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leanprover-community-bot committed Mar 21, 2023
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16 changes: 8 additions & 8 deletions Mathbin/Algebra/Algebra/Subalgebra/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -2300,27 +2300,27 @@ theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (
rfl
#align subalgebra.smul_def Subalgebra.smul_def

/- warning: subalgebra.smul_comm_class_left -> Subalgebra.sMulCommClass_left is a dubious translation:
/- warning: subalgebra.smul_comm_class_left -> Subalgebra.smulCommClass_left is a dubious translation:
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u2, u4} A β] [_inst_7 : SMul.{u3, u4} α β] [_inst_8 : SMulCommClass.{u2, u3, u4} A α β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u2, u3, u4} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) α β (Subalgebra.hasSmul.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_6 S) _inst_7
but is expected to have type
forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u2, u4} A β] [_inst_7 : SMul.{u3, u4} α β] [_inst_8 : SMulCommClass.{u2, u3, u4} A α β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u2, u3, u4} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) α β (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_6 S) _inst_7
Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_leftₓ'. -/
instance sMulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_leftₓ'. -/
instance smulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
SMulCommClass S α β :=
S.toSubsemiring.smulCommClass_left
#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_left
#align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_left

/- warning: subalgebra.smul_comm_class_right -> Subalgebra.sMulCommClass_right is a dubious translation:
/- warning: subalgebra.smul_comm_class_right -> Subalgebra.smulCommClass_right is a dubious translation:
lean 3 declaration is
forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u3, u4} α β] [_inst_7 : SMul.{u2, u4} A β] [_inst_8 : SMulCommClass.{u3, u2, u4} α A β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u3, u2, u4} α (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) β _inst_6 (Subalgebra.hasSmul.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_7 S)
but is expected to have type
forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u3, u4} α β] [_inst_7 : SMul.{u2, u4} A β] [_inst_8 : SMulCommClass.{u3, u2, u4} α A β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u3, u2, u4} α (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) β _inst_6 (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_7 S)
Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_rightₓ'. -/
instance sMulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_rightₓ'. -/
instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
SMulCommClass α S β :=
S.toSubsemiring.smulCommClass_right
#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_right
#align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right

/- warning: subalgebra.is_scalar_tower_left -> Subalgebra.isScalarTower_left is a dubious translation:
lean 3 declaration is
Expand Down
3 changes: 1 addition & 2 deletions Mathbin/Analysis/Complex/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -468,8 +468,7 @@ section ComplexOrder
open ComplexOrder

theorem eq_coe_norm_of_nonneg {z : ℂ} (hz : 0 ≤ z) : z = ↑‖z‖ := by
rw [eq_re_of_real_le hz, IsROrC.norm_of_real,
Real.norm_of_nonneg (Complex.ComplexOrder.le_def.2 hz).1]
rw [eq_re_of_real_le hz, IsROrC.norm_of_real, Real.norm_of_nonneg (Complex.le_def.2 hz).1]
#align complex.eq_coe_norm_of_nonneg Complex.eq_coe_norm_of_nonneg

end ComplexOrder
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Original file line number Diff line number Diff line change
Expand Up @@ -107,8 +107,8 @@ theorem spectrum_star_mul_self_of_isStarNormal :
rw [gelfand_transform_apply_apply ℂ _ (star a' * a') φ, map_mul φ, map_star φ]
rw [Complex.eq_coe_norm_of_nonneg star_mul_self_nonneg, ← map_star, ← map_mul]
exact
⟨Complex.ComplexOrder.zero_le_real.2 (norm_nonneg _),
Complex.ComplexOrder.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
⟨Complex.zero_le_real.2 (norm_nonneg _),
Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
#align spectrum_star_mul_self_of_is_star_normal spectrum_star_mul_self_of_isStarNormal

variable {a}
Expand Down Expand Up @@ -165,9 +165,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
by
replace hz := Set.image_subset _ (spectrum_star_mul_self_of_isStarNormal a) hz
rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz
refine'
lt_of_le_of_ne
(Complex.ComplexOrder.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
refine' lt_of_le_of_ne (Complex.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
· intro hz'
replace hz' := congr_arg (fun x : ℝ≥0 => ((x : ℝ) : ℂ)) hz'
simp only [coe_nnnorm] at hz'
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6 changes: 3 additions & 3 deletions Mathbin/CategoryTheory/Limits/Constructions/ZeroObjects.lean
Original file line number Diff line number Diff line change
Expand Up @@ -191,13 +191,13 @@ def coprodZeroIso (X : C) : X ⨿ (0 : C) ≅ X :=
#align category_theory.limits.coprod_zero_iso CategoryTheory.Limits.coprodZeroIso
-/

#print CategoryTheory.Limits.inr_coprod_zeroiso_hom /-
#print CategoryTheory.Limits.inr_coprodZeroIso_hom /-
@[simp]
theorem inr_coprod_zeroiso_hom (X : C) : coprod.inl ≫ (coprodZeroIso X).Hom = 𝟙 X :=
theorem inr_coprodZeroIso_hom (X : C) : coprod.inl ≫ (coprodZeroIso X).Hom = 𝟙 X :=
by
dsimp [coprod_zero_iso, binary_cofan_zero_right]
simp
#align category_theory.limits.inr_coprod_zeroiso_hom CategoryTheory.Limits.inr_coprod_zeroiso_hom
#align category_theory.limits.inr_coprod_zeroiso_hom CategoryTheory.Limits.inr_coprodZeroIso_hom
-/

#print CategoryTheory.Limits.coprodZeroIso_inv /-
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