module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Algebra.Lie.Basis | {
"line": 302,
"column": 2
} | {
"line": 302,
"column": 38
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nthis : ((Int.castRingHom R).mapMatrix b.A).Nondegenerate\nv : ι → Dual R ↥b.cartan :=\n ((Basis.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 359,
"column": 4
} | {
"line": 360,
"column": 68
} | [
{
"pp": "R : Type u_3\ninst✝ : CommSemiring R\nN : ℕ\nφ : MvPolynomial (Fin (N + 1)) R\nn : ℕ\nhφ : φ.IsHomogeneous n\ni j : ℕ\nh : i + j = n\nd : Fin N →₀ ℕ\nhd : coeff (cons i d) φ ≠ 0\n⊢ (weight 1) (cons i d) = i + j",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.CartanCriterion | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 41
} | [
{
"pp": "R : Type u_1\nL : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CharZero R\ninst✝⁴ : IsDomain R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : IsNoetherian R L\ninst✝ : Module.Free R L\n⊢ LieIdeal.killingCompl R L ⊤ ≤ radical R L",
"usedConstants": [
"LieAlgebra.toModule",
"LieSubmodu... | rw [← LieIdeal.solvable_iff_le_radical] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Lie.CartanCriterion | {
"line": 258,
"column": 32
} | {
"line": 258,
"column": 43
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁷ : CommRing R\ninst✝⁶ : CharZero R\ninst✝⁵ : IsDomain R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : IsNoetherian R L\ninst✝¹ : Module.Free R L\ninst✝ : HasTrivialRadical R L\n⊢ LieIdeal.killingCompl R L ⊤ = ⊥",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Zero | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 42
} | [
{
"pp": "case h\nR : Type u_1\nM : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Module.Finite R M\ninst✝¹ : Free R M\ninst✝ : IsNoetherian R M\nφ : End R M\ntfae_1_to_2 : IsNilpotent φ → charpoly φ = X ^ finrank R M\nh : charpoly φ = X ^ finrank R M\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 415,
"column": 6
} | {
"line": 415,
"column": 17
} | [
{
"pp": "case neg\nR : Type u_3\ninst✝ : CommSemiring R\nN : ℕ\nF : MvPolynomial (Fin N.succ) R\nn : ℕ\nhF : F.IsHomogeneous n\nhF₀ : F ≠ 0\nhdeg : ((finSuccEquiv R N) F).natDegree < n + 1\naux : ∀ i ∈ Finset.range n, constantCoeff (((finSuccEquiv R N) F).coeff i) = 0\nhFn : constantCoeff (((finSuccEquiv R N) F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 339,
"column": 49
} | {
"line": 339,
"column": 73
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx : L\nhx : x ∈ b.borelUpper\n⊢ x ∈ lieSpan R L (range b.e)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 433,
"column": 4
} | {
"line": 433,
"column": 67
} | [
{
"pp": "case h.a\nR : Type u_5\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nF : MvPolynomial (Fin 0) R\nn : ℕ\nhF : F.IsHomogeneous n\nhnR : ↑n ≤ #R\nhF₀ : (eval 0) F = 0\nd : Fin 0 →₀ ℕ\n⊢ coeff d F = coeff d 0",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semirin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 439,
"column": 65
} | {
"line": 439,
"column": 76
} | [
{
"pp": "R : Type u_5\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nN : ℕ\nIH : ∀ {F : MvPolynomial (Fin N) R} {n : ℕ}, F.IsHomogeneous n → F ≠ 0 → ↑n ≤ #R → ∃ r, (eval r) F ≠ 0\nF : MvPolynomial (Fin (N + 1)) R\nn : ℕ\nhF : F.IsHomogeneous n\nhnR : ↑n ≤ #R\nhdeg : ((finSuccEquiv R N) F).natDegree < n + 1\nhF₀ : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 459,
"column": 6
} | {
"line": 459,
"column": 17
} | [
{
"pp": "R : Type u_5\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nN : ℕ\nIH : ∀ {F : MvPolynomial (Fin N) R} {n : ℕ}, F.IsHomogeneous n → F ≠ 0 → ↑n ≤ #R → ∃ r, (eval r) F ≠ 0\nF : MvPolynomial (Fin (N + 1)) R\nhF₀ : F ≠ 0\ni : ℕ\nhi : ((finSuccEquiv R N) F).coeff i ≠ 0\nj : ℕ\nr : Fin N → R\nhr : (eval r) (((fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Homogeneous | {
"line": 487,
"column": 2
} | {
"line": 487,
"column": 27
} | [
{
"pp": "R : Type u_5\nσ : Type u_6\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nF G : MvPolynomial σ R\nn : ℕ\nhF : F.IsHomogeneous n\nhG : G.IsHomogeneous n\nh : ∀ (r : σ → R), (eval r) F = (eval r) G\nhnR : ↑n ≤ #R\n⊢ ∀ (r : σ → R), (eval r) (F - G) = 0",
"usedConstants": [
"Finsupp.instAddZeroClass",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Zero | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 58
} | [
{
"pp": "K : Type u_2\nM : Type u_3\ninst✝³ : Field K\ninst✝² : AddCommGroup M\ninst✝¹ : Module K M\ninst✝ : Module.Finite K M\nφ : End K M\ntfae_1_iff_2 : φ.HasEigenvalue 0 ↔ (minpoly K φ).IsRoot 0\ntfae_2_to_3 : (minpoly K φ).IsRoot 0 → constantCoeff (charpoly φ) = 0\ntfae_3_to_4 : constantCoeff (charpoly φ) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Zero | {
"line": 114,
"column": 2
} | {
"line": 117,
"column": 61
} | [
{
"pp": "K : Type u_2\nM : Type u_3\ninst✝³ : Field K\ninst✝² : AddCommGroup M\ninst✝¹ : Module K M\ninst✝ : Module.Finite K M\nφ : End K M\ntfae_1_iff_2 : φ.HasEigenvalue 0 ↔ (minpoly K φ).IsRoot 0\ntfae_2_to_3 : (minpoly K φ).IsRoot 0 → constantCoeff (charpoly φ) = 0\ntfae_3_to_4 : constantCoeff (charpoly φ) ... | tfae_have 6 → 1
| ⟨x, h1, h2⟩ => by
apply Module.End.hasEigenvalue_of_hasEigenvector ⟨_, h1⟩
simpa only [Module.End.eigenspace_zero, mem_ker] using h2 | Mathlib.Tactic.TFAE._aux_Mathlib_Tactic_TFAE___macroRules_Mathlib_Tactic_TFAE_tfaeHave_1 | Mathlib.Tactic.TFAE.tfaeHave |
Mathlib.Algebra.Lie.Basis | {
"line": 365,
"column": 8
} | {
"line": 365,
"column": 19
} | [
{
"pp": "case refine_1.a.h.h\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v✝ : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v✝ ∈ lieSpan R L (range ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 368,
"column": 8
} | {
"line": 368,
"column": 19
} | [
{
"pp": "case h.a.h\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v ∈ lieSpan R L (range b.e)\nhu : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Zero | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 31
} | [
{
"pp": "K : Type u_2\nM : Type u_3\ninst✝³ : Field K\ninst✝² : AddCommGroup M\ninst✝¹ : Module K M\ninst✝ : Module.Finite K M\nφ : End K M\nthis :\n [¬φ.HasEigenvalue 0, ¬(minpoly K φ).IsRoot 0, constantCoeff (charpoly φ) ≠ 0, LinearMap.det φ ≠ 0, ¬⊥ < ker φ,\n ∀ (m : M), m ≠ 0 → φ m ≠ 0].TFAE\naux₁ : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 379,
"column": 2
} | {
"line": 379,
"column": 34
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\n⊢ b.borelLower ≤ ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n i • ⇑((-b.baseSupp) i))",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 412,
"column": 33
} | {
"line": 412,
"column": 50
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 416,
"column": 6
} | {
"line": 416,
"column": 23
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LinearMap.Polynomial | {
"line": 488,
"column": 2
} | {
"line": 488,
"column": 57
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁹ : CommRing R\ninst✝⁸ : AddCommGroup L\ninst✝⁷ : Module R L\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nφ : L →ₗ[R] End R M\ninst✝⁴ : Free R M\ninst✝³ : Module.Finite R M\ninst✝² : Module.Finite R L\ninst✝¹ : Free R L\ninst✝ : Nontrivial R\n⊢ φ.nilRank... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 420,
"column": 34
} | {
"line": 420,
"column": 45
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Matrix | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 15
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\n⊢ Function.Injective ⇑(toEnd R (Matrix n n R) (n → R))",
"usedConstants": [
"LieHom",
"Module.End.instRing",
"Eq.mpr",
"Pi.Function.module",
"lieEquivMatrix'",
"Matrix.instLie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 424,
"column": 33
} | {
"line": 424,
"column": 50
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 428,
"column": 6
} | {
"line": 428,
"column": 23
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 432,
"column": 34
} | {
"line": 432,
"column": 45
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 437,
"column": 6
} | {
"line": 437,
"column": 23
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 439,
"column": 6
} | {
"line": 439,
"column": 23
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 450,
"column": 4
} | {
"line": 450,
"column": 15
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.SymplecticGroup | {
"line": 152,
"column": 16
} | {
"line": 152,
"column": 27
} | [
{
"pp": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\nhA : Aᵀ ∈ symplecticGroup l R\n⊢ A ∈ symplecticGroup l R",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 495,
"column": 4
} | {
"line": 495,
"column": 49
} | [
{
"pp": "case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁵ : Fintype ι\ninst✝⁴ : Field K\ninst✝³ : CharZero K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : FiniteDimensional K L\nb : Basis ι K L\ni : ι\n⊢ { toFun := ⇑(b.baseSupp i), genWeightSpace_ne_bot' := ⋯ } ∈ root",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 504,
"column": 49
} | {
"line": 504,
"column": 72
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.SkewAdjoint | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 15
} | [
{
"pp": "case mp\nR : Type u\nn : Type w\ninst✝² : CommRing R\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\nu : Rˣ\nJ A : Matrix n n R\nh : Aᵀ * u • J = u • J * -A\n⊢ Aᵀ * J = J * -A",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 522,
"column": 4
} | {
"line": 522,
"column": 57
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nχ : ↥root\nthis✝ : ∀ (n : ι → ℕ), ∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 529,
"column": 32
} | {
"line": 529,
"column": 43
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 532,
"column": 4
} | {
"line": 532,
"column": 92
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 533,
"column": 73
} | {
"line": 533,
"column": 89
} | [
{
"pp": "case refine_1\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 533,
"column": 73
} | {
"line": 533,
"column": 89
} | [
{
"pp": "case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 86
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Classical | {
"line": 148,
"column": 2
} | {
"line": 148,
"column": 63
} | [
{
"pp": "n : Type u_1\nR : Type u₂\ninst✝³ : DecidableEq n\ninst✝² : CommRing R\ninst✝¹ : Fintype n\ninst✝ : Nontrivial R\nh : 1 < Fintype.card n\ni j : n\nhij : i ≠ j\nA : ↥(sl n R) := (single i j hij) 1\nB : ↥(sl n R) := (single j i ⋯) 1\nc : IsLieAbelian ↥(sl n R)\nc' : ↑A * ↑B = ↑B * ↑A\n⊢ False",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Classical | {
"line": 190,
"column": 13
} | {
"line": 190,
"column": 36
} | [
{
"pp": "case a\np : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\nx y : p ⊕ q\n⊢ (Pso p q R i * Pso p q R (-i)) x y = 1 x y",
"usedConstants": []
}
] | rcases x with ⟨x⟩ | ⟨x⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Algebra.Lie.Classical | {
"line": 209,
"column": 13
} | {
"line": 209,
"column": 36
} | [
{
"pp": "case a\np : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\nx y : p ⊕ q\n⊢ ((Pso p q R i)ᵀ * indefiniteDiagonal p q R * Pso p q R i) x y = 1 x y",
"usedConstants": []
}
] | rcases x with ⟨x⟩ | ⟨x⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Algebra.Lie.CartanExists | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 24
} | [
{
"pp": "case inl\nK : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\ny : L\nhyU : y ∈ U\nEy : ↑{x | ∃ y ∈ U, engel K y = x} := ⟨engel K y, ⋯⟩\nhxU : 0 ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x}... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.CartanExists | {
"line": 226,
"column": 6
} | {
"line": 226,
"column": 92
} | [
{
"pp": "case inr.refine_1\nK : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\nx : L\nhxU : x ∈ U\ny : L\nhyU : y ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x} := ⟨engel K x, ⋯⟩\nEy : ↑{x | ∃ y ∈ U... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.CartanExists | {
"line": 246,
"column": 6
} | {
"line": 247,
"column": 13
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\nx : L\nhxU : x ∈ U\ny : L\nhyU : y ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x} := ⟨engel K x, ⋯⟩\nEy : ↑{x | ∃ y ∈ U, engel K y = x} :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.DirectSum | {
"line": 112,
"column": 6
} | {
"line": 112,
"column": 51
} | [
{
"pp": "case w\nR : Type u\nι : Type v\ninst✝² : CommRing R\nL : ι → Type w\ninst✝¹ : (i : ι) → LieRing (L i)\ninst✝ : (i : ι) → LieAlgebra R (L i)\nx y z : ⨁ (i : ι), L i\ni✝ : ι\n⊢ (zipWith (fun x x_1 y ↦ ⁅x_1, y⁆) ⋯ x (y + z)) i✝ =\n (zipWith (fun x x_1 y ↦ ⁅x_1, y⁆) ⋯ x y + zipWith (fun x x_1 y ↦ ⁅x_1, ... | simp only [zipWith_apply, add_apply, lie_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Lie.CartanExists | {
"line": 312,
"column": 4
} | {
"line": 312,
"column": 76
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\nx : L\nhxU : x ∈ U\ny : L\nhyU : y ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x} := ⟨engel K x, ⋯⟩\nEy : ↑{x | ∃ y ∈ U, engel K y = x} :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.CartanExists | {
"line": 322,
"column": 2
} | {
"line": 332,
"column": 75
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\nx : L\nhxU : x ∈ U\ny : L\nhyU : y ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x} := ⟨engel K x, ⋯⟩\nEy : ↑{x | ∃ y ∈ U, engel K y = x} :=... | have hz' : ∃ n : ℕ, (toEnd K U Q v ^ n) z' = 0 := by
rw [mem_engel_iff] at hz
obtain ⟨n, hn⟩ := hz
use n
apply_fun LieSubmodule.Quotient.mk' E at hn
rw [map_zero] at hn
rw [← hn]
clear hn
induction n with
| zero => simp only [z', pow_zero, Module.End.one_apply]
| succ n ih => rw ... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Algebra.Lie.UniversalEnveloping | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 13
} | [
{
"pp": "R : Type u₁\nL : Type u₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nA : Type u₃\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nf : L →ₗ⁅R⁆ A\nx : L\n⊢ ((lift R) f) ((mkAlgHom R L) (ιₜ x)) = f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.CartanExists | {
"line": 339,
"column": 4
} | {
"line": 339,
"column": 58
} | [
{
"pp": "case inl\nK : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : Module.Finite K L\nhLK : ↑(finrank K L) ≤ #K\nU : LieSubalgebra K L\nx : L\nhxU : x ∈ U\ny : L\nhyU : y ∈ U\nEx : ↑{x | ∃ x_1 ∈ U, engel K x_1 = x} := ⟨engel K x, ⋯⟩\nEy : ↑{x | ∃ y ∈ U, engel K... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 33
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b : lib R X\nh : Rel R X a b\n⊢ Rel R X (-a) (-b)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 35
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X b c\n⊢ Rel R X (a - b) (a - c)",
"usedConstants": [
"Eq.mpr",
"FreeNonUnitalNonAssocAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 35
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X a b\n⊢ Rel R X (a - c) (b - c)",
"usedConstants": [
"Eq.mpr",
"FreeNonUnitalNonAssocAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 165,
"column": 13
} | {
"line": 165,
"column": 87
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\n⊢ ∀ (x y z : FreeLieAlgebra R X),\n Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ (x + y) z =\n Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ x z + Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ y z",
"usedConstants": [
"add_mul",
"FreeLieAlgebra.Rel.mul_left",
... | by rintro ⟨a⟩ ⟨b⟩ ⟨c⟩; change Quot.mk _ _ = Quot.mk _ _; simp_rw [add_mul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Lie.Cochain | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 63
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\nL : Type u_2\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nM : Type u_3\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\na : ↥(twoCochain R L M)\nx y : L\n⊢ (a y) x + (a x) y = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 53,
"column": 6
} | {
"line": 53,
"column": 63
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 15
} | [
{
"pp": "case h\nk : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 55,
"column": 2
} | {
"line": 59,
"column": 46
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | have aux : radical k L = center k L := by
refine le_antisymm (fun x hx ↦ (mem_maxTrivSubmodule k L L x).mpr ?_) (center_le_radical k L)
intro y
simp [← toEnd_eq_zero_iff (R := k) (L := L) (M := M), LieHom.map_lie, hχ _ hx, lie_smul,
(toEnd k L M y).commute_id_right.lie_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 26
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 87,
"column": 16
} | {
"line": 87,
"column": 27
} | [
{
"pp": "case mem\nL : Type u_2\nM : Type u_3\ninst✝⁶ : LieRing L\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : LieRingModule L M\nR : Type u_4\ninst✝³ : CommRing R\ninst✝² : LieAlgebra R L\ninst✝¹ : Module R M\ninst✝ : LieModule R L M\ns : Set L\nhs : ∀ x ∈ s, (trace R M) ((toEnd R L M) x) = 0\nx u : L\nhu : u ∈ s\n⊢ (tr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | [
{
"pp": "case h1\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.attach.Nodup\nhn : 2 ≤ l.attach.length\n⊢ ∀ σ ∈ [l.attach.formPerm], σ.IsCycle",
"usedConstants": [
"Eq.mpr",
"False",
"congrArg",
"Membership.mem",
"id",
"Subtype",
"List.not_mem_nil._simp_1"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 36
} | [
{
"pp": "case mk\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Cycle α\nx✝ : α\nh : Nodup (Quot.mk ⇑(IsRotated.setoid α) [x✝])\nhn : Nontrivial (Quot.mk ⇑(IsRotated.setoid α) [x✝])\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 13
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nx : α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\nhx : x ∉ Quot.mk (⇑(IsRotated.setoid α)) a✝\n⊢ (formPerm (Quot.mk (⇑(IsRotated.setoid α)) a✝) h) x = x",
"usedConstants": [
"Equiv.instEquivLike",
"List.IsRotated.setoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 13
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nx : α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\nhx : x ∈ Quot.mk (⇑(IsRotated.setoid α)) a✝\n⊢ (formPerm (Quot.mk (⇑(IsRotated.setoid α)) a✝) h) x = next (Quot.mk (⇑(IsRotated.setoid α)) a✝) h x hx",
"usedConstants": [
"Equiv.in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 13
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : DecidableEq α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\n⊢ (reverse (Quot.mk (⇑(IsRotated.setoid α)) a✝)).formPerm ⋯ = (formPerm (Quot.mk (⇑(IsRotated.setoid α)) a✝) h)⁻¹",
"usedConstants": [
"Iff.mpr",
"Cycle.nodup_reverse_iff",
"E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 13
} | [
{
"pp": "case h\nα : Type u_2\ninst✝ : DecidableEq α\na₁✝ a₂✝ : List α\nhs : Nodup (Quotient.mk'' a₁✝)\nhs' : Nodup (Quotient.mk'' a₂✝)\n⊢ formPerm (Quotient.mk'' a₁✝) hs = formPerm (Quotient.mk'' a₂✝) hs' ↔\n Quotient.mk'' a₁✝ = Quotient.mk'' a₂✝ ∨ length (Quotient.mk'' a₁✝) ≤ 1 ∧ length (Quotient.mk'' a₂✝)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 35
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nH : p.toList x = [y]\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 234,
"column": 4
} | {
"line": 234,
"column": 15
} | [
{
"pp": "case mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nh : p.SameCycle x y\nhx : x ∈ p.support\n⊢ ∃ m < (p.cycleOf x).support.card, (p ^ m) x = y",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 273,
"column": 33
} | {
"line": 273,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nhy✝ : y ∈ p.toList x\nhy : p.SameCycle x y ∧ x ∈ p.support\nk : ℕ\nhk : k < (p.cycleOf x).support.card\nhk' : (p ^ k) x = y\n⊢ k < (p.toList x).length",
"usedConstants": [
"Equiv.Perm.instDecidableRelSameCycle",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nk : ℕ\n⊢ p.toList ((p ^ k) x) = (p.toList x).rotate k",
"usedConstants": [
"Equiv.Perm.toList",
"List.ext_getElem",
"Equiv.instEquivLike",
"Equiv.Perm.instPowNat",
"HPow.hPow",
"Equiv.Per... | apply ext_getElem | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 331,
"column": 4
} | {
"line": 331,
"column": 15
} | [
{
"pp": "case hl\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ 2 ≤ (l.rotate ↑k).length",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.length_rotate",
"id",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 15
} | [
{
"pp": "case hn\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ (l.rotate ↑k).Nodup",
"usedConstants": [
"Eq.mpr",
"id",
"Fin.val",
"List.Nodup",
"Eq",
"Li... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 374,
"column": 2
} | {
"line": 374,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\nx : α\nhx : f x ≠ x\n⊢ (f.toCycle hf).Nodup",
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.toList",
"congrArg",
"Equiv.Perm.toCycle",
"id",
"List.Nodup",
"Equiv.Perm.toCycle_eq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 410,
"column": 4
} | {
"line": 410,
"column": 94
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : { f // f.IsCycle }\nx : α\nhx : ↑f x ≠ x\n⊢ (fun s ↦ ⟨(↑s).formPerm ⋯, ⋯⟩) ((fun f ↦ ⟨(↑f).toCycle ⋯, ⋯⟩) f) = f",
"usedConstants": [
"Equiv.Perm.instDecidableRelSameCycle",
"Eq.mpr",
"Equiv.Perm.toLi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 415,
"column": 33
} | {
"line": 415,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhx : x ∈ Quot.mk (⇑(IsRotated.setoid α)) s\n⊢ 2 ≤ s.length",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 424,
"column": 8
} | {
"line": 424,
"column": 19
} | [
{
"pp": "case mk.a\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn✝ : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhl : 2 ≤ s.length\nhn : s.Nodup\nhx : x ∈ s\n⊢ x ∈ s.toFinset",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 449,
"column": 6
} | {
"line": 449,
"column": 17
} | [
{
"pp": "case intro.refine_2.mk.refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nval✝ : Fintype α\nx : α\ny✝ : Cycle α\nl : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) l)\nhf : (Cycle.formPerm (Quot.mk (⇑(IsRotated.setoid α)) l) hn).IsCycle\nhx : (Cycle.formPerm (Quot.mk (⇑(IsRota... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhs : s.Nodup\nhf : (s.formPerm hs).IsCycle\nhs' : ∀ (y : Cycle α), (fun s_1 ↦ ∃ (h : s_1.Nodup), s_1.formPerm h = s.formPerm hs) y → y = s\nt : Cycle α\nht : t.Nodup\nht' : (↑⟨t, ht⟩).formPerm ⋯ = s.formPerm hs\n⊢ ⟨t, ht⟩ = ⟨s, hs⟩",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 466,
"column": 4
} | {
"line": 466,
"column": 15
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhn : s.Nodup\nhf : ((↑⟨s, hn⟩).formPerm ⋯).IsCycle\nhs' : ∀ (y : { s // s.Nodup }), (fun s_1 ↦ (↑s_1).formPerm ⋯ = (↑⟨s, hn⟩).formPerm ⋯) y → y = ⟨s, hn⟩\nH : s.Subsingleton\n⊢ (↑⟨s, hn⟩).formPerm ⋯ = 1",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 467,
"column": 4
} | {
"line": 467,
"column": 15
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\n⊢ (fun s ↦ (↑s).formPerm ⋯ = f) ⟨s, ⋯⟩",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 469,
"column": 4
} | {
"line": 469,
"column": 15
} | [
{
"pp": "case refine_3\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\nt : Cycle α\nht : t.Nodup\nht' : t.Nontrivial\nht'' : (↑⟨t, ⋯⟩).fo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Loop | {
"line": 103,
"column": 47
} | {
"line": 103,
"column": 58
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : AddCommGroup A\ninst✝¹ : DistribSMul A R\ninst✝ : SMulCommClass A R R\nΦ : LinearMap.BilinForm R L\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\nx y : lo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 138,
"column": 4
} | {
"line": 138,
"column": 32
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | simp [hv'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 61
} | [
{
"pp": "k : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L V\nA : LieIdeal ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Extension | {
"line": 312,
"column": 20
} | {
"line": 312,
"column": 49
} | [
{
"pp": "R : Type u_1\nN : Type u_2\nL : Type u_3\nM : Type u_4\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing M\ninst✝ : LieAlgebra R M\nE : Extension R M L\nx : ↥E.proj.ker\n⊢ (fun m ↦ ⟨E.incl m, ⋯⟩) ((⇑(Equiv.ofInjective ⇑E.incl ⋯).symm ∘ ⇑(IsExtension.kerEquivRange E.inc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Loop | {
"line": 132,
"column": 77
} | {
"line": 132,
"column": 93
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Loop | {
"line": 135,
"column": 25
} | {
"line": 135,
"column": 36
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Matrix.Cartan | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 37
} | [
{
"pp": "case mpr.inl\nι : Type u_1\ninst✝ : LinearOrder ι\nA : Matrix ι ι ℤ\nhA : A.IsSymm\nh : ∀ ⦃i j : ι⦄, j < i → A i j = 0 ∨ A i j = -1\ni j : ι\nhij✝ : i ≠ j\nhij : i < j\n⊢ A i j = 0 ∨ A i j = -1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 48
} | [
{
"pp": "case h.refine_2\nk : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 218,
"column": 6
} | {
"line": 218,
"column": 69
} | [
{
"pp": "case h\nk : Type u_1\ninst✝¹² : Field k\nV : Type u_3\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : Module k V\ninst✝⁹ : CharZero k\ninst✝⁸ : Module.Finite k V\ninst✝⁷ : Nontrivial V\nL : Type u_4\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra k L\ninst✝⁴ : LieRingModule L V\ninst✝³ : LieModule k L V\ninst✝² : IsSolv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 15
} | [
{
"pp": "case h.refine_2\nk : Type u_1\ninst✝¹¹ : Field k\nL : Type u_2\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : LieRingModule L V\ninst✝⁵ : LieModule k L V\ninst✝⁴ : CharZero k\ninst✝³ : Module.Finite k V\ninst✝² : Nontrivial V\ninst✝¹ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.LinearRecurrence | {
"line": 234,
"column": 4
} | {
"line": 234,
"column": 29
} | [
{
"pp": "case mp\nR : Type u_1\ninst✝ : CommRing R\nE : LinearRecurrence R\nq : R\nh : E.IsSolution fun n ↦ q ^ n\n⊢ q ^ E.order - ∑ x, E.coeffs x * q ^ ↑x = 0",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Finset.univ",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Extension | {
"line": 448,
"column": 4
} | {
"line": 449,
"column": 37
} | [
{
"pp": "R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Extension | {
"line": 452,
"column": 4
} | {
"line": 452,
"column": 38
} | [
{
"pp": "R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Bimodule | {
"line": 88,
"column": 26
} | {
"line": 88,
"column": 75
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Module A M\ninst✝⁵ : Module B M\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : IsScalarTower R A M\ninst✝¹ : IsScal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Bimodule | {
"line": 89,
"column": 31
} | {
"line": 89,
"column": 58
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Module A M\ninst✝⁵ : Module B M\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : IsScalarTower R A M\ninst✝¹ : IsScal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 48,
"column": 8
} | {
"line": 48,
"column": 55
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np : Associates M\nh₁ : p ≠ 0\nhp : IsAtom p\n⊢ ¬IsUnit p",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"congrArg",
"IsUnit",
"id",
"CommMonoidWithZero.toMonoidWithZero",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 55,
"column": 8
} | {
"line": 55,
"column": 78
} | [
{
"pp": "M : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\np : Associates M\nh₁ : p ≠ 0\nhp : Irreducible p\n⊢ p ≠ ⊥",
"usedConstants": [
"CommMonoidWithZero.toCommMonoid",
"OrderBot.toBot",
"Preorder.toLE",
"id",
"Ne",
"Bot.bot",
"CommMonoidWi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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