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24 changes: 0 additions & 24 deletions Mathlib/Algebra/Category/Grp/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -603,27 +603,3 @@ abbrev AddCommGrpMax.{u1, u2} := AddCommGrp.{max u1 u2}
/-!
Deprecated lemmas for `MonoidHom.comp` and categorical identities.
-/

@[to_additive (attr := deprecated
"Proven by `simp only [Grp.hom_id, comp_id]`"
(since := "2025-01-28"))]
theorem MonoidHom.comp_id_grp {G : Grp.{u}} {H : Type u} [Monoid H] (f : G →* H) :
f.comp (Grp.Hom.hom (𝟙 G)) = f := by simp
@[to_additive (attr := deprecated
"Proven by `simp only [Grp.hom_id, id_comp]`"
(since := "2025-01-28"))]
theorem MonoidHom.id_grp_comp {G : Type u} [Monoid G] {H : Grp.{u}} (f : G →* H) :
MonoidHom.comp (Grp.Hom.hom (𝟙 H)) f = f := by simp

@[to_additive (attr := deprecated
"Proven by `simp only [CommGrp.hom_id, comp_id]`"
(since := "2025-01-28"))]
theorem MonoidHom.comp_id_commGrp {G : CommGrp.{u}} {H : Type u} [Monoid H] (f : G →* H) :
f.comp (CommGrp.Hom.hom (𝟙 G)) = f := by
simp
@[to_additive (attr := deprecated
"Proven by `simp only [CommGrp.hom_id, id_comp]`"
(since := "2025-01-28"))]
theorem MonoidHom.id_commGrp_comp {G : Type u} [Monoid G] {H : CommGrp.{u}} (f : G →* H) :
MonoidHom.comp (CommGrp.Hom.hom (𝟙 H)) f = f := by
simp
3 changes: 0 additions & 3 deletions Mathlib/Algebra/Category/ModuleCat/Presheaf/Pullback.lean
Original file line number Diff line number Diff line change
Expand Up @@ -48,9 +48,6 @@ on a certain object `M : PresheafOfModules S`. -/
abbrev pullbackObjIsDefined : ObjectProperty (PresheafOfModules.{v} S) :=
(pushforward φ).leftAdjointObjIsDefined

@[deprecated (since := "2025-03-06")]
alias PullbackObjIsDefined := pullbackObjIsDefined

end

section
Expand Down
24 changes: 0 additions & 24 deletions Mathlib/Algebra/Category/MonCat/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -504,30 +504,6 @@ example : (forget₂ CommMonCat MonCat).ReflectsIsomorphisms := inferInstance
`@[simp]` lemmas for `MonoidHom.comp` and categorical identities.
-/

@[to_additive (attr := deprecated
"Proven by `simp only [MonCat.hom_id, comp_id]`"
(since := "2025-01-28"))]
theorem MonoidHom.comp_id_monCat {G : MonCat.{u}} {H : Type u} [Monoid H] (f : G →* H) :
f.comp (MonCat.Hom.hom (𝟙 G)) = f := by simp
@[to_additive (attr := deprecated
"Proven by `simp only [MonCat.hom_id, id_comp]`"
(since := "2025-01-28"))]
theorem MonoidHom.id_monCat_comp {G : Type u} [Monoid G] {H : MonCat.{u}} (f : G →* H) :
MonoidHom.comp (MonCat.Hom.hom (𝟙 H)) f = f := by simp

@[to_additive (attr := deprecated
"Proven by `simp only [CommMonCat.hom_id, comp_id]`"
(since := "2025-01-28"))]
theorem MonoidHom.comp_id_commMonCat {G : CommMonCat.{u}} {H : Type u} [CommMonoid H] (f : G →* H) :
f.comp (CommMonCat.Hom.hom (𝟙 G)) = f := by
simp
@[to_additive (attr := deprecated
"Proven by `simp only [CommMonCat.hom_id, id_comp]`"
(since := "2025-01-28"))]
theorem MonoidHom.id_commMonCat_comp {G : Type u} [CommMonoid G] {H : CommMonCat.{u}} (f : G →* H) :
MonoidHom.comp (CommMonCat.Hom.hom (𝟙 H)) f = f := by
simp

/-- The equivalence between `AddMonCat` and `MonCat`. -/
@[simps]
def AddMonCat.equivalence : AddMonCat ≌ MonCat where
Expand Down
6 changes: 0 additions & 6 deletions Mathlib/Algebra/Group/Action/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -115,12 +115,6 @@ theorem smul_bijective {m : α} (hm : IsUnit m) :
lift m to αˣ using hm
exact MulAction.bijective m

@[deprecated (since := "2025-03-03")]
alias _root_.AddAction.vadd_bijective_of_is_addUnit := IsAddUnit.vadd_bijective

@[to_additive existing, deprecated (since := "2025-03-03")]
alias _root_.MulAction.smul_bijective_of_is_unit := IsUnit.smul_bijective

@[to_additive]
lemma smul_left_cancel {a : α} (ha : IsUnit a) {x y : β} : a • x = a • y ↔ x = y :=
let ⟨u, hu⟩ := ha
Expand Down
3 changes: 0 additions & 3 deletions Mathlib/Algebra/Group/Action/Pointwise/Set/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -41,9 +41,6 @@ lemma smul_set_prod {M α : Type*} [SMul M α] [SMul M β] (c : M) (s : Set α)
c • (s ×ˢ t) = (c • s) ×ˢ (c • t) :=
prodMap_image_prod (c • ·) (c • ·) s t

@[deprecated (since := "2025-03-11")]
alias vadd_set_sum := vadd_set_prod

@[to_additive]
lemma smul_set_pi {G ι : Type*} {α : ι → Type*} [Group G] [∀ i, MulAction G (α i)]
(c : G) (I : Set ι) (s : ∀ i, Set (α i)) : c • I.pi s = I.pi (c • s) :=
Expand Down
24 changes: 0 additions & 24 deletions Mathlib/Algebra/Group/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -224,37 +224,25 @@ theorem mul_eq_left : a * b = a ↔ b = 1 := calc
a * b = a ↔ a * b = a * 1 := by rw [mul_one]
_ ↔ b = 1 := mul_left_cancel_iff

@[deprecated (since := "2025-03-05")] alias mul_right_eq_self := mul_eq_left
@[deprecated (since := "2025-03-05")] alias add_right_eq_self := add_eq_left

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] mul_right_eq_self

@[to_additive (attr := simp)]
theorem left_eq_mul : a = a * b ↔ b = 1 :=
eq_comm.trans mul_eq_left

@[deprecated (since := "2025-03-05")] alias self_eq_mul_right := left_eq_mul
@[deprecated (since := "2025-03-05")] alias self_eq_add_right := left_eq_add

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] self_eq_mul_right

@[to_additive]
theorem mul_ne_left : a * b ≠ a ↔ b ≠ 1 := mul_eq_left.not

@[deprecated (since := "2025-03-05")] alias mul_right_ne_self := mul_ne_left
@[deprecated (since := "2025-03-05")] alias add_right_ne_self := add_ne_left

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] mul_right_ne_self

@[to_additive]
theorem left_ne_mul : a ≠ a * b ↔ b ≠ 1 := left_eq_mul.not

@[deprecated (since := "2025-03-05")] alias self_ne_mul_right := left_ne_mul
@[deprecated (since := "2025-03-05")] alias self_ne_add_right := left_ne_add

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] self_ne_mul_right

Expand All @@ -269,37 +257,25 @@ theorem mul_eq_right : a * b = b ↔ a = 1 := calc
a * b = b ↔ a * b = 1 * b := by rw [one_mul]
_ ↔ a = 1 := mul_right_cancel_iff

@[deprecated (since := "2025-03-05")] alias mul_left_eq_self := mul_eq_right
@[deprecated (since := "2025-03-05")] alias add_left_eq_self := add_eq_right

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] mul_left_eq_self

@[to_additive (attr := simp)]
theorem right_eq_mul : b = a * b ↔ a = 1 :=
eq_comm.trans mul_eq_right

@[deprecated (since := "2025-03-05")] alias self_eq_mul_left := right_eq_mul
@[deprecated (since := "2025-03-05")] alias self_eq_add_left := right_eq_add

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] self_eq_mul_left

@[to_additive]
theorem mul_ne_right : a * b ≠ b ↔ a ≠ 1 := mul_eq_right.not

@[deprecated (since := "2025-03-05")] alias mul_left_ne_self := mul_ne_right
@[deprecated (since := "2025-03-05")] alias add_left_ne_self := add_ne_right

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] mul_left_ne_self

@[to_additive]
theorem right_ne_mul : b ≠ a * b ↔ a ≠ 1 := right_eq_mul.not

@[deprecated (since := "2025-03-05")] alias self_ne_mul_left := right_ne_mul
@[deprecated (since := "2025-03-05")] alias self_ne_add_left := right_ne_add

set_option linter.existingAttributeWarning false in
attribute [to_additive existing] self_ne_mul_left

Expand Down
6 changes: 0 additions & 6 deletions Mathlib/Algebra/Group/Graph.lean
Original file line number Diff line number Diff line change
Expand Up @@ -56,9 +56,6 @@ lemma mem_mgraph {f : G →* H} {x : G × H} : x ∈ f.mgraph ↔ f x.1 = x.2 :=
@[to_additive mgraph_eq_mrange_prod]
lemma mgraph_eq_mrange_prod (f : G →* H) : f.mgraph = mrange ((id _).prod f) := by aesop

@[deprecated (since := "2025-03-11")]
alias _root_.AddMonoidHom.mgraph_eq_mrange_sum := AddMonoidHom.mgraph_eq_mrange_prod

/-- **Vertical line test** for monoid homomorphisms.

Let `f : G → H × I` be a homomorphism to a product of monoids. Assume that `f` is surjective on the
Expand Down Expand Up @@ -171,9 +168,6 @@ lemma mem_graph {f : G →* H} {x : G × H} : x ∈ f.graph ↔ f x.1 = x.2 := .
@[to_additive graph_eq_range_prod]
lemma graph_eq_range_prod (f : G →* H) : f.graph = range ((id _).prod f) := by aesop

@[deprecated (since := "2025-03-11")]
alias AddMonoidHom.graph_eq_range_sum := graph_eq_range_prod

/-- **Vertical line test** for group homomorphisms.

Let `f : G → H × I` be a homomorphism to a product of groups. Assume that `f` is surjective on the
Expand Down
9 changes: 0 additions & 9 deletions Mathlib/Algebra/Group/Pointwise/Set/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -130,9 +130,6 @@ theorem coe_singletonOneHom : (singletonOneHom : α → Set α) = singleton :=
@[to_additive (attr := simp) zero_prod_zero]
lemma one_prod_one [One β] : (1 ×ˢ 1 : Set (α × β)) = 1 := by ext; simp [Prod.ext_iff]

@[deprecated (since := "2025-03-11")]
alias zero_sum_zero := zero_prod_zero

end One

/-! ### Set negation/inversion -/
Expand Down Expand Up @@ -187,9 +184,6 @@ theorem compl_inv : sᶜ⁻¹ = s⁻¹ᶜ :=
@[to_additive (attr := simp) neg_prod]
lemma inv_prod [Inv β] (s : Set α) (t : Set β) : (s ×ˢ t)⁻¹ = s⁻¹ ×ˢ t⁻¹ := rfl

@[deprecated (since := "2025-03-11")]
alias neg_sum := neg_prod

end Inv

section InvolutiveInv
Expand Down Expand Up @@ -392,9 +386,6 @@ theorem image_op_mul : op '' (s * t) = op '' t * op '' s :=
lemma prod_mul_prod_comm [Mul β] (s₁ s₂ : Set α) (t₁ t₂ : Set β) :
(s₁ ×ˢ t₁) * (s₂ ×ˢ t₂) = (s₁ * s₂) ×ˢ (t₁ * t₂) := by ext; simp [mem_mul]; aesop

@[deprecated (since := "2025-03-11")]
alias sum_add_sum_comm := prod_add_prod_comm

end Mul

/-! ### Set subtraction/division -/
Expand Down
22 changes: 0 additions & 22 deletions Mathlib/Algebra/Group/Subgroup/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -126,9 +126,6 @@ theorem top_prod_top : (⊤ : Subgroup G).prod (⊤ : Subgroup N) = ⊤ :=
theorem bot_prod_bot : (⊥ : Subgroup G).prod (⊥ : Subgroup N) = ⊥ :=
SetLike.coe_injective <| by simp [coe_prod]

@[deprecated (since := "2025-03-11")]
alias _root_.AddSubgroup.bot_sum_bot := AddSubgroup.bot_prod_bot

@[to_additive le_prod_iff]
theorem le_prod_iff {H : Subgroup G} {K : Subgroup N} {J : Subgroup (G × N)} :
J ≤ H.prod K ↔ map (MonoidHom.fst G N) J ≤ H ∧ map (MonoidHom.snd G N) J ≤ K := by
Expand Down Expand Up @@ -569,17 +566,11 @@ theorem prodMap_comap_prod {G' : Type*} {N' : Type*} [Group G'] [Group N'] (f :
(S.prod S').comap (prodMap f g) = (S.comap f).prod (S'.comap g) :=
SetLike.coe_injective <| Set.preimage_prod_map_prod f g _ _

@[deprecated (since := "2025-03-11")]
alias _root_.AddMonoidHom.sumMap_comap_sum := AddMonoidHom.prodMap_comap_prod

@[to_additive ker_prodMap]
theorem ker_prodMap {G' : Type*} {N' : Type*} [Group G'] [Group N'] (f : G →* N) (g : G' →* N') :
(prodMap f g).ker = f.ker.prod g.ker := by
rw [← comap_bot, ← comap_bot, ← comap_bot, ← prodMap_comap_prod, bot_prod_bot]

@[deprecated (since := "2025-03-11")]
alias _root_.AddMonoidHom.ker_sumMap := AddMonoidHom.ker_prodMap

@[to_additive (attr := simp)]
lemma ker_fst : ker (fst G G') = .prod ⊥ ⊤ := SetLike.ext fun _ => (iff_of_eq (and_true _)).symm

Expand Down Expand Up @@ -618,13 +609,6 @@ theorem comap_normalizer_eq_of_surjective (H : Subgroup G) {f : N →* G}
(hf : Function.Surjective f) : H.normalizer.comap f = (H.comap f).normalizer :=
comap_normalizer_eq_of_le_range fun x _ ↦ hf x

@[deprecated (since := "2025-03-13")]
alias comap_normalizer_eq_of_injective_of_le_range := comap_normalizer_eq_of_le_range

@[deprecated (since := "2025-03-13")]
alias _root_.AddSubgroup.comap_normalizer_eq_of_injective_of_le_range :=
AddSubgroup.comap_normalizer_eq_of_le_range

/-- The image of the normalizer is equal to the normalizer of the image of an isomorphism. -/
@[to_additive
/-- The image of the normalizer is equal to the normalizer of the image of an
Expand Down Expand Up @@ -816,19 +800,13 @@ instance prod_subgroupOf_prod_normal {H₁ K₁ : Subgroup G} {H₂ K₂ : Subgr
h₂.conj_mem ⟨(n : G × N).snd, (mem_prod.mp n.2).2⟩ hgHK.2
⟨(g : G × N).snd, (mem_prod.mp g.2).2⟩⟩

@[deprecated (since := "2025-03-11")]
alias _root_.AddSubgroup.sum_addSubgroupOf_sum_normal := AddSubgroup.prod_addSubgroupOf_prod_normal

@[to_additive prod_normal]
instance prod_normal (H : Subgroup G) (K : Subgroup N) [hH : H.Normal] [hK : K.Normal] :
(H.prod K).Normal where
conj_mem n hg g :=
⟨hH.conj_mem n.fst (Subgroup.mem_prod.mp hg).1 g.fst,
hK.conj_mem n.snd (Subgroup.mem_prod.mp hg).2 g.snd⟩

@[deprecated (since := "2025-03-11")]
alias _root_.AddSubgroup.sum_normal := AddSubgroup.prod_normal

@[to_additive]
theorem inf_subgroupOf_inf_normal_of_right (A B' B : Subgroup G)
[hN : (B'.subgroupOf B).Normal] : ((A ⊓ B').subgroupOf (A ⊓ B)).Normal := by
Expand Down
3 changes: 0 additions & 3 deletions Mathlib/Algebra/Group/Subgroup/Ker.lean
Original file line number Diff line number Diff line change
Expand Up @@ -306,9 +306,6 @@ theorem ker_prod {M N : Type*} [MulOneClass M] [MulOneClass N] (f : G →* M) (g
(f.prod g).ker = f.ker ⊓ g.ker :=
SetLike.ext fun _ => Prod.mk_eq_one

@[deprecated (since := "2025-03-11")]
alias _root_.AddMonoidHom.ker_sum := AddMonoidHom.ker_prod

@[to_additive]
theorem range_le_ker_iff (f : G →* G') (g : G' →* G'') : f.range ≤ g.ker ↔ g.comp f = 1 :=
⟨fun h => ext fun x => h ⟨x, rfl⟩, by rintro h _ ⟨y, rfl⟩; exact DFunLike.congr_fun h y⟩
Expand Down
2 changes: 0 additions & 2 deletions Mathlib/Algebra/Group/Subgroup/Pointwise.lean
Original file line number Diff line number Diff line change
Expand Up @@ -460,8 +460,6 @@ theorem Normal.conjAct {H : Subgroup G} (hH : H.Normal) (g : ConjAct G) : g •
theorem Normal.conj_smul_eq_self (g : G) (H : Subgroup G) [h : Normal H] : MulAut.conj g • H = H :=
h.conjAct g

@[deprecated (since := "2025-03-01")] alias smul_normal := Normal.conj_smul_eq_self

theorem Normal.of_conjugate_fixed {H : Subgroup G} (h : ∀ g : G, (MulAut.conj g) • H = H) :
H.Normal := by
constructor
Expand Down
3 changes: 0 additions & 3 deletions Mathlib/Algebra/MvPolynomial/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -402,9 +402,6 @@ theorem monomial_add_induction_on {motive : MvPolynomial σ R → Prop} (p : MvP
motive p :=
Finsupp.induction p (C_0.rec <| C 0) monomial_add

@[deprecated (since := "2025-03-11")]
alias induction_on''' := monomial_add_induction_on

/--
Similar to `MvPolynomial.induction_on` but only a yet weaker form of `h_add` is required.
In particular, this version only requires us to show
Expand Down
3 changes: 0 additions & 3 deletions Mathlib/Algebra/Order/Group/Abs.lean
Original file line number Diff line number Diff line change
Expand Up @@ -193,9 +193,6 @@ theorem mabs_div_le_of_le_of_le {a b lb ub : G} (hal : lb ≤ a) (hau : a ≤ ub
(hbu : b ≤ ub) : |a / b|ₘ ≤ ub / lb :=
mabs_div_le_iff.2 ⟨div_le_div'' hau hbl, div_le_div'' hbu hal⟩

@[deprecated (since := "2025-03-02")]
alias dist_bdd_within_interval := abs_sub_le_of_le_of_le

@[to_additive]
theorem eq_of_mabs_div_le_one (h : |a / b|ₘ ≤ 1) : a = b :=
eq_of_mabs_div_eq_one (le_antisymm h (one_le_mabs (a / b)))
Expand Down
2 changes: 0 additions & 2 deletions Mathlib/Algebra/Order/Group/Unbundled/Int.lean
Original file line number Diff line number Diff line change
Expand Up @@ -133,8 +133,6 @@ protected theorem sign_eq_ediv_abs' (a : ℤ) : sign a = a / |a| :=
if az : a = 0 then by simp [az]
else (Int.ediv_eq_of_eq_mul_left (mt abs_eq_zero.1 az) (sign_mul_abs _).symm).symm

@[deprecated (since := "2025-03-10")] alias sign_eq_ediv_abs := Int.sign_eq_ediv_abs'

protected theorem sign_eq_abs_ediv (a : ℤ) : sign a = |a| / a :=
if az : a = 0 then by simp [az]
else (Int.ediv_eq_of_eq_mul_left az (sign_mul_self_eq_abs _).symm).symm
Expand Down
18 changes: 0 additions & 18 deletions Mathlib/Algebra/Order/Round.lean
Original file line number Diff line number Diff line change
Expand Up @@ -62,9 +62,6 @@ theorem round_add_intCast (x : α) (y : ℤ) : round (x + y) = round x + y := by
rw [round, round, Int.fract_add_intCast, Int.floor_add_intCast, Int.ceil_add_intCast,
← apply_ite₂, ite_self]

@[deprecated (since := "2025-03-23")]
alias round_add_int := round_add_intCast

@[simp]
theorem round_add_one (a : α) : round (a + 1) = round a + 1 := by
rw [← round_add_intCast a 1, cast_one]
Expand All @@ -75,9 +72,6 @@ theorem round_sub_intCast (x : α) (y : ℤ) : round (x - y) = round x - y := by
norm_cast
rw [round_add_intCast, sub_eq_add_neg]

@[deprecated (since := "2025-03-23")]
alias round_sub_int := round_sub_intCast

@[simp]
theorem round_sub_one (a : α) : round (a - 1) = round a - 1 := by
rw [← round_sub_intCast a 1, cast_one]
Expand All @@ -86,9 +80,6 @@ theorem round_sub_one (a : α) : round (a - 1) = round a - 1 := by
theorem round_add_natCast (x : α) (y : ℕ) : round (x + y) = round x + y :=
mod_cast round_add_intCast x y

@[deprecated (since := "2025-03-23")]
alias round_add_nat := round_add_natCast

@[simp]
theorem round_add_ofNat (x : α) (n : ℕ) [n.AtLeastTwo] :
round (x + ofNat(n)) = round x + ofNat(n) :=
Expand All @@ -98,9 +89,6 @@ theorem round_add_ofNat (x : α) (n : ℕ) [n.AtLeastTwo] :
theorem round_sub_natCast (x : α) (y : ℕ) : round (x - y) = round x - y :=
mod_cast round_sub_intCast x y

@[deprecated (since := "2025-03-23")]
alias round_sub_nat := round_sub_natCast

@[simp]
theorem round_sub_ofNat (x : α) (n : ℕ) [n.AtLeastTwo] :
round (x - ofNat(n)) = round x - ofNat(n) :=
Expand All @@ -110,16 +98,10 @@ theorem round_sub_ofNat (x : α) (n : ℕ) [n.AtLeastTwo] :
theorem round_intCast_add (x : α) (y : ℤ) : round ((y : α) + x) = y + round x := by
rw [add_comm, round_add_intCast, add_comm]

@[deprecated (since := "2025-03-23")]
alias round_int_add := round_intCast_add

@[simp]
theorem round_natCast_add (x : α) (y : ℕ) : round ((y : α) + x) = y + round x := by
rw [add_comm, round_add_natCast, add_comm]

@[deprecated (since := "2025-03-23")]
alias round_nat_add := round_natCast_add

@[simp]
theorem round_ofNat_add (n : ℕ) [n.AtLeastTwo] (x : α) :
round (ofNat(n) + x) = ofNat(n) + round x :=
Expand Down
6 changes: 0 additions & 6 deletions Mathlib/AlgebraicGeometry/EllipticCurve/Affine/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -246,12 +246,6 @@ lemma equation_iff_nonsingular [Nontrivial R] [W.IsElliptic] {x y : R} :
W.toAffine.Equation x y ↔ W.toAffine.Nonsingular x y :=
W.toAffine.equation_iff_nonsingular_of_Δ_ne_zero <| W.coe_Δ' ▸ W.Δ'.ne_zero

@[deprecated (since := "2025-03-01")] alias nonsingular_zero_of_Δ_ne_zero :=
equation_iff_nonsingular_of_Δ_ne_zero
@[deprecated (since := "2025-03-01")] alias nonsingular_of_Δ_ne_zero :=
equation_iff_nonsingular_of_Δ_ne_zero
@[deprecated (since := "2025-03-01")] alias nonsingular := equation_iff_nonsingular

/-! ## Maps and base changes -/

variable (f : R →+* S) (x y : R)
Expand Down
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