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[Merged by Bors] - chore(*): Fix syntactic tautologies #8811

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[Merged by Bors] - chore(*): Fix syntactic tautologies #8811

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3906aa7
Fix syntactic tautologies
alexjbest Aug 22, 2021
6f2cd50
Update src/analysis/normed_space/linear_isometry.lean
alexjbest Aug 22, 2021
0bbcc78
swap direction and remove notation
alexjbest Aug 22, 2021
253812e
try again to reverse
alexjbest Aug 24, 2021
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2 changes: 1 addition & 1 deletion src/analysis/normed_space/affine_isometry.lean
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Expand Up @@ -157,7 +157,7 @@ include V
/-- The identity affine isometry. -/
def id : P →ᵃⁱ[𝕜] P := ⟨affine_map.id 𝕜 P, λ x, rfl⟩

@[simp] lemma coe_id : ⇑(id : P →ᵃⁱ[𝕜] P) = id := rfl
@[simp] lemma coe_id : ⇑(id : P →ᵃⁱ[𝕜] P) = _root_.id := rfl

@[simp] lemma id_apply (x : P) : (affine_isometry.id : P →ᵃⁱ[𝕜] P) x = x := rfl

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2 changes: 1 addition & 1 deletion src/analysis/normed_space/linear_isometry.lean
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Expand Up @@ -104,7 +104,7 @@ f.isometry.comp_continuous_iff
/-- The identity linear isometry. -/
def id : E →ₗᵢ[R] E := ⟨linear_map.id, λ x, rfl⟩

@[simp] lemma coe_id : ⇑(id : E →ₗᵢ[R] E) = id := rfl
@[simp] lemma coe_id : ⇑(id : E →ₗᵢ[R] E) = _root_.id := rfl

@[simp] lemma id_apply (x : E) : (id : E →ₗᵢ[R] E) x = x := rfl

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12 changes: 8 additions & 4 deletions src/category_theory/sums/basic.lean
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Expand Up @@ -50,10 +50,14 @@ instance sum : category.{v₁} (C ⊕ D) :=
| inr X, inr Y, inr Z, f, g := f ≫ g
end }

@[simp] lemma sum_comp_inl {P Q R : C} (f : (inl P : C ⊕ D) ⟶ inl Q) (g : inl Q ⟶ inl R) :
f ≫ g = (f : P ⟶ Q) ≫ (g : Q ⟶ R) := rfl
@[simp] lemma sum_comp_inr {P Q R : D} (f : (inr P : C ⊕ D) ⟶ inr Q) (g : inr Q ⟶ inr R) :
f ≫ g = (f : P ⟶ Q) ≫ (g : Q ⟶ R) := rfl
@[simp] lemma sum_comp_inl {P Q R : C} (f : (inl P : C ⊕ D) ⟶ inl Q)
(g : (inl Q : C ⊕ D) ⟶ inl R) :
@category_struct.comp _ _ P Q R (f : P ⟶ Q) (g : Q ⟶ R) =
@category_struct.comp _ _ (inl P) (inl Q) (inl R) (f : P ⟶ Q) (g : Q ⟶ R) := rfl
@[simp] lemma sum_comp_inr {P Q R : D} (f : (inr P : C ⊕ D) ⟶ inr Q)
(g : (inr Q : C ⊕ D) ⟶ inr R) :
@category_struct.comp _ _ P Q R (f : P ⟶ Q) (g : Q ⟶ R) =
@category_struct.comp _ _ (inr P) (inr Q) (inr R) (f : P ⟶ Q) (g : Q ⟶ R) := rfl
end

namespace sum
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3 changes: 2 additions & 1 deletion src/linear_algebra/basic.lean
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Expand Up @@ -1330,7 +1330,8 @@ namespace quotient
when `p` is a submodule of `M`. -/
def mk {p : submodule R M} : M → quotient p := quotient.mk'

@[simp] theorem mk_eq_mk {p : submodule R M} (x : M) : (quotient.mk x : quotient p) = mk x := rfl
@[simp] theorem mk_eq_mk {p : submodule R M} (x : M) :
(@_root_.quotient.mk _ (quotient_rel p) x) = mk x := rfl
@[simp] theorem mk'_eq_mk {p : submodule R M} (x : M) : (quotient.mk' x : quotient p) = mk x := rfl
@[simp] theorem quot_mk_eq_mk {p : submodule R M} (x : M) : (quot.mk _ x : quotient p) = mk x := rfl

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