algebra.ring.add_aut
⟷
Mathlib.Algebra.Ring.AddAut
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.GroupTheory.GroupAction.Group
-import Mathbin.Algebra.Module.Basic
+import GroupTheory.GroupAction.Group
+import Algebra.Module.Basic
#align_import algebra.ring.add_aut from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.ring.add_aut
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.GroupTheory.GroupAction.Group
import Mathbin.Algebra.Module.Basic
+#align_import algebra.ring.add_aut from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Multiplication on the left/right as additive automorphisms
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -29,26 +29,34 @@ namespace AddAut
variable {R : Type _} [Semiring R]
+#print AddAut.mulLeft /-
/-- Left multiplication by a unit of a semiring as an additive automorphism. -/
@[simps (config := { simpRhs := true })]
def mulLeft : Rˣ →* AddAut R :=
DistribMulAction.toAddAut _ _
#align add_aut.mul_left AddAut.mulLeft
+-/
+#print AddAut.mulRight /-
/-- Right multiplication by a unit of a semiring as an additive automorphism. -/
def mulRight (u : Rˣ) : AddAut R :=
DistribMulAction.toAddAut Rᵐᵒᵖˣ R (Units.opEquiv.symm <| MulOpposite.op u)
#align add_aut.mul_right AddAut.mulRight
+-/
+#print AddAut.mulRight_apply /-
@[simp]
theorem mulRight_apply (u : Rˣ) (x : R) : mulRight u x = x * u :=
rfl
#align add_aut.mul_right_apply AddAut.mulRight_apply
+-/
+#print AddAut.mulRight_symm_apply /-
@[simp]
theorem mulRight_symm_apply (u : Rˣ) (x : R) : (mulRight u).symm x = x * ↑u⁻¹ :=
rfl
#align add_aut.mul_right_symm_apply AddAut.mulRight_symm_apply
+-/
end AddAut
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -29,46 +29,22 @@ namespace AddAut
variable {R : Type _} [Semiring R]
-/- warning: add_aut.mul_left -> AddAut.mulLeft is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], MonoidHom.{u1, u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Units.mulOneClass.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DivInvMonoid.toMonoid.{u1} (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Group.toDivInvMonoid.{u1} (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddAut.group.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
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- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], MonoidHom.{u1, u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Units.instMulOneClassUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Monoid.toMulOneClass.{u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (DivInvMonoid.toMonoid.{u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Group.toDivInvMonoid.{u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddAut.group.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align add_aut.mul_left AddAut.mulLeftₓ'. -/
/-- Left multiplication by a unit of a semiring as an additive automorphism. -/
@[simps (config := { simpRhs := true })]
def mulLeft : Rˣ →* AddAut R :=
DistribMulAction.toAddAut _ _
#align add_aut.mul_left AddAut.mulLeft
-/- warning: add_aut.mul_right -> AddAut.mulRight is a dubious translation:
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- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) -> (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
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- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) -> (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align add_aut.mul_right AddAut.mulRightₓ'. -/
/-- Right multiplication by a unit of a semiring as an additive automorphism. -/
def mulRight (u : Rˣ) : AddAut R :=
DistribMulAction.toAddAut Rᵐᵒᵖˣ R (Units.opEquiv.symm <| MulOpposite.op u)
#align add_aut.mul_right AddAut.mulRight
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-Case conversion may be inaccurate. Consider using '#align add_aut.mul_right_apply AddAut.mulRight_applyₓ'. -/
@[simp]
theorem mulRight_apply (u : Rˣ) (x : R) : mulRight u x = x * u :=
rfl
#align add_aut.mul_right_apply AddAut.mulRight_apply
-/- warning: add_aut.mul_right_symm_apply -> AddAut.mulRight_symm_apply is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align add_aut.mul_right_symm_apply AddAut.mulRight_symm_applyₓ'. -/
@[simp]
theorem mulRight_symm_apply (u : Rˣ) (x : R) : (mulRight u).symm x = x * ↑u⁻¹ :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -56,7 +56,7 @@ def mulRight (u : Rˣ) : AddAut R :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (AddAut.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : AddEquiv.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => R -> R) (AddEquiv.hasCoeToFun.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddAut.mulRight.{u1} R _inst_1 u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (Units.hasCoe.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) u))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (AddEquivClass.toEquivLike.{u1, u1, u1} (AddAut.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (AddAut.mulRight.{u1} R _inst_1 u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) u))
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (AddAut.mulRight.{u1} R _inst_1 u) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) u))
Case conversion may be inaccurate. Consider using '#align add_aut.mul_right_apply AddAut.mulRight_applyₓ'. -/
@[simp]
theorem mulRight_apply (u : Rˣ) (x : R) : mulRight u x = x * u :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -67,7 +67,7 @@ theorem mulRight_apply (u : Rˣ) (x : R) : mulRight u x = x * u :=
lean 3 declaration is
forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} R (coeFn.{succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : AddEquiv.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => R -> R) (AddEquiv.hasCoeToFun.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (AddEquiv.symm.{u1, u1} R R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddAut.mulRight.{u1} R _inst_1 u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) x ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (HasLiftT.mk.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (CoeTCₓ.coe.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (coeBase.{succ u1, succ u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) R (Units.hasCoe.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Units.hasInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) u)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (AddEquiv.symm.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddAut.mulRight.{u1} R _inst_1 u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Units.instInvUnits.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) u)))
+ forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (u : Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (x : R), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) x) (FunLike.coe.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : R) => R) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (AddEquivClass.toEquivLike.{u1, u1, u1} (AddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddEquiv.instAddEquivClassAddEquiv.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (AddEquiv.symm.{u1, u1} R R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddAut.mulRight.{u1} R _inst_1 u)) x) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x (Units.val.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (Inv.inv.{u1} (Units.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) (Units.instInv.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) u)))
Case conversion may be inaccurate. Consider using '#align add_aut.mul_right_symm_apply AddAut.mulRight_symm_applyₓ'. -/
@[simp]
theorem mulRight_symm_apply (u : Rˣ) (x : R) : (mulRight u).symm x = x * ↑u⁻¹ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Similar to #12486, which did this for Algebra.Algebra.Basic
.
Splits Algebra.Module.Defs
off Algebra.Module.Basic
. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Module.Basic
is now a grab-bag of unrelated results, and should probably be split further or rehomed.
This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Module.Basic.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.GroupTheory.GroupAction.Group
-import Mathlib.Algebra.Module.Basic
+import Mathlib.Algebra.Module.Defs
#align_import algebra.ring.add_aut from "leanprover-community/mathlib"@"a437a2499163d85d670479f69f625f461cc5fef9"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -21,7 +21,7 @@ See also `AddMonoidHom.mulLeft`, `AddMonoidHom.mulRight`, `AddMonoid.End.mulLeft
namespace AddAut
-variable {R : Type _} [Semiring R]
+variable {R : Type*} [Semiring R]
/-- Left multiplication by a unit of a semiring as an additive automorphism. -/
@[simps! (config := { simpRhs := true })]
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.ring.add_aut
-! leanprover-community/mathlib commit a437a2499163d85d670479f69f625f461cc5fef9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.GroupTheory.GroupAction.Group
import Mathlib.Algebra.Module.Basic
+#align_import algebra.ring.add_aut from "leanprover-community/mathlib"@"a437a2499163d85d670479f69f625f461cc5fef9"
+
/-!
# Multiplication on the left/right as additive automorphisms
@@ -32,7 +32,7 @@ def mulLeft : Rˣ →* AddAut R :=
DistribMulAction.toAddAut _ _
#align add_aut.mul_left AddAut.mulLeft
#align add_aut.mul_left_apply_apply AddAut.mulLeft_apply_apply
-#align add_aut.mul_left_apply_symm_apply AddAut.mulLeft_apply_symmApply
+#align add_aut.mul_left_apply_symm_apply AddAut.mulLeft_apply_symm_apply
/-- Right multiplication by a unit of a semiring as an additive automorphism. -/
def mulRight (u : Rˣ) : AddAut R :=
simps
, just raises a linter error if you run simps
in a more expensive mode without writing !
.to_additive, simps
. Will do that systematically in future PR.OmegaCompletePartialOrder.ContinuousHom.ofMono
a bitCo-authored-by: Yury G. Kudryashov <urkud@urkud.name>
@@ -27,7 +27,7 @@ namespace AddAut
variable {R : Type _} [Semiring R]
/-- Left multiplication by a unit of a semiring as an additive automorphism. -/
-@[simps (config := { simpRhs := true })]
+@[simps! (config := { simpRhs := true })]
def mulLeft : Rˣ →* AddAut R :=
DistribMulAction.toAddAut _ _
#align add_aut.mul_left AddAut.mulLeft
This PR is the result of a slight variant on the following "algorithm"
_
and make all uppercase letters into lowercase_
and make all uppercase letters into lowercase(original_lean3_name, OriginalLean4Name)
#align
statement just before the next empty line#align
statement to have been inserted too early)@@ -31,6 +31,8 @@ variable {R : Type _} [Semiring R]
def mulLeft : Rˣ →* AddAut R :=
DistribMulAction.toAddAut _ _
#align add_aut.mul_left AddAut.mulLeft
+#align add_aut.mul_left_apply_apply AddAut.mulLeft_apply_apply
+#align add_aut.mul_left_apply_symm_apply AddAut.mulLeft_apply_symmApply
/-- Right multiplication by a unit of a semiring as an additive automorphism. -/
def mulRight (u : Rˣ) : AddAut R :=
The unported dependencies are