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.CategoryTheory.Topos.Sheaf | {
"line": 200,
"column": 6
} | {
"line": 200,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nF G : Sheaf J (Type (max u v))\nm : F ⟶ G\ninst✝ : Mono m\n⊢ 𝟙 G.obj ≫ Presheaf.χ m.hom = Subfunctor.lift (Presheaf.χ m.hom) ⋯ ≫ (closedSieves J).ι",
"usedConstants": [
"CategoryTheory.Functor",
"Opposite",
"Cate... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.Generators | {
"line": 163,
"column": 4
} | {
"line": 163,
"column": 24
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : Preadditive C\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nP : ObjectProperty C\na : ℤ\nX : C\nhX : ∃ n, P.triangEnvelopeIter n X\n⊢ P.triangEnvelope.shift a X",
"... | obtain ⟨n, hn⟩ := hX | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Triangulated.Opposite.Triangulated | {
"line": 54,
"column": 6
} | {
"line": 54,
"column": 38
} | [
{
"pp": "case refine_3\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : HasShift C ℤ\ninst✝⁴ : HasZeroObject C\ninst✝³ : Preadditive C\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\ninst✝ : IsTriangulated C\nX₁ X₂ X₃ Z₁₂ Z₂₃ Z₁₃ : Cᵒᵖ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nu₁₃ : X₁... | have := op_distinguished _ o.mem | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 116,
"column": 6
} | {
"line": 116,
"column": 45
} | [
{
"pp": "case a\nC : Type u_1\nA : Type u_2\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : Pretriangulated C\ninst✝³ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (s... | eq_zero_of_hom_shift_pos hι l (by lia), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 30
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : Pretriangulated C\ninst✝³ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftFunc... | replace hk := ι.congr_map hk | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 132,
"column": 6
} | {
"line": 132,
"column": 45
} | [
{
"pp": "C : Type u_1\nA : Type u_2\ninst✝⁹ : Category.{v_1, u_1} C\ninst✝⁸ : HasZeroObject C\ninst✝⁷ : Preadditive C\ninst✝⁶ : HasShift C ℤ\ninst✝⁵ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝⁴ : Pretriangulated C\ninst✝³ : Category.{v_2, u_2} A\nι : A ⥤ C\nhι : ∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (shiftFunc... | eq_zero_of_hom_shift_pos hι l (by lia), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.TStructure.SpectralObject | {
"line": 81,
"column": 2
} | {
"line": 83,
"column": 83
} | [
{
"pp": "case w.h\nC : Type u_1\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Preadditive C\ninst✝⁴ : HasZeroObject C\ninst✝³ : HasShift C ℤ\ninst✝² : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝¹ : Pretriangulated C\nt : TStructure C\ninst✝ : IsTriangulated C\na b c : EInt\nhab : a ≤ b\nhbc : b ≤ c\na' b' c' : EI... | simp only [ω₁δ_app, ← Functor.map_comp, NatTrans.naturality_assoc, Functor.comp_map,
Category.assoc, ← Functor.map_comp_assoc, NatTrans.naturality_app_assoc,
Functor.whiskeringRight_obj_map, Functor.whiskerRight_app, NatTrans.naturality] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.Additive.RuzsaCovering | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 98
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nK : ℝ\nA B : Finset G\nhB₀ : (↑B).Nonempty\nhK : ↑(Nat.card ↑(↑A * ↑B)) ≤ K * ↑(Nat.card ↑↑B)\n⊢ ∃ F ⊆ ↑A, ↑(Nat.card ↑F) ≤ K ∧ ↑A ⊆ F * (↑B / ↑B) ∧ F.Finite",
"usedConstants": [
"Real.instLE",
"Real",
"HMul.hMul",
"_private.Mathlib.Combinatori... | obtain ⟨F, hFA, hF, hAF⟩ := Finset.ruzsa_covering_mul hB₀ (by simpa [← Finset.coe_mul] using hK) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Combinatorics.Additive.AP.Three.Behrend | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 100
} | [
{
"pp": "n d : ℕ\n⊢ ∃ k ∈ range (n * (d - 1) ^ 2 + 1), ↑(d ^ n) / (↑(n * (d - 1) ^ 2) + 1) ≤ ↑(#(sphere n d k))",
"usedConstants": [
"Real",
"instHDiv",
"HMul.hMul",
"Finset.univ",
"Finset",
"Finset.nonempty_range_add_one",
"Nat.instMonoid",
"Real.instDivInvMo... | refine exists_le_card_fiber_of_nsmul_le_card_of_maps_to (fun x hx => ?_) nonempty_range_add_one ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 126,
"column": 47
} | {
"line": 128,
"column": 48
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf₁ f₂ : α → β\nn : ℕ\nhf₁ : IsMulFreimanHom n A B f₁\nh : EqOn f₁ f₂ A\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nhs : s.card = n\nht : t.card = n\nh' : s.prod = t.prod... | by
rw [map_congr rfl fun x hx => (h (hsA hx)).symm, map_congr rfl fun x hx => (h (htA hx)).symm,
hf₁.map_prod_eq_map_prod hsA htA hs ht h'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 266,
"column": 38
} | {
"line": 266,
"column": 46
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : MapsTo f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → s.prod = t.prod → (map f s).prod = (map f t).prod",
"us... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 266,
"column": 38
} | {
"line": 266,
"column": 46
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : MapsTo f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → s.prod = t.prod → (map f s).prod = (map f t).prod",
"us... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 266,
"column": 38
} | {
"line": 266,
"column": 46
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : MapsTo f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → s.prod = t.prod → (map f s).prod = (map f t).prod",
"us... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 270,
"column": 37
} | {
"line": 270,
"column": 45
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : BijOn f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → ((map f s).prod = (map f t).prod ↔ s.prod = t.prod)",
"u... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 270,
"column": 37
} | {
"line": 270,
"column": 45
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : BijOn f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → ((map f s).prod = (map f t).prod ↔ s.prod = t.prod)",
"u... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 270,
"column": 37
} | {
"line": 270,
"column": 45
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CommMonoid β\nA : Set α\nB : Set β\nf : α → β\nh : BijOn f A B\n⊢ ∀ ⦃s t : Multiset α⦄,\n (∀ ⦃x : α⦄, x ∈ s → x ∈ A) →\n (∀ ⦃x : α⦄, x ∈ t → x ∈ A) → s.card = 0 → t.card = 0 → ((map f s).prod = (map f t).prod ↔ s.prod = t.prod)",
"u... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 132,
"column": 4
} | {
"line": 134,
"column": 70
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA₁ : 1 ∈ A\nhAsymm : A⁻¹ = A\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\n⊢ CovBySMul G (K ^ 3) ((↑A ^ 2) ^ 2) (↑A ^ 2)",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Combinatorics.Additive.ApproximateSubgroup.0.IsApproxim... | replace hA := calc (#(A ^ 4 * A) : ℝ)
_ = #(A ^ 5) := by rw [← pow_succ]
_ ≤ K ^ 3 * #A := small_pow_of_small_tripling (by lia) hA hAsymm | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 145,
"column": 79
} | {
"line": 145,
"column": 93
} | [
{
"pp": "case bc\nG : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B : Finset G\nhA : ∀ A' ⊆ A, #(A * B) * #A' ≤ #(A' * B) * #A\nx : G\nC : Finset G\na✝ : x ∉ C\nih : #(C * A * B) * #A ≤ #(A * B) * #(C * A)\nA' : Finset G := A ∩ ({x}⁻¹ * C * A)\nhA' : A' = A ∩ ({x}⁻¹ * C * A)\nC' : Finset G := insert x ... | mul_assoc {_}, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 146,
"column": 10
} | {
"line": 146,
"column": 24
} | [
{
"pp": "case bc\nG : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B : Finset G\nhA : ∀ A' ⊆ A, #(A * B) * #A' ≤ #(A' * B) * #A\nx : G\nC : Finset G\na✝ : x ∉ C\nih : #(C * A * B) * #A ≤ #(A * B) * #(C * A)\nA' : Finset G := A ∩ ({x}⁻¹ * C * A)\nhA' : A' = A ∩ ({x}⁻¹ * C * A)\nC' : Finset G := insert x ... | mul_assoc {_}, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 247,
"column": 42
} | {
"line": 247,
"column": 60
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : CommGroup G\nA : Finset G\nhA : A.Nonempty\nB : Finset G\nm n : ℕ\nhA' : A ∈ A.powerset.erase ∅\nC : Finset G\nhCmin : ∀ x' ∈ A.powerset.erase ∅, ↑(#(C * B)) / ↑(#C) ≤ ↑(#(x' * B)) / ↑(#x')\nhC : C.Nonempty\nhCA : C ⊆ A\n⊢ ↑(#(B ^ m * C)) * ↑(#(B ^ n * C)) ... | simp_rw [mul_comm] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 247,
"column": 42
} | {
"line": 247,
"column": 60
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : CommGroup G\nA : Finset G\nhA : A.Nonempty\nB : Finset G\nm n : ℕ\nhA' : A ∈ A.powerset.erase ∅\nC : Finset G\nhCmin : ∀ x' ∈ A.powerset.erase ∅, ↑(#(C * B)) / ↑(#C) ≤ ↑(#(x' * B)) / ↑(#x')\nhC : C.Nonempty\nhCA : C ⊆ A\n⊢ ↑(#(B ^ m * C)) * ↑(#(B ^ n * C)) ... | simp_rw [mul_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 247,
"column": 42
} | {
"line": 247,
"column": 60
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : CommGroup G\nA : Finset G\nhA : A.Nonempty\nB : Finset G\nm n : ℕ\nhA' : A ∈ A.powerset.erase ∅\nC : Finset G\nhCmin : ∀ x' ∈ A.powerset.erase ∅, ↑(#(C * B)) / ↑(#C) ≤ ↑(#(x' * B)) / ↑(#x')\nhC : C.Nonempty\nhCA : C ⊆ A\n⊢ ↑(#(B ^ m * C)) * ↑(#(B ^ n * C)) ... | simp_rw [mul_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Maps | {
"line": 121,
"column": 42
} | {
"line": 122,
"column": 25
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nf : V ↪ W\nG : SimpleGraph V\n⊢ (SimpleGraph.map (⇑f) G).support = ⇑f '' G.support",
"usedConstants": [
"Set.ext",
"and_true",
"congrArg",
"SimpleGraph.Adj",
"Set.mem_image._simp_1",
"Membership.mem",
"Exists",
"Eq.mp",
... | by
ext; simp [mem_support] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Set.Equitable | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 47
} | [
{
"pp": "α : Type u_1\ns : Finset α\nf : α → ℕ\n⊢ (↑s).EquitableOn f ↔ ∀ a ∈ s, (∑ i ∈ s, f i) / #s ≤ f a ∧ f a ≤ (∑ i ∈ s, f i) / #s + 1",
"usedConstants": [
"Set.EquitableOn",
"Eq.mpr",
"instHDiv",
"Nat.instOne",
"congrArg",
"Finset",
"Set.equitableOn_iff_exists_l... | rw [Set.equitableOn_iff_exists_le_le_add_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 49
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv : V\ninst✝¹ : Fintype ↑(G.neighborSet v)\ninst✝ : Fintype ↑G.edgeSet\n⊢ #(G.incidenceFinset v) ≤ #G.edgeFinset",
"usedConstants": [
"Finset.card_le_card",
"Classical.propDecidable",
"SimpleGraph.incidenceFinset_subset",
"SimpleGraph.edgeFin... | exact card_le_card (G.incidenceFinset_subset v) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Partition.Equipartition | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 36
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nP : Finpartition s\nhP : P.IsEquipartition\nz :\n (#({x ∈ P.parts | #x = #s / #P.parts + 1}) + #({p ∈ P.parts | ¬#p = #s / #P.parts + 1})) * (#s / #P.parts) +\n #({x ∈ P.parts | #x = #s / #P.parts + 1}) =\n #s\n⊢ #({p ∈ P.parts | #p = #s / #P.... | card_filter_add_card_filter_not, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Partition.Equipartition | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 37
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nhs : s ≠ ∅\n⊢ {s}.EquitableOn Finset.card",
"usedConstants": [
"Finset",
"Set.equitableOn_singleton",
"IsStrictOrderedRing.toIsOrderedRing",
"Nat",
"Nat.instPartialOrder",
"Finset.card",
"Nat.instSemiring",... | exact Set.equitableOn_singleton s _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Density | {
"line": 155,
"column": 64
} | {
"line": 159,
"column": 76
} | [
{
"pp": "α : Type u_4\nβ : Type u_5\nr : α → β → Prop\ninst✝¹ : (a : α) → DecidablePred (r a)\nt : Finset β\ninst✝ : DecidableEq β\ns : Finset α\nP : Finpartition t\n⊢ #(interedges r s t) = ∑ b ∈ P.parts, #(interedges r s b)",
"usedConstants": [
"Eq.mpr",
"Rel.interedges",
"Finpartition.di... | by
classical
simp_rw [← P.biUnion_parts, interedges_biUnion_right, id]
rw [card_biUnion]
exact fun x hx y hy h ↦ interedges_disjoint_right r _ (P.disjoint hx hy h) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nP : Finpartition univ\nh : 1 ≤ 4 ^ #P.parts\n| 4 ^ #P.parts",
"usedConstants": [
"Finset.univ",
"congrArg",
"Finset",
"Nat.instMonoid",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"Finpartition.p... | ← Nat.sub_add_cancel h | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Order.Partition.Finpartition | {
"line": 471,
"column": 4
} | {
"line": 471,
"column": 12
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝³ : DistribLattice α\ninst✝² : OrderBot α\ninst✝¹ : DecidableEq α\nparts : Finset α\nhdisjoint : (↑parts).PairwiseDisjoint id\nX : Type u_2\ninst✝ : AddCommMonoid X\nf : α → X\nhf : f ⊥ = 0\nhbot : ⊥ ∉ parts\n⊢ ∑ p ∈ (ofPairwiseDisjoint parts hdisjoint).parts, f p = ∑ p ∈ p... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Order.Partition.Finpartition | {
"line": 471,
"column": 4
} | {
"line": 471,
"column": 12
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝³ : DistribLattice α\ninst✝² : OrderBot α\ninst✝¹ : DecidableEq α\nparts : Finset α\nhdisjoint : (↑parts).PairwiseDisjoint id\nX : Type u_2\ninst✝ : AddCommMonoid X\nf : α → X\nhf : f ⊥ = 0\nhbot : ⊥ ∉ parts\n⊢ ∑ p ∈ (ofPairwiseDisjoint parts hdisjoint).parts, f p = ∑ p ∈ p... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Partition.Finpartition | {
"line": 471,
"column": 4
} | {
"line": 471,
"column": 12
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝³ : DistribLattice α\ninst✝² : OrderBot α\ninst✝¹ : DecidableEq α\nparts : Finset α\nhdisjoint : (↑parts).PairwiseDisjoint id\nX : Type u_2\ninst✝ : AddCommMonoid X\nf : α → X\nhf : f ⊥ = 0\nhbot : ⊥ ∉ parts\n⊢ ∑ p ∈ (ofPairwiseDisjoint parts hdisjoint).parts, f p = ∑ p ∈ p... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Partition.Finpartition | {
"line": 694,
"column": 4
} | {
"line": 694,
"column": 12
} | [
{
"pp": "case mp\nα : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nP : Finpartition s\na : α\nht : P.part a ∈ P.parts\n⊢ a ∈ P.part a",
"usedConstants": [
"Finpartition.part_mem._simp_1",
"Finpartition.mem_part_self._simp_1",
"Finset",
"Finpartition.part",
"Membership.mem",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise | {
"line": 102,
"column": 36
} | {
"line": 102,
"column": 46
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : DecidableEq α\nm : ℕ\nm_pos : m > 0\ns : Finset α\nih :\n ∀ t ⊂ s,\n ∀ {a b : ℕ} {P : Finpartition t},\n a * m + b * (m + 1) = #t →\n ∃ Q,\n (∀ x ∈ Q.parts, #x = m ∨ #x = m + 1) ∧\n (∀ x ∈ P.parts, #(x \\ {y ∈ Q.parts | y ⊆ x}.biUnion ... | if_neg ha, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 45
} | [
{
"pp": "case pos\nα : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\nh : ¬G.IsUniform ε s t\nh✝ : WellOrderingRel s t\n⊢ (G.nonuniformWitnesses ε s t).1 ⊆ s",
"usedConstants": [
... | exact G.left_nonuniformWitnesses_subset h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 45
} | [
{
"pp": "case pos\nα : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\nh : ¬G.IsUniform ε s t\nh✝ : WellOrderingRel s t\n⊢ (G.nonuniformWitnesses ε s t).1 ⊆ s",
"usedConstants": [
... | exact G.left_nonuniformWitnesses_subset h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 45
} | [
{
"pp": "case pos\nα : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\nh : ¬G.IsUniform ε s t\nh✝ : WellOrderingRel s t\n⊢ (G.nonuniformWitnesses ε s t).1 ⊆ s",
"usedConstants": [
... | exact G.left_nonuniformWitnesses_subset h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 334,
"column": 4
} | {
"line": 334,
"column": 68
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : DecidableEq α\nA : Finset α\nP : Finpartition A\nhP : P.IsEquipartition\nh : P.parts.Nonempty\nU : Finset α\nhU : U ∈ P.parts\nthis : (#U - 1) * #U ≤ #A / #P.parts * (#A / #P.parts + 1)\n⊢ ... | rwa [Nat.mul_sub_right_distrib, one_mul, ← offDiag_card] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 334,
"column": 4
} | {
"line": 334,
"column": 68
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : DecidableEq α\nA : Finset α\nP : Finpartition A\nhP : P.IsEquipartition\nh : P.parts.Nonempty\nU : Finset α\nhU : U ∈ P.parts\nthis : (#U - 1) * #U ≤ #A / #P.parts * (#A / #P.parts + 1)\n⊢ ... | rwa [Nat.mul_sub_right_distrib, one_mul, ← offDiag_card] at this | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 334,
"column": 4
} | {
"line": 334,
"column": 68
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\ninst✝ : DecidableEq α\nA : Finset α\nP : Finpartition A\nhP : P.IsEquipartition\nh : P.parts.Nonempty\nU : Finset α\nhU : U ∈ P.parts\nthis : (#U - 1) * #U ≤ #A / #P.parts * (#A / #P.parts + 1)\n⊢ ... | rwa [Nat.mul_sub_right_distrib, one_mul, ← offDiag_card] at this | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 80
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nx : V\n⊢ (fromEdgeSet (G.incidenceSet x)).edgeSet = G.incidenceSet x",
"usedConstants": [
"Eq.mpr",
"SimpleGraph.edgeSet_fromEdgeSet",
"SimpleGraph.incidenceSet",
"congrArg",
"SimpleGraph.fromEdgeSet",
"Compl.compl",
"Set.su... | rw [edgeSet_fromEdgeSet, sdiff_eq_left, ← Set.subset_compl_iff_disjoint_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | {
"line": 107,
"column": 6
} | {
"line": 109,
"column": 10
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nl : ℕ\nhε : 0 < ε\nhl : l ≤ Fintype.card α\nhα : bound ε l ≤ Fintype.card α\nt : ℕ := initialBound ε l\nhtα : t ≤ #univ\ndum : Finpartition univ\nhdum₁ : dum.IsEquipartition\nh... | rw [iterate_succ_apply', stepBound, bound]
gcongr
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | {
"line": 107,
"column": 6
} | {
"line": 109,
"column": 10
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nl : ℕ\nhε : 0 < ε\nhl : l ≤ Fintype.card α\nhα : bound ε l ≤ Fintype.card α\nt : ℕ := initialBound ε l\nhtα : t ≤ #univ\ndum : Finpartition univ\nhdum₁ : dum.IsEquipartition\nh... | rw [iterate_succ_apply', stepBound, bound]
gcongr
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 28
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nl : ℕ\nhε : 0 < ε\nhl : l ≤ Fintype.card α\nhα : bound ε l ≤ Fintype.card α\nt : ℕ := initialBound ε l\nhtα : t ≤ #univ\ndum : Finpartition univ\nhdum₁ : dum.IsEquipartition\nhdum₂ ... | rw [iterate_succ_apply'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Increment | {
"line": 77,
"column": 6
} | {
"line": 77,
"column": 38
} | [
{
"pp": "case e_a\nα : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nhP : P.IsEquipartition\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nhPα : #P.parts * 16 ^ #P.parts ≤ Fintype.card α\nhPG : ¬P.IsUniform G ε\nhPα' : stepBound #P.parts ≤ Fintype.card α\nhPpos : 0 < stepB... | card_filter_add_card_filter_not, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 75,
"column": 32
} | {
"line": 75,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nhn : ¬G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔ G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s",
"usedConstants": [
"False",
"Sym2.Rel",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 75,
"column": 32
} | {
"line": 75,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nhn : ¬G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔ G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s",
"usedConstants": [
"False",
"Sym2.Rel",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 75,
"column": 32
} | {
"line": 75,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nhn : ¬G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔ G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s",
"usedConstants": [
"False",
"Sym2.Rel",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 81,
"column": 32
} | {
"line": 81,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nha : G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔\n (G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s) ∧\n s(x✝, y✝) ∉ {s(t, t)}",
"usedConstants": [... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 81,
"column": 32
} | {
"line": 81,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nha : G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔\n (G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s) ∧\n s(x✝, y✝) ∉ {s(t, t)}",
"usedConstants": [... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 81,
"column": 32
} | {
"line": 81,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝ : DecidableEq V\nha : G.Adj s t\ne : Sym2 V\nx✝ y✝ : V\nh✝¹ : x✝ = t\nh✝ : y✝ = t\n⊢ False ↔\n (G.Adj x✝ y✝ ∧ ¬(G.Adj x✝ y✝ ∧ (t = x✝ ∨ t = y✝)) ∨ s(x✝, y✝) ∈ (fun x ↦ s(x, t)) '' G.neighborSet s) ∧\n s(x✝, y✝) ∉ {s(t, t)}",
"usedConstants": [... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 158,
"column": 22
} | {
"line": 158,
"column": 30
} | [
{
"pp": "case Adj.h.h.a\nV : Type u_1\ns x✝¹ x✝ : V\n⊢ (x✝¹ = s ∧ x✝ = s ∨ x✝¹ = s ∧ x✝ = s) ∧ x✝¹ ≠ x✝ ↔ ⊥.Adj x✝¹ x✝",
"usedConstants": [
"False",
"iff_false",
"congrArg",
"SimpleGraph.Adj",
"not_true_eq_false",
"Ne",
"Bot.bot",
"SimpleGraph",
"And",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 213,
"column": 62
} | {
"line": 213,
"column": 70
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype ↑(G ⊔ edge s t).edgeSet\nhn : ¬G.Adj s t\nh : s ≠ t\n⊢ s(s, t) ∉ G.edgeFinset",
"usedConstants": [
"False",
"eq_false",
"Sym2.mk",
"congrArg",
"Finset",
"Si... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 213,
"column": 62
} | {
"line": 213,
"column": 70
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype ↑(G ⊔ edge s t).edgeSet\nhn : ¬G.Adj s t\nh : s ≠ t\n⊢ s(s, t) ∉ G.edgeFinset",
"usedConstants": [
"False",
"eq_false",
"Sym2.mk",
"congrArg",
"Finset",
"Si... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Operations | {
"line": 213,
"column": 62
} | {
"line": 213,
"column": 70
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns t : V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype ↑(G ⊔ edge s t).edgeSet\nhn : ¬G.Adj s t\nh : s ≠ t\n⊢ s(s, t) ∉ G.edgeFinset",
"usedConstants": [
"False",
"eq_false",
"Sym2.mk",
"congrArg",
"Finset",
"Si... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Walk.Traversal | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 56
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v w : V\nn : ℕ\np : G.Walk v w\nh : G.Adj u v\nhn : n ≠ 0\n⊢ (cons h p).getVert n = p.getVert (n - 1)",
"usedConstants": [
"Nat.exists_eq_add_one_of_ne_zero"
]
}
] | obtain ⟨n, rfl⟩ := Nat.exists_eq_add_one_of_ne_zero hn | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1350,
"column": 33
} | {
"line": 1350,
"column": 41
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : G.Subgraph\ns✝ s : Set V\nx✝ : ↑{v | ↑v ∉ s}\nv : ↑G'.verts\nhv : v ∈ {v | ↑v ∉ s}\n⊢ ↑v ∈ (G'.deleteVerts s).verts",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"and_self",
"Membership.mem",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1350,
"column": 33
} | {
"line": 1350,
"column": 41
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : G.Subgraph\ns✝ s : Set V\nx✝ : ↑{v | ↑v ∉ s}\nv : ↑G'.verts\nhv : v ∈ {v | ↑v ∉ s}\n⊢ ↑v ∈ (G'.deleteVerts s).verts",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"and_self",
"Membership.mem",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1350,
"column": 33
} | {
"line": 1350,
"column": 41
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : G.Subgraph\ns✝ s : Set V\nx✝ : ↑{v | ↑v ∉ s}\nv : ↑G'.verts\nhv : v ∈ {v | ↑v ∉ s}\n⊢ ↑v ∈ (G'.deleteVerts s).verts",
"usedConstants": [
"False",
"eq_false",
"congrArg",
"and_self",
"Membership.mem",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Walk.Basic | {
"line": 264,
"column": 18
} | {
"line": 264,
"column": 26
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu v u✝ : V\n⊢ nil.support[nil.length] = u✝",
"usedConstants": [
"eq_self",
"of_eq_true",
"Eq"
]
}
] | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Basic | {
"line": 264,
"column": 18
} | {
"line": 264,
"column": 26
} | [
{
"pp": "case cons\nV : Type u\nG : SimpleGraph V\nu v u✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\np_ih✝ : p✝.support[p✝.length] = w✝\n⊢ (cons h✝ p✝).support[(cons h✝ p✝).length] = w✝",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.length",
"SimpleGraph.Walk.support",
"GetE... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 118,
"column": 4
} | {
"line": 122,
"column": 11
} | [
{
"pp": "case cons\nV : Type u\nV' : Type v\nG : SimpleGraph V\nG' : SimpleGraph V'\nf : G →g G'\nhinj : Function.Injective ⇑f\nu v u✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\nih : ∀ ⦃p' : G.Walk v✝ w✝⦄, Walk.map f p✝ = Walk.map f p' → p✝ = p'\np' : G.Walk u✝ w✝\nh : Walk.map f (cons h✝ p✝) = Walk.map f ... | cases p' with
| nil => simp at h
| cons _ _ =>
simp only [map_cons, cons.injEq] at h
grind | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 118,
"column": 4
} | {
"line": 122,
"column": 11
} | [
{
"pp": "case cons\nV : Type u\nV' : Type v\nG : SimpleGraph V\nG' : SimpleGraph V'\nf : G →g G'\nhinj : Function.Injective ⇑f\nu v u✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\nih : ∀ ⦃p' : G.Walk v✝ w✝⦄, Walk.map f p✝ = Walk.map f p' → p✝ = p'\np' : G.Walk u✝ w✝\nh : Walk.map f (cons h✝ p✝) = Walk.map f ... | cases p' with
| nil => simp at h
| cons _ _ =>
simp only [map_cons, cons.injEq] at h
grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 118,
"column": 4
} | {
"line": 122,
"column": 11
} | [
{
"pp": "case cons\nV : Type u\nV' : Type v\nG : SimpleGraph V\nG' : SimpleGraph V'\nf : G →g G'\nhinj : Function.Injective ⇑f\nu v u✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\nih : ∀ ⦃p' : G.Walk v✝ w✝⦄, Walk.map f p✝ = Walk.map f p' → p✝ = p'\np' : G.Walk u✝ w✝\nh : Walk.map f (cons h✝ p✝) = Walk.map f ... | cases p' with
| nil => simp at h
| cons _ _ =>
simp only [map_cons, cons.injEq] at h
grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 102,
"column": 4
} | {
"line": 103,
"column": 48
} | [
{
"pp": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nhP : P.IsEquipartition\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nU : Finset α\nhU : U ∈ P.parts\nV : Finset α\nhV : V ∈ P.parts\nhUV : U ≠ V\nh₂ : ¬G.IsUniform ε U V\nhX : G.nonuniformWitness ε U V ∈ P.nonunif... | simp only [not_exists, mem_biUnion, and_imp, mem_filter,
not_and, mem_sdiff, id, mem_sdiff] at hx ⊢ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 205,
"column": 77
} | {
"line": 205,
"column": 85
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu✝ v✝¹ u'✝ v' w✝ : V\np : G.Walk u✝ v✝¹\nH : SimpleGraph V\ns s' : Set V\nu v✝ v u' : V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 205,
"column": 77
} | {
"line": 205,
"column": 85
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu✝ v✝¹ u'✝ v' w✝ : V\np : G.Walk u✝ v✝¹\nH : SimpleGraph V\ns s' : Set V\nu v✝ v u' : V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 205,
"column": 77
} | {
"line": 205,
"column": 85
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu✝ v✝¹ u'✝ v' w✝ : V\np : G.Walk u✝ v✝¹\nH : SimpleGraph V\ns s' : Set V\nu v✝ v u' : V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 210,
"column": 76
} | {
"line": 210,
"column": 84
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' w✝ : V\np : G.Walk u v\nH : SimpleGraph V\ns s' : Set V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ∈ w.support, x ∈ s",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 210,
"column": 76
} | {
"line": 210,
"column": 84
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' w✝ : V\np : G.Walk u v\nH : SimpleGraph V\ns s' : Set V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ∈ w.support, x ∈ s",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Walk.Maps | {
"line": 210,
"column": 76
} | {
"line": 210,
"column": 84
} | [
{
"pp": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' w✝ : V\np : G.Walk u v\nH : SimpleGraph V\ns s' : Set V\nhuu' : G.Adj u u'\nw : G.Walk u' v\nhw : ∀ x ∈ (cons huu' w).support, x ∈ s\n⊢ ∀ x ∈ w.support, x ∈ s",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | {
"line": 84,
"column": 6
} | {
"line": 84,
"column": 26
} | [
{
"pp": "case cons.mp\nV : Type u_1\nG : SimpleGraph V\nu v u' v✝ : V\nh : G.Adj u v✝\np : G.Walk v✝ v\n⊢ (cons h p).IsSubwalk nil → ∃ (hu : u' = u) (hv : u' = v), cons h p = nil.copy hu hv",
"usedConstants": [
"SimpleGraph.Walk.cons",
"SimpleGraph.Walk.IsSubwalk",
"SimpleGraph.Walk.nil"
... | rintro ⟨_ | _, _, h⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Combinatorics.SimpleGraph.Walk.Operations | {
"line": 656,
"column": 41
} | {
"line": 656,
"column": 64
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\nn : ℕ\np : G.Walk u v\nh : p.length ≤ n\n⊢ p.length - n = 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.length",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"instHSub",
"Nat",
"... | Nat.sub_eq_zero_of_le h | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 244,
"column": 24
} | {
"line": 244,
"column": 32
} | [
{
"pp": "case inl\nV : Type u\nG : SimpleGraph V\nw : V\ninst✝ : DecidableEq V\nu v : V\nn : ℕ\np : G.Walk u v\nhw : w ∈ p.support\nhn : n ≤ (p.takeUntil w hw).length\nh✝ : n < (p.takeUntil w hw).length\n⊢ (p.takeUntil w hw).getVert n =\n if n < (p.takeUntil w hw).length then (p.takeUntil w hw).getVert n\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 244,
"column": 24
} | {
"line": 244,
"column": 32
} | [
{
"pp": "case inr\nV : Type u\nG : SimpleGraph V\nw : V\ninst✝ : DecidableEq V\nu v : V\nn : ℕ\np : G.Walk u v\nhw : w ∈ p.support\nhn : n ≤ (p.takeUntil w hw).length\nh✝ : n = (p.takeUntil w hw).length\n⊢ (p.takeUntil w hw).getVert n =\n if n < (p.takeUntil w hw).length then (p.takeUntil w hw).getVert n\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 293,
"column": 4
} | {
"line": 293,
"column": 33
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv u : V\ninst✝ : DecidableEq V\np : G.Walk u v\nw x : V\nh : x ≠ w\nhw : w ∈ p.support\nhx : x ∈ (p.takeUntil w hw).support\nhw' : w ∈ ((p.takeUntil w hw).takeUntil x hx).support\nh1 : (((p.takeUntil w hw).takeUntil x hx).takeUntil w hw').length < ((p.takeUntil w hw).take... | exact length_takeUntil_lt _ h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 40
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v w : V\np : G.Walk u v\nq : G.Walk v w\n⊢ (p.append q).IsPath → p.IsPath",
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.support",
"id",
"List.tail",
"List.Nodup",
"instHAppendOfAppend",
"List",
"im... | simp only [isPath_def, support_append] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 390,
"column": 11
} | {
"line": 390,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu v u✝ : V\nhp : Walk.nil.IsPath\nn : ℕ\nhn : n ∈ {i | i ≤ Walk.nil.length}\nm : ℕ\nhm : m ∈ {i | i ≤ Walk.nil.length}\nhnm : Walk.nil.getVert n = Walk.nil.getVert m\n⊢ n = m",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.length",
"setO... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 390,
"column": 11
} | {
"line": 390,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu v u✝ : V\nhp : Walk.nil.IsPath\nn : ℕ\nhn : n ∈ {i | i ≤ Walk.nil.length}\nm : ℕ\nhm : m ∈ {i | i ≤ Walk.nil.length}\nhnm : Walk.nil.getVert n = Walk.nil.getVert m\n⊢ n = m",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.length",
"setO... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 390,
"column": 11
} | {
"line": 390,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu v u✝ : V\nhp : Walk.nil.IsPath\nn : ℕ\nhn : n ∈ {i | i ≤ Walk.nil.length}\nm : ℕ\nhm : m ∈ {i | i ≤ Walk.nil.length}\nhnm : Walk.nil.getVert n = Walk.nil.getVert m\n⊢ n = m",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.length",
"setO... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 399,
"column": 37
} | {
"line": 399,
"column": 45
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu✝ v✝ v w u : V\nh : G.Adj v w\np : G.Walk w u\nihp :\n p.IsPath → ∀ ⦃n : ℕ⦄, n ∈ {i | i ≤ p.length} → ∀ ⦃m : ℕ⦄, m ∈ {i | i ≤ p.length} → p.getVert n = p.getVert m → n = m\nhp : (cons h p).IsPath\nn : ℕ\nhn : n ≤ p.length + 1\nm : ℕ\nhm : m ≤ p.length + 1\nhn0 : ¬n = 0\... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 408,
"column": 25
} | {
"line": 408,
"column": 33
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu w : V\ni : ℕ\np : G.Walk u w\nhp : p.IsPath\nh : ¬p.Nil\n⊢ i = 0 → p.getVert i = u",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.getVert_zero",
"instOfNatNat",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 408,
"column": 25
} | {
"line": 408,
"column": 33
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu w : V\ni : ℕ\np : G.Walk u w\nhp : p.IsPath\nh : ¬p.Nil\n⊢ i = 0 → p.getVert i = u",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.getVert_zero",
"instOfNatNat",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 408,
"column": 25
} | {
"line": 408,
"column": 33
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu w : V\ni : ℕ\np : G.Walk u w\nhp : p.IsPath\nh : ¬p.Nil\n⊢ i = 0 → p.getVert i = u",
"usedConstants": [
"congrArg",
"SimpleGraph.Walk.getVert_zero",
"instOfNatNat",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 414,
"column": 4
} | {
"line": 414,
"column": 12
} | [
{
"pp": "case neg\nV : Type u\nG : SimpleGraph V\nw : V\ni : ℕ\np : G.Walk w w\nhp : p.IsPath\nh : ¬p.Nil\nh' : ¬i ≤ p.length\n⊢ i = 0",
"usedConstants": [
"False",
"eq_false",
"False.elim",
"SimpleGraph.Walk",
"Eq.mp",
"instOfNatNat",
"SimpleGraph.Walk.isPath_iff_e... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 456,
"column": 50
} | {
"line": 456,
"column": 58
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu v w u✝ : V\nhp : Walk.nil.IsPath\nhnil : ¬Walk.nil.Nil\nhmem : ((u✝, w) = (u✝, Walk.nil.snd) ∨ (u✝, w) = (u✝, Walk.nil.snd).swap) ∨ s(u✝, w) ∈ Walk.nil.tail.edges\n⊢ u✝ ∉ Walk.nil.tail.support",
"usedConstants": [
"False",
"congrArg",
"Fa... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 456,
"column": 50
} | {
"line": 456,
"column": 58
} | [
{
"pp": "case cons\nV : Type u\nG : SimpleGraph V\nu v w u✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\np_ih✝ :\n p✝.IsPath →\n ¬p✝.Nil → ((v✝, w) = (v✝, p✝.snd) ∨ (v✝, w) = (v✝, p✝.snd).swap) ∨ s(v✝, w) ∈ p✝.tail.edges → v✝ ∉ p✝.tail.support\nhp : (cons h✝ p✝).IsPath\nhnil : ¬(cons h✝ p✝).Nil\nhmem : (... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 485,
"column": 8
} | {
"line": 485,
"column": 16
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu : V\np : G.Walk u u\nhpc✝ : p.IsCycle\nhpc : (cons ⋯ p.tail).IsCycle\nn : ℕ\nhn : 1 ≤ n ∧ n ≤ p.tail.length + 1\nm : ℕ\nhm : 1 ≤ m ∧ m ≤ p.tail.length + 1\nhnm : p.getVert n = p.getVert m\n⊢ p.tail.getVert (n - 1) = p.tail.getVert (m - 1)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 485,
"column": 8
} | {
"line": 485,
"column": 16
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu : V\np : G.Walk u u\nhpc✝ : p.IsCycle\nhpc : (cons ⋯ p.tail).IsCycle\nn : ℕ\nhn : 1 ≤ n ∧ n ≤ p.tail.length + 1\nm : ℕ\nhm : 1 ≤ m ∧ m ≤ p.tail.length + 1\nhnm : p.getVert n = p.getVert m\n⊢ p.tail.getVert (n - 1) = p.tail.getVert (m - 1)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 485,
"column": 8
} | {
"line": 485,
"column": 16
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu : V\np : G.Walk u u\nhpc✝ : p.IsCycle\nhpc : (cons ⋯ p.tail).IsCycle\nn : ℕ\nhn : 1 ≤ n ∧ n ≤ p.tail.length + 1\nm : ℕ\nhm : 1 ≤ m ∧ m ≤ p.tail.length + 1\nhnm : p.getVert n = p.getVert m\n⊢ p.tail.getVert (n - 1) = p.tail.getVert (m - 1)",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 530,
"column": 11
} | {
"line": 530,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu : V\nx✝ : nil.tail.IsPath ∧ 3 ≤ nil.length\nh₁ : nil.tail.IsPath\nh₂ : 3 ≤ nil.length\n⊢ nil.IsCycle",
"usedConstants": [
"False",
"congrArg",
"SimpleGraph.Walk.length",
"False.elim",
"noConfusion_of_Nat",
"SimpleGraph.W... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 530,
"column": 11
} | {
"line": 530,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu : V\nx✝ : nil.tail.IsPath ∧ 3 ≤ nil.length\nh₁ : nil.tail.IsPath\nh₂ : 3 ≤ nil.length\n⊢ nil.IsCycle",
"usedConstants": [
"False",
"congrArg",
"SimpleGraph.Walk.length",
"False.elim",
"noConfusion_of_Nat",
"SimpleGraph.W... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 530,
"column": 11
} | {
"line": 530,
"column": 19
} | [
{
"pp": "case nil\nV : Type u\nG : SimpleGraph V\nu : V\nx✝ : nil.tail.IsPath ∧ 3 ≤ nil.length\nh₁ : nil.tail.IsPath\nh₂ : 3 ≤ nil.length\n⊢ nil.IsCycle",
"usedConstants": [
"False",
"congrArg",
"SimpleGraph.Walk.length",
"False.elim",
"noConfusion_of_Nat",
"SimpleGraph.W... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Clique | {
"line": 194,
"column": 32
} | {
"line": 198,
"column": 50
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : SimpleGraph α\nf : ⊤.Copy G\n⊢ G.IsClique (Set.range ⇑f)",
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Copy.topEmbedding",
"SimpleGraph.Copy.topEmbedding_apply",
"congrArg",
"SimpleGraph.Embedding.map_adj_iff",
"SimpleGraph.Adj",
... | by
intro _ ⟨_, h⟩ _ ⟨_, h'⟩ nh
rw [← h, ← Copy.topEmbedding_apply, ← h', ← Copy.topEmbedding_apply] at nh ⊢
rwa [← f.topEmbedding.coe_toEmbedding, (f.topEmbedding.apply_eq_iff_eq _ _).ne,
← top_adj, ← f.topEmbedding.map_adj_iff] at nh | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Paths | {
"line": 853,
"column": 8
} | {
"line": 853,
"column": 28
} | [
{
"pp": "case cons\nV : Type u\nV' : Type v\nG : SimpleGraph V\nG' : SimpleGraph V'\nf : G →g G'\nu v : V\np : G.Walk u v\nhinj : Injective ⇑f\nu✝ v✝ w✝ : V\nh✝ : G.Adj u✝ v✝\np✝ : G.Walk v✝ w✝\nih : p✝.IsPath → (Walk.map f p✝).IsPath\nhp : (cons h✝ p✝).IsPath\n⊢ (Walk.map f (cons h✝ p✝)).IsPath",
"usedCons... | Walk.cons_isPath_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Triangle.Counting | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 60
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\ninst✝¹ : DecidableRel G.Adj\nε : ℝ\ns t u : Finset α\ninst✝ : DecidableEq α\ndst : 2 * ε ≤ ↑(G.edgeDensity s t)\ndsu : 2 * ε ≤ ↑(G.edgeDensity s u)\ndtu : 2 * ε ≤ ↑(G.edgeDensity t u)\nutu : G.IsUniform ε t u\nx : α\nhx :\n x ∈ s ∧ x ∉ s ∨\n x ∈ s ∧\n (↑(G.edge... | simp only [false_or, and_not_self, mul_comm (_ - _)] at hx | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Clique | {
"line": 424,
"column": 6
} | {
"line": 424,
"column": 20
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\nn : ℕ\ninst✝ : Fintype α\nhc : Fintype.card α < n\n⊢ G.CliqueFree n",
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Copy",
"SimpleGraph.completeGraph",
"id",
"SimpleGraph.cliqueFree_iff",
"IsEmpty",
"SimpleGrap... | cliqueFree_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Clique | {
"line": 582,
"column": 2
} | {
"line": 582,
"column": 31
} | [
{
"pp": "case refine_2\nα : Type u_1\nG : SimpleGraph α\ns : Set α\n⊢ s.Pairwise G.Adjᶜ → ∀ ⦃t : Finset α⦄, ↑t ⊆ s → G.IsClique ↑t → ∀ (x x_1 : α), x ≠ x_1 → ¬t = {x, x_1}",
"usedConstants": [
"Compl.compl",
"SimpleGraph.Adj",
"Prop.instCompl",
"Pi.instCompl",
"Set.Pairwise"
... | rintro h t hst ht a b hab rfl | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Combinatorics.Additive.DoublingConst | {
"line": 83,
"column": 71
} | {
"line": 84,
"column": 34
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA B : Finset G\n⊢ ↑(#A) * σₘ[A, B] = ↑(#(A * B))",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Finset.mulConst_mul_card",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toNonU... | by
rw [mul_comm, mulConst_mul_card] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.Energy | {
"line": 142,
"column": 60
} | {
"line": 151,
"column": 53
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Mul α\ns t u : Finset α\n⊢ #({xy ∈ s ×ˢ t | xy.1 * xy.2 ∈ u}) ^ 2 ≤ #u * Eₘ[s, t]",
"usedConstants": [
"instPowNat",
"one_pow",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mu... | by
calc
_ = (∑ c ∈ u, #{xy ∈ s ×ˢ t | xy.1 * xy.2 = c}) ^ 2 := by
rw [← sum_card_fiberwise_eq_card_filter]
_ ≤ #u * ∑ c ∈ u, #{xy ∈ s ×ˢ t | xy.1 * xy.2 = c} ^ 2 := by
simpa using sum_mul_sq_le_sq_mul_sq (R := ℕ) _ 1 _
_ ≤ #u * ∑ c ∈ s * t, #{xy ∈ s ×ˢ t | xy.1 * xy.2 = c} ^ 2 := by
... | [anonymous] | Lean.Parser.Term.byTactic |
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