Ioi (by norm_num)) (convex_Ioi 0.5)
     convert ((strictConcaveOn_sqrt_mul_log_Ioi.concaveOn.comp_linearMap
       ((2 : ℝ) • LinearMap.id))) using 1
-    . ext x
+    · ext x
       simp only [Set.mem_Ioi, Set.mem_preimage, LinearMap.smul_apply,
         LinearMap.id_coe, id_eq, smul_eq_mul]
       rw [← mul_lt_mul_left (two_pos)]
@@ -90,7 +90,7 @@ theorem real_main_inequality {x : ℝ} (n_large : (512 : ℝ) ≤ x) :
     obtain ⟨x1, x2, h1, h2, h0, h3, h4⟩ := this
     exact (h.right_le_of_le_left'' h1 ((h1.trans h2).trans_le h0) h2 h0 (h4.trans h3)).trans h4
   refine' ⟨18, 512, by norm_num1, by norm_num1, n_large, _, _⟩
-  . have : sqrt (2 * 18) = 6 := (sqrt_eq_iff_mul_self_eq_of_pos (by norm_num1)).mpr (by norm_num1)
+  · have : sqrt (2 * 18) = 6 := (sqrt_eq_iff_mul_self_eq_of_pos (by norm_num1)).mpr (by norm_num1)
     rw [hf, log_nonneg_iff, this]
     rw [one_le_div] <;> norm_num1
     apply le_trans _ (le_mul_of_one_le_left _ _) <;> norm_num1
@@ -99,17 +99,17 @@ theorem real_main_inequality {x : ℝ} (n_large : (512 : ℝ) ≤ x) :
     apply rpow_pos_of_pos ; norm_num1
     apply hf' 18 ; norm_num1
     norm_num1
-  . have : sqrt (2 * 512) = 32 :=
+  · have : sqrt (2 * 512) = 32 :=
       (sqrt_eq_iff_mul_self_eq_of_pos (by norm_num1)).mpr (by norm_num1)
     rw [hf, log_nonpos_iff (hf' _ _), this, div_le_one] <;> norm_num1
     have : (512 : ℝ) = 2 ^ (9 : ℕ)
-    . rw [rpow_nat_cast 2 9] ; norm_num1
+    · rw [rpow_nat_cast 2 9] ; norm_num1
     conv_lhs => rw [this]
     have : (1024 : ℝ) = 2 ^ (10 : ℕ)
-    . rw [rpow_nat_cast 2 10] ; norm_num1
+    · rw [rpow_nat_cast 2 10] ; norm_num1
     rw [this, ← rpow_mul, ← rpow_add] <;> norm_num1
     have : (4 : ℝ) = 2 ^ (2 : ℕ)
-    . rw [rpow_nat_cast 2 2] ; norm_num1
+    · rw [rpow_nat_cast 2 2] ; norm_num1
     rw [this, ← rpow_mul] <;> norm_num1
     apply rpow_le_rpow_of_exponent_le <;> norm_num1
     apply rpow_pos_of_pos four_pos
diff --git a/Mathlib/NumberTheory/ClassNumber/Finite.lean b/Mathlib/NumberTheory/ClassNumber/Finite.lean
index 9e3e5fd69f37d..44e7cd7ea6d7a 100644
--- a/Mathlib/NumberTheory/ClassNumber/Finite.lean
+++ b/Mathlib/NumberTheory/ClassNumber/Finite.lean
@@ -102,7 +102,7 @@ theorem norm_le (a : S) {y : ℤ} (hy : ∀ k, abv (bS.repr a k) ≤ y) :
   --   exact finset.mem_image.mpr ⟨⟨i, j, k⟩, Finset.mem_univ _, rfl⟩
   rw [← LinearMap.det_toMatrix bS]
   convert Matrix.det_sum_smul_le (n := ι) Finset.univ _ hy using 3
-  . simp; rfl
+  · simp; rfl
   · rw [Finset.card_univ, smul_mul_assoc, mul_comm]
   · intro i j k
     apply Finset.le_max'
diff --git a/Mathlib/NumberTheory/Cyclotomic/Basic.lean b/Mathlib/NumberTheory/Cyclotomic/Basic.lean
index dc298fabae79a..14694e3047211 100644
--- a/Mathlib/NumberTheory/Cyclotomic/Basic.lean
+++ b/Mathlib/NumberTheory/Cyclotomic/Basic.lean
@@ -555,9 +555,9 @@ instance isCyclotomicExtension [NeZero ((n : ℕ) : K)] :
   rw [← eval_map, ← IsRoot.def, map_cyclotomic, isRoot_cyclotomic_iff] at hζ
 -- Porting note: the first `?_` was `forall_eq.2 ⟨ζ, hζ⟩` that now fails.
   refine ⟨?_, ?_⟩
-  . simp only [mem_singleton_iff, forall_eq]
+  · simp only [mem_singleton_iff, forall_eq]
     exact ⟨ζ, hζ⟩
-  . rw [← Algebra.eq_top_iff, ← SplittingField.adjoin_rootSet, eq_comm]
+  · rw [← Algebra.eq_top_iff, ← SplittingField.adjoin_rootSet, eq_comm]
     exact IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots hζ
 #align cyclotomic_field.is_cyclotomic_extension CyclotomicField.isCyclotomicExtension
 
diff --git a/Mathlib/NumberTheory/PellMatiyasevic.lean b/Mathlib/NumberTheory/PellMatiyasevic.lean
index fe88b1c56b13b..15515c624719c 100644
--- a/Mathlib/NumberTheory/PellMatiyasevic.lean
+++ b/Mathlib/NumberTheory/PellMatiyasevic.lean
@@ -809,7 +809,7 @@ theorem modEq_of_xn_modEq {i j n} (ipos : 0 < i) (hin : i ≤ n)
   have jj : j ≡ j' [MOD 4 * n] := by delta ModEq; rw [Nat.mod_eq_of_lt jl]
   have : ∀ j q, xn a1 (j + 4 * n * q) ≡ xn a1 j [MOD xn a1 n] := by
     intro j q; induction' q with q IH
-    . simp [ModEq.refl]
+    · simp [ModEq.refl]
     rw [Nat.mul_succ, ← add_assoc, add_comm]
     exact (xn_modEq_x4n_add _ _ _).trans IH
   Or.imp (fun ji : j' = i => by rwa [← ji])
diff --git a/Mathlib/Order/Atoms.lean b/Mathlib/Order/Atoms.lean
index 8544a76ae28c8..6c460832d5de0 100644
--- a/Mathlib/Order/Atoms.lean
+++ b/Mathlib/Order/Atoms.lean
@@ -586,7 +586,7 @@ protected def booleanAlgebra {α} [DecidableEq α] [Lattice α] [BoundedOrder α
     inf_compl_le_bot := fun x => by
       rcases eq_bot_or_eq_top x with (rfl | rfl)
       · simp
-      . simp
+      · simp
     top_le_sup_compl := fun x => by rcases eq_bot_or_eq_top x with (rfl | rfl) <;> simp }
 #align is_simple_order.boolean_algebra IsSimpleOrder.booleanAlgebra
 
diff --git a/Mathlib/Order/Bounds/Basic.lean b/Mathlib/Order/Bounds/Basic.lean
index d77be44fe167f..02f571ce1033b 100644
--- a/Mathlib/Order/Bounds/Basic.lean
+++ b/Mathlib/Order/Bounds/Basic.lean
@@ -1593,8 +1593,7 @@ theorem isLUB_prod [Preorder α] [Preorder β] {s : Set (α × β)} (p : α × 
   · suffices h : (p.1, a) ∈ upperBounds s from (H.2 h).2
     exact fun q hq => ⟨(H.1 hq).1, ha <| mem_image_of_mem _ hq⟩
   · exact fun q hq => ⟨H.1.1 <| mem_image_of_mem _ hq, H.2.1 <| mem_image_of_mem _ hq⟩
-  ·
-    exact fun q hq =>
+  · exact fun q hq =>
       ⟨H.1.2 <| monotone_fst.mem_upperBounds_image hq,
         H.2.2 <| monotone_snd.mem_upperBounds_image hq⟩
 #align is_lub_prod isLUB_prod
diff --git a/Mathlib/Order/CompleteLattice.lean b/Mathlib/Order/CompleteLattice.lean
index 2b88dc9ddb983..4b95baffcd675 100644
--- a/Mathlib/Order/CompleteLattice.lean
+++ b/Mathlib/Order/CompleteLattice.lean
@@ -391,12 +391,12 @@ instance CompleteLinearOrder.toLinearOrder [i : CompleteLinearOrder α] : Linear
     max := Sup.sup
     min_def := fun a b => by
       split_ifs with h
-      . simp [h]
-      . simp [(CompleteLinearOrder.le_total a b).resolve_left h]
+      · simp [h]
+      · simp [(CompleteLinearOrder.le_total a b).resolve_left h]
     max_def :=  fun a b => by
       split_ifs with h
-      . simp [h]
-      . simp [(CompleteLinearOrder.le_total a b).resolve_left h] }
+      · simp [h]
+      · simp [(CompleteLinearOrder.le_total a b).resolve_left h] }
 
 namespace OrderDual
 
diff --git a/Mathlib/Order/ConditionallyCompleteLattice/Basic.lean b/Mathlib/Order/ConditionallyCompleteLattice/Basic.lean
index d58b6c225bf8b..2106e150cc114 100644
--- a/Mathlib/Order/ConditionallyCompleteLattice/Basic.lean
+++ b/Mathlib/Order/ConditionallyCompleteLattice/Basic.lean
@@ -1190,8 +1190,7 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
         intro b hb
         exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
       · refine' some_le_some.2 (le_csInf _ _)
-        ·
-          classical
+        · classical
             contrapose! h
             rintro (⟨⟩ | a) ha
             · exact mem_singleton ⊤
diff --git a/Mathlib/Order/OmegaCompletePartialOrder.lean b/Mathlib/Order/OmegaCompletePartialOrder.lean
index 723d2d42d517a..1e7dd0cb4861a 100644
--- a/Mathlib/Order/OmegaCompletePartialOrder.lean
+++ b/Mathlib/Order/OmegaCompletePartialOrder.lean
@@ -316,8 +316,8 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   cases' hb with j hb; replace hb := hb.symm
   rw [eq_some_iff] at ha hb
   cases' le_total i j with hij hji
-  . have := c.monotone hij _ ha; apply mem_unique this hb
-  . have := c.monotone hji _ hb; apply Eq.symm; apply mem_unique this ha
+  · have := c.monotone hij _ ha; apply mem_unique this hb
+  · have := c.monotone hji _ hb; apply Eq.symm; apply mem_unique this ha
   --Porting note: Old proof
   -- wlog h : i ≤ j := le_total i j using a b i j, b a j i
   -- rw [eq_some_iff] at ha hb
diff --git a/Mathlib/Order/SuccPred/Basic.lean b/Mathlib/Order/SuccPred/Basic.lean
index 37222926569b2..0331d2324539d 100644
--- a/Mathlib/Order/SuccPred/Basic.lean
+++ b/Mathlib/Order/SuccPred/Basic.lean
@@ -1021,7 +1021,7 @@ instance : SuccOrder (WithTop α) where
     · exact le_top
     change _ ≤ ite _ _ _
     split_ifs
-    . exact le_top
+    · exact le_top
     · exact some_le_some.2 (le_succ a)
   max_of_succ_le {a} ha := by
     cases a
diff --git a/Mathlib/Order/WithBot.lean b/Mathlib/Order/WithBot.lean
index 3591e02fad35f..65ee0c3a13f47 100644
--- a/Mathlib/Order/WithBot.lean
+++ b/Mathlib/Order/WithBot.lean
@@ -393,7 +393,7 @@ theorem unbot'_bot_le_iff [LE α] [OrderBot α] {a : WithBot α} {b : α} :
 theorem unbot'_lt_iff [LT α] {a : WithBot α} {b c : α} (ha : a ≠ ⊥) : a.unbot' b < c ↔ a < c := by
   cases a
   · exact (ha rfl).elim
-  . rw [some_eq_coe, unbot'_coe, coe_lt_coe]
+  · rw [some_eq_coe, unbot'_coe, coe_lt_coe]
 #align with_bot.unbot'_lt_iff WithBot.unbot'_lt_iff
 
 instance semilatticeSup [SemilatticeSup α] : SemilatticeSup (WithBot α) :=
@@ -1289,10 +1289,10 @@ instance trichotomous.lt [Preorder α] [IsTrichotomous α (· < ·)] :
     IsTrichotomous (WithTop α) (· < ·) :=
   ⟨by
     rintro (a | a) (b | b)
-    . simp
-    . simp
-    . simp
-    . simpa [some_eq_coe, IsTrichotomous, coe_eq_coe] using @trichotomous α (. < .) _ a b⟩
+    · simp
+    · simp
+    · simp
+    · simpa [some_eq_coe, IsTrichotomous, coe_eq_coe] using @trichotomous α (. < .) _ a b⟩
 #align with_top.trichotomous.lt WithTop.trichotomous.lt
 
 instance IsWellOrder.lt [Preorder α] [h : IsWellOrder α (· < ·)] :
@@ -1303,10 +1303,10 @@ instance trichotomous.gt [Preorder α] [IsTrichotomous α (· > ·)] :
     IsTrichotomous (WithTop α) (· > ·) :=
   ⟨by
     rintro (a | a) (b | b)
-    . simp
-    . simp
-    . simp
-    . simpa [some_eq_coe, IsTrichotomous, coe_eq_coe] using @trichotomous α (. > .) _ a b⟩
+    · simp
+    · simp
+    · simp
+    · simpa [some_eq_coe, IsTrichotomous, coe_eq_coe] using @trichotomous α (. > .) _ a b⟩
 #align with_top.trichotomous.gt WithTop.trichotomous.gt
 
 instance IsWellOrder.gt [Preorder α] [h : IsWellOrder α (· > ·)] :
diff --git a/Mathlib/Order/Zorn.lean b/Mathlib/Order/Zorn.lean
index 073ad165df0a9..72ad43e4e20eb 100644
--- a/Mathlib/Order/Zorn.lean
+++ b/Mathlib/Order/Zorn.lean
@@ -137,7 +137,7 @@ theorem zorn_nonempty_preorder₀ (s : Set α)
   -- rcases zorn_preorder₀ ({ y ∈ s | x ≤ y }) fun c hcs hc => ?_ with ⟨m, ⟨hms, hxm⟩, hm⟩
   -- · exact ⟨m, hms, hxm, fun z hzs hmz => hm _ ⟨hzs, hxm.trans hmz⟩ hmz⟩
   have H := zorn_preorder₀ ({ y ∈ s | x ≤ y }) fun c hcs hc => ?_
-  . rcases H with ⟨m, ⟨hms, hxm⟩, hm⟩
+  · rcases H with ⟨m, ⟨hms, hxm⟩, hm⟩
     exact ⟨m, hms, hxm, fun z hzs hmz => hm _ ⟨hzs, hxm.trans hmz⟩ hmz⟩
   · rcases c.eq_empty_or_nonempty with (rfl | ⟨y, hy⟩)
     · exact ⟨x, ⟨hxs, le_rfl⟩, fun z => False.elim⟩
diff --git a/Mathlib/Probability/Kernel/CondCdf.lean b/Mathlib/Probability/Kernel/CondCdf.lean
index d972770e5e570..8957b876587e7 100644
--- a/Mathlib/Probability/Kernel/CondCdf.lean
+++ b/Mathlib/Probability/Kernel/CondCdf.lean
@@ -94,8 +94,7 @@ theorem Real.iInter_Iic_rat : ⋂ r : ℚ, Iic (r : ℝ) = ∅ := by
 theorem atBot_le_nhds_bot {α : Type _} [TopologicalSpace α] [LinearOrder α] [OrderBot α]
     [OrderTopology α] : (atBot : Filter α) ≤ 𝓝 ⊥ := by
   cases subsingleton_or_nontrivial α
-  ·
-    simp only [nhds_discrete, le_pure_iff, mem_atBot_sets, mem_singleton_iff,
+  · simp only [nhds_discrete, le_pure_iff, mem_atBot_sets, mem_singleton_iff,
       eq_iff_true_of_subsingleton, imp_true_iff, exists_const]
   have h : atBot.HasBasis (fun _ : α => True) Iic := @atBot_basis α _ _
   have h_nhds : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a => Iio a := @nhds_bot_basis α _ _ _ _ _
@@ -730,8 +729,7 @@ theorem condCdf'_eq_condCdfRat (ρ : Measure (α × ℝ)) (a : α) (r : ℚ) :
     condCdf' ρ a r = condCdfRat ρ a r := by
   rw [← inf_gt_condCdfRat ρ a r, condCdf']
   refine' Equiv.iInf_congr _ _
-  ·
-    exact
+  · exact
       { toFun := fun t => ⟨t.1, by exact_mod_cast t.2⟩
         invFun := fun t => ⟨t.1, by exact_mod_cast t.2⟩
         left_inv := fun t => by simp only [Subtype.coe_eta]
diff --git a/Mathlib/RingTheory/Adjoin/Basic.lean b/Mathlib/RingTheory/Adjoin/Basic.lean
index 8380fd0480330..99f375c271eb7 100644
--- a/Mathlib/RingTheory/Adjoin/Basic.lean
+++ b/Mathlib/RingTheory/Adjoin/Basic.lean
@@ -254,8 +254,7 @@ theorem adjoin_inl_union_inr_eq_prod (s) (t) :
     adjoin R (LinearMap.inl R A B '' (s ∪ {1}) ∪ LinearMap.inr R A B '' (t ∪ {1})) =
       (adjoin R s).prod (adjoin R t) := by
   apply le_antisymm
-  ·
-    simp only [adjoin_le_iff, Set.insert_subset_iff, Subalgebra.zero_mem, Subalgebra.one_mem,
+  · simp only [adjoin_le_iff, Set.insert_subset_iff, Subalgebra.zero_mem, Subalgebra.one_mem,
       subset_adjoin,-- the rest comes from `squeeze_simp`
       Set.union_subset_iff,
       LinearMap.coe_inl, Set.mk_preimage_prod_right, Set.image_subset_iff, SetLike.mem_coe,
diff --git a/Mathlib/RingTheory/AdjoinRoot.lean b/Mathlib/RingTheory/AdjoinRoot.lean
index 830349fac7223..69fc9947b6b47 100644
--- a/Mathlib/RingTheory/AdjoinRoot.lean
+++ b/Mathlib/RingTheory/AdjoinRoot.lean
@@ -402,8 +402,8 @@ noncomputable instance field [Fact (Irreducible f)] : Field (AdjoinRoot f) :=
       -- porting note: was
       -- `rw [Rat.cast_mk' (K := ℚ), _root_.map_mul, _root_.map_intCast, map_inv₀, map_natCast]`
       convert_to ((Rat.mk' a b h1 h2 : K) : AdjoinRoot f) = ((↑a * (↑b)⁻¹ : K) : AdjoinRoot f)
-      . simp only [_root_.map_mul, map_intCast, map_inv₀, map_natCast]
-      . simp only [Rat.cast_mk', _root_.map_mul, map_intCast, map_inv₀, map_natCast]
+      · simp only [_root_.map_mul, map_intCast, map_inv₀, map_natCast]
+      · simp only [Rat.cast_mk', _root_.map_mul, map_intCast, map_inv₀, map_natCast]
     qsmul := (· • ·)
     qsmul_eq_mul' := fun a x =>
       -- porting note: I gave the explicit motive and changed `rw` to `simp`.
diff --git a/Mathlib/RingTheory/Artinian.lean b/Mathlib/RingTheory/Artinian.lean
index 16d9647bf92db..bf0a4f853a717 100644
--- a/Mathlib/RingTheory/Artinian.lean
+++ b/Mathlib/RingTheory/Artinian.lean
@@ -344,8 +344,8 @@ theorem isArtinian_of_fg_of_artinian {R M} [Ring R] [AddCommGroup M] [Module R M
   haveI := Classical.decEq R
   have : ∀ x ∈ s, x ∈ N := fun x hx => hs ▸ Submodule.subset_span hx
   refine' @isArtinian_of_surjective _ ((↑s : Set M) →₀ R) N _ _ _ _ _ _ _ isArtinian_finsupp
-  . exact Finsupp.total (↑s : Set M) N R (fun i => ⟨i, hs ▸ subset_span i.2⟩)
-  . rw [← LinearMap.range_eq_top, eq_top_iff,
+  · exact Finsupp.total (↑s : Set M) N R (fun i => ⟨i, hs ▸ subset_span i.2⟩)
+  · rw [← LinearMap.range_eq_top, eq_top_iff,
        ← map_le_map_iff_of_injective (show Injective (Submodule.subtype N)
          from Subtype.val_injective), Submodule.map_top, range_subtype,
          ← Submodule.map_top, ← Submodule.map_comp, Submodule.map_top]
diff --git a/Mathlib/RingTheory/HahnSeries.lean b/Mathlib/RingTheory/HahnSeries.lean
index b581e6e642bc1..e0b2a7b063eed 100644
--- a/Mathlib/RingTheory/HahnSeries.lean
+++ b/Mathlib/RingTheory/HahnSeries.lean
@@ -391,7 +391,7 @@ theorem min_order_le_order_add {Γ} [LinearOrderedCancelAddCommMonoid Γ] {x y :
   by_cases hy : y = 0; · simp [hy]
   rw [order_of_ne hx, order_of_ne hy, order_of_ne hxy]
   refine' le_of_eq_of_le _ (Set.IsWf.min_le_min_of_subset (support_add_subset (x := x) (y := y)))
-  . exact (Set.IsWf.min_union _ _ _ _).symm
+  · exact (Set.IsWf.min_union _ _ _ _).symm
 #align hahn_series.min_order_le_order_add HahnSeries.min_order_le_order_add
 
 /-- `single` as an additive monoid/group homomorphism -/
@@ -1226,7 +1226,7 @@ theorem ofPowerSeries_X_pow {R} [CommSemiring R] (n : ℕ) :
   induction' n with n ih
   · simp
     rfl
-  . rw [pow_succ, pow_succ, ih, ofPowerSeries_X, mul_comm, single_mul_single, one_mul,
+  · rw [pow_succ, pow_succ, ih, ofPowerSeries_X, mul_comm, single_mul_single, one_mul,
       Nat.cast_succ, add_comm]
 #align hahn_series.of_power_series_X_pow HahnSeries.ofPowerSeries_X_pow
 
diff --git a/Mathlib/RingTheory/Ideal/Basic.lean b/Mathlib/RingTheory/Ideal/Basic.lean
index 49542d64b38ec..186131a7ac107 100644
--- a/Mathlib/RingTheory/Ideal/Basic.lean
+++ b/Mathlib/RingTheory/Ideal/Basic.lean
@@ -780,8 +780,7 @@ division (semi)ring.
 This result actually holds for all division semirings, but we lack the predicate to state it. -/
 theorem isField_iff_isSimpleOrder_ideal : IsField R ↔ IsSimpleOrder (Ideal R) := by
   cases subsingleton_or_nontrivial R
-  ·
-    exact
+  · exact
       ⟨fun h => (not_isField_of_subsingleton _ h).elim, fun h =>
         (false_of_nontrivial_of_subsingleton <| Ideal R).elim⟩
   rw [← not_iff_not, Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top, ← not_iff_not]
diff --git a/Mathlib/RingTheory/Ideal/LocalRing.lean b/Mathlib/RingTheory/Ideal/LocalRing.lean
index b0f2d52b31571..0fbef5b27ec98 100644
--- a/Mathlib/RingTheory/Ideal/LocalRing.lean
+++ b/Mathlib/RingTheory/Ideal/LocalRing.lean
@@ -300,22 +300,22 @@ theorem local_hom_TFAE (f : R →+* S) :
         (maximalIdeal R).map f ≤ maximalIdeal S, maximalIdeal R ≤ (maximalIdeal S).comap f,
         (maximalIdeal S).comap f = maximalIdeal R] := by
   tfae_have 1 → 2
-  . rintro _ _ ⟨a, ha, rfl⟩
+  · rintro _ _ ⟨a, ha, rfl⟩
     exact map_nonunit f a ha
   tfae_have 2 → 4
-  . exact Set.image_subset_iff.1
+  · exact Set.image_subset_iff.1
   tfae_have 3 ↔ 4
-  . exact Ideal.map_le_iff_le_comap
+  · exact Ideal.map_le_iff_le_comap
   tfae_have 4 → 1
-  . intro h
+  · intro h
     constructor
     exact fun x => not_imp_not.1 (@h x)
   tfae_have 1 → 5
-  . intro
+  · intro
     ext
     exact not_iff_not.2 (isUnit_map_iff f _)
   tfae_have 5 → 4
-  . exact fun h => le_of_eq h.symm
+  · exact fun h => le_of_eq h.symm
   tfae_finish
 #align local_ring.local_hom_tfae LocalRing.local_hom_TFAE
 
diff --git a/Mathlib/RingTheory/Ideal/MinimalPrime.lean b/Mathlib/RingTheory/Ideal/MinimalPrime.lean
index 065846b5aa402..ccabc314606e8 100644
--- a/Mathlib/RingTheory/Ideal/MinimalPrime.lean
+++ b/Mathlib/RingTheory/Ideal/MinimalPrime.lean
@@ -77,11 +77,11 @@ theorem Ideal.radical_minimalPrimes : I.radical.minimalPrimes = I.minimalPrimes
   congr
   ext p
   refine' ⟨_, _⟩ <;> rintro ⟨⟨a, ha⟩, b⟩
-  . refine' ⟨⟨a, a.radical_le_iff.1 ha⟩, _⟩
-    . simp only [Set.mem_setOf_eq, and_imp] at *
+  · refine' ⟨⟨a, a.radical_le_iff.1 ha⟩, _⟩
+    · simp only [Set.mem_setOf_eq, and_imp] at *
       exact fun _ h2 h3 h4 => b h2 (h2.radical_le_iff.2 h3) h4
-  . refine' ⟨⟨a, a.radical_le_iff.2 ha⟩, _⟩
-    . simp only [Set.mem_setOf_eq, and_imp] at *
+  · refine' ⟨⟨a, a.radical_le_iff.2 ha⟩, _⟩
+    · simp only [Set.mem_setOf_eq, and_imp] at *
       exact fun _ h2 h3 h4 => b h2 (h2.radical_le_iff.1 h3) h4
 #align ideal.radical_minimal_primes Ideal.radical_minimalPrimes
 
@@ -138,7 +138,7 @@ theorem Ideal.exists_comap_eq_of_mem_minimalPrimes {I : Ideal S} (f : R →+* S)
       (RingHom.kerLift_injective f') (p.map <| Ideal.Quotient.mk <| RingHom.ker f') this
     refine' ⟨p'.comap <| Ideal.Quotient.mk I, Ideal.IsPrime.comap _, _, _⟩
     · exact Ideal.mk_ker.symm.trans_le (Ideal.comap_mono bot_le)
-    . convert congr_arg (Ideal.comap <| Ideal.Quotient.mk <| RingHom.ker f') hp₂
+    · convert congr_arg (Ideal.comap <| Ideal.Quotient.mk <| RingHom.ker f') hp₂
       rwa [Ideal.comap_map_of_surjective (Ideal.Quotient.mk <| RingHom.ker f')
         Ideal.Quotient.mk_surjective, eq_comm, sup_eq_left]
   refine' ⟨⟨_, bot_le⟩, _⟩
@@ -199,8 +199,7 @@ theorem Ideal.minimalPrimes_eq_comap :
 theorem Ideal.minimalPrimes_eq_subsingleton (hI : I.IsPrimary) : I.minimalPrimes = {I.radical} := by
   ext J
   constructor
-  ·
-    exact fun H =>
+  · exact fun H =>
       let e := H.1.1.radical_le_iff.mpr H.1.2
       (H.2 ⟨Ideal.isPrime_radical hI, Ideal.le_radical⟩ e).antisymm e
   · rintro (rfl : J = I.radical)
diff --git a/Mathlib/RingTheory/Ideal/Over.lean b/Mathlib/RingTheory/Ideal/Over.lean
index 70eead40c0623..13686c4a60883 100644
--- a/Mathlib/RingTheory/Ideal/Over.lean
+++ b/Mathlib/RingTheory/Ideal/Over.lean
@@ -69,8 +69,8 @@ theorem exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem {r : S}
     rw [eval₂_mul, eval₂_X] at hp
     obtain ⟨i, hi, mem⟩ := ih p_nonzero (r_non_zero_divisor hp)
     refine' ⟨i + 1, _, _⟩
-    . simp [hi, mem]
-    . simpa [hi] using mem
+    · simp [hi, mem]
+    · simpa [hi] using mem
 #align ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem
 
 /-- Let `P` be an ideal in `R[x]`.  The map
diff --git a/Mathlib/RingTheory/IntegralDomain.lean b/Mathlib/RingTheory/IntegralDomain.lean
index 3696b85ed6dd7..edcc2b8199a3e 100644
--- a/Mathlib/RingTheory/IntegralDomain.lean
+++ b/Mathlib/RingTheory/IntegralDomain.lean
@@ -160,8 +160,8 @@ variable (S : Subgroup Rˣ) [Finite S]
 instance subgroup_units_cyclic : IsCyclic S := by
   -- porting note: the original proof used a `coe`, but I was not able to get it to work.
   apply isCyclic_of_subgroup_isDomain (R := R) (G := S) _ _
-  . exact MonoidHom.mk (OneHom.mk (fun s => ↑s.val) rfl) (by simp)
-  . exact Units.ext.comp Subtype.val_injective
+  · exact MonoidHom.mk (OneHom.mk (fun s => ↑s.val) rfl) (by simp)
+  · exact Units.ext.comp Subtype.val_injective
 #align subgroup_units_cyclic subgroup_units_cyclic
 
 end
diff --git a/Mathlib/RingTheory/Polynomial/Basic.lean b/Mathlib/RingTheory/Polynomial/Basic.lean
index 6dbb40d12eebe..aab83fd53462d 100644
--- a/Mathlib/RingTheory/Polynomial/Basic.lean
+++ b/Mathlib/RingTheory/Polynomial/Basic.lean
@@ -498,10 +498,10 @@ theorem coeff_isUnit_isNilpotent_of_isUnit {P : Polynomial R} (hunit : IsUnit P)
     IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) := by
   obtain ⟨Q, hQ⟩ := IsUnit.exists_right_inv hunit
   constructor
-  . refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
+  · refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
     have h := (mul_coeff_zero P Q).symm
     rwa [hQ, coeff_one_zero] at h
-  . intros n hn
+  · intros n hn
     rw [nilpotent_iff_mem_prime]
     intros I hI
     let f := mapRingHom (Ideal.Quotient.mk I)
diff --git a/Mathlib/RingTheory/Polynomial/Content.lean b/Mathlib/RingTheory/Polynomial/Content.lean
index ddce458bd0401..12cd5d429a653 100644
--- a/Mathlib/RingTheory/Polynomial/Content.lean
+++ b/Mathlib/RingTheory/Polynomial/Content.lean
@@ -180,8 +180,8 @@ theorem normalize_content {p : R[X]} : normalize p.content = p.content :=
 @[simp]
 theorem normUnit_content {p : R[X]} : normUnit (content p) = 1 := by
   by_cases hp0 : p.content = 0
-  . simp [hp0]
-  . ext
+  · simp [hp0]
+  · ext
     apply mul_left_cancel₀ hp0
     erw [← normalize_apply, normalize_content, mul_one]
 
@@ -388,8 +388,7 @@ theorem content_mul {p q : R[X]} : (p * q).content = p.content * q.content := by
       ← Nat.cast_withBot, ← degree_eq_natDegree q.primPart_ne_zero] at heq
     rw [p.eq_C_content_mul_primPart, q.eq_C_content_mul_primPart]
     suffices h : (q.primPart * p.primPart).content = 1
-    ·
-      rw [mul_assoc, content_C_mul, content_C_mul, mul_comm p.primPart, mul_assoc, content_C_mul,
+    · rw [mul_assoc, content_C_mul, content_C_mul, mul_comm p.primPart, mul_assoc, content_C_mul,
         content_C_mul, h, mul_one, content_primPart, content_primPart, mul_one, mul_one]
     rw [← normalize_content, normalize_eq_one, isUnit_iff_dvd_one,
       content_eq_gcd_leadingCoeff_content_eraseLead, leadingCoeff_mul, gcd_comm]
diff --git a/Mathlib/RingTheory/TensorProduct.lean b/Mathlib/RingTheory/TensorProduct.lean
index 4838164037fe0..06d1c49491571 100644
--- a/Mathlib/RingTheory/TensorProduct.lean
+++ b/Mathlib/RingTheory/TensorProduct.lean
@@ -731,11 +731,11 @@ algEquivOfLinearEquivTensorProduct f (fun x₁ x₂ c₁ c₂ => by
   try
     intros
     trivial
-  . intros ab₁ ab₂ h₁ h₂ a b
+  · intros ab₁ ab₂ h₁ h₂ a b
     rw [mul_add, add_tmul, map_add, h₁, h₂, map_add, mul_add]
-  . intros a b ab₁ ab₂ h₁ h₂
+  · intros a b ab₁ ab₂ h₁ h₂
     rw [add_mul, add_tmul, map_add, h₁, h₂, map_add, add_mul]
-  . intros ab₁ ab₂ _ _ x y hx hy
+  · intros ab₁ ab₂ _ _ x y hx hy
     rw [add_mul, add_tmul, map_add, hx, hy, map_add, map_add, mul_add, mul_add, add_mul, mul_add])
   w₂
 #align algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product Algebra.TensorProduct.algEquivOfLinearEquivTripleTensorProduct
diff --git a/Mathlib/RingTheory/UniqueFactorizationDomain.lean b/Mathlib/RingTheory/UniqueFactorizationDomain.lean
index 353d41a21dada..5191e523d0443 100644
--- a/Mathlib/RingTheory/UniqueFactorizationDomain.lean
+++ b/Mathlib/RingTheory/UniqueFactorizationDomain.lean
@@ -1266,7 +1266,7 @@ theorem prod_mono : ∀ {a b : FactorSet α}, a ≤ b → a.prod ≤ b.prod
 theorem FactorSet.prod_eq_zero_iff [Nontrivial α] (p : FactorSet α) : p.prod = 0 ↔ p = ⊤ := by
   induction p using WithTop.recTopCoe
   · simp only [iff_self_iff, eq_self_iff_true, Associates.prod_top]
-  . rw [prod_coe, Multiset.prod_eq_zero_iff, Multiset.mem_map, eq_false WithTop.coe_ne_top,
+  · rw [prod_coe, Multiset.prod_eq_zero_iff, Multiset.mem_map, eq_false WithTop.coe_ne_top,
       iff_false_iff, not_exists]
     exact fun a => not_and_of_not_right _ a.prop.ne_zero
 #align associates.factor_set.prod_eq_zero_iff Associates.FactorSet.prod_eq_zero_iff
diff --git a/Mathlib/RingTheory/WittVector/WittPolynomial.lean b/Mathlib/RingTheory/WittVector/WittPolynomial.lean
index d2402f1e5ee23..83400362ee0b3 100644
--- a/Mathlib/RingTheory/WittVector/WittPolynomial.lean
+++ b/Mathlib/RingTheory/WittVector/WittPolynomial.lean
@@ -273,14 +273,14 @@ theorem xInTermsOfW_vars_aux (n : ℕ) :
     rcases H with ⟨j, hj, H⟩
     rw [vars_C_mul] at H
     swap
-    . apply pow_ne_zero
+    · apply pow_ne_zero
       exact_mod_cast hp.1.ne_zero
     rw [mem_range] at hj
     replace H := (ih j hj).2 (vars_pow _ _ H)
     rw [mem_range] at H
-  . rw [mem_range]
+  · rw [mem_range]
     linarith
-  . linarith
+  · linarith
 set_option linter.uppercaseLean3 false in
 #align X_in_terms_of_W_vars_aux xInTermsOfW_vars_aux
 
diff --git a/Mathlib/SetTheory/Cardinal/Basic.lean b/Mathlib/SetTheory/Cardinal/Basic.lean
index dc371000d85f3..eb78c82c9c1b7 100644
--- a/Mathlib/SetTheory/Cardinal/Basic.lean
+++ b/Mathlib/SetTheory/Cardinal/Basic.lean
@@ -1958,7 +1958,7 @@ theorem toPartENat_lift (c : Cardinal.{v}) : toPartENat (lift.{u, v} c) = toPart
     simp only [toNat_lift]
     rw [lift_lt_aleph0]
     exact hc
-  . rw [toPartENat_apply_of_aleph0_le hc, toPartENat_apply_of_aleph0_le _]
+  · rw [toPartENat_apply_of_aleph0_le hc, toPartENat_apply_of_aleph0_le _]
     rw [aleph0_le_lift]
     exact hc
 #align cardinal.to_part_enat_lift Cardinal.toPartENat_lift
diff --git a/Mathlib/SetTheory/Cardinal/Cofinality.lean b/Mathlib/SetTheory/Cardinal/Cofinality.lean
index 87337162fa9b0..32194fb94773a 100644
--- a/Mathlib/SetTheory/Cardinal/Cofinality.lean
+++ b/Mathlib/SetTheory/Cardinal/Cofinality.lean
@@ -529,7 +529,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2
       · suffices : r x a ∨ ∃ _ : PUnit.{u}, ↑a = x
-        . convert this
+        · convert this
           dsimp [RelEmbedding.ofMonotone]; simp
         rcases trichotomous_of r x a with (h | h | h)
         · exact Or.inl h
diff --git a/Mathlib/SetTheory/Cardinal/Ordinal.lean b/Mathlib/SetTheory/Cardinal/Ordinal.lean
index 4fb76d149b3b0..1e184ccfd73a5 100644
--- a/Mathlib/SetTheory/Cardinal/Ordinal.lean
+++ b/Mathlib/SetTheory/Cardinal/Ordinal.lean
@@ -528,8 +528,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
         typein_inj, mem_setOf_eq] at h
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
     suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit
-    ·
-      exact
+    · exact
         ⟨(Set.embeddingOfSubset _ _ this).trans
             ((Equiv.Set.prod _ _).trans (H.prodCongr H)).toEmbedding⟩
     refine' (Equiv.Set.insert _).trans ((Equiv.refl _).sumCongr punitEquivPUnit)
@@ -1032,8 +1031,7 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : #(Finset α) = #α :
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
     #(α →₀ β) = max (lift.{v} #α) (lift.{u} #β) := by
   apply le_antisymm
-  ·
-    calc
+  · calc
       #(α →₀ β) ≤ #(Finset (α × β)) := mk_le_of_injective (Finsupp.graph_injective α β)
       _ = #(α × β) := mk_finset_of_infinite _
       _ = max (lift.{v} #α) (lift.{u} #β) :=
diff --git a/Mathlib/SetTheory/Lists.lean b/Mathlib/SetTheory/Lists.lean
index ec4ce866511b9..f971dffea6286 100644
--- a/Mathlib/SetTheory/Lists.lean
+++ b/Mathlib/SetTheory/Lists.lean
@@ -301,7 +301,7 @@ theorem Equiv.antisymm_iff {l₁ l₂ : Lists' α true} : of' l₁ ~ of' l₂ 
   refine' ⟨fun h => _, fun ⟨h₁, h₂⟩ => Equiv.antisymm h₁ h₂⟩
   cases' h with _ _ _ h₁ h₂
   · simp [Lists'.Subset.refl]
-  . exact ⟨h₁, h₂⟩
+  · exact ⟨h₁, h₂⟩
 #align lists.equiv.antisymm_iff Lists.Equiv.antisymm_iff
 
 attribute [refl] Equiv.refl
@@ -347,9 +347,9 @@ theorem Equiv.trans : ∀ {l₁ l₂ l₃ : Lists α}, l₁ ~ l₂ → l₂ ~ l
     -- Assumption fails.
     simp only [Lists'.toList, Sigma.eta, List.find?, List.mem_cons, forall_eq_or_imp]
     constructor
-    . intros l₂ l₃ h₁ h₂
+    · intros l₂ l₃ h₁ h₂
       exact IH₁ h₁ h₂
-    . intros a h₁ l₂ l₃ h₂ h₃
+    · intros a h₁ l₂ l₃ h₂ h₃
       exact IH _ h₁ h₂ h₃
 #align lists.equiv.trans Lists.Equiv.trans
 
diff --git a/Mathlib/SetTheory/Ordinal/Arithmetic.lean b/Mathlib/SetTheory/Ordinal/Arithmetic.lean
index 62f8fb71c0a69..b151d561c1383 100644
--- a/Mathlib/SetTheory/Ordinal/Arithmetic.lean
+++ b/Mathlib/SetTheory/Ordinal/Arithmetic.lean
@@ -910,8 +910,7 @@ theorem le_div {a b c : Ordinal} (c0 : c ≠ 0) : a ≤ b / c ↔ c * a ≤ b :=
   · simp only [mul_zero, Ordinal.zero_le]
   · intros
     rw [succ_le_iff, lt_div c0]
-  ·
-    simp (config := { contextual := true }) only [mul_le_of_limit, limit_le, iff_self_iff,
+  · simp (config := { contextual := true }) only [mul_le_of_limit, limit_le, iff_self_iff,
       forall_true_iff]
 #align ordinal.le_div Ordinal.le_div
 
diff --git a/Mathlib/SetTheory/Ordinal/Exponential.lean b/Mathlib/SetTheory/Ordinal/Exponential.lean
index f5f2455514b1f..fcc3652431aa1 100644
--- a/Mathlib/SetTheory/Ordinal/Exponential.lean
+++ b/Mathlib/SetTheory/Ordinal/Exponential.lean
@@ -156,8 +156,7 @@ theorem opow_le_opow_left {a b : Ordinal} (c) (ab : a ≤ b) : (a^c) ≤ (b^c) :
     · simp only [opow_zero, le_refl]
     · intro c IH
       simpa only [opow_succ] using mul_le_mul' IH ab
-    ·
-      exact fun c l IH =>
+    · exact fun c l IH =>
         (opow_le_of_limit a0 l).2 fun b' h =>
           (IH _ h).trans (opow_le_opow_right ((Ordinal.pos_iff_ne_zero.2 a0).trans_le ab) h.le)
 #align ordinal.opow_le_opow_left Ordinal.opow_le_opow_left
diff --git a/Mathlib/SetTheory/Ordinal/Notation.lean b/Mathlib/SetTheory/Ordinal/Notation.lean
index bdcc465c7c600..7002c8f958347 100644
--- a/Mathlib/SetTheory/Ordinal/Notation.lean
+++ b/Mathlib/SetTheory/Ordinal/Notation.lean
@@ -341,21 +341,21 @@ theorem cmp_compares : ∀ (a b : ONote) [NF a] [NF b], (cmp a b).Compares a b
       rw [cmpUsing, ite_eq_iff, not_lt] at nh
       case lt =>
         cases' nh with nh nh
-        . exact oadd_lt_oadd_2 h₁ nh.left
-        . rw [ite_eq_iff] at nh; cases' nh.right with nh nh <;> cases nh <;> contradiction
+        · exact oadd_lt_oadd_2 h₁ nh.left
+        · rw [ite_eq_iff] at nh; cases' nh.right with nh nh <;> cases nh <;> contradiction
       case gt =>
         cases' nh with nh nh
-        . cases nh; contradiction
-        . cases' nh with _ nh
+        · cases nh; contradiction
+        · cases' nh with _ nh
           rw [ite_eq_iff] at nh; cases' nh with nh nh
-          . exact oadd_lt_oadd_2 h₂ nh.left
-          . cases nh; contradiction
+          · exact oadd_lt_oadd_2 h₂ nh.left
+          · cases nh; contradiction
       cases' nh with nh nh
-      . cases nh; contradiction
+      · cases nh; contradiction
       cases' nh with nhl nhr
       rw [ite_eq_iff] at nhr
       cases' nhr with nhr nhr
-      . cases nhr; contradiction
+      · cases nhr; contradiction
       obtain rfl := Subtype.eq (eq_of_incomp ⟨(not_lt_of_ge nhl), nhr.left⟩)
       have IHa := @cmp_compares _ _ h₁.snd h₂.snd
       revert IHa; cases cmp a₁ a₂ <;> intro IHa <;> dsimp at IHa
@@ -540,7 +540,7 @@ theorem repr_sub : ∀ (o₁ o₂) [NF o₁] [NF o₂], repr (o₁ - o₂) = rep
     have ee := @cmp_compares _ _ h₁.fst h₂.fst
     cases h : cmp e₁ e₂ <;> simp only [h] at ee
     · rw [Ordinal.sub_eq_zero_iff_le.2]
-      . rfl
+      · rfl
       exact le_of_lt (oadd_lt_oadd_1 h₁ ee)
     · change e₁ = e₂ at ee
       subst e₂
@@ -817,10 +817,10 @@ instance nf_opowAux (e a0 a) [NF e] [NF a0] [NF a] : ∀ k m, NF (opowAux e a0 a
   intro k m
   unfold opowAux
   cases' m with m m
-  . cases k <;> exact NF.zero
+  · cases k <;> exact NF.zero
   cases' k with k k
-  . exact NF.oadd_zero _ _
-  . haveI := nf_opowAux e a0 a k
+  · exact NF.oadd_zero _ _
+  · haveI := nf_opowAux e a0 a k
     simp only [Nat.succ_ne_zero m] ; infer_instance
 #align onote.NF_opow_aux ONote.nf_opowAux
 
@@ -839,8 +839,8 @@ instance nf_opow (o₁ o₂) [NF o₁] [NF o₂] : NF (o₁ ^ o₂) := by
   · simp [(· ^ ·),Pow.pow,pow, opow, opowAux2, e₁, e₂, split_eq_scale_split' e₂]
     have := na.fst
     cases' k with k <;> simp <;> skip <;> dsimp
-    . infer_instance
-    . cases k <;> cases m <;> infer_instance
+    · infer_instance
+    · cases k <;> cases m <;> infer_instance
 #align onote.NF_opow ONote.nf_opow
 
 theorem scale_opowAux (e a0 a : ONote) [NF e] [NF a0] [NF a] :
diff --git a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
index b794d53206755..ac0649adb4513 100644
--- a/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
+++ b/Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
@@ -697,8 +697,8 @@ theorem tsum_iSup_decode₂ [CompleteLattice β] (m : β → α) (m0 : m ⊥ = 0
     intro n h
     generalize decode₂ γ n = foo at *
     cases' foo with b
-    . refine' (h <| by simp [m0]).elim
-    . exact rfl
+    · refine' (h <| by simp [m0]).elim
+    · exact rfl
   symm
   refine' tsum_eq_tsum_of_ne_zero_bij (fun a => Option.get _ (H a.1 a.2)) _ _ _
   · dsimp only []
@@ -842,7 +842,7 @@ theorem HasSum.update (hf : HasSum f a₁) (b : β) [DecidableEq β] (a : α) :
   by_cases h : b' = b
   · rw [h, update_same]
     simp [eq_self_iff_true, if_true, sub_add_cancel]
-  . simp only [h, update_noteq, if_false, Ne.def, zero_add, not_false_iff]
+  · simp only [h, update_noteq, if_false, Ne.def, zero_add, not_false_iff]
 #align has_sum.update HasSum.update
 
 theorem Summable.update (hf : Summable f) (b : β) [DecidableEq β] (a : α) :
diff --git a/Mathlib/Topology/Category/TopCat/Opens.lean b/Mathlib/Topology/Category/TopCat/Opens.lean
index 6628717490148..6ac7564f09de1 100644
--- a/Mathlib/Topology/Category/TopCat/Opens.lean
+++ b/Mathlib/Topology/Category/TopCat/Opens.lean
@@ -355,10 +355,10 @@ theorem adjunction_counit_app_self {X : TopCat} (U : Opens X) :
 theorem inclusion_top_functor (X : TopCat) :
     (@Opens.openEmbedding X ⊤).isOpenMap.functor = map (inclusionTopIso X).inv := by
   refine' CategoryTheory.Functor.ext _ _
-  . intro U
+  · intro U
     ext x
     exact ⟨fun ⟨⟨_, _⟩, h, rfl⟩ => h, fun h => ⟨⟨x, trivial⟩, h, rfl⟩⟩
-  . intros U V f
+  · intros U V f
     apply Subsingleton.elim
 #align topological_space.opens.inclusion_top_functor TopologicalSpace.Opens.inclusion_top_functor
 
@@ -377,9 +377,9 @@ lemma set_range_forget_map_inclusion {X : TopCat} (U : Opens X) :
     Set.range ((forget TopCat).map (inclusion U)) = (U : Set X) := by
   ext x
   constructor
-  . rintro ⟨x, rfl⟩
+  · rintro ⟨x, rfl⟩
     exact x.2
-  . intro h
+  · intro h
     exact ⟨⟨x, h⟩, rfl⟩
 
 @[simp]
diff --git a/Mathlib/Topology/Instances/RatLemmas.lean b/Mathlib/Topology/Instances/RatLemmas.lean
index 7a27bf59f5976..2bcc661a48494 100644
--- a/Mathlib/Topology/Instances/RatLemmas.lean
+++ b/Mathlib/Topology/Instances/RatLemmas.lean
@@ -86,7 +86,7 @@ instance : TotallyDisconnectedSpace ℚ := by
   refine' ⟨fun s hsu hs x hx y hy => _⟩; clear hsu
   by_contra' H : x ≠ y
   wlog hlt : x < y
-  . refine' this s hs y hy x hx H.symm <| H.lt_or_lt.resolve_left hlt <;> assumption
+  · refine' this s hs y hy x hx H.symm <| H.lt_or_lt.resolve_left hlt <;> assumption
   rcases exists_irrational_btwn (Rat.cast_lt.2 hlt) with ⟨z, hz, hxz, hzy⟩
   have := hs.image _ continuous_coe_real.continuousOn
   rw [isPreconnected_iff_ordConnected] at this
diff --git a/Mathlib/Topology/MetricSpace/Kuratowski.lean b/Mathlib/Topology/MetricSpace/Kuratowski.lean
index 0eee480494ce1..a584e9bbf929d 100644
--- a/Mathlib/Topology/MetricSpace/Kuratowski.lean
+++ b/Mathlib/Topology/MetricSpace/Kuratowski.lean
@@ -150,10 +150,10 @@ theorem LipschitzOnWith.extend_lp_infty [PseudoMetricSpace α] {s : Set α} {f :
     exact LipschitzOnWith.extend_real (hfl i) -- use the nonlinear Hahn-Banach theorem here!
   choose g hgl hgeq using this
   rcases s.eq_empty_or_nonempty with rfl | ⟨a₀, ha₀_in_s⟩
-  . exact ⟨0, LipschitzWith.const' 0, by simp⟩
+  · exact ⟨0, LipschitzWith.const' 0, by simp⟩
   · -- Show that the extensions are uniformly bounded
     have hf_extb : ∀ a : α, Memℓp (swap g a) ∞
-    . apply LipschitzWith.uniformly_bounded (swap g) hgl a₀
+    · apply LipschitzWith.uniformly_bounded (swap g) hgl a₀
       use ‖f a₀‖
       rintro - ⟨i, rfl⟩
       simp_rw [←hgeq i ha₀_in_s]
diff --git a/Mathlib/Topology/Sheaves/Functors.lean b/Mathlib/Topology/Sheaves/Functors.lean
index 9c42ad85beadb..f94b7b6065d24 100644
--- a/Mathlib/Topology/Sheaves/Functors.lean
+++ b/Mathlib/Topology/Sheaves/Functors.lean
@@ -46,7 +46,7 @@ theorem map_diagram :
     Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) := by
   have obj_eq : ∀ (j : Pairwise ι), (Pairwise.diagram U ⋙ Opens.map f).obj j =
     (Pairwise.diagram ((Opens.map f).toPrefunctor.obj ∘ U)).obj j
-  . rintro ⟨i⟩ <;> rfl
+  · rintro ⟨i⟩ <;> rfl
   refine Functor.hext obj_eq ?_
   intro i j g; apply Subsingleton.helim
   rw [obj_eq, obj_eq]
diff --git a/Mathlib/Topology/Sheaves/LocalPredicate.lean b/Mathlib/Topology/Sheaves/LocalPredicate.lean
index 3a2bf05f874f3..d8c06528e4016 100644
--- a/Mathlib/Topology/Sheaves/LocalPredicate.lean
+++ b/Mathlib/Topology/Sheaves/LocalPredicate.lean
@@ -299,8 +299,8 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     -- and put it back together again in the correct order.
     refine' ⟨op W, fun w => fU (iU w : (unop U).1), P.res _ _ hU, _⟩
     rcases W with ⟨W, m⟩
-    . exact iU
-    . exact ⟨colimit_sound iU.op (Subtype.eq rfl), colimit_sound iV.op (Subtype.eq (funext w).symm)⟩
+    · exact iU
+    · exact ⟨colimit_sound iU.op (Subtype.eq rfl), colimit_sound iV.op (Subtype.eq (funext w).symm)⟩
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective
 
diff --git a/Mathlib/Topology/Sheaves/Operations.lean b/Mathlib/Topology/Sheaves/Operations.lean
index ccde073d32f3a..f816b687c5175 100644
--- a/Mathlib/Topology/Sheaves/Operations.lean
+++ b/Mathlib/Topology/Sheaves/Operations.lean
@@ -121,7 +121,7 @@ instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf
   -- Porting note : was an `apply (config := { instances := false })`
   -- See https://github.com/leanprover/lean4/issues/2273
   suffices : ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U)
-  . apply NatTrans.mono_of_mono_app
+  · apply NatTrans.mono_of_mono_app
   intro U
   apply ConcreteCategory.mono_of_injective
   dsimp [toTotalQuotientPresheaf, CommRingCat.ofHom]
diff --git a/Mathlib/Topology/Sheaves/Presheaf.lean b/Mathlib/Topology/Sheaves/Presheaf.lean
index 0074c99d17204..b6a29327ade8d 100644
--- a/Mathlib/Topology/Sheaves/Presheaf.lean
+++ b/Mathlib/Topology/Sheaves/Presheaf.lean
@@ -327,10 +327,10 @@ def pullbackObjObjOfImageOpen {X Y : TopCat.{v}} (f : X ⟶ Y) (ℱ : Y.Presheaf
     { lift := fun s ↦ by
         fapply CostructuredArrow.homMk
         change op (unop _) ⟶ op (⟨_, H⟩ : Opens _)
-        . refine' (homOfLE _).op
+        · refine' (homOfLE _).op
           apply (Set.image_subset f s.pt.hom.unop.le).trans
           exact Set.image_preimage.l_u_le (SetLike.coe s.pt.left.unop)
-        . simp
+        · simp
       -- porting note : add `fac`, `uniq` manually
       fac := fun _ _ => by ext; simp
       uniq := fun _ _ _ => by ext; simp }
@@ -398,7 +398,7 @@ theorem id_pushforward {X : TopCat.{w}} : pushforward C (𝟙 X) = 𝟭 (X.Presh
   apply CategoryTheory.Functor.ext
   · intros a b f
     ext U
-    . erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
+    · erw [NatTrans.congr f (Opens.op_map_id_obj (op U))]
       simp only [Functor.op_obj, eqToHom_refl, CategoryTheory.Functor.map_id,
         Category.comp_id, Category.id_comp, Functor.id_obj, Functor.id_map]
       apply Pushforward.id_eq
diff --git a/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean b/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
index 40a6a3c9cd54f..d09e301f99dcd 100644
--- a/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
+++ b/Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean
@@ -378,7 +378,7 @@ def interUnionPullbackConeLift : s.pt ⟶ F.1.obj (op (U ⊔ V)) := by
   rcases g with ⟨⟩ <;>
   dsimp [Pairwise.diagram] <;>
   simp only [Category.id_comp, s.condition, CategoryTheory.Functor.map_id, Category.comp_id]
-  . rw [← cancel_mono (F.1.map (eqToHom <| inf_comm : U ⊓ V ⟶ _).op), Category.assoc,
+  · rw [← cancel_mono (F.1.map (eqToHom <| inf_comm : U ⊓ V ⟶ _).op), Category.assoc,
       Category.assoc, ←F.1.map_comp, ←F.1.map_comp]
     exact s.condition.symm
 set_option linter.uppercaseLean3 false in
diff --git a/Mathlib/Topology/Sheaves/Skyscraper.lean b/Mathlib/Topology/Sheaves/Skyscraper.lean
index f042497d3124b..6637607f45aae 100644
--- a/Mathlib/Topology/Sheaves/Skyscraper.lean
+++ b/Mathlib/Topology/Sheaves/Skyscraper.lean
@@ -235,8 +235,8 @@ theorem skyscraperPresheaf_isSheaf : (skyscraperPresheaf p₀ A).IsSheaf := by
         (Presheaf.isSheaf_on_pUnit_of_isTerminal _ (by
           dsimp [skyscraperPresheaf]
           rw [if_neg]
-          . exact terminalIsTerminal
-          . exact Set.not_mem_empty PUnit.unit)))
+          · exact terminalIsTerminal
+          · exact Set.not_mem_empty PUnit.unit)))
 #align skyscraper_presheaf_is_sheaf skyscraperPresheaf_isSheaf
 
 /--
diff --git a/Mathlib/Topology/UniformSpace/Completion.lean b/Mathlib/Topology/UniformSpace/Completion.lean
index fad2ddb7316b9..3cb5a07217caa 100644
--- a/Mathlib/Topology/UniformSpace/Completion.lean
+++ b/Mathlib/Topology/UniformSpace/Completion.lean
@@ -192,10 +192,10 @@ theorem denseRange_pureCauchy : DenseRange (pureCauchy : α → CauchyFilter α)
   simp only [closure_eq_cluster_pts, ClusterPt, nhds_eq_uniformity, lift'_inf_principal_eq,
     Set.inter_comm _ (range pureCauchy), mem_setOf_eq]
   refine (lift'_neBot_iff ?_).mpr (fun s hs => ?_)
-  . refine monotone_const.inter ?_
+  · refine monotone_const.inter ?_
     simp_rw [UniformSpace.ball]
     exact monotone_preimage
-  . let ⟨y, hy⟩ := h_ex s hs
+  · let ⟨y, hy⟩ := h_ex s hs
     have : pureCauchy y ∈ range pureCauchy ∩ { y : CauchyFilter α | (f, y) ∈ s } :=
       ⟨mem_range_self y, hy⟩
     exact ⟨_, this⟩
@@ -644,16 +644,16 @@ def completionSeparationQuotientEquiv (α : Type u) [UniformSpace α] :
     -- porting note: had to insert rewrites to switch between Quot.mk, Quotient.mk, Quotient.mk'
     rw [← Quotient.mk,extension_coe (SeparationQuotient.uniformContinuous_lift _),
       SeparationQuotient.lift_mk (uniformContinuous_coe α), map_coe]
-    . rfl
-    . exact uniformContinuous_quotient_mk
+    · rfl
+    · exact uniformContinuous_quotient_mk
   · intro a
     refine' Completion.induction_on a
         (isClosed_eq (continuous_extension.comp continuous_map) continuous_id) fun a => _
     rw [map_coe]
     -- porting note: add SeparationQuotient.lift_mk' for Quotient.mk' ?
-    . rw [extension_coe (SeparationQuotient.uniformContinuous_lift _), Quotient.mk',
+    · rw [extension_coe (SeparationQuotient.uniformContinuous_lift _), Quotient.mk',
         SeparationQuotient.lift_mk (uniformContinuous_coe α) _]
-    . exact uniformContinuous_quotient_mk
+    · exact uniformContinuous_quotient_mk
 #align uniform_space.completion.completion_separation_quotient_equiv UniformSpace.Completion.completionSeparationQuotientEquiv
 
 theorem uniformContinuous_completionSeparationQuotientEquiv :
diff --git a/scripts/lint-style.py b/scripts/lint-style.py
index f712c20e99e33..083c8819b20b7 100755
--- a/scripts/lint-style.py
+++ b/scripts/lint-style.py
@@ -47,6 +47,7 @@
 ERR_TAC = 9 # imported Mathlib.Tactic
 ERR_UNF = 10 # unfreeze_local_instances
 ERR_IBY = 11 # isolated by
+ERR_DOT = 12 # isolated or low focusing dot
 
 exceptions = []
 
@@ -231,7 +232,7 @@ def banned_import_check(lines, path):
             errors += [(ERR_TAC, line_nr, path)]
     return errors
 
-def isolated_by_check(lines, path):
+def isolated_by_dot_check(lines, path):
     errors = []
     for line_nr, line in enumerate(lines, 1):
         if line.strip() == "by":
@@ -241,6 +242,8 @@ def isolated_by_check(lines, path):
             prev_line = lines[line_nr - 2].rstrip()
             if not prev_line.endswith(",") and not re.search(", fun [^,]* =>$", prev_line):
                 errors += [(ERR_IBY, line_nr, path)]
+        if line.lstrip().startswith(". ") or line.strip() in (".", "·"):
+            errors += [(ERR_DOT, line_nr, path)]
     return errors
 
 def output_message(path, line_nr, code, msg):
@@ -283,13 +286,15 @@ def format_errors(errors):
             output_message(path, line_nr, "ERR_TAC", "Files in mathlib cannot import the whole tactic folder")
         if errno == ERR_IBY:
             output_message(path, line_nr, "ERR_IBY", "Line is an isolated 'by'")
+        if errno == ERR_DOT:
+            output_message(path, line_nr, "ERR_DOT", "Line is an isolated focusing dot or uses . instead of ·")
 
 def lint(path):
     with path.open(encoding="utf-8") as f:
         lines = f.readlines()
         errs = long_lines_check(lines, path)
         format_errors(errs)
-        errs = isolated_by_check(lines, path)
+        errs = isolated_by_dot_check(lines, path)
         format_errors(errs)
         (b, errs) = import_only_check(lines, path)
         if b:
diff --git a/test/interval_cases.lean b/test/interval_cases.lean
index 9095332f3530c..ef7a8d848b8fd 100644
--- a/test/interval_cases.lean
+++ b/test/interval_cases.lean
@@ -27,59 +27,59 @@ example (n : ℕ) (w₂ : n < 1) : n = 0 := by
 
 example (n : ℕ) (w₂ : n < 2) : n = 0 ∨ n = 1 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : 1 ≤ n) (w₂ : n < 3) : n = 1 ∨ n = 2 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : 1 ≤ n) (w₂ : n < 3) : n = 1 ∨ n = 2 := by
   interval_cases using w₁, w₂
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 -- make sure we only pick up bounds on the specified variable:
 example (n m : ℕ) (w₁ : 1 ≤ n) (w₂ : n < 3) (_ : m < 2) : n = 1 ∨ n = 2 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : 1 < n) (w₂ : n < 4) : n = 2 ∨ n = 3 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : n ≥ 3) (w₂ : n < 5) : n = 3 ∨ n = 4 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₀ : n ≥ 2) (w₁ : n ≥ 3) (w₂ : n < 5) : n = 3 ∨ n = 4 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : n > 2) (w₂ : n < 5) : n = 3 ∨ n = 4 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : n > 2) (w₂ : n ≤ 4) : n = 3 ∨ n = 4 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (w₁ : 2 < n) (w₂ : 4 ≥ n) : n = 3 ∨ n = 4 := by
   interval_cases n
-  . left; rfl
-  . right; rfl
+  · left; rfl
+  · right; rfl
 
 example (n : ℕ) (h1 : 4 < n) (h2 : n ≤ 6) : n < 20 := by
   interval_cases n
-  . guard_target =ₛ 5 < 20; norm_num
-  . guard_target =ₛ 6 < 20; norm_num
+  · guard_target =ₛ 5 < 20; norm_num
+  · guard_target =ₛ 6 < 20; norm_num
 
 example (n : ℕ) (w₁ : n % 3 < 1) : n % 3 = 0 := by
   interval_cases h : n % 3
@@ -124,15 +124,15 @@ example (z : ℤ) (h1 : z ≥ -3) (h2 : z < 2) : z < 20 := by
 
 example (z : ℤ) (h1 : z ≥ -3) (h2 : z < 2) : z < 20 := by
   interval_cases z
-  . guard_target =ₛ (-3 : ℤ) < 20
+  · guard_target =ₛ (-3 : ℤ) < 20
     norm_num
-  . guard_target =ₛ (-2 : ℤ) < 20
+  · guard_target =ₛ (-2 : ℤ) < 20
     norm_num
-  . guard_target =ₛ (-1 : ℤ) < 20
+  · guard_target =ₛ (-1 : ℤ) < 20
     norm_num
-  . guard_target =ₛ (0 : ℤ) < 20
+  · guard_target =ₛ (0 : ℤ) < 20
     norm_num
-  . guard_target =ₛ (1 : ℤ) < 20
+  · guard_target =ₛ (1 : ℤ) < 20
     norm_num
 
 example (n : ℕ) : n % 2 = 0 ∨ n % 2 = 1 := by
@@ -140,9 +140,9 @@ example (n : ℕ) : n % 2 = 0 ∨ n % 2 = 1 := by
   have h2 : r < 2 := by
     exact Nat.mod_lt _ (by decide)
   interval_cases hrv : r -- Porting note: old syntax was `interval_cases r with hrv`
-  . left; exact hrv.symm.trans hrv
+  · left; exact hrv.symm.trans hrv
                --^ hover says `hrv : r = 0` and jumps to `hrv :` above
-  . right; exact hrv.symm.trans hrv
+  · right; exact hrv.symm.trans hrv
                --^ hover says `hrv : r = 1` and jumps to `hrv :` above
 
 /- https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/interval_cases.20bug -/
@@ -151,8 +151,8 @@ example {x : ℕ} (hx2 : x < 2) (h : False) : False := by
   -- `interval_cases` deliberately not focussed,
   -- this is testing that the `interval_cases` only acts on `have` side goal, not on both
   interval_cases x
-  . exact zero_le_one
-  . rfl -- done for free in the mathlib3 version
+  · exact zero_le_one
+  · rfl -- done for free in the mathlib3 version
   exact h
 
 /-