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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.Algebraic.Pi | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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{
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Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.Artinian.Algebra | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.AdicCompletion.Completeness | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Coalgebra.GroupLike | {
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Mathlib.RingTheory.Flat.Domain | {
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{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R N\nP : Type u_4\nQ : Type u_5\ninst✝⁴ : AddCommGroup P\ninst✝³ : Module R P\ninst✝² : AddCommGroup Q\ninst✝¹ : Module R Q\nf : P ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Flat.Domain | {
"line": 63,
"column": 61
} | {
"line": 63,
"column": 63
} | {
"line": 64,
"column": 2
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nι : Type u_6\nκ : Type u_7\nv : ι → M\nw : κ → N\nhv : LinearIndependent R v\nhw : LinearIndependent R w\n⊢ LinearIndependent R ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.GroupLike | {
"line": 150,
"column": 26
} | {
"line": 150,
"column": 28
} | {
"line": 150,
"column": 29
} | [
{
"pp": "R : Type u_2\nA : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : AddCommGroup A\ninst✝² : Module R A\ninst✝¹ : Coalgebra R A\ninst✝ : IsTorsionFree R A\na : A\ns : Finset A\nhas : a ∉ s\nha : IsGroupLikeElem R a\nhs : ∀ a ∈ s, IsGroupLikeElem R a\nd : R\nc : A → R\nih :\n ∀ (f g : A × A ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.GroupLike | {
"line": 140,
"column": 42
} | {
"line": 140,
"column": 44
} | {
"line": 142,
"column": 4
} | [
{
"pp": "R : Type u_2\nA : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : AddCommGroup A\ninst✝² : Module R A\ninst✝¹ : Coalgebra R A\ninst✝ : IsTorsionFree R A\na : A\ns : Finset A\nhas : a ∉ s\nha : IsGroupLikeElem R a\nhs : ∀ a ∈ s, IsGroupLikeElem R a\nd : R\nc : A → R\nhc : ∑ a ∈ s, c a • a =... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Coalgebra.GroupLike | {
"line": 103,
"column": 90
} | {
"line": 103,
"column": 92
} | {
"line": 104,
"column": 2
} | [
{
"pp": "R : Type u_2\nA : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : AddCommGroup A\ninst✝² : Module R A\ninst✝¹ : Coalgebra R A\ninst✝ : IsTorsionFree R A\n⊢ LinearIndepOn R id {a | IsGroupLikeElem R a}",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"TensorProduc... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.GroupLike | {
"line": 157,
"column": 90
} | {
"line": 157,
"column": 92
} | {
"line": 158,
"column": 2
} | [
{
"pp": "R : Type u_2\nA : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : AddCommGroup A\ninst✝² : Module R A\ninst✝¹ : Coalgebra R A\ninst✝ : IsTorsionFree R A\n⊢ LinearIndependent R GroupLike.val",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Equiv.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.Quotient | {
"line": 48,
"column": 89
} | {
"line": 48,
"column": 91
} | {
"line": 49,
"column": 2
} | [
{
"pp": "R : Type u_1\nC : Type u_2\ninst✝³ : CommRing R\ninst✝² : AddCommGroup C\ninst✝¹ : Module R C\ninst✝ : CoalgebraStruct R C\nI : Submodule R C\n⊢ I.IsCoideal ↔ (∀ x ∈ I, counit x = 0) ∧ ∀ x ∈ I, comul x ∈ (lTensor C I.subtype).range ⊔ (rTensor C I.subtype).range",
"ppTerm": "?m.99",
"assigned": ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.Quotient | {
"line": 86,
"column": 34
} | {
"line": 86,
"column": 36
} | {
"line": 87,
"column": 2
} | [
{
"pp": "R : Type u_1\nC : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup C\ninst✝² : Module R C\ninst✝¹ : Coalgebra R C\nI : Submodule R C\ninst✝ : I.IsCoideal\n⊢ Coalgebra R (C ⧸ I)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"Eq.mpr",
"NonAsso... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 471,
"column": 41
} | {
"line": 471,
"column": 43
} | {
"line": 472,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\nA : Rep k G\nS : Subgroup G\ninst✝¹ : S.Normal\ninst✝ : Representation.IsTrivial (MonoidHom.comp A.ρ S.subtype)\n⊢ (H1CoresCoinfOfTrivial A S).Exact",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"add_sub... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 553,
"column": 10
} | {
"line": 553,
"column": 12
} | {
"line": 553,
"column": 13
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k G\nB : Rep k H\nf : G →* H\nφ : A ⟶ res f B\nn : ℕ\nS : Subgroup G\ninst✝ : S.Normal\n⊢ map S.subtype (𝟙 (res S.subtype A)) 1 ≫ map (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S) 1 = 0",
"ppTerm": "?m.84",
"assig... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 562,
"column": 48
} | {
"line": 562,
"column": 50
} | {
"line": 563,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\n⊢ Submodule.comap\n (ModuleCat.Hom.hom\n ((mapShortComplexH1 (MonoidHom.id G) (A.coinvariantsShortComplex S).f).τ₂ ≫ (shortComplexH1 A).pOpcycles))\n (ModuleCat.Hom.hom\n ((mapS... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Bialgebra.Quotient | {
"line": 59,
"column": 34
} | {
"line": 59,
"column": 36
} | {
"line": 60,
"column": 2
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Bialgebra R A\nI : Ideal A\ninst✝¹ : I.IsTwoSided\ninst✝ : (Submodule.restrictScalars R I).IsCoideal\n⊢ Bialgebra R (A ⧸ I)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"AlgHom.toLinearMap",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 597,
"column": 60
} | {
"line": 597,
"column": 62
} | {
"line": 598,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k G\nB : Rep k H\nf : G →* H\nφ : A ⟶ res f B\nn : ℕ\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ (A.quotientToCoinvariants S))\ny : ↑(ModuleCat.of k ↥(cycles₁ (A.toCoinvariants S)))\nhy : (ConcreteCategory.hom (mapCyc... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 605,
"column": 52
} | {
"line": 605,
"column": 54
} | {
"line": 606,
"column": 4
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k G\nB : Rep k H\nf : G →* H\nφ : A ⟶ res f B\nn : ℕ\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ (A.quotientToCoinvariants S))\ny : ↑(ModuleCat.of k ↥(cycles₁ (A.toCoinvariants S)))\nhy : (ConcreteCategory.hom (mapCyc... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 585,
"column": 39
} | {
"line": 585,
"column": 41
} | {
"line": 586,
"column": 2
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k G\nB : Rep k H\nf : G →* H\nφ : A ⟶ res f B\nn : ℕ\nS : Subgroup G\ninst✝ : S.Normal\n⊢ Epi (H1CoresCoinf A S).g",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finsupp.instF... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 639,
"column": 74
} | {
"line": 639,
"column": 76
} | {
"line": 640,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(ModuleCat.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 659,
"column": 45
} | {
"line": 659,
"column": 47
} | {
"line": 660,
"column": 6
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(ModuleCat.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Bialgebra.SymmetricAlgebra | {
"line": 32,
"column": 5
} | {
"line": 32,
"column": 7
} | {
"line": 33,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ (↑(Algebra.TensorProduct.assoc R R R (SymmetricAlgebra R M) (SymmetricAlgebra R M) (SymmetricAlgebra R M))).comp\n ((Algebra.TensorProduct.map\n (lift\n ((TensorProduct.mk R... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Bialgebra.SymmetricAlgebra | {
"line": 36,
"column": 5
} | {
"line": 36,
"column": 7
} | {
"line": 36,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ (Algebra.TensorProduct.map algebraMapInv (AlgHom.id R (SymmetricAlgebra R M))).comp\n (lift\n ((TensorProduct.mk R (SymmetricAlgebra R M) (SymmetricAlgebra R M)).flip 1 ∘ₗ ι R M +\n ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Bialgebra.SymmetricAlgebra | {
"line": 37,
"column": 5
} | {
"line": 37,
"column": 7
} | {
"line": 37,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ (Algebra.TensorProduct.map (AlgHom.id R (SymmetricAlgebra R M)) algebraMapInv).comp\n (lift\n ((TensorProduct.mk R (SymmetricAlgebra R M) (SymmetricAlgebra R M)).flip 1 ∘ₗ ι R M +\n ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Bialgebra.SymmetricAlgebra | {
"line": 53,
"column": 58
} | {
"line": 53,
"column": 60
} | {
"line": 54,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ (↑(Algebra.TensorProduct.comm R (SymmetricAlgebra R M) (SymmetricAlgebra R M))).comp\n (Bialgebra.comulAlgHom R (SymmetricAlgebra R M)) =\n Bialgebra.comulAlgHom R (SymmetricAlgebra R M)",
"... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Bialgebra.SymmetricAlgebra | {
"line": 50,
"column": 21
} | {
"line": 50,
"column": 23
} | {
"line": 51,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ ↑(TensorProduct.comm R (SymmetricAlgebra R M) (SymmetricAlgebra R M)) ∘ₗ CoalgebraStruct.comul = CoalgebraStruct.comul",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Bialge... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.MulOpposite | {
"line": 40,
"column": 26
} | {
"line": 40,
"column": 28
} | {
"line": 41,
"column": 4
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Module R A\ninst✝ : Coalgebra R A\nx✝ : Aᵐᵒᵖ\n⊢ (↑(TensorProduct.assoc R Aᵐᵒᵖ Aᵐᵒᵖ Aᵐᵒᵖ) ∘ₗ rTensor Aᵐᵒᵖ comul ∘ₗ comul) x✝ = (lTensor Aᵐᵒᵖ comul ∘ₗ comul) x✝",
"ppTerm": "?m.62",
"assigned": true,
"used... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.MulOpposite | {
"line": 45,
"column": 44
} | {
"line": 45,
"column": 46
} | {
"line": 46,
"column": 4
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Module R A\ninst✝ : Coalgebra R A\nx✝ : Aᵐᵒᵖ\n⊢ (rTensor Aᵐᵒᵖ counit ∘ₗ comul) x✝ = ((TensorProduct.mk R R Aᵐᵒᵖ) 1) x✝",
"ppTerm": "?m.109",
"assigned": true,
"usedConstants": [
"LinearMap.id",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 680,
"column": 5
} | {
"line": 680,
"column": 7
} | {
"line": 680,
"column": 8
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(ModuleCat.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Coalgebra.MulOpposite | {
"line": 48,
"column": 44
} | {
"line": 48,
"column": 46
} | {
"line": 49,
"column": 4
} | [
{
"pp": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Module R A\ninst✝ : Coalgebra R A\nx✝ : Aᵐᵒᵖ\n⊢ (lTensor Aᵐᵒᵖ counit ∘ₗ comul) x✝ = ((TensorProduct.mk R Aᵐᵒᵖ R).flip 1) x✝",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"Coalgebra.lTe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Congruence.Star | {
"line": 28,
"column": 17
} | {
"line": 28,
"column": 19
} | {
"line": 29,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : StarRing R\nr : R → R → Prop\nhr : ∀ (a b : R), r a b → r (Star.star a) (Star.star b)\na b w✝ x✝ y✝ z✝ : R\nh1 : Rel r w✝ x✝\nh2 : Rel r y✝ z✝\n⊢ Rel r (Star.star (w✝ * y✝)) (Star.star (x✝ * z✝))",
"ppTerm": "?m.110",
"assigned": true,... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Congruence.Star | {
"line": 31,
"column": 17
} | {
"line": 31,
"column": 19
} | {
"line": 32,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : StarRing R\nr : R → R → Prop\nhr : ∀ (a b : R), r a b → r (Star.star a) (Star.star b)\na b w✝ x✝ y✝ z✝ : R\nh1 : Rel r w✝ x✝\nh2 : Rel r y✝ z✝\n⊢ Rel r (Star.star (w✝ + y✝)) (Star.star (x✝ + z✝))",
"ppTerm": "?m.128",
"assigned": true,... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 682,
"column": 2
} | {
"line": 682,
"column": 76
} | {
"line": 684,
"column": 2
} | [
{
"pp": "case h.h\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(... | [
"case h.h\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(ModuleCat.of... | rcases (moduleCat_pOpcycles_eq_iff _ _ _).1 hα with ⟨(δ : G × G →₀ A), hβ⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | {
"line": 684,
"column": 66
} | {
"line": 684,
"column": 68
} | {
"line": 685,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cycles₁ A)\nhx :\n (ConcreteCategory.hom (H1π (A.quotientToCoinvariants S)))\n ((ConcreteCategory.hom (mapCycles₁ (QuotientGroup.mk' S) (A.toCoinvariantsMkQ S))) x) =\n 0\ny : ↑(ModuleCat.... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 54,
"column": 9
} | {
"line": 54,
"column": 11
} | {
"line": 54,
"column": 12
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra A B\ninst✝² : Module.IsTorsionFree A B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\nα : (FractionRing A)ˣ\n⊢ (IsFractionRing.map ⋯) ↑α ≠ 0",
"ppTerm": "?m.91",
"assigned": true,
"usedConstants": [
"Uni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 50,
"column": 5
} | {
"line": 50,
"column": 7
} | {
"line": 51,
"column": 6
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra A B\ninst✝² : Module.IsTorsionFree A B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\n⊢ (toPrincipalIdeal A (FractionRing A)).range ≤\n Subgroup.comap (Units.map ↑(FractionalIdeal.extendedHom (FractionRing B) B))\n ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 61,
"column": 84
} | {
"line": 61,
"column": 86
} | {
"line": 62,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra A B\ninst✝² : Module.IsTorsionFree A B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\nα : (FractionalIdeal A⁰ (FractionRing A))ˣ\n⊢ (extendedHom A B) ↑α = ↑((Units.map ↑(FractionalIdeal.extendedHom (FractionRing B) B)) α)... | [] | by | [anonymous] | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 67,
"column": 86
} | {
"line": 67,
"column": 88
} | {
"line": 68,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra A B\ninst✝² : Module.IsTorsionFree A B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\nI : (FractionalIdeal A⁰ (FractionRing A))ˣ\n⊢ (extendedHom A B) ((mk (FractionRing A)) I) =\n (mk (FractionRing B)) ((Units.map ↑(Fr... | [] | by | [anonymous] | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 81,
"column": 69
} | {
"line": 81,
"column": 71
} | {
"line": 82,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : Algebra A B\ninst✝⁹ : Module.IsTorsionFree A B\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDomain B\nC : Type u_3\ninst✝⁶ : CommRing C\ninst✝⁵ : IsDomain C\ninst✝⁴ : Algebra B C\ninst✝³ : Algebra A C\ninst✝² : IsScalarTower A B C\ni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.ClassGroup.ExtendedHom | {
"line": 95,
"column": 51
} | {
"line": 95,
"column": 53
} | {
"line": 96,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : Algebra A B\ninst✝² : Module.IsTorsionFree A B\ninst✝¹ : IsDedekindDomain A\ninst✝ : IsDomain B\nI : ↥(Ideal A)⁰\n⊢ (extendedHom A B) (mk0 I) =\n (mk (FractionRing B))\n ((Units.map ↑(FractionalIdeal.extendedHom (Fra... | [] | by | [anonymous] | by |
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