module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Limits.Shapes.Kernels | {
"line": 947,
"column": 2
} | {
"line": 947,
"column": 15
} | {
"line": 949,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nX Y Z : C\nf g : X ⟶ Y\ninst✝¹ : HasCokernel f\ninst✝ : HasCokernel g\nh : f = g\ne : Y ⟶ Z\nhe : f ≫ e = 0\n⊢ (cokernelIsoOfEq h).inv ≫ cokernel.desc f e he = cokernel.desc g e ⋯",
"ppTerm": "?m.65",
"assigned": true,
"us... | [] | cases h; simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Kernels | {
"line": 947,
"column": 2
} | {
"line": 947,
"column": 15
} | {
"line": 949,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nX Y Z : C\nf g : X ⟶ Y\ninst✝¹ : HasCokernel f\ninst✝ : HasCokernel g\nh : f = g\ne : Y ⟶ Z\nhe : f ≫ e = 0\n⊢ (cokernelIsoOfEq h).inv ≫ cokernel.desc f e he = cokernel.desc g e ⋯",
"ppTerm": "?m.65",
"assigned": true,
"us... | [] | cases h; simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Biproducts | {
"line": 453,
"column": 94
} | {
"line": 454,
"column": 40
} | {
"line": 456,
"column": 0
} | [
{
"pp": "J : Type w\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : DecidableEq J\nf : J → C\ninst✝ : HasBiproduct f\nj j' : J\n⊢ ι f j ≫ π f j' = if h : j = j' then eqToHom ⋯ else 0",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categ... | [] | by
convert! (biproduct.bicone f).ι_π j j' | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Biproducts | {
"line": 708,
"column": 14
} | {
"line": 710,
"column": 41
} | {
"line": 711,
"column": 12
} | [
{
"pp": "case pos\nJ✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nι : Type u_3\nf : ι → T... | [] | cases w
simp only [heq_eq_eq, forall_true_left] at h
simp [biproduct.ι_π_ne _ h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Biproducts | {
"line": 708,
"column": 14
} | {
"line": 710,
"column": 41
} | {
"line": 711,
"column": 12
} | [
{
"pp": "case pos\nJ✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nι : Type u_3\nf : ι → T... | [] | cases w
simp only [heq_eq_eq, forall_true_left] at h
simp [biproduct.ι_π_ne _ h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | {
"line": 697,
"column": 2
} | {
"line": 697,
"column": 79
} | {
"line": 699,
"column": 0
} | [
{
"pp": "C : Type uC\ninst✝³ : Category.{uC', uC} C\ninst✝² : HasZeroMorphisms C\nW X Y Z : C\ninst✝¹ : HasBinaryBiproduct W X\ninst✝ : HasBinaryBiproduct Y Z\nf : W ⟶ Y\ng : X ⟶ Z\n⊢ inr ≫ map' f g = g ≫ inr",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.IsCo... | [] | exact IsColimit.ι_map (BinaryBiproduct.isColimit W X) _ _ ⟨WalkingPair.right⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Limits.Shapes.Biproducts | {
"line": 849,
"column": 6
} | {
"line": 849,
"column": 16
} | {
"line": 850,
"column": 6
} | [
{
"pp": "J✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nf : J → C\ni : J\ninst✝¹ : HasBip... | [
"J✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nf : J → C\ni : J\ninst✝¹ : HasBiproduct f\nin... | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.CategoryTheory.Limits.Shapes.Biproducts | {
"line": 875,
"column": 6
} | {
"line": 875,
"column": 16
} | {
"line": 876,
"column": 6
} | [
{
"pp": "J✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nf : J → C\ni : J\ninst✝¹ : HasBip... | [
"J✝ : Type w\nC✝ : Type uC\ninst✝⁷ : Category.{uC', uC} C✝\ninst✝⁶ : HasZeroMorphisms C✝\nD : Type uD\ninst✝⁵ : Category.{uD', uD} D\ninst✝⁴ : HasZeroMorphisms D\nF : J✝ → C✝\nJ : Type w\nK : Type u_1\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\nf : J → C\ni : J\ninst✝¹ : HasBiproduct f\nin... | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Order.Fin.Tuple | {
"line": 104,
"column": 39
} | {
"line": 104,
"column": 45
} | {
"line": 107,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nn : ℕ\nf : Fin (n + 1) → α\na : α\n⊢ Monotone ![1, 2, 2, 3]",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"id",
"forall_prop_decidab... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Order.Fin.Tuple | {
"line": 104,
"column": 39
} | {
"line": 104,
"column": 45
} | {
"line": 107,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nn : ℕ\nf : Fin (n + 1) → α\na : α\n⊢ Monotone ![1, 2, 2, 3]",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"id",
"forall_prop_decidab... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Fin.Tuple | {
"line": 104,
"column": 39
} | {
"line": 104,
"column": 45
} | {
"line": 107,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nn : ℕ\nf : Fin (n + 1) → α\na : α\n⊢ Monotone ![1, 2, 2, 3]",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"id",
"forall_prop_decidab... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.ModuleCat.Basic | {
"line": 673,
"column": 2
} | {
"line": 676,
"column": 47
} | {
"line": 677,
"column": 0
} | [
{
"pp": "R✝ : Type u\ninst✝⁴ : Ring R✝\nX₁ X₂ : Type v\nR : Type u_1\nS : Type u_2\ninst✝³ : Ring R\ninst✝² : Ring S\nF : ModuleCat R ⥤ ModuleCat S\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nM : ModuleCat R\nh : Nontrivial ↑M\n⊢ Nontrivial ↑(F.obj M)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants"... | [] | by_contra!
exact ((not_iff_not.2 ModuleCat.isZero_iff_subsingleton).2 <|
not_subsingleton_iff_nontrivial.2 h) <| IsZero.of_full_of_faithful_of_isZero F _ <|
ModuleCat.isZero_of_subsingleton <| F.obj M | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.ModuleCat.Basic | {
"line": 673,
"column": 2
} | {
"line": 676,
"column": 47
} | {
"line": 677,
"column": 0
} | [
{
"pp": "R✝ : Type u\ninst✝⁴ : Ring R✝\nX₁ X₂ : Type v\nR : Type u_1\nS : Type u_2\ninst✝³ : Ring R\ninst✝² : Ring S\nF : ModuleCat R ⥤ ModuleCat S\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nM : ModuleCat R\nh : Nontrivial ↑M\n⊢ Nontrivial ↑(F.obj M)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants"... | [] | by_contra!
exact ((not_iff_not.2 ModuleCat.isZero_iff_subsingleton).2 <|
not_subsingleton_iff_nontrivial.2 h) <| IsZero.of_full_of_faithful_of_isZero F _ <|
ModuleCat.isZero_of_subsingleton <| F.obj M | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.NatAntidiagonal | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 12
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case elim0.zero\nk : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 0 ↔ ∑ i, i.elim0 = 0",
"ppTerm": "?elim0.zero",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Finset.univ",
"instLawfulBEq",
"Membership.mem",
"id",
"instOfNatNat",
"instBEqOfDec... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Fin.Tuple.NatAntidiagonal | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 12
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case elim0.zero\nk : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 0 ↔ ∑ i, i.elim0 = 0",
"ppTerm": "?elim0.zero",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Finset.univ",
"instLawfulBEq",
"Membership.mem",
"id",
"instOfNatNat",
"instBEqOfDec... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.NatAntidiagonal | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 12
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case elim0.zero\nk : ℕ\n⊢ Fin.elim0 ∈ antidiagonalTuple 0 0 ↔ ∑ i, i.elim0 = 0",
"ppTerm": "?elim0.zero",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Finset.univ",
"instLawfulBEq",
"Membership.mem",
"id",
"instOfNatNat",
"instBEqOfDec... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.NatAntidiagonal | {
"line": 152,
"column": 4
} | {
"line": 152,
"column": 67
} | {
"line": 153,
"column": 4
} | [
{
"pp": "k n : ℕ\n⊢ (∀ (a b : ℕ),\n a + b = n →\n Pairwise (fun a b ↦ Pi.Lex (fun x1 x2 ↦ x1 < x2) (fun i x1 x2 ↦ x1 < x2) a b) (antidiagonalTuple k b)) ∧\n Pairwise\n (fun a₁ a₂ ↦\n ∀ a ∈ antidiagonalTuple k a₁.2,\n ∀ a_2 ∈ antidiagonalTuple k a₂.2,\n a₁.1 < a₂.1 ... | [
"k n : ℕ\n⊢ Pairwise\n (fun a₁ a₂ ↦\n ∀ a ∈ antidiagonalTuple k a₁.2,\n ∀ a_2 ∈ antidiagonalTuple k a₂.2,\n a₁.1 < a₂.1 ∨ a₁.1 = a₂.1 ∧ Pi.Lex (fun x1 x2 ↦ x1 < x2) (fun i x1 x2 ↦ x1 < x2) a a_2)\n (antidiagonal n)"
] | refine ⟨fun _ _ _ => antidiagonalTuple_pairwise_pi_lex k _, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 112,
"column": 2
} | {
"line": 122,
"column": 12
} | {
"line": 124,
"column": 0
} | [
{
"pp": "ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\nn✝ : μ\ns : Finset ι\nn : μ\n⊢ Finset (ι → μ)",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
... | [] | refine (Fintype.truncEquivFinOfCardEq <| Fintype.card_coe s).lift
(fun e ↦ (finAntidiagonal s.card n).map ⟨fun f i ↦ if hi : i ∈ s then f (e ⟨i, hi⟩) else 0, ?_⟩)
fun e₁ e₂ ↦ ?_
· rintro f g hfg
ext i
simpa using congr_fun hfg (e.symm i)
· ext f
simp only [mem_map, mem_finAntidiagonal]
refin... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 112,
"column": 2
} | {
"line": 122,
"column": 12
} | {
"line": 124,
"column": 0
} | [
{
"pp": "ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\nn✝ : μ\ns : Finset ι\nn : μ\n⊢ Finset (ι → μ)",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
... | [] | refine (Fintype.truncEquivFinOfCardEq <| Fintype.card_coe s).lift
(fun e ↦ (finAntidiagonal s.card n).map ⟨fun f i ↦ if hi : i ∈ s then f (e ⟨i, hi⟩) else 0, ?_⟩)
fun e₁ e₂ ↦ ?_
· rintro f g hfg
ext i
simpa using congr_fun hfg (e.symm i)
· ext f
simp only [mem_map, mem_finAntidiagonal]
refin... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 128,
"column": 84
} | {
"line": 128,
"column": 89
} | {
"line": 128,
"column": 89
} | [
{
"pp": "case a\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ι → μ\ne : ↥s ≃ Fin #s\n⊢ f ∈\n Trunc.lift\n (fun e ↦ map { toFun := fun f i ↦ if hi : i ∈ s then f (e ⟨i, hi⟩) else 0, inj' := ⋯... | [
"case a\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ι → μ\ne : ↥s ≃ Fin #s\n⊢ f ∈\n Trunc.lift\n (fun e ↦ map { toFun := fun f i ↦ if hi : i ∈ s then f (e ⟨i, hi⟩) else 0, inj' := ⋯ } (finAntid... | | _ e
=> | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 77
} | {
"line": 130,
"column": 2
} | [
{
"pp": "case a\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ι → μ\ne : ↥s ≃ Fin #s\n⊢ f ∈\n Trunc.lift\n (fun e ↦ map { toFun := fun f i ↦ if hi : i ∈ s then f (e ⟨i, hi⟩) else 0, inj' := ⋯... | [
"case a\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ι → μ\ne : ↥s ≃ Fin #s\n⊢ (∃ a, ∑ i, a i = n ∧ (fun i ↦ if hi : i ∈ s then a (e ⟨i, hi⟩) else 0) = f) ↔ s.sum f = n ∧ ∀ (i : ι), f i ≠ 0 → i ∈ s"
] | simp only [Trunc.lift_mk, mem_map, mem_finAntidiagonal, Embedding.coeFn_mk] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 19
} | {
"line": 179,
"column": 4
} | [
{
"pp": "case mp\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCancelCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ni : ι\ns : Finset ι\nhi : i ∉ s\nn : μ\nf : ι → μ\n⊢ (f i + ∑ x ∈ s, f x = n ∧ ∀ (i_1 : ι), ¬f i_1 = 0 → i_1 = i ∨ i_1 ∈ s) →\n ∃ a b,\n a + b = n ∧\n ... | [
"case mp\nι : Type u_1\nμ : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : AddCancelCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ni : ι\ns : Finset ι\nhi : i ∉ s\nn : μ\nf : ι → μ\nhn : f i + ∑ x ∈ s, f x = n\nhf : ∀ (i_1 : ι), ¬f i_1 = 0 → i_1 = i ∨ i_1 ∈ s\n⊢ ∃ a b,\n a + b = n ∧\n ∃ a_1,\n... | rintro ⟨hn, hf⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.CategoryTheory.Preadditive.Biproducts | {
"line": 824,
"column": 6
} | {
"line": 827,
"column": 13
} | {
"line": 828,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⊞ X ⟶ Y ⊞ Z\ninst✝ : IsIso f\nnz : 𝟙 W ≠ 0\na₁ : biprod.inl ≫ f ≫ biprod.fst = 0\na₂ : biprod.inl ≫ f ≫ biprod.snd = 0\nx : W ⟶ W := biprod.inl ≫ f ≫ inv f ≫ biprod.fst\nh₁ : x = 𝟙 W\n| ... | [
"case a.a.a.a\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⊞ X ⟶ Y ⊞ Z\ninst✝ : IsIso f\nnz : 𝟙 W ≠ 0\na₁ : biprod.inl ≫ f ≫ biprod.fst = 0\na₂ : biprod.inl ≫ f ≫ biprod.snd = 0\nx : W ⟶ W := biprod.inl ≫ f ≫ inv f ≫ biprod.fst\nh₁ : x = 𝟙 W\n... | congr
next => skip
slice 1 3
rw [a₂] | Lean.Elab.Tactic.Conv.evalConvSeq1Indented | Lean.Parser.Tactic.Conv.convSeq1Indented |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 405,
"column": 2
} | {
"line": 405,
"column": 6
} | {
"line": 406,
"column": 2
} | [
{
"pp": "n : ℕ\nc : Composition n\ni : Fin c.length\nj : Fin (c.blocksFun i)\n⊢ c.index ((c.embedding i) j) = i",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Composition.length",
"Composition.blocksFun",
"instLEFin",
"Composition.embedding",
"Composition.ind... | [
"n : ℕ\nc : Composition n\ni : Fin c.length\nj : Fin (c.blocksFun i)\n⊢ i = c.index ((c.embedding i) j)"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.CategoryTheory.Preadditive.Biproducts | {
"line": 824,
"column": 6
} | {
"line": 827,
"column": 13
} | {
"line": 828,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⊞ X ⟶ Y ⊞ Z\ninst✝ : IsIso f\nnz : 𝟙 W ≠ 0\na₁ : biprod.inl ≫ f ≫ biprod.fst = 0\na₂ : biprod.inl ≫ f ≫ biprod.snd = 0\nx : W ⟶ W := biprod.inl ≫ f ≫ inv f ≫ biprod.fst\nh₁ : x = 𝟙 W\n| ... | [
"case a.a.a.a\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⊞ X ⟶ Y ⊞ Z\ninst✝ : IsIso f\nnz : 𝟙 W ≠ 0\na₁ : biprod.inl ≫ f ≫ biprod.fst = 0\na₂ : biprod.inl ≫ f ≫ biprod.snd = 0\nx : W ⟶ W := biprod.inl ≫ f ≫ inv f ≫ biprod.fst\nh₁ : x = 𝟙 W\n... | congr
next => skip
slice 1 3
rw [a₂] | Lean.Elab.Tactic.Conv.evalConvSeq | Lean.Parser.Tactic.Conv.convSeq |
Mathlib.GroupTheory.Perm.Support | {
"line": 160,
"column": 21
} | {
"line": 163,
"column": 52
} | {
"line": 165,
"column": 0
} | [
{
"pp": "α : Type u_1\nf : Perm α\nx : α\nhffx : f (f x) = x\nn : ℕ\n⊢ (f ^ Int.negSucc n) x = x ∨ (f ^ Int.negSucc n) x = f x",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"Equiv.instEquivLike",
"HMul.hMul",
"Equiv.Perm.instI... | [] | by
rw [zpow_negSucc, inv_eq_iff_eq, ← f.injective.eq_iff, ← mul_apply, ← pow_succ', eq_comm,
inv_eq_iff_eq, ← mul_apply, ← pow_succ, @eq_comm _ x, or_comm]
exact pow_apply_eq_of_apply_apply_eq_self hffx _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.Support | {
"line": 288,
"column": 2
} | {
"line": 291,
"column": 13
} | {
"line": 293,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx : α\n⊢ x ∈ (f * g).support → x ∈ f.support ⊔ g.support",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.support",
"Lattice.toSemilatticeSup",
"Equiv.instEquivLike"... | [] | simp only [sup_eq_union]
rw [mem_union, mem_support, mem_support, mem_support, mul_apply, ← not_and_or, not_imp_not]
rintro ⟨hf, hg⟩
rw [hg, hf] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Support | {
"line": 288,
"column": 2
} | {
"line": 291,
"column": 13
} | {
"line": 293,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx : α\n⊢ x ∈ (f * g).support → x ∈ f.support ⊔ g.support",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.support",
"Lattice.toSemilatticeSup",
"Equiv.instEquivLike"... | [] | simp only [sup_eq_union]
rw [mem_union, mem_support, mem_support, mem_support, mul_apply, ← not_and_or, not_imp_not]
rintro ⟨hf, hg⟩
rw [hg, hf] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 512,
"column": 47
} | {
"line": 519,
"column": 9
} | {
"line": 520,
"column": 6
} | [
{
"pp": "n : ℕ\nc : Composition n\nH : ¬c = ones n\nlength_n : c.length = n\n⊢ ∑ i, 1 < ∑ i, c.blocksFun i",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Finset.mem_univ",
"Composition.ofFn_blocksFun",
"Set.mem_range",
"Preorder.toLT",
"Nat.instIsOrderedAddM... | [] | by
{
obtain ⟨i, hi, i_blocks⟩ : ∃ i ∈ c.blocks, 1 < i := ne_ones_iff.1 H
rw [← ofFn_blocksFun, mem_ofFn' c.blocksFun, Set.mem_range] at hi
obtain ⟨j : Fin c.length, hj : c.blocksFun j = i⟩ := hi
rw [← hj] at i_blocks
exact Finset.sum_lt_sum (fun i _ => one_le_blocksFun c ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 729,
"column": 2
} | {
"line": 729,
"column": 19
} | {
"line": 730,
"column": 2
} | [
{
"pp": "α : Type u_1\nns : List ℕ\n⊢ ∀ {l : List α}, ns.sum ≤ l.length → map length (l.splitWrtCompositionAux ns) = ns",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Nat.instCanonicallyOrderedAdd",
"Nat.instMulZeroClass",
"instIsBotZeroClass",
"zero_le._simp_1",
... | [] | induction ns with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 741,
"column": 2
} | {
"line": 742,
"column": 25
} | {
"line": 743,
"column": 2
} | [
{
"pp": "α : Type u_1\nl l' : List α\nc : Composition l.length\nh : l' ∈ l.splitWrtComposition c\n⊢ 0 < l'.length",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"List.map",
"Membership.mem",
"List",
"List.splitWrtComposition",
"List.instMembership",
"Na... | [
"α : Type u_1\nl l' : List α\nc : Composition l.length\nh : l' ∈ l.splitWrtComposition c\nthis : l'.length ∈ map length (l.splitWrtComposition c)\n⊢ 0 < l'.length"
] | have : l'.length ∈ (l.splitWrtComposition c).map List.length :=
List.mem_map_of_mem h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 779,
"column": 2
} | {
"line": 779,
"column": 19
} | {
"line": 780,
"column": 2
} | [
{
"pp": "α : Type u_1\nns : List ℕ\n⊢ ∀ {l : List α}, ns.sum = l.length → (l.splitWrtCompositionAux ns).flatten = l",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Nat.instOrderedSub",
"Nat.instIsOrderedAddMonoid",
"AddLeftCan... | [] | induction ns with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.GroupTheory.Perm.Support | {
"line": 386,
"column": 4
} | {
"line": 386,
"column": 80
} | {
"line": 388,
"column": 0
} | [
{
"pp": "case succ.a\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : ∀ x ∈ f.support ∩ g.support, f x = g x\nk : ℕ\nhk : ∀ x ∈ f.support ∩ g.support, (f ^ k) x = (g ^ k) x\nx : α\nhx : x ∈ f.support ∩ g.support\n⊢ g x ∈ f.support ∩ g.support",
"ppTerm": "?succ.a",
"assigned":... | [] | rwa [mem_inter, apply_mem_support, ← h _ hx, apply_mem_support, ← mem_inter] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.GroupTheory.Perm.Finite | {
"line": 50,
"column": 4
} | {
"line": 50,
"column": 38
} | {
"line": 51,
"column": 2
} | [
{
"pp": "case pos\nα : Type u\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ τ : Perm α\nf : { x // x ∈ ↑σ.support } ≃ { x // x ∈ ↑τ.support }\nhf : ∀ (x : α) (hx : x ∈ ↑σ.support), ↑(f ⟨σ x, ⋯⟩) = τ ↑(f ⟨x, hx⟩)\nx : α\nhx : x ∈ σ.support\n⊢ ↑(f ⟨σ x, ?pos.hx✝⟩) = τ ↑(f ⟨x, ?pos.hx✝¹⟩)",
"ppTerm": "?pos✝",
... | [] | · exact hf x (Finset.mem_coe.2 hx) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.Perm.List | {
"line": 201,
"column": 8
} | {
"line": 201,
"column": 25
} | {
"line": 201,
"column": 26
} | [
{
"pp": "case a\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\nh' : ∀ (x : α), l ≠ [x]\nn : ℕ\nhn : n < l.length\nhx : l[n] ∈ l\n⊢ l[n] ∈ {x | l.formPerm x ≠ x}",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
... | [
"case a\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\nh' : ∀ (x : α), l ≠ [x]\nn : ℕ\nhn : n < l.length\nhx : l[n] ∈ l\n⊢ l.formPerm l[n] ≠ l[n]"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.List | {
"line": 276,
"column": 10
} | {
"line": 276,
"column": 27
} | {
"line": 276,
"column": 28
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\n⊢ x' ∈ {z | (x :: y :: l).formPerm z ≠ z}",
"ppTerm": "?m.58",
"assigned": true,
"usedConst... | [
"α : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\n⊢ (x :: y :: l).formPerm x' ≠ x'"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.List | {
"line": 311,
"column": 4
} | {
"line": 311,
"column": 53
} | {
"line": 312,
"column": 2
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nk : ℕ\nhk : k < l.length\nhx : l[k] ∈ l\nhn : l.length = 0\n⊢ (k + 1) % 0 = k ↔ 0 ≤ 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.zero_le",
"Nat.instMod",
"instHMod",
"Eq.le"... | [] | exact absurd k.zero_le (hk.trans_le hn.le).not_ge | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.Perm.List | {
"line": 311,
"column": 4
} | {
"line": 311,
"column": 53
} | {
"line": 312,
"column": 2
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nk : ℕ\nhk : k < l.length\nhx : l[k] ∈ l\nhn : l.length = 0\n⊢ (k + 1) % 0 = k ↔ 0 ≤ 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.zero_le",
"Nat.instMod",
"instHMod",
"Eq.le"... | [] | exact absurd k.zero_le (hk.trans_le hn.le).not_ge | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.List | {
"line": 311,
"column": 4
} | {
"line": 311,
"column": 53
} | {
"line": 312,
"column": 2
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nk : ℕ\nhk : k < l.length\nhx : l[k] ∈ l\nhn : l.length = 0\n⊢ (k + 1) % 0 = k ↔ 0 ≤ 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.zero_le",
"Nat.instMod",
"instHMod",
"Eq.le"... | [] | exact absurd k.zero_le (hk.trans_le hn.le).not_ge | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Closure | {
"line": 92,
"column": 6
} | {
"line": 92,
"column": 17
} | {
"line": 92,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nh1 : σ.IsCycle\nh2 : σ.support = univ\nx : α\nH : Subgroup (Perm α) := closure {σ, swap x (σ x)}\nh3 : σ ∈ H\nh4 : swap x (σ x) ∈ H\nstep1 : ∀ (n : ℕ), swap ((σ ^ n) x) ((σ ^ (n + 1)) x) ∈ H\nstep2 : ∀ (n : ℕ), swap x ((σ ^ n) x) ∈ H\... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nh1 : σ.IsCycle\nh2 : σ.support = univ\nx : α\nH : Subgroup (Perm α) := closure {σ, swap x (σ x)}\nh3 : σ ∈ H\nh4 : swap x (σ x) ∈ H\nstep1 : ∀ (n : ℕ), swap ((σ ^ n) x) ((σ ^ (n + 1)) x) ∈ H\nstep2 : ∀ (n : ℕ), swap x ((σ ^ n) x) ∈ H\nstep3 : ∀ (... | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 42
} | {
"line": 266,
"column": 48
} | {
"line": 266,
"column": 48
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 0 < 2",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 42
} | {
"line": 266,
"column": 48
} | {
"line": 266,
"column": 48
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 0 < 2",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 42
} | {
"line": 266,
"column": 48
} | {
"line": 266,
"column": 48
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 0 < 2",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 86
} | {
"line": 266,
"column": 92
} | {
"line": 266,
"column": 92
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 1 < 2",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 86
} | {
"line": 266,
"column": 92
} | {
"line": 266,
"column": 92
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 1 < 2",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Sign | {
"line": 266,
"column": 86
} | {
"line": 266,
"column": 92
} | {
"line": 266,
"column": 92
} | [
{
"pp": "α : Type u\ninst✝ : DecidableEq α\nβ : Type v\nn : ℕ\nhn : 2 ≤ n\n⊢ 1 < 2",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Closure | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 17
} | {
"line": 106,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nσ : Perm α\nh0 : n.Coprime (orderOf σ)\nh1 : σ.IsCycle\nh2 : σ.support = univ\nx : α\nm : ℕ\nhm : (σ ^ n) ^ m = σ\nh2' : (σ ^ n).support = univ\nh1' : (σ ^ n).IsCycle\n⊢ closure {σ, swap x ((σ ^ n) x)} = ⊤",
"ppTerm": "?m.140",
"as... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nσ : Perm α\nh0 : n.Coprime (orderOf σ)\nh1 : σ.IsCycle\nh2 : σ.support = univ\nx : α\nm : ℕ\nhm : (σ ^ n) ^ m = σ\nh2' : (σ ^ n).support = univ\nh1' : (σ ^ n).IsCycle\n⊢ ⊤ ≤ closure {σ, swap x ((σ ^ n) x)}"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.Finite | {
"line": 231,
"column": 10
} | {
"line": 231,
"column": 46
} | {
"line": 233,
"column": 0
} | [
{
"pp": "case neg\nα : Type u\ninst✝ : DecidableEq α\ng : Perm α\nu : Perm ↑(fixedPoints ⇑g)\nx : α\nhx : x ∉ fixedPoints ⇑g\n⊢ (ofSubtype u) x = x",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"MonoidHom",... | [] | rw [ofSubtype_apply_of_not_mem u hx] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 750,
"column": 4
} | {
"line": 750,
"column": 51
} | {
"line": 751,
"column": 4
} | [
{
"pp": "case inr\nα : Type u_2\nf : Perm α\na : α\ns : Finset α\nhf : f.IsCycleOn ↑s\nha : a ∈ s\nn : ℕ\nhs : s.Nontrivial\n⊢ (f ^ n) a = a ↔ #s ∣ n",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Finset",
"Equiv.Perm.IsCycleOn.apply_ne",
"Me... | [
"case inr\nα : Type u_2\nf : Perm α\na : α\ns : Finset α\nhf : f.IsCycleOn ↑s\nha : a ∈ s\nn : ℕ\nhs : s.Nontrivial\nh : ∀ (x : ↥s), ¬f ↑x = ↑x\n⊢ (f ^ n) a = a ↔ #s ∣ n"
] | have h (x : s) : ¬f x = x := hf.apply_ne hs x.2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 839,
"column": 2
} | {
"line": 839,
"column": 57
} | {
"line": 840,
"column": 2
} | [
{
"pp": "α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\na : α\nha : a ∈ {a | a ∈ l}\nb : α\nhb : b ∈ {a | a ∈ l}\n⊢ l.formPerm.SameCycle a b",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"instLawfulBEq",
"congrArg",
"setOf",
"Membership.mem",
... | [
"α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\na : α\nha : idxOf a l < l.length\nb : α\nhb : idxOf b l < l.length\n⊢ l.formPerm.SameCycle a b"
] | rw [Set.mem_setOf, ← List.idxOf_lt_length_iff] at ha hb | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.Perm.Sign | {
"line": 484,
"column": 16
} | {
"line": 484,
"column": 35
} | {
"line": 485,
"column": 16
} | [
{
"pp": "α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nf : Perm α\ng : Perm β\ni : (x : α) → f x ≠ x → β\nh : ∀ (x : α) (hx : f x ≠ x) (hx' : f (f x) ≠ f x), i (f x) hx' = g (i x hx)\nhi : ∀ (x₁ x₂ : α) (hx₁ : f x₁ ≠ x₁) (hx₂ : f x₂ ≠ x₂), i x₁ hx... | [
"α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nf : Perm α\ng : Perm β\ni : (x : α) → f x ≠ x → β\nh : ∀ (x : α) (hx : f x ≠ x) (hx' : f (f x) ≠ f x), i (f x) hx' = g (i x hx)\nhi : ∀ (x₁ x₂ : α) (hx₁ : f x₁ ≠ x₁) (hx₂ : f x₂ ≠ x₂), i x₁ hx₁ = i x₂ hx₂... | rw [← h _ x.2 this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 1030,
"column": 11
} | {
"line": 1030,
"column": 27
} | {
"line": 1030,
"column": 28
} | [
{
"pp": "α : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng c : Perm α\nhc : c.IsCycle\n⊢ Commute g c ↔ ∃ (hc' : ∀ (x : α), g x ∈ c.support ↔ x ∈ c.support), ofSubtype (g.subtypePerm hc') ∈ Subgroup.zpowers c",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Eq... | [
"α : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng c : Perm α\nhc : c.IsCycle\n⊢ (∃ (hc' : ∀ (x : α), g x ∈ c.support ↔ x ∈ c.support), g.subtypePerm hc' ∈ Subgroup.zpowers c.subtypePermOfSupport) ↔\n ∃ (hc' : ∀ (x : α), g x ∈ c.support ↔ x ∈ c.support), ofSubtype (g.subtypePerm hc') ∈ Subgroup.zpowers ... | hc.commute_iff', | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.GroupTheory.Perm.Sign | {
"line": 531,
"column": 42
} | {
"line": 532,
"column": 82
} | {
"line": 532,
"column": 82
} | [
{
"pp": "α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\na : α\nσ : Perm β\nx✝¹ x✝ : α × β\na₁ : α\nb₁ : β\nhab₁ : (prodExtendRight a σ) (a₁, b₁) ≠ (a₁, b₁)\na₂ : α\nb₂ : β\nhab₂ : (prodExtendRight a σ) (a₂, b₂) ≠ (a₂, b₂)\nh : (a₁, b₁).2 = (a₂, b₂)... | [] | by
simpa [eq_of_prodExtendRight_ne hab₁, eq_of_prodExtendRight_ne hab₂] using h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.NoncommPiCoprod | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 6
} | {
"line": 277,
"column": 2
} | [
{
"pp": "case h\nG : Type u_1\ninst✝³ : Group G\nι : Type u_2\nH : ι → Type u_3\ninst✝² : (i : ι) → Group (H i)\nϕ : (i : ι) → H i →* G\nhcomm : Pairwise fun i j ↦ ∀ (x : H i) (y : H j), Commute ((ϕ i) x) ((ϕ j) y)\ninst✝¹ : Finite ι\ninst✝ : (i : ι) → Fintype (H i)\nhcoprime : Pairwise fun i j ↦ (Fintype.card ... | [
"case h\nG : Type u_1\ninst✝³ : Group G\nι : Type u_2\nH : ι → Type u_3\ninst✝² : (i : ι) → Group (H i)\nϕ : (i : ι) → H i →* G\nhcomm : Pairwise fun i j ↦ ∀ (x : H i) (y : H j), Commute ((ϕ i) x) ((ϕ j) y)\ninst✝¹ : Finite ι\ninst✝ : (i : ι) → Fintype (H i)\nhcoprime : Pairwise fun i j ↦ (Fintype.card (H i)).Copri... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.GroupTheory.Perm.Fin | {
"line": 173,
"column": 2
} | {
"line": 182,
"column": 40
} | {
"line": 184,
"column": 0
} | [
{
"pp": "n : ℕ\ni j : Fin n\nh : i ≤ j\n⊢ ↑(j.cycleRange i) = if i = j then 0 else ↑i + 1",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Trans.trans",
"le_rfl",
"Equiv.instEquivLike",
"congrArg",
"instDecidableEqF... | [] | rcases n with - | n
· exact absurd le_rfl j.pos.not_ge
rw [cycleRange_of_le h]
split_ifs with h'
· rfl
exact
val_add_one_of_lt
(calc
(i : ℕ) < j := Fin.lt_def.mp (lt_of_le_of_ne h h')
_ ≤ n := Nat.lt_succ_iff.mp j.2) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Fin | {
"line": 173,
"column": 2
} | {
"line": 182,
"column": 40
} | {
"line": 184,
"column": 0
} | [
{
"pp": "n : ℕ\ni j : Fin n\nh : i ≤ j\n⊢ ↑(j.cycleRange i) = if i = j then 0 else ↑i + 1",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Trans.trans",
"le_rfl",
"Equiv.instEquivLike",
"congrArg",
"instDecidableEqF... | [] | rcases n with - | n
· exact absurd le_rfl j.pos.not_ge
rw [cycleRange_of_le h]
split_ifs with h'
· rfl
exact
val_add_one_of_lt
(calc
(i : ℕ) < j := Fin.lt_def.mp (lt_of_le_of_ne h h')
_ ≤ n := Nat.lt_succ_iff.mp j.2) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Fin | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 74
} | {
"line": 204,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ninst✝ : NeZero n\ni j : Fin n\nh₁ : ¬j < i\nh₂ : ¬j = i\n⊢ i.cycleRange j = j",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"le_of_not_gt",
"Ne.symm",
"Fin.instLinearOrder",
"Fin.instPartialOrder",
"Fin.cycleRange_of_gt",
"Fin... | [] | exact cycleRange_of_gt (lt_of_le_of_ne (le_of_not_gt h₁) (Ne.symm h₂)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.Perm.Fin | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 74
} | {
"line": 204,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ninst✝ : NeZero n\ni j : Fin n\nh₁ : ¬j < i\nh₂ : ¬j = i\n⊢ i.cycleRange j = j",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"le_of_not_gt",
"Ne.symm",
"Fin.instLinearOrder",
"Fin.instPartialOrder",
"Fin.cycleRange_of_gt",
"Fin... | [] | exact cycleRange_of_gt (lt_of_le_of_ne (le_of_not_gt h₁) (Ne.symm h₂)) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Fin | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 74
} | {
"line": 204,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ninst✝ : NeZero n\ni j : Fin n\nh₁ : ¬j < i\nh₂ : ¬j = i\n⊢ i.cycleRange j = j",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"le_of_not_gt",
"Ne.symm",
"Fin.instLinearOrder",
"Fin.instPartialOrder",
"Fin.cycleRange_of_gt",
"Fin... | [] | exact cycleRange_of_gt (lt_of_le_of_ne (le_of_not_gt h₁) (Ne.symm h₂)) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Fin | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 14
} | {
"line": 356,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ni j k : Fin n\nh : k < i\nhij : ¬i ≤ j\n⊢ (i.cycleIcc j) k = k",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"eq_false",
"congrArg",
"LE.le",
"instLEFin",
"Equi... | [] | · simp [hij] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.Perm.Fin | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 14
} | {
"line": 378,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ni j k : Fin n\nh : j < k\nhij : ¬i ≤ j\n⊢ (i.cycleIcc j) k = k",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"eq_false",
"congrArg",
"LE.le",
"instLEFin",
"Equi... | [] | · simp [hij] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.Perm.Fin | {
"line": 419,
"column": 2
} | {
"line": 419,
"column": 14
} | {
"line": 420,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni j : Fin n\nhij✝ : i ≤ j\ninst✝ : NeZero n\nhij : i < j\n⊢ j.cycleIcc i = 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Equiv.Perm.instOne",
"congrArg",
"Fin.cycleIcc_def_gt",
"Equiv.Perm",
"True",
"eq_self",
"of_eq_t... | [
"case inr\nn : ℕ\ni j : Fin n\nhij✝ : i ≤ j\ninst✝ : NeZero n\nhij : i = j\n⊢ j.cycleIcc i = 1"
] | · simp [hij] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 451,
"column": 4
} | {
"line": 458,
"column": 58
} | {
"line": 460,
"column": 0
} | [
{
"pp": "α : Type u_4\ninst✝ : Finite α\nl₁ l₂ : List (Perm α)\nh₀ : l₁.prod = l₂.prod\nh₁l₁ : ∀ σ ∈ l₁, σ.IsCycle\nh₁l₂ : ∀ σ ∈ l₂, σ.IsCycle\nh₂l₁ : List.Pairwise Disjoint l₁\nh₂l₂ : List.Pairwise Disjoint l₂\n⊢ l₁ ~ l₂",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [] | refine
(List.perm_ext_iff_of_nodup (nodup_of_pairwise_disjoint_cycles h₁l₁ h₂l₁)
(nodup_of_pairwise_disjoint_cycles h₁l₂ h₂l₂)).mpr
fun σ => ?_
by_cases hσ : σ.IsCycle
· obtain _ := not_forall.mp (mt ext hσ.ne_one)
rw [mem_list_cycles_iff h₁l₁ h₂l₁, mem_list_cycles_iff h₁l₂ h₂l₂,... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 451,
"column": 4
} | {
"line": 458,
"column": 58
} | {
"line": 460,
"column": 0
} | [
{
"pp": "α : Type u_4\ninst✝ : Finite α\nl₁ l₂ : List (Perm α)\nh₀ : l₁.prod = l₂.prod\nh₁l₁ : ∀ σ ∈ l₁, σ.IsCycle\nh₁l₂ : ∀ σ ∈ l₂, σ.IsCycle\nh₂l₁ : List.Pairwise Disjoint l₁\nh₂l₂ : List.Pairwise Disjoint l₂\n⊢ l₁ ~ l₂",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [] | refine
(List.perm_ext_iff_of_nodup (nodup_of_pairwise_disjoint_cycles h₁l₁ h₂l₁)
(nodup_of_pairwise_disjoint_cycles h₁l₂ h₂l₂)).mpr
fun σ => ?_
by_cases hσ : σ.IsCycle
· obtain _ := not_forall.mp (mt ext hσ.ne_one)
rw [mem_list_cycles_iff h₁l₁ h₂l₁, mem_list_cycles_iff h₁l₂ h₂l₂,... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 504,
"column": 4
} | {
"line": 504,
"column": 23
} | {
"line": 505,
"column": 4
} | [
{
"pp": "case mpr\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nl : List (Perm α)\nhn : l.Nodup\nl' : List (Perm α)\nhp' : l'.prod = σ\nhc' : ∀ g ∈ l', g.IsCycle\nhd' : List.Pairwise Disjoint l'\nhl : Trunc.mk ⟨l', ⋯⟩ = σ.truncCycleFactors\nht : σ.cycleFactorsFinset = l'.toFinset\n⊢ (∀ f... | [
"case mpr\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nl : List (Perm α)\nhn : l.Nodup\nl' : List (Perm α)\nhp' : l'.prod = σ\nhc' : ∀ g ∈ l', g.IsCycle\nhd' : List.Pairwise Disjoint l'\nhl : Trunc.mk ⟨l', ⋯⟩ = σ.truncCycleFactors\nht : σ.cycleFactorsFinset = l'.toFinset\nhc : ∀ f ∈ l, f.Is... | rintro ⟨hc, hd, hp⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 22
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g1 : Perm α\nh1 h2 : g1 ∈ f.cycleFactorsFinset\n⊢ Commute g1 g1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Commute.refl",
"Equiv.Perm",
"Equiv.Perm.instMul"
],
"usedFVars": [
... | [] | apply Commute.refl | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 22
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g1 : Perm α\nh1 h2 : g1 ∈ f.cycleFactorsFinset\n⊢ Commute g1 g1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Commute.refl",
"Equiv.Perm",
"Equiv.Perm.instMul"
],
"usedFVars": [
... | [] | apply Commute.refl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 22
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g1 : Perm α\nh1 h2 : g1 ∈ f.cycleFactorsFinset\n⊢ Commute g1 g1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Commute.refl",
"Equiv.Perm",
"Equiv.Perm.instMul"
],
"usedFVars": [
... | [] | apply Commute.refl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 166,
"column": 24
} | {
"line": 166,
"column": 52
} | {
"line": 167,
"column": 2
} | [
{
"pp": "case base_cycles\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : σ.IsCycle\n⊢ sign σ = (Multiset.map (fun n ↦ -(-1) ^ n) σ.cycleType).prod",
"ppTerm": "?base_cycles",
"assigned": true,
"usedConstants": [
"Int.instCommMonoid",
"Equiv.Perm.support",
... | [] | simp [hσ.cycleType, hσ.sign] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 166,
"column": 24
} | {
"line": 166,
"column": 52
} | {
"line": 167,
"column": 2
} | [
{
"pp": "case base_cycles\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : σ.IsCycle\n⊢ sign σ = (Multiset.map (fun n ↦ -(-1) ^ n) σ.cycleType).prod",
"ppTerm": "?base_cycles",
"assigned": true,
"usedConstants": [
"Int.instCommMonoid",
"Equiv.Perm.support",
... | [] | simp [hσ.cycleType, hσ.sign] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 166,
"column": 24
} | {
"line": 166,
"column": 52
} | {
"line": 167,
"column": 2
} | [
{
"pp": "case base_cycles\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : σ.IsCycle\n⊢ sign σ = (Multiset.map (fun n ↦ -(-1) ^ n) σ.cycleType).prod",
"ppTerm": "?base_cycles",
"assigned": true,
"usedConstants": [
"Int.instCommMonoid",
"Equiv.Perm.support",
... | [] | simp [hσ.cycleType, hσ.sign] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 210,
"column": 4
} | {
"line": 212,
"column": 19
} | {
"line": 213,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : Nat.Prime (orderOf σ)\n⊢ σ.cycleType.card = σ.cycleType.card - 1 + 1",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.to... | [] | rw [tsub_add_cancel_of_le]
rw [Nat.succ_le_iff, card_cycleType_pos, Ne, ← orderOf_eq_one_iff]
exact hσ.ne_one | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 210,
"column": 4
} | {
"line": 212,
"column": 19
} | {
"line": 213,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : Nat.Prime (orderOf σ)\n⊢ σ.cycleType.card = σ.cycleType.card - 1 + 1",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.to... | [] | rw [tsub_add_cancel_of_le]
rw [Nat.succ_le_iff, card_cycleType_pos, Ne, ← orderOf_eq_one_iff]
exact hσ.ne_one | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 52
} | {
"line": 630,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ f.cycleFactorsFinset = ∅ ↔ f = 1",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"False",
"Finset.coe_empty",
"Equiv.Perm.instOne",
"Function.onFun"... | [] | simpa [cycleFactorsFinset_eq_finset] using eq_comm | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 52
} | {
"line": 630,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ f.cycleFactorsFinset = ∅ ↔ f = 1",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"False",
"Finset.coe_empty",
"Equiv.Perm.instOne",
"Function.onFun"... | [] | simpa [cycleFactorsFinset_eq_finset] using eq_comm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 52
} | {
"line": 630,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ f.cycleFactorsFinset = ∅ ↔ f = 1",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"False",
"Finset.coe_empty",
"Equiv.Perm.instOne",
"Function.onFun"... | [] | simpa [cycleFactorsFinset_eq_finset] using eq_comm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 516,
"column": 50
} | {
"line": 516,
"column": 85
} | {
"line": 517,
"column": 2
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Group G\ninst✝ : Fintype G\np : ℕ\nhp : Fact (Nat.Prime p)\nhdvd : p ∣ Fintype.card G\nhp' : p - 1 ≠ 0\nScard : p ∣ Fintype.card ↑(vectorsProdEqOne G p)\nf : ℕ → ↑(vectorsProdEqOne G p) → ↑(vectorsProdEqOne G p) := fun k v ↦ VectorsProdEqOne.rotate v k\nhf1 : ∀ (v : ↑(vectorsProd... | [] | by rw [pow_one, hσ, hf3, one_apply] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 559,
"column": 6
} | {
"line": 559,
"column": 17
} | {
"line": 559,
"column": 18
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nH : Subgroup (Perm α)\nd : DecidablePred fun x ↦ x ∈ H\nτ : Perm α\nh0 : Nat.Prime (Fintype.card α)\nh1 : Fintype.card α ∣ Fintype.card ↥H\nh2 : τ ∈ H\nh3 : τ.IsSwap\nthis : Fact (Nat.Prime (Fintype.card α))\nσ : ↥H\nhσ : orderOf σ = Fintype.card... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nH : Subgroup (Perm α)\nd : DecidablePred fun x ↦ x ∈ H\nτ : Perm α\nh0 : Nat.Prime (Fintype.card α)\nh1 : Fintype.card α ∣ Fintype.card ↥H\nh2 : τ ∈ H\nh3 : τ.IsSwap\nthis : Fact (Nat.Prime (Fintype.card α))\nσ : ↥H\nhσ : orderOf σ = Fintype.card α\nhσ1 : or... | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 586,
"column": 2
} | {
"line": 586,
"column": 8
} | {
"line": 588,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\na : ℕ\nh : a ∈ Multiset.replicate (Fintype.card α - #σ.support) 1\n⊢ ¬2 ≤ 1",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 698,
"column": 4
} | {
"line": 698,
"column": 8
} | {
"line": 699,
"column": 4
} | [
{
"pp": "case mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : a ∈ g.support\n⊢ g.support = {a, g a, g (g a)}",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Equiv.Perm.support",
"Equiv.instEquivLike",
"Finset",
... | [
"case mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : a ∈ g.support\n⊢ {a, g a, g (g a)} = g.support"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 10
} | {
"line": 60,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nd : n → R\nσ : Perm n\nhσ : σ = 1\n⊢ ¬1 = -1",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Comm... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 302,
"column": 4
} | {
"line": 302,
"column": 59
} | {
"line": 303,
"column": 2
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 302,
"column": 4
} | {
"line": 302,
"column": 59
} | {
"line": 303,
"column": 2
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 302,
"column": 4
} | {
"line": 302,
"column": 59
} | {
"line": 303,
"column": 2
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 59
} | {
"line": 306,
"column": 0
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 59
} | {
"line": 306,
"column": 0
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 59
} | {
"line": 306,
"column": 0
} | [
{
"pp": "R : Type uR\nS : Type uS\nι : Type uι\nn✝ : ℕ\nM : Fin n✝.succ → Type v\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₁'' : ι → Type v₁''\nM₂ : Type v₂\nM₃ : Type v₃\nM₄ : Type v₄\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin n✝.succ) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ni... | [] | simp [dite_comp_equiv_update (s.orderIsoOfFin hk).symm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 443,
"column": 12
} | {
"line": 443,
"column": 15
} | {
"line": 443,
"column": 16
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : Semiring R\ninst✝⁴ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : DecidableEq ι\nm : (i : ι) → M₁ i\nt✝ : Finset ι\ni : ι\nt : F... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : Semiring R\ninst✝⁴ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : DecidableEq ι\nm : (i : ι) → M₁ i\nt✝ : Finset ι\ni : ι\nt : Finset ι\nhit... | hit | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 504,
"column": 4
} | {
"line": 513,
"column": 83
} | {
"line": 514,
"column": 4
} | [
{
"pp": "case pos\nR : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : Decidab... | [
"case pos\nR : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : DecidableEq ι\ninst... | have :
∀ r : ∀ i, α i, r ∈ piFinset A → (f fun i => g i (r i)) = f fun i => ∑ j ∈ A i, g i j := by
intro r hr
congr with i
have : ∀ j ∈ A i, g i j = g i (r i) := by
intro j hj
congr
apply Finset.card_le_one_iff.1 (Ai_singleton i) hj
exact mem_piFinset.mp hr i
... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 882,
"column": 2
} | {
"line": 882,
"column": 43
} | {
"line": 884,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁸ : Semiring R\nM : Type u_2\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nN' : Type u_6\ninst✝⁵ : AddCommGroup N'\ninst✝⁴ : Module R N'\nι : Type u_7\nN'₂ : Type u_10\ninst✝³ : AddCommGroup N'₂\ninst✝² : Module R N'₂\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\ng : N' →ₗ[R] N'₂\nf ... | [] | simp [MultilinearMap.alternatization_def] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 902,
"column": 2
} | {
"line": 904,
"column": 44
} | {
"line": 906,
"column": 0
} | [
{
"pp": "case neg\nι : Type u_7\nι₁ : Type u_10\ninst✝⁵ : Finite ι\nR' : Type u_11\nN₁ : Type u_12\nN₂ : Type u_13\ninst✝⁴ : CommSemiring R'\ninst✝³ : AddCommMonoid N₁\ninst✝² : AddCommMonoid N₂\ninst✝¹ : Module R' N₁\ninst✝ : Module R' N₂\nf g : N₁ [⋀^ι]→ₗ[R'] N₂\ne : Basis ι₁ R' N₁\nh : ∀ (v : ι → ι₁), Functi... | [] | · have : ¬Function.Injective fun i => e (v i) := hi.imp Function.Injective.of_comp
rw [coe_multilinearMap, coe_multilinearMap, f.map_eq_zero_of_not_injective _ this,
g.map_eq_zero_of_not_injective _ this] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 547,
"column": 8
} | {
"line": 547,
"column": 12
} | {
"line": 548,
"column": 8
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : DecidableEq ι\nin... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : DecidableEq ι\ninst✝ : Fintyp... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 265,
"column": 6
} | {
"line": 265,
"column": 49
} | {
"line": 266,
"column": 6
} | [
{
"pp": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : ColimitType F\n⊢ descFun F s (x + y) = descFun F s x + descFun F s y",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"... | [
"J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : ColimitType F\na b : Prequotient F\n⊢ descFun F s (Quot.mk (⇑(colimitSetoid F)) a + Quot.mk (⇑(colimitSetoid F)) b) =\n descFun F s (Quot.mk (⇑(colimitSetoid F)) a) + descFun F s (Quot.mk (⇑(colimitSetoid F)) b)"
] | refine Quot.induction_on₂ x y fun a b => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 11
} | {
"line": 225,
"column": 17
} | {
"line": 225,
"column": 17
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ 1 ≠ -1",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 11
} | {
"line": 225,
"column": 17
} | {
"line": 225,
"column": 17
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ 1 ≠ -1",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 11
} | {
"line": 225,
"column": 17
} | {
"line": 225,
"column": 17
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ 1 ≠ -1",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 31
} | {
"line": 225,
"column": 37
} | {
"line": 225,
"column": 37
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ -1 ≠ 1",
"ppTerm": "?m.88",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 31
} | {
"line": 225,
"column": 37
} | {
"line": 225,
"column": 37
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ -1 ≠ 1",
"ppTerm": "?m.88",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 225,
"column": 31
} | {
"line": 225,
"column": 37
} | {
"line": 225,
"column": 37
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A * detp t B)\n⊢ -1 ≠ 1",
"ppTerm": "?m.88",
"assigned": true,
"usedConstants": [
"instD... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 242,
"column": 11
} | {
"line": 242,
"column": 17
} | {
"line": 242,
"column": 17
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA B : Matrix n n R\nd : n → R\nhAB : A * B = diagonal d\nh : ∀ {s t : ℤˣ}, s ≠ t → IsAddUnit (detp s A • (B * adjp t B))\n⊢ 1 ≠ -1",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants": [
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
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