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.NumberTheory.Padics.PadicNumbers | {
"line": 312,
"column": 2
} | {
"line": 312,
"column": 17
} | [
{
"pp": "case h\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : ¬f ≈ 0\nH : ↑f (stationaryPoint hf) = 0\nε : ℚ\nhε : ε > 0\nn : ℕ\nhn : n ≥ stationaryPoint hf\n⊢ padicNorm p (↑f (stationaryPoint hf)) < ε",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Rat.instOfNat",
"Eq.mpr"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 390,
"column": 2
} | {
"line": 390,
"column": 18
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : PadicSeq p\nha : ¬a ≈ 0\nk : ℚ\nhk : a.norm = padicNorm p k\nhk' : k ≠ 0\n⊢ ∃ z, a.norm = ↑p ^ (-z)",
"usedConstants": [
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"Rat",
"DivI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 453,
"column": 38
} | {
"line": 453,
"column": 87
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfg : ¬f + g ≈ 0\nhf : (f - 0).LimZero\n⊢ LimZero (f + g - g)",
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"CauSeq.addGroup",
"Eq.mpr",
"NormedRing.toRing",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 462,
"column": 40
} | {
"line": 462,
"column": 88
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfg : ¬f + g ≈ 0\nhf : ¬f ≈ 0\nhg : (g - 0).LimZero\n⊢ LimZero (f + g - f)",
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedRing.toRing",
"congrArg",
"add_su... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 497,
"column": 2
} | {
"line": 497,
"column": 29
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : f + g ≈ 0\nthis✝¹ : (f + g - 0).LimZero\nthis✝ : f ≈ -g\nthis : f.norm = (-g).norm\n⊢ f.norm = g.norm",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.Representability | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | [
{
"pp": "case a\nF : Sheaf zariskiTopology (Type u)\nι : Type u\nX : ι → Scheme\nf : (i : ι) → yoneda.obj (X i) ⟶ F.obj\nhf : ∀ (i : ι), IsOpenImmersion.presheaf (f i)\ni : ι\n⊢ (ConcreteCategory.hom\n ({ hom := yonedaEquiv.symm ((glueData hf).sheafValGluedMk (fun i ↦ yonedaEquiv (f i)) ⋯) }.hom.app (op ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.Representability | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 69
} | [
{
"pp": "case h\nF : Sheaf zariskiTopology (Type u)\nι : Type u\nX : ι → Scheme\nf : (i : ι) → yoneda.obj (X i) ⟶ F.obj\nhf : ∀ (i : ι), IsOpenImmersion.presheaf (f i)\ni✝ j✝ k : ι\nU : Scheme\nα β : U ⟶ (glueData hf).glued\nmem :\n Sieve.ofArrows (glueData hf).openCover.X (glueData hf).openCover.f ∈\n (gro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 195,
"column": 66
} | {
"line": 195,
"column": 77
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y : D\nf : X ⟶ Y\nhf : F.relativelyRepresentable f\na✝ : C\ng : F.obj a✝ ⟶ Y\ninst✝ : F.Faithful\nc : C\na b : c ⟶ hf.pullback g\nh₁ : F.map a ≫ hf.fst g = F.map b ≫ hf.fst g\nh₂ : a ≫ hf.snd g = b ≫ hf.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 205,
"column": 18
} | {
"line": 205,
"column": 40
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nY : D\nb✝ : C\nf' : F.obj b✝ ⟶ Y\nhf' : F.relativelyRepresentable f'\na✝ : C\ng : F.obj a✝ ⟶ Y\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nc : C\na b : c ⟶ hf'.pullback g\nh₁ : a ≫ hf'.fst' g = b ≫ hf'.fst' g\nh₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y : D\nf : X ⟶ Y\nhf : F.relativelyRepresentable f\na : C\ng : F.obj a ⟶ Y\nc : C\ni : F.obj c ⟶ X\nh : c ⟶ a\nhi : i ≫ f = F.map h ≫ g\ninst✝ : F.Full\n⊢ F.map (hf.lift i h hi) ≫ hf.fst g = i",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 222,
"column": 24
} | {
"line": 222,
"column": 42
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y : D\nf : X ⟶ Y\nhf : F.relativelyRepresentable f\na : C\ng : F.obj a ⟶ Y\nc : C\ni : F.obj c ⟶ X\nh : c ⟶ a\nhi : i ≫ f = F.map h ≫ g\ninst✝¹ : F.Full\ninst✝ : F.Faithful\n⊢ F.map (hf.lift i h hi ≫ hf.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 291,
"column": 9
} | {
"line": 291,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF✝ : C ⥤ D\nF G H : D\nf : F ⟶ G\ng : G ⟶ H\nhf : F✝.relativelyRepresentable f\nhg : F✝.relativelyRepresentable g\nX : C\nh : F✝.obj X ⟶ H\n⊢ IsPullback (hf.fst (hg.fst h)) (F✝.map (hf.snd (hg.fst h) ≫ hg.snd h)) (f ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 296,
"column": 70
} | {
"line": 296,
"column": 81
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF : C ⥤ D\nX Y Y' X' : D\nf : X ⟶ X'\ng : Y ⟶ X'\nf' : Y' ⟶ Y\ng' : Y' ⟶ X\nP₁ : IsPullback f' g' g f\nhg : F.relativelyRepresentable g\na : C\nh : F.obj a ⟶ X\n⊢ hg.fst (h ≫ f) ≫ g = (F.map (hg.snd (h ≫ f)) ≫ h) ≫ f",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 403,
"column": 42
} | {
"line": 403,
"column": 53
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nF✝ : C ⥤ D\nX✝ Y : D\nP : MorphismProperty C\ninst✝² : F✝.Faithful\ninst✝¹ : F✝.Full\ninst✝ : P.IsStableUnderComposition\nF G H : D\nf : F ⟶ G\ng : G ⟶ H\nhf : relative F✝ P f\nhg : relative F✝ P g\nZ X : C\np : F✝.ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 417,
"column": 30
} | {
"line": 417,
"column": 41
} | [
{
"pp": "C : Type u₁\ninst✝⁵ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁴ : Category.{v₂, u₂} D\nF : C ⥤ D\nX✝ Y✝ : D\nP : MorphismProperty C\ninst✝³ : F.Faithful\ninst✝² : F.Full\ninst✝¹ : P.IsMultiplicative\ninst✝ : P.RespectsIso\nX : D\nY : C\ng : F.obj Y ⟶ X\n⊢ IsPullback g (F.map (𝟙 Y)) (𝟙 X) g",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 434,
"column": 4
} | {
"line": 434,
"column": 15
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nF G : Cᵒᵖ ⥤ Type v₁\nf : F ⟶ G\nhf : (monomorphisms C).presheaf f\nX : C\na b : yoneda.obj X ⟶ F\nh : a ≫ f = b ≫ f\nthis : ⋯.lift a (𝟙 X) ⋯ = ⋯.lift b (𝟙 X) ⋯\n⊢ a = b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Faces | {
"line": 62,
"column": 49
} | {
"line": 62,
"column": 79
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY : C\nn q : ℕ\nφ : Y ⟶ X _⦋n + 1⦌\nv : HigherFacesVanish (q + 1) φ\nj : Fin (n + 1)\nhj : n + 1 ≤ ↑j + q\n⊢ n + 1 ≤ ↑j + (q + 1)",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.AlgebraicTopolo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 780,
"column": 18
} | {
"line": 780,
"column": 36
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx y z : ℚ_[p]\n⊢ dist x z ≤ max (dist x y) (dist y z)",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Lattice.toSemilatticeSup",
"padicNormE",
"congrArg",
"Real.instRatCast",
"Rat",
"PartialOrder.toPreor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 815,
"column": 44
} | {
"line": 815,
"column": 55
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nq : ℚ_[p]\nε : ℝ\nhε : 0 < ε\nε' : ℚ\nhε'l : 0 < ↑ε'\nhε'r : ↑ε' < ε\n⊢ 0 < ε'",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 816,
"column": 19
} | {
"line": 816,
"column": 42
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nq : ℚ_[p]\nε : ℝ\nhε : 0 < ε\nε' : ℚ\nhε'l : 0 < ↑ε'\nhε'r : ↑ε' < ε\nr : ℚ\nhr : padicNormE (q - ↑r) < ε'\n⊢ ‖q - ↑r‖ < ↑ε'",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real",
"Preorder.toLT",
"padicNormE",
"DivisionRing.toRatC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Projections | {
"line": 71,
"column": 2
} | {
"line": 72,
"column": 6
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ P q + Q q = 𝟙 K[X]",
"usedConstants": [
"Eq.mpr",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Q... | rw [Q]
abel | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.DoldKan.Projections | {
"line": 71,
"column": 2
} | {
"line": 72,
"column": 6
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ P q + Q q = 𝟙 K[X]",
"usedConstants": [
"Eq.mpr",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Q... | rw [Q]
abel | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 936,
"column": 30
} | {
"line": 936,
"column": 41
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ\n⊢ ‖↑x‖ ≤ 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 944,
"column": 2
} | {
"line": 944,
"column": 39
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ ‖↑n‖ < 1 ↔ p ∣ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 957,
"column": 2
} | {
"line": 957,
"column": 30
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ ‖↑n‖ = 1 ↔ p.Coprime n",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Nat.Coprime",
"Real",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"Real.inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 982,
"column": 2
} | {
"line": 982,
"column": 35
} | [
{
"pp": "case h\np : ℕ\nhp : Fact (Nat.Prime p)\nz1 z2 : ℚ_[p]\nh : ‖z1 - z2‖ < ‖z1‖\n⊢ ‖z2 - z1‖ < ‖z1‖",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 987,
"column": 2
} | {
"line": 988,
"column": 70
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑(p - 1)‖ = 1",
"usedConstants": [
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"Nat.Coprime",
"Real",
"Nat.Prime",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"id",
"Nat.coprime_self_sub_ri... | rw [norm_natCast_eq_one_iff]
exact (coprime_self_sub_right hp.out.one_le).mpr p.coprime_one_right | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 987,
"column": 2
} | {
"line": 988,
"column": 70
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑(p - 1)‖ = 1",
"usedConstants": [
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"Nat.Coprime",
"Real",
"Nat.Prime",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"id",
"Nat.coprime_self_sub_ri... | rw [norm_natCast_eq_one_iff]
exact (coprime_self_sub_right hp.out.one_le).mpr p.coprime_one_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.DoldKan.PInfty | {
"line": 54,
"column": 4
} | {
"line": 55,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ (fun n ↦ (P n).f n) (n + 1) ≫ K[X].d (n + 1) n = K[X].d (n + 1) n ≫ (fun n ↦ (P n).f n) n",
"usedConstants": [
"Eq.mpr",
"le_refl",
"instHSMul",
"Opposite",
"SimplexCa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1028,
"column": 2
} | {
"line": 1028,
"column": 30
} | [
{
"pp": "case a\np : ℕ\nhp : Fact (Nat.Prime p)\nu : ℕ → ℚ_[p]\nhu : CauchySeq u\nc : CauSeq ℚ_[p] norm := ⟨u, ⋯⟩\n⊢ ∃ a, Tendsto u atTop (nhds a)",
"usedConstants": [
"Filter.instMembership",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"PseudoMetricSpace.toUnif... | refine ⟨c.lim, fun s h ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1060,
"column": 4
} | {
"line": 1060,
"column": 15
} | [
{
"pp": "case h.hf.a\np : ℕ\nhp : Fact (Nat.Prime p)\nf : CauSeq ℚ (padicNorm p)\nhf : f - 0 ≈ 0\n⊢ f ≈ const (padicNorm p) 0",
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"Rat",
"Rat.linearOrder",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1073,
"column": 45
} | {
"line": 1073,
"column": 63
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\n⊢ padicValRat p ↑n = ↑(padicValInt p n)",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"congrArg",
"padicValInt",
"Rat",
"Rat.instIntCast",
"id",
"Int",
"padicValRat",
"Nat.cast",
"padicValRat.of_in... | padicValRat.of_int | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1095,
"column": 4
} | {
"line": 1095,
"column": 35
} | [
{
"pp": "case pos\np : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\nhxy : x + y ≠ 0\nhx : x = 0\n⊢ min x.valuation y.valuation ≤ (x + y).valuation",
"usedConstants": [
"Eq.mpr",
"instAddPadic",
"instZeroPadic",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1097,
"column": 4
} | {
"line": 1097,
"column": 35
} | [
{
"pp": "case pos\np : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\nhxy : x + y ≠ 0\nhx : ¬x = 0\nhy : y = 0\n⊢ min x.valuation y.valuation ≤ (x + y).valuation",
"usedConstants": [
"Eq.mpr",
"instAddPadic",
"instZeroPadic",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Decomposition | {
"line": 70,
"column": 10
} | {
"line": 70,
"column": 17
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn q : ℕ\nhq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev\nhqn : q ≤ n\na : ℕ\nha : q + a = n\n⊢ (Q (q + 1)).f (n + 1) = ∑ i with ↑i < q + 1, (P ↑i).f (n + 1) ≫ X.... | Q_succ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1187,
"column": 4
} | {
"line": 1187,
"column": 15
} | [
{
"pp": "case neg\np : ℕ\nhp : Fact (Nat.Prime p)\nx✝¹ x✝ : ℚ_[p]\nh✝² : ¬x✝¹ + x✝ = 0\nh✝¹ : ¬x✝¹ = 0\nh✝ : ¬x✝ = 0\n⊢ x✝¹.valuation ≤ (x✝¹ + x✝).valuation ∨ x✝.valuation ≤ (x✝¹ + x✝).valuation",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Decomposition | {
"line": 79,
"column": 6
} | {
"line": 81,
"column": 11
} | [
{
"pp": "case neg.e_a.e_s\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn q : ℕ\nhq : (Q q).f (n + 1) = ∑ i with ↑i < q, (P ↑i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev\nhqn : q ≤ n\na : ℕ\nha : q + a = n\nq' : Fin (n + 1) := ⟨q, ⋯⟩\n⊢ {i | ↑i < q + 1}.erase q' = {i... | · ext ⟨i, hi⟩
simp_rw [Finset.mem_erase, Finset.mem_filter_univ, q', ne_eq, Fin.mk.injEq]
lia | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.DoldKan.Faces | {
"line": 187,
"column": 4
} | {
"line": 187,
"column": 69
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY : C\nq a m : ℕ\nφ : Y ⟶ X _⦋m + 1 + 1⦌\nv : HigherFacesVanish q φ\nj : Fin (m + 1 + 1)\nhj₁ : m + 1 + 1 ≤ ↑j + (q + 1)\nhqn : q ≤ m + 1\nha : q + a = m + 1\nhj₂ : ¬a = ↑j\nhaj : a < ↑j\nham : a ≤ m\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.Split | {
"line": 97,
"column": 8
} | {
"line": 97,
"column": 39
} | [
{
"pp": "case len\nC : Type u_1\nD : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Category.{v_2, u_2} D\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\nΔ₁ : SimplexCategory\nα₁ : { α // Epi α }\nΔ₂ : SimplexCategory\nα₂ : { α // Epi α }\nh₁ : Δ₁.len = Δ₂.len ∧ ⇑(Hom.toOrderHom (e ⟨op Δ₁, α₁⟩)) ≍ ⇑(Hom.toOrderHom (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 187,
"column": 4
} | {
"line": 187,
"column": 37
} | [
{
"pp": "case succ\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nT : C\nn : ℕ\nf : X _⦋n + 1⦌ ⟶ T\n⊢ DegeneraciesVanish f ↔ QInfty.f (n + 1) ≫ f = 0",
"usedConstants": [
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruc... | refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence | {
"line": 67,
"column": 6
} | {
"line": 68,
"column": 43
} | [
{
"pp": "case zero\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\n⊢ PInfty.f 0 =\n (((dNext 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) + (prevD 0) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +\n (𝟙 K[X]).f 0",
"usedConstants": [
"AlgebraicT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 49
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nK : ChainComplex C ℕ\nΔ : SimplexCategory\ni : Δ ⟶ Δ\ninst✝ : Mono i\nhi : Isδ₀ i\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence | {
"line": 69,
"column": 6
} | {
"line": 73,
"column": 13
} | [
{
"pp": "case succ\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ PInfty.f (n + 1) =\n (((dNext (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +\n (prevD (n + 1)) fun i j ↦ (homotopyPToId X (j + 1)).hom i j) +\n (𝟙 K[X]).f (n + 1)",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.Normalized | {
"line": 112,
"column": 4
} | {
"line": 114,
"column": 45
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Category.{v_1, u_1} A\ninst✝ : Abelian A\nX✝ X : SimplicialObject A\n⊢ inclusionOfMooreComplexMap X ≫ PInftyToNormalizedMooreComplex X = 𝟙 ((normalizedMooreComplex A).obj X)",
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.ass... | simp only [← cancel_mono (inclusionOfMooreComplexMap X), assoc, id_comp,
PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap,
inclusionOfMooreComplexMap_comp_PInfty] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.DoldKan.Normalized | {
"line": 112,
"column": 4
} | {
"line": 114,
"column": 45
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Category.{v_1, u_1} A\ninst✝ : Abelian A\nX✝ X : SimplicialObject A\n⊢ inclusionOfMooreComplexMap X ≫ PInftyToNormalizedMooreComplex X = 𝟙 ((normalizedMooreComplex A).obj X)",
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.ass... | simp only [← cancel_mono (inclusionOfMooreComplexMap X), assoc, id_comp,
PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap,
inclusionOfMooreComplexMap_comp_PInfty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.DoldKan.Normalized | {
"line": 112,
"column": 4
} | {
"line": 114,
"column": 45
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Category.{v_1, u_1} A\ninst✝ : Abelian A\nX✝ X : SimplicialObject A\n⊢ inclusionOfMooreComplexMap X ≫ PInftyToNormalizedMooreComplex X = 𝟙 ((normalizedMooreComplex A).obj X)",
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.ass... | simp only [← cancel_mono (inclusionOfMooreComplexMap X), assoc, id_comp,
PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap,
inclusionOfMooreComplexMap_comp_PInfty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Idempotents.HomologicalComplex | {
"line": 74,
"column": 6
} | {
"line": 74,
"column": 50
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nι : Type u_2\nc : ComplexShape ι\nP : Karoubi (HomologicalComplex C c)\nn : ι\n⊢ P.p.f n ≫ P.p.f n = P.p.f n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.HomologicalComplex | {
"line": 104,
"column": 8
} | {
"line": 104,
"column": 33
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nι : Type u_2\nc : ComplexShape ι\nK : HomologicalComplex (Karoubi C) c\ni j k : ι\nx✝¹ : c.Rel i j\nx✝ : c.Rel j k\n⊢ (K.d i j).f ≫ (K.d j k).f = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.HomologicalComplex | {
"line": 113,
"column": 33
} | {
"line": 113,
"column": 58
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nι : Type u_2\nc : ComplexShape ι\nK L : HomologicalComplex (Karoubi C) c\nf : K ⟶ L\ni j : ι\nhij : c.Rel i j\n⊢ (f.f i).f ≫ (obj L).X.d i j = (obj K).X.d i j ≫ (f.f j).f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : Karoubi (Karoubi C)\n⊢ P.p.f ≫ P.p.f = P.p.f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP Q : Karoubi (Karoubi C)\nf : P ⟶ Q\n⊢ P.p.f ≫ f.f.f = f.f.f ≫ Q.p.f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi | {
"line": 44,
"column": 29
} | {
"line": 44,
"column": 59
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nP : Karoubi (Karoubi C)\n⊢ P.p.f ≫ P.p.f = P.p.f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi | {
"line": 45,
"column": 22
} | {
"line": 45,
"column": 52
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nX✝ Y✝ : Karoubi (Karoubi C)\nf : X✝ ⟶ Y✝\n⊢ { X := X✝.X.X, p := X✝.p.f, idem := ⋯ }.p ≫ f.f.f ≫ { X := Y✝.X.X, p := Y✝.p.f, idem := ⋯ }.p = f.f.f",
"usedConstants": [
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.Idempotents.Kar... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | {
"line": 276,
"column": 2
} | {
"line": 278,
"column": 37
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\nK : ChainComplex C ℕ\ninst✝¹ : HasFiniteCoproducts C\nΔ Δ' : SimplexCategory\ne : Δ' ⟶ Δ\ninst✝ : Epi e\n⊢ ((splitting K).cofan (op Δ)).inj (Splitting.IndexSet.id (op Δ)) ≫ (obj K).map e.op =\n ((splitting K).cofan (op Δ')).inj (S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.GammaCompN | {
"line": 63,
"column": 10
} | {
"line": 63,
"column": 37
} | [
{
"pp": "case h₂\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\nn : ℕ\ni : Fin (n + 2)\nhi : i ≠ 0\n⊢ ¬Isδ₀ (SimplexCategory.δ i)",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.AlgebraicTopology.DoldKan.GammaCompN.0.A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | {
"line": 335,
"column": 42
} | {
"line": 335,
"column": 69
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\nn : ℕ\nj : Fin (n + 1)\na✝ : n + 1 ≤ ↑j + (n + 1)\neq :\n ((Γ₀.splitting K).cofan (op ⦋n + 1⦌)).inj (Splitting.IndexSet.id (op ⦋n + 1⦌)) ≫\n (Γ₀.obj K).map (SimplexCategory.δ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | {
"line": 345,
"column": 4
} | {
"line": 345,
"column": 31
} | [
{
"pp": "case zero\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\n⊢ ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌)) ≫ (P 0).f 0 =\n ((Γ₀.splitting K).cofan (op ⦋0⦌)).inj (Splitting.IndexSet.id (op ⦋0⦌))",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.NCompGamma | {
"line": 54,
"column": 19
} | {
"line": 54,
"column": 73
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nm : ℕ\nh₁ : ⦋m⦌.len ≠ m + 1\nj : Fin (m + 2)\nhi : Mono (SimplexCategory.δ j)\nh₂ : ¬j = 0\nh : ¬1 ≤ ↑j\n⊢ j = 0",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.AlgebraicTopology.DoldKan.NCompG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.NCompGamma | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 73
} | [
{
"pp": "case mk.zero\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nm : ℕ\nh₁ : ⦋m⦌.len ≠ m + 1\nj : Fin (m + 2)\nhi : Mono (SimplexCategory.δ j)\nh₂ : ¬j = 0\nh₃ : 1 ≤ ↑j\n⊢ PInfty.f (m + 1) ≫ X.map (SimplexCategory.δ j).op = 0",
"usedConstants": [
"Alg... | exact (HigherFacesVanish.of_P (m + 1) m).comp_δ_eq_zero j h₂ (by lia) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 13
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX : SimplicialObject C\ns : X.Splitting\ninst✝ : Preadditive C\n⊢ s.toKaroubiNondegComplexIsoN₁.hom.f ≫ PInfty = s.toKaroubiNondegComplexIsoN₁.hom.f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.DoldKan.NCompGamma | {
"line": 228,
"column": 2
} | {
"line": 236,
"column": 36
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\n⊢ IsIso Γ₂N₂.natTrans",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Functor",
"ChainComplex",
"HomologicalComplex.instCategory",
"CategoryTheory.IsIso",
"Opposit... | have : ∀ P : Karoubi (SimplicialObject C), IsIso (Γ₂N₂.natTrans.app P) := by
intro P
have : IsIso (N₂.map (Γ₂N₂.natTrans.app P)) := by
have h := identity_N₂_objectwise P
dsimp only [Functor.id_obj, Functor.comp_obj] at h
rw [hom_comp_eq_id] at h
rw [h]
infer_instance
exact isIs... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Product | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 57
} | [
{
"pp": "case h_map\nA : TopCat\nB : TopCat\nx₀ : ↑A\nx₁ : ↑B\ny₀ : ↑A\ny₁ : ↑B\nf : { as := (x₀, x₁) } ⟶ { as := (y₀, y₁) }\n⊢ ((projLeft A B).prod' (projRight A B) ⋙ prodToProdTop A B).map f ≍ (𝟭 ↑(π.obj (TopCat.of (↑A × ↑B)))).map f",
"usedConstants": [
"Eq.mpr",
"Path.Homotopic.projLeft",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Basic | {
"line": 613,
"column": 21
} | {
"line": 613,
"column": 50
} | [
{
"pp": "F✝ : Type u_1\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\nι : Type u_2\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nf₀✝ f₁✝ f₂ : C(X, Y)\nS : Set X\nf₀ f₁ g₀ g₁ : C(X, Y)\nF : f₀.HomotopyRel f₁ S\nh₀ : f₀ = g₀\nh₁ : f₁ = g₁\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Path | {
"line": 408,
"column": 2
} | {
"line": 408,
"column": 51
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\nx₀ x₁ x₃ : X\np₁ : Path x₀ x₁\np₂ : Path x₀ x₃\nhp : ∀ (t : ↑I), p₁ t = p₂ t\n⊢ ⟦p₁⟧ ≍ ⟦p₂⟧",
"usedConstants": [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"congrArg",
"HEq.refl",
"Real.semiring"... | obtain rfl : x₁ = x₃ := by convert! hp 1 <;> simp | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps | {
"line": 88,
"column": 4
} | {
"line": 89,
"column": 11
} | [
{
"pp": "case η\nX✝ : Type u_1\nY✝ : Type u_2\ninst✝³ : TopologicalSpace X✝\ninst✝² : TopologicalSpace Y✝\nf g : C(X✝, Y✝)\nX : Type u_3\nY : Type u_4\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nhequiv : X ≃ₕ Y\n⊢ 𝟭 (FundamentalGroupoid X) ≅ map hequiv.toFun ⋙ map hequiv.invFun",
"usedConstan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps | {
"line": 90,
"column": 4
} | {
"line": 91,
"column": 11
} | [
{
"pp": "case ε\nX✝ : Type u_1\nY✝ : Type u_2\ninst✝³ : TopologicalSpace X✝\ninst✝² : TopologicalSpace Y✝\nf g : C(X✝, Y✝)\nX : Type u_3\nY : Type u_4\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nhequiv : X ≃ₕ Y\n⊢ map hequiv.invFun ⋙ map hequiv.toFun ≅ 𝟭 (FundamentalGroupoid Y)",
"usedConstan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected | {
"line": 121,
"column": 6
} | {
"line": 121,
"column": 17
} | [
{
"pp": "Y : Type u_2\ninst✝ : TopologicalSpace Y\nhpc : PathConnectedSpace Y\nx y : Y\np₁ p₂ : Path x y\nhloops : ∀ (x : Y) (γ : Path x x), ⟦γ⟧ = ⟦Path.refl x⟧\n⊢ Path.Homotopic.Quotient.trans ⟦p₁⟧ (Path.Homotopic.Quotient.symm ⟦p₂⟧) = Path.Homotopic.Quotient.refl x",
"usedConstants": [
"id",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected | {
"line": 106,
"column": 89
} | {
"line": 124,
"column": 26
} | [
{
"pp": "Y : Type u_2\ninst✝ : TopologicalSpace Y\n⊢ SimplyConnectedSpace Y ↔ PathConnectedSpace Y ∧ ∀ (x : Y) (γ : Path x x), γ.Homotopic (Path.refl x)",
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected.0.simply_connected_iff_loops_nullhomotopic._proof_1_5",
... | by
rw [simply_connected_iff_paths_homotopic']
constructor
· -- Forward: all paths homotopic implies all loops null-homotopic
intro ⟨hpc, hall⟩
exact ⟨hpc, fun x γ => hall γ (Path.refl x)⟩
· -- Backward: all loops null-homotopic implies all paths homotopic
intro ⟨hpc, hloops⟩
refine ⟨hpc, fun {x ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.FundamentalGroupoid.SimplyConnected | {
"line": 168,
"column": 25
} | {
"line": 168,
"column": 36
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\nh : ∀ (x : ↑s) (γ : Path x x), γ.Homotopic (Path.refl x)\nx : X\np : Path x x\nhp : ∀ (t : ↑unitInterval), p t ∈ s\n⊢ x ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 52,
"column": 4
} | {
"line": 55,
"column": 33
} | [
{
"pp": "case pos\nx : ↑I × ↑I\nh✝ : ↑x.2 ≤ 1 / 2\n⊢ ↑x.1 * 2 * ↑x.2 ∈ I",
"usedConstants": [
"Real.instIsOrderedRing",
"Eq.mpr",
"mul_nonneg",
"Real.partialOrder",
"Semigroup.toMul",
"Real",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"Real.instZero",
... | constructor
· apply mul_nonneg <;> grind
· rw [mul_assoc]
apply mul_le_one₀ <;> grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 52,
"column": 4
} | {
"line": 55,
"column": 33
} | [
{
"pp": "case pos\nx : ↑I × ↑I\nh✝ : ↑x.2 ≤ 1 / 2\n⊢ ↑x.1 * 2 * ↑x.2 ∈ I",
"usedConstants": [
"Real.instIsOrderedRing",
"Eq.mpr",
"mul_nonneg",
"Real.partialOrder",
"Semigroup.toMul",
"Real",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"Real.instZero",
... | constructor
· apply mul_nonneg <;> grind
· rw [mul_assoc]
apply mul_le_one₀ <;> grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 85,
"column": 6
} | {
"line": 85,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : ModelCategory C\nX Y Z : C\nf g : X ⟶ Y\ninst✝¹ : IsFibrant Y\nh✝ : RightHomotopyRel f g\nQ : Cylinder X\ninst✝ : Q.IsGood\nP : PathObject Y := ⋯.choose\nh : ⋯.choose.RightHomotopy f g\nh' : ⋯.choose.IsGood\nsq : CommSq (coprod.desc (f ≫ P.ι) h.h) Q.i P.... | rw [Q.inl_i_assoc, coprod.inl_desc] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 227,
"column": 2
} | {
"line": 227,
"column": 13
} | [
{
"pp": "case a\nC : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\ng : Y ⟶ X\nhg : LeftHomotopyRel (f ≫ g) (𝟙 X)\n⊢ LeftHomotopyRel (f ≫ g ≫ f) f",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 234,
"column": 2
} | {
"line": 235,
"column": 36
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ ∃ g, LeftHomotopyRel (f ≫ g) (𝟙 X) ∧ LeftHomotopyRel (g ≫ f) (𝟙 Y)",
"usedConstants": [
... | simp only [leftHomotopyRel_iff_rightHomotopyRel]
apply RightHomotopyClass.whitehead | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.ModelCategory.Homotopy | {
"line": 234,
"column": 2
} | {
"line": 235,
"column": 36
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\ninst✝⁵ : ModelCategory C\nX Y : C\ninst✝⁴ : IsCofibrant X\ninst✝³ : IsCofibrant Y\ninst✝² : IsFibrant X\ninst✝¹ : IsFibrant Y\nf : X ⟶ Y\ninst✝ : WeakEquivalence f\n⊢ ∃ g, LeftHomotopyRel (f ≫ g) (𝟙 X) ∧ LeftHomotopyRel (g ≫ f) (𝟙 Y)",
"usedConstants": [
... | simp only [leftHomotopyRel_iff_rightHomotopyRel]
apply RightHomotopyClass.whitehead | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction | {
"line": 53,
"column": 6
} | {
"line": 53,
"column": 89
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\ninst✝² : Category.{v_1, u_1} C₁\ninst✝¹ : Category.{v_2, u_2} C₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\nadj : G ⊣ F\nW : MorphismProperty C₁\ninst✝ : W.IsMultiplicative\nhW : W.IsInvertedBy G\nhW' : W.functorCategory C₁ adj.unit\nX Y T : C₁\ns : T ⟶ X\nw✝ : W s\nf : T ⟶ Y\nthis✝ : IsI... | rw [reassoc_of% this, Functor.map_inv, IsIso.hom_inv_id_assoc, adj.unit_naturality] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 13
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} C₁\ninst✝² : Category.{v_2, u_2} C₂\nG : C₁ ⥤ C₂\nF : C₂ ⥤ C₁\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nadj : F ⊣ G\nW : MorphismProperty C₁\nhW : W.IsInvertedBy G\nhW' : W.functorCategory C₁ adj.counit\n⊢ G.IsLocalization W",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 199,
"column": 2
} | {
"line": 199,
"column": 41
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (refl x₀).trans (mk γ) = mk γ",
"usedConstants": [
"Eq.mpr",
"Path.trans",
"id",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopic.Quotient.refl_trans._simp_1_3",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 41
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).trans (refl x₁) = mk γ",
"usedConstants": [
"Eq.mpr",
"Path.trans",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopic.Quotient.trans_refl._simp_1_3",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 52
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).trans (mk γ).symm = refl x₀",
"usedConstants": [
"Eq.mpr",
"Path.symm",
"Path.trans",
"id",
"Path.Homotopic.Quotient",
"Path.Homotopic.Quotient.refl",
"Path.Homotopic.Quo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 52
} | [
{
"pp": "case mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ : X\nγ : Path x₀ x₁\n⊢ (mk γ).symm.trans (mk γ) = refl x₁",
"usedConstants": [
"Eq.mpr",
"Path.symm",
"Path.trans",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopic.Quotient.symm_trans._si... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | {
"line": 228,
"column": 2
} | {
"line": 228,
"column": 30
} | [
{
"pp": "case mk.mk.mk\nX : Type u_1\ninst✝ : TopologicalSpace X\nx₀ x₁ x₂ x₃ : X\nγ₀ : Path x₀ x₁\nγ₁ : Path x₁ x₂\nγ₂ : Path x₂ x₃\n⊢ ((mk γ₀).trans (mk γ₁)).trans (mk γ₂) = (mk γ₀).trans ((mk γ₁).trans (mk γ₂))",
"usedConstants": [
"Eq.mpr",
"Path.trans",
"id",
"_private.Mathlib.A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy | {
"line": 198,
"column": 36
} | {
"line": 198,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ LeftHomotopyRel (resolutionMap (𝟙 X) ≫ pResolutionObj X) (𝟙 (mk (resolutionObj X)).obj ≫ pResolutionObj X)",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy | {
"line": 201,
"column": 36
} | {
"line": 201,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX₁ X₂ X₃ : C\nf : X₁ ⟶ X₂\ng : X₂ ⟶ X₃\n⊢ LeftHomotopyRel (resolutionMap (f ≫ g) ≫ pResolutionObj X₃)\n (((homMk (resolutionMap f)).hom ≫ (homMk (resolutionMap g)).hom) ≫ pResolutionObj X₃)",
"usedConstants": [
"Eq.mpr"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy | {
"line": 211,
"column": 4
} | {
"line": 213,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nx✝² x✝¹ : C\nx✝ : x✝² ⟶ x✝¹\nh : weakEquivalences C x✝\n⊢ (weakEquivalences (HoCat C)).inverseImage resolution x✝",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : ModelCategory C\nD : Type u_2\ninst✝¹ : Category.{v_2, u_2} D\nL : C ⥤ D\ninst✝ : L.IsLocalization (weakEquivalences C)\nx✝¹ x✝ : C\nf : x✝¹ ⟶ x✝\n⊢ (resolution ⋙ toLocalization L).map f ≫ L.map (pResolutionObj x✝) = L.map (pResolutionObj x✝¹) ≫ L.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 201,
"column": 36
} | {
"line": 201,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ RightHomotopyRel (iResolutionObj X ≫ resolutionMap (𝟙 X)) (iResolutionObj X ≫ 𝟙 (mk (resolutionObj X)).obj)",
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.Cat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 204,
"column": 36
} | {
"line": 204,
"column": 47
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nX₁ X₂ X₃ : C\nf : X₁ ⟶ X₂\ng : X₂ ⟶ X₃\n⊢ RightHomotopyRel (iResolutionObj X₁ ≫ resolutionMap (f ≫ g))\n (iResolutionObj X₁ ≫ (homMk (resolutionMap f)).hom ≫ (homMk (resolutionMap g)).hom)",
"usedConstants": [
"Eq.mpr",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 214,
"column": 4
} | {
"line": 216,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : ModelCategory C\nx✝² x✝¹ : C\nx✝ : x✝² ⟶ x✝¹\nh : weakEquivalences C x✝\n⊢ (weakEquivalences (HoCat C)).inverseImage resolution x✝",
"usedConstants": [
"Eq.mpr",
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.Category... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 39
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : ModelCategory C\nD : Type u_2\ninst✝¹ : Category.{v_2, u_2} D\nL : C ⥤ D\ninst✝ : L.IsLocalization (weakEquivalences C)\nx✝¹ x✝ : C\nf : x✝¹ ⟶ x✝\n⊢ L.map f ≫ L.map (iResolutionObj x✝) = L.map (iResolutionObj x✝¹) ≫ (resolution ⋙ toLocalization L).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 49
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : ModelCategory C\nX Y : C\ninst✝³ : IsCofibrant X\ninst✝² : IsCofibrant Y\ninst✝¹ : IsFibrant X\ninst✝ : IsFibrant Y\nx✝¹ x✝ : (toHoCat.obj (mk X)).as ⟶ (toHoCat.obj (mk Y)).as\nh : HomRel.CompClosure (homRel C) x✝¹ x✝\n⊢ (fun f ↦ RightHomotopyClass.mk f.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | {
"line": 183,
"column": 6
} | {
"line": 184,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nx✝³ x✝² : BifibrantObject C\nx✝¹ x✝ : x✝³ ⟶ x✝²\nh : homRel C x✝¹ x✝\n⊢ (BifibrantObject.ιFibrantObject ⋙ FibrantObject.toHoCat).map x✝¹ =\n (BifibrantObject.ιFibrantObject ⋙ FibrantObject.toHoCat).map x✝",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | {
"line": 330,
"column": 2
} | {
"line": 330,
"column": 13
} | [
{
"pp": "case a\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nX : CofibrantObject C\nY : BifibrantObject C\nf g : X.bifibrantResolutionObj ⟶ Y\nh :\n RightHomotopyClass.mk (X.iBifibrantResolutionObj ≫ BifibrantObject.ιCofibrantObject.map f).hom =\n RightHomotopyClass.mk (X.iBifibrantReso... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | {
"line": 350,
"column": 4
} | {
"line": 350,
"column": 56
} | [
{
"pp": "case h\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : ModelCategory C\nX Y : CofibrantObject C\nf g : X ⟶ Y\nh : homRel C f g\n⊢ toHoCat.map X.iBifibrantResolutionObj ≫ BifibrantObject.HoCat.ιCofibrantObject.map (bifibrantResolution'.map f) =\n toHoCat.map X.iBifibrantResolutionObj ≫ BifibrantObje... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 65
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 64
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\ninst✝⁵ : Category.{v₁, u₁} C₁\ninst✝⁴ : Category.{v₂, u₂} C₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nD₁ : Type u_1\nD₂ : Type u_2\ninst✝³ : Category.{v_1, u_1} D₁\ninst✝² : Category.{v_2, u_2} D₂\nL₁ : C₁ ⥤ D₁\nL₂ : C₂ ⥤ D₂\ninst✝¹ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Opposite | {
"line": 47,
"column": 29
} | {
"line": 47,
"column": 40
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\nX₃ : C₃ᵒᵖ\nX₂ : C₂ᵒᵖ\ng : B.op.obj X₃ ⟶ R.op.obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 40
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : ModelCategory C\nX : C\nR : (localizerMorphism C).LeftResolution X\n⊢ WeakEquivalence R.w",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.CofibrantObject.loca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureCofibrant | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 26
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{u_2, u_1} C\ninst✝ : ModelCategory C\nX : C\n⊢ weakEquivalences C (HoCat.pResolutionObj X)",
"usedConstants": [
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.CofibrantObject.localizerMorphism",
"HomotopicalAl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.GuitartExact.Opposite | {
"line": 105,
"column": 2
} | {
"line": 106,
"column": 18
} | [
{
"pp": "case mpr\nC₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\nC₄ : Type u₄\ninst✝³ : Category.{v₁, u₁} C₁\ninst✝² : Category.{v₂, u₂} C₂\ninst✝¹ : Category.{v₃, u₃} C₃\ninst✝ : Category.{v₄, u₄} C₄\nT : C₁ ⥤ C₂\nL : C₁ ⥤ C₃\nR : C₂ ⥤ C₄\nB : C₃ ⥤ C₄\nw : TwoSquare T L R B\n⊢ w.GuitartExact → w.op.GuitartExact",
... | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
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