Skip to content

Commit

Permalink
bump to nightly-2023-03-14-02
Browse files Browse the repository at this point in the history
  • Loading branch information
leanprover-community-bot committed Mar 14, 2023
1 parent e3b6a9d commit d4b38a4
Show file tree
Hide file tree
Showing 144 changed files with 726 additions and 318 deletions.
5 changes: 4 additions & 1 deletion Mathbin/Algebra/Algebra/Subalgebra/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov

! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
! leanprover-community/mathlib commit c4658a649d216f57e99621708b09dcb3dcccbd23
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -16,6 +16,9 @@ import Mathbin.RingTheory.Ideal.Operations
/-!
# Subalgebras over Commutative Semiring

> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.

In this file we define `subalgebra`s and the usual operations on them (`map`, `comap`).

More lemmas about `adjoin` can be found in `ring_theory.adjoin`.
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/Algebra/Subalgebra/Tower.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
! This file was ported from Lean 3 source module algebra.algebra.subalgebra.tower
! leanprover-community/mathlib commit a35ddf20601f85f78cd57e7f5b09ed528d71b7af
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.Algebra.Algebra.Tower
/-!
# Subalgebras in towers of algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
In this file we prove facts about subalgebras in towers of algebra.
An algebra tower A/S/R is expressed by having instances of `algebra A S`,
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/FreeNonUnitalNonAssocAlgebra.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
! This file was ported from Lean 3 source module algebra.free_non_unital_non_assoc_algebra
! leanprover-community/mathlib commit 2f1a4aff21c9aadf7cfb96911734754d6c228029
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.Algebra.MonoidAlgebra.Basic
/-!
# Free algebras
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Given a semiring `R` and a type `X`, we construct the free non-unital, non-associative algebra on
`X` with coefficients in `R`, together with its universal property. The construction is valuable
because it can be used to build free algebras with more structure, e.g., free Lie algebras.
Expand Down
41 changes: 6 additions & 35 deletions Mathbin/Algebra/Group/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Simon Hudon, Mario Carneiro
! This file was ported from Lean 3 source module algebra.group.basic
! leanprover-community/mathlib commit 4060545f1f2b865a399c46f14391e2dba0fe3667
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -424,40 +424,11 @@ theorem inv_inj {a b : G} : a⁻¹ = b⁻¹ ↔ a = b :=
#align inv_inj inv_inj
#align neg_inj neg_inj

/- warning: eq_inv_of_eq_inv -> eq_inv_of_eq_inv is a dubious translation:
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, (Eq.{succ u1} G a (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) b)) -> (Eq.{succ u1} G b (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) a))
but is expected to have type
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, (Eq.{succ u1} G a (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) b)) -> (Eq.{succ u1} G b (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) a))
Case conversion may be inaccurate. Consider using '#align eq_inv_of_eq_inv eq_inv_of_eq_invₓ'. -/
@[to_additive]
theorem eq_inv_of_eq_inv (h : a = b⁻¹) : b = a⁻¹ := by simp [h]
#align eq_inv_of_eq_inv eq_inv_of_eq_inv
#align eq_neg_of_eq_neg eq_neg_of_eq_neg

/- warning: eq_inv_iff_eq_inv -> eq_inv_iff_eq_inv is a dubious translation:
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, Iff (Eq.{succ u1} G a (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) b)) (Eq.{succ u1} G b (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) a))
but is expected to have type
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, Iff (Eq.{succ u1} G a (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) b)) (Eq.{succ u1} G b (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) a))
Case conversion may be inaccurate. Consider using '#align eq_inv_iff_eq_inv eq_inv_iff_eq_invₓ'. -/
@[to_additive]
theorem eq_inv_iff_eq_inv : a = b⁻¹ ↔ b = a⁻¹ :=
⟨eq_inv_of_eq_inv, eq_inv_of_eq_inv⟩
#align eq_inv_iff_eq_inv eq_inv_iff_eq_inv
#align eq_neg_iff_eq_neg eq_neg_iff_eq_neg

/- warning: inv_eq_iff_inv_eq -> inv_eq_iff_inv_eq is a dubious translation:
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, Iff (Eq.{succ u1} G (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) a) b) (Eq.{succ u1} G (Inv.inv.{u1} G (InvolutiveInv.toHasInv.{u1} G _inst_1) b) a)
but is expected to have type
forall {G : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} G] {a : G} {b : G}, Iff (Eq.{succ u1} G (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) a) b) (Eq.{succ u1} G (Inv.inv.{u1} G (InvolutiveInv.toInv.{u1} G _inst_1) b) a)
Case conversion may be inaccurate. Consider using '#align inv_eq_iff_inv_eq inv_eq_iff_inv_eqₓ'. -/
@[to_additive]
theorem inv_eq_iff_inv_eq : a⁻¹ = b ↔ b⁻¹ = a :=
eq_comm.trans <| eq_inv_iff_eq_inv.trans eq_comm
#align inv_eq_iff_inv_eq inv_eq_iff_inv_eq
#align neg_eq_iff_neg_eq neg_eq_iff_neg_eq
theorem inv_eq_iff_eq_inv : a⁻¹ = b ↔ a = b⁻¹ :=
fun h => h ▸ (inv_inv a).symm, fun h => h.symm ▸ inv_inv b⟩
#align inv_eq_iff_eq_inv inv_eq_iff_eq_inv
#align neg_eq_iff_eq_neg neg_eq_iff_eq_neg

variable (G)

Expand Down Expand Up @@ -1269,7 +1240,7 @@ but is expected to have type
Case conversion may be inaccurate. Consider using '#align mul_eq_one_iff_inv_eq mul_eq_one_iff_inv_eqₓ'. -/
@[to_additive]
theorem mul_eq_one_iff_inv_eq : a * b = 1 ↔ a⁻¹ = b := by
rw [mul_eq_one_iff_eq_inv, eq_inv_iff_eq_inv, eq_comm]
rw [mul_eq_one_iff_eq_inv, inv_eq_iff_eq_inv]
#align mul_eq_one_iff_inv_eq mul_eq_one_iff_inv_eq
#align add_eq_zero_iff_neg_eq add_eq_zero_iff_neg_eq

Expand Down
4 changes: 2 additions & 2 deletions Mathbin/Algebra/GroupWithZero/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
! This file was ported from Lean 3 source module algebra.group_with_zero.basic
! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -625,7 +625,7 @@ but is expected to have type
forall {G₀ : Type.{u1}} [_inst_1 : GroupWithZero.{u1} G₀] {a : G₀}, Iff (Eq.{succ u1} G₀ (Inv.inv.{u1} G₀ (GroupWithZero.toInv.{u1} G₀ _inst_1) a) (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (MonoidWithZero.toZero.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ _inst_1))))) (Eq.{succ u1} G₀ a (OfNat.ofNat.{u1} G₀ 0 (Zero.toOfNat0.{u1} G₀ (MonoidWithZero.toZero.{u1} G₀ (GroupWithZero.toMonoidWithZero.{u1} G₀ _inst_1)))))
Case conversion may be inaccurate. Consider using '#align inv_eq_zero inv_eq_zeroₓ'. -/
@[simp]
theorem inv_eq_zero {a : G₀} : a⁻¹ = 0 ↔ a = 0 := by rw [inv_eq_iff_inv_eq, inv_zero, eq_comm]
theorem inv_eq_zero {a : G₀} : a⁻¹ = 0 ↔ a = 0 := by rw [inv_eq_iff_eq_inv, inv_zero]
#align inv_eq_zero inv_eq_zero

/- warning: zero_eq_inv -> zero_eq_inv is a dubious translation:
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/MonoidAlgebra/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury G. Kudryashov, Scott Morrison

! This file was ported from Lean 3 source module algebra.monoid_algebra.basic
! leanprover-community/mathlib commit 6623e6af705e97002a9054c1c05a980180276fc1
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -17,6 +17,9 @@ import Mathbin.LinearAlgebra.Finsupp
/-!
# Monoid algebras

> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.

When the domain of a `finsupp` has a multiplicative or additive structure, we can define
a convolution product. To mathematicians this structure is known as the "monoid algebra",
i.e. the finite formal linear combinations over a given semiring of elements of the monoid.
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/MonoidAlgebra/Support.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,14 +4,17 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
! This file was ported from Lean 3 source module algebra.monoid_algebra.support
! leanprover-community/mathlib commit 16749fc4661828cba18cd0f4e3c5eb66a8e80598
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Algebra.MonoidAlgebra.Basic

/-!
# Lemmas about the support of a finitely supported function
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
-/


Expand Down
6 changes: 3 additions & 3 deletions Mathbin/Algebra/Order/Group/Abs.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
! This file was ported from Lean 3 source module algebra.order.group.abs
! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -161,7 +161,7 @@ but is expected to have type
forall {α : Type.{u1}} [_inst_1 : AddGroup.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α}, (Eq.{succ u1} α (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) b) -> (Or (Eq.{succ u1} α a b) (Eq.{succ u1} α a (Neg.neg.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (AddGroup.toSubtractionMonoid.{u1} α _inst_1)))) b)))
Case conversion may be inaccurate. Consider using '#align eq_or_eq_neg_of_abs_eq eq_or_eq_neg_of_abs_eqₓ'. -/
theorem eq_or_eq_neg_of_abs_eq {a b : α} (h : |a| = b) : a = b ∨ a = -b := by
simpa only [← h, eq_comm, eq_neg_iff_eq_neg] using abs_choice a
simpa only [← h, eq_comm, neg_eq_iff_eq_neg] using abs_choice a
#align eq_or_eq_neg_of_abs_eq eq_or_eq_neg_of_abs_eq

/- warning: abs_eq_abs -> abs_eq_abs is a dubious translation:
Expand All @@ -175,7 +175,7 @@ theorem abs_eq_abs {a b : α} : |a| = |b| ↔ a = b ∨ a = -b :=
refine' ⟨fun h => _, fun h => _⟩
·
obtain rfl | rfl := eq_or_eq_neg_of_abs_eq h <;>
simpa only [neg_eq_iff_neg_eq, neg_inj, or_comm, @eq_comm _ (-b)] using abs_choice b
simpa only [neg_eq_iff_eq_neg, neg_inj, or_comm] using abs_choice b
· cases h <;> simp only [h, abs_neg]
#align abs_eq_abs abs_eq_abs

Expand Down
4 changes: 2 additions & 2 deletions Mathbin/Algebra/Order/ToIntervalMod.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
! This file was ported from Lean 3 source module algebra.order.to_interval_mod
! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -378,7 +378,7 @@ theorem toIcoDiv_neg (a : α) {b : α} (hb : 0 < b) (x : α) :
by
suffices toIcoDiv a hb (-x) = -toIocDiv (-(a + b)) hb x by
rwa [neg_add, ← sub_eq_add_neg, ← toIocDiv_add_right', toIocDiv_add_right] at this
rw [eq_neg_iff_eq_neg, eq_comm]
rw [← neg_eq_iff_eq_neg]
apply eq_toIocDiv_of_sub_zsmul_mem_Ioc
obtain ⟨hc, ho⟩ := sub_toIcoDiv_zsmul_mem_Ico a hb (-x)
rw [← neg_lt_neg_iff, neg_sub' (-x), neg_neg, ← neg_smul] at ho
Expand Down
6 changes: 3 additions & 3 deletions Mathbin/Algebra/Periodic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
! This file was ported from Lean 3 source module algebra.periodic
! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -723,7 +723,7 @@ but is expected to have type
Case conversion may be inaccurate. Consider using '#align function.antiperiodic.funext' Function.Antiperiodic.funext'ₓ'. -/
protected theorem Antiperiodic.funext' [Add α] [InvolutiveNeg β] (h : Antiperiodic f c) :
(fun x => -f (x + c)) = f :=
(eq_neg_iff_eq_neg.mp h.funext).symm
neg_eq_iff_eq_neg.mpr h.funext
#align function.antiperiodic.funext' Function.Antiperiodic.funext'

/- warning: function.antiperiodic.periodic -> Function.Antiperiodic.periodic is a dubious translation:
Expand Down Expand Up @@ -799,7 +799,7 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {f : α -> β} {c : α} [_inst_1 : AddGroup.{u2} α] [_inst_2 : InvolutiveNeg.{u1} β], (Function.Antiperiodic.{u2, u1} α β (AddZeroClass.toAdd.{u2} α (AddMonoid.toAddZeroClass.{u2} α (SubNegMonoid.toAddMonoid.{u2} α (AddGroup.toSubNegMonoid.{u2} α _inst_1)))) (InvolutiveNeg.toNeg.{u1} β _inst_2) f c) -> (forall (x : α), Eq.{succ u1} β (f (HSub.hSub.{u2, u2, u2} α α α (instHSub.{u2} α (SubNegMonoid.toSub.{u2} α (AddGroup.toSubNegMonoid.{u2} α _inst_1))) x c)) (Neg.neg.{u1} β (InvolutiveNeg.toNeg.{u1} β _inst_2) (f x)))
Case conversion may be inaccurate. Consider using '#align function.antiperiodic.sub_eq Function.Antiperiodic.sub_eqₓ'. -/
theorem Antiperiodic.sub_eq [AddGroup α] [InvolutiveNeg β] (h : Antiperiodic f c) (x : α) :
f (x - c) = -f x := by simp only [eq_neg_iff_eq_neg.mp (h (x - c)), sub_add_cancel]
f (x - c) = -f x := by rw [← neg_eq_iff_eq_neg, ← h (x - c), sub_add_cancel]
#align function.antiperiodic.sub_eq Function.Antiperiodic.sub_eq

/- warning: function.antiperiodic.sub_eq' -> Function.Antiperiodic.sub_eq' is a dubious translation:
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/Polynomial/BigOperators.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark
! This file was ported from Lean 3 source module algebra.polynomial.big_operators
! leanprover-community/mathlib commit 47adfab39a11a072db552f47594bf8ed2cf8a722
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -14,6 +14,9 @@ import Mathbin.Data.Polynomial.Monic
/-!
# Lemmas for the interaction between polynomials and `∑` and `∏`.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
Recall that `∑` and `∏` are notation for `finset.sum` and `finset.prod` respectively.
## Main results
Expand Down
19 changes: 18 additions & 1 deletion Mathbin/Algebra/Star/SelfAdjoint.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
! This file was ported from Lean 3 source module algebra.star.self_adjoint
! leanprover-community/mathlib commit 671d5d9a0cca76de2933cff8ee3c29b7533f9caf
! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -38,6 +38,7 @@ We also define `is_star_normal R`, a `Prop` that states that an element `x` sati
## TODO
* Define `is_skew_adjoint` to match `is_self_adjoint`.
* Define `λ z x, z * x * star z` (i.e. conjugation by `z`) as a monoid action of `R` on `R`
(similar to the existing `conj_act` for groups), and then state the fact that `self_adjoint R` is
invariant under it.
Expand Down Expand Up @@ -759,6 +760,22 @@ end SMul

end skewAdjoint

/-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
skew-adjoint element. -/
theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
[StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
(ha : IsSelfAdjoint a) : r • a ∈ skewAdjoint A :=
(star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
#align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint

/-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
self-adjoint element. -/
theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]
[StarAddMonoid R] [StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
(ha : a ∈ skewAdjoint A) : IsSelfAdjoint (r • a) :=
(star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul_neg _ _
#align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjoint

/- warning: is_star_normal_zero -> isStarNormal_zero is a dubious translation:
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)], IsStarNormal.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
Expand Down
5 changes: 4 additions & 1 deletion Mathbin/Algebra/Star/Subalgebra.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Jireh Loreaux

! This file was ported from Lean 3 source module algebra.star.subalgebra
! leanprover-community/mathlib commit 160ef3e338a2a4f21a280e4c152d4016156e516d
! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand All @@ -17,6 +17,9 @@ import Mathbin.RingTheory.Adjoin.Basic
/-!
# Star subalgebras

> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.

A *-subalgebra is a subalgebra of a *-algebra which is closed under *.

The centralizer of a *-closed set is a *-subalgebra.
Expand Down
4 changes: 2 additions & 2 deletions Mathbin/AlgebraicGeometry/EllipticCurve/Point.lean
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
! This file was ported from Lean 3 source module algebraic_geometry.elliptic_curve.point
! leanprover-community/mathlib commit 03994e05d8bfc59a41d2ec99523d6553d21848ac
! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
Expand Down Expand Up @@ -693,7 +693,7 @@ theorem add_eq_zero (P Q : W.Point) : P + Q = 0 ↔ P = -Q :=
by
rcases P, Q with ⟨_ | @⟨x₁, y₁, _⟩, _ | @⟨x₂, y₂, _⟩⟩
any_goals rfl
· rw [zero_def, zero_add, eq_neg_iff_eq_neg, neg_zero]
· rw [zero_def, zero_add, ← neg_eq_iff_eq_neg, neg_zero, eq_comm]
· simp only [neg_some]
constructor
· intro h
Expand Down
Loading

0 comments on commit d4b38a4

Please sign in to comment.