module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Triangulated.Opposite.Functor | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 30
} | {
"line": 155,
"column": 31
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\ninst✝² : HasShift C ℤ\ninst✝¹ : HasShift D ℤ\nF : C ⥤ D\ninst✝ : F.CommShift ℤ\nX : Cᵒᵖ\nn : ℤ\n⊢ (F.map ((shiftFunctorOpIso C n (-n) ⋯).hom.app (op ((shiftFunctor C n).obj (unop X)))).unop).op ≫\n ((commSh... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\ninst✝² : HasShift C ℤ\ninst✝¹ : HasShift D ℤ\nF : C ⥤ D\ninst✝ : F.CommShift ℤ\nX : Cᵒᵖ\nn : ℤ\n⊢ (F.map ((shiftFunctorOpIso C n (-n) ⋯).hom.app (op ((shiftFunctor C n).obj (unop X)))).unop).op ≫\n ((commShiftIso F (-n... | NatTrans.naturality_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.Opposite.Functor | {
"line": 168,
"column": 2
} | {
"line": 170,
"column": 23
} | {
"line": 171,
"column": 2
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\ninst✝² : HasShift C ℤ\ninst✝¹ : HasShift D ℤ\nF : C ⥤ D\ninst✝ : F.CommShift ℤ\nX : Cᵒᵖ\nn : ℤ\n⊢ F.map (𝟙 (unop X)) =\n (((opShiftFunctorEquivalence D n).counitIso.hom.app (op (F.obj (unop X)))).unop ≫\n ... | [
"C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\ninst✝² : HasShift C ℤ\ninst✝¹ : HasShift D ℤ\nF : C ⥤ D\ninst✝ : F.CommShift ℤ\nX : Cᵒᵖ\nn : ℤ\n⊢ 𝟙 (F.obj (unop X)) =\n ((opShiftFunctorEquivalence D n).counitIso.inv.app (op (F.obj (unop X))) ≫\n (shiftFunctor ... | simp only [map_id, assoc, ← Functor.map_comp_assoc,
← unop_comp, Iso.inv_hom_id_app_assoc, ← op_comp,
Iso.inv_hom_id_app] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 162,
"column": 6
} | {
"line": 163,
"column": 85
} | {
"line": 163,
"column": 85
} | [
{
"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... | [] | have := mono_ιK hι hT hT'
rw [← cancel_mono (ιK f₃ α), (exists_lift_ιK hι hT hT' x₁ hx₁).choose_spec, hm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | {
"line": 162,
"column": 6
} | {
"line": 163,
"column": 85
} | {
"line": 163,
"column": 85
} | [
{
"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... | [] | have := mono_ιK hι hT hT'
rw [← cancel_mono (ιK f₃ α), (exists_lift_ιK hι hT hT' x₁ hx₁).choose_spec, hm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 314,
"column": 66
} | {
"line": 320,
"column": 18
} | {
"line": 322,
"column": 0
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝³ : DecidableEq α\ninst✝² : Monoid α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid β\ns : Finset α\nt : Finset β\n⊢ mulRothNumber s * mulRothNumber t ≤ mulRothNumber (s ×ˢ t)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"E... | [] | by
obtain ⟨u, hus, hucard, hu⟩ := mulRothNumber_spec s
obtain ⟨v, hvt, hvcard, hv⟩ := mulRothNumber_spec t
rw [← hucard, ← hvcard, ← card_product]
refine ThreeGPFree.le_mulRothNumber ?_ (product_subset_product hus hvt)
rw [coe_product]
exact hu.prod hv | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.AP.Three.Defs | {
"line": 442,
"column": 6
} | {
"line": 442,
"column": 19
} | {
"line": 442,
"column": 20
} | [
{
"pp": "case e'_2\na b : ℕ\nh : a ≤ b\n⊢ Ico a b = map (addLeftEmbedding a) (range (b - a))",
"ppTerm": "?e'_2",
"assigned": true,
"usedConstants": [
"addLeftEmbedding",
"Eq.mpr",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"congrArg",
"Finset",
"AddMonoid.toAddZ... | [
"case e'_2\na b : ℕ\nh : a ≤ b\n⊢ Ico a b = map (addLeftEmbedding a) (Ico 0 (b - a))"
] | range_eq_Ico, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.AP.Three.Behrend | {
"line": 433,
"column": 68
} | {
"line": 433,
"column": 81
} | {
"line": 434,
"column": 4
} | [
{
"pp": "N : ℕ\nhN : 4096 ≤ N\nn : ℕ := nValue N\nhn : 0 < ↑n\nhd : 0 < dValue N\nhN₀ : 0 < ↑N\nhn₂ : 2 < n\nthis : (2 * dValue N - 1) ^ n ≤ N\n⊢ ↑N * rexp (-4 * √(log ↑N)) ≤ ↑N ^ (1 - 2 / ↑n) / rexp 1 ^ (↑n - 2) / ↑n",
"ppTerm": "?m.285",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"N : ℕ\nhN : 4096 ≤ N\nn : ℕ := nValue N\nhn : 0 < ↑n\nhd : 0 < dValue N\nhN₀ : 0 < ↑N\nhn₂ : 2 < n\nthis : (2 * dValue N - 1) ^ n ≤ N\n⊢ ↑N * rexp (-4 * √(log ↑N)) ≤ ↑N ^ (1 - 2 / ↑n) / rexp (↑n - 2) / ↑n"
] | exp_one_rpow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 96,
"column": 34
} | {
"line": 96,
"column": 75
} | {
"line": 97,
"column": 6
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA : IsApproximateSubgroup K ↑A\nn : ℕ\nF : Finset G\nhF : ↑(#F) ≤ K\nhSF : ↑A ^ 2 ⊆ ↑F • ↑A\n⊢ ↑(#(F ^ (n + 1))) * ↑(#A) ≤ ↑(#F) ^ (n + 1) * ↑(#A)",
"ppTerm": "?m.198",
"assigned": true,
"usedConstants": [
"R... | [] | gcongr; exact mod_cast Finset.card_pow_le | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 96,
"column": 34
} | {
"line": 96,
"column": 75
} | {
"line": 97,
"column": 6
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA : IsApproximateSubgroup K ↑A\nn : ℕ\nF : Finset G\nhF : ↑(#F) ≤ K\nhSF : ↑A ^ 2 ⊆ ↑F • ↑A\n⊢ ↑(#(F ^ (n + 1))) * ↑(#A) ≤ ↑(#F) ^ (n + 1) * ↑(#A)",
"ppTerm": "?m.198",
"assigned": true,
"usedConstants": [
"R... | [] | gcongr; exact mod_cast Finset.card_pow_le | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Maps | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 30
} | {
"line": 390,
"column": 2
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nhinj : Injective ⇑f\ne₁ : Sym2 V\nh₁ : e₁ ∈ G.edgeSet\ne₂ : Sym2 V\nh₂ : e₂ ∈ G.edgeSet\n⊢ ⟨Sym2.map (⇑f) e₁, ⋯⟩ = ⟨Sym2.map (⇑f) e₂, ⋯⟩ → ⟨e₁, h₁⟩ = ⟨e₂, h₂⟩",
"ppTerm": "?m.31",
"assigned": true,
"usedConstant... | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nhinj : Injective ⇑f\ne₁ : Sym2 V\nh₁ : e₁ ∈ G.edgeSet\ne₂ : Sym2 V\nh₂ : e₂ ∈ G.edgeSet\n⊢ Sym2.map (⇑f) e₁ = Sym2.map (⇑f) e₂ → e₁ = e₂"
] | repeat rw [Subtype.mk_eq_mk] | Lean.Elab.Tactic.evalRepeat | Lean.Parser.Tactic.tacticRepeat_ |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 79,
"column": 71
} | {
"line": 79,
"column": 88
} | {
"line": 81,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset = G₂.edgeFinset ↔ G₁ = G₂",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"RelEmbedding.instEmbeddingLike",
"LE.le",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 79,
"column": 71
} | {
"line": 79,
"column": 88
} | {
"line": 81,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset = G₂.edgeFinset ↔ G₁ = G₂",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"RelEmbedding.instEmbeddingLike",
"LE.le",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 79,
"column": 71
} | {
"line": 79,
"column": 88
} | {
"line": 81,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset = G₂.edgeFinset ↔ G₁ = G₂",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"RelEmbedding.instEmbeddingLike",
"LE.le",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 19
} | {
"line": 85,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊆ G₂.edgeFinset ↔ G₁ ≤ G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 19
} | {
"line": 85,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊆ G₂.edgeFinset ↔ G₁ ≤ G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 19
} | {
"line": 85,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊆ G₂.edgeFinset ↔ G₁ ≤ G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 19
} | {
"line": 89,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊂ G₂.edgeFinset ↔ G₁ < G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 19
} | {
"line": 89,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊂ G₂.edgeFinset ↔ G₁ < G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 19
} | {
"line": 89,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝¹ : Fintype ↑G₁.edgeSet\ninst✝ : Fintype ↑G₂.edgeSet\n⊢ G₁.edgeFinset ⊂ G₂.edgeFinset ↔ G₁ < G₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 95,
"column": 66
} | {
"line": 95,
"column": 83
} | {
"line": 97,
"column": 0
} | [
{
"pp": "V : Type u_1\n⊢ ⊥.edgeFinset = ∅",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_congr",
"SimpleGraph.edgeSet_bot",
"Bot.bot",
"Set.toFinset",
"Set.toFinset_empty",
"Finset.instEmptyCollection",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 95,
"column": 66
} | {
"line": 95,
"column": 83
} | {
"line": 97,
"column": 0
} | [
{
"pp": "V : Type u_1\n⊢ ⊥.edgeFinset = ∅",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_congr",
"SimpleGraph.edgeSet_bot",
"Bot.bot",
"Set.toFinset",
"Set.toFinset_empty",
"Finset.instEmptyCollection",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 95,
"column": 66
} | {
"line": 95,
"column": 83
} | {
"line": 97,
"column": 0
} | [
{
"pp": "V : Type u_1\n⊢ ⊥.edgeFinset = ∅",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_congr",
"SimpleGraph.edgeSet_bot",
"Bot.bot",
"Set.toFinset",
"Set.toFinset_empty",
"Finset.instEmptyCollection",
... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 99,
"column": 63
} | {
"line": 99,
"column": 80
} | {
"line": 101,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑G₁.edgeSet\ninst✝² : Fintype ↑G₂.edgeSet\ninst✝¹ : Fintype ↑(G₁ ⊔ G₂).edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊔ G₂).edgeFinset = G₁.edgeFinset ∪ G₂.edgeFinset",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.toFinset_u... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 99,
"column": 63
} | {
"line": 99,
"column": 80
} | {
"line": 101,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑G₁.edgeSet\ninst✝² : Fintype ↑G₂.edgeSet\ninst✝¹ : Fintype ↑(G₁ ⊔ G₂).edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊔ G₂).edgeFinset = G₁.edgeFinset ∪ G₂.edgeFinset",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.toFinset_u... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 99,
"column": 63
} | {
"line": 99,
"column": 80
} | {
"line": 101,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑G₁.edgeSet\ninst✝² : Fintype ↑G₂.edgeSet\ninst✝¹ : Fintype ↑(G₁ ⊔ G₂).edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊔ G₂).edgeFinset = G₁.edgeFinset ∪ G₂.edgeFinset",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.toFinset_u... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 19
} | {
"line": 105,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊓ G₂).edgeFinset = G₁.edgeFinset ∩ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SimpleGraph.instMin",
"congrArg",
"Fins... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 19
} | {
"line": 105,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊓ G₂).edgeFinset = G₁.edgeFinset ∩ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SimpleGraph.instMin",
"congrArg",
"Fins... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 19
} | {
"line": 105,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ ⊓ G₂).edgeFinset = G₁.edgeFinset ∩ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"SimpleGraph.instMin",
"congrArg",
"Fins... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 107,
"column": 63
} | {
"line": 107,
"column": 80
} | {
"line": 109,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ \\ G₂).edgeFinset = G₁.edgeFinset \\ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_co... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 107,
"column": 63
} | {
"line": 107,
"column": 80
} | {
"line": 109,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ \\ G₂).edgeFinset = G₁.edgeFinset \\ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_co... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 107,
"column": 63
} | {
"line": 107,
"column": 80
} | {
"line": 109,
"column": 0
} | [
{
"pp": "V : Type u_1\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑G₁.edgeSet\ninst✝¹ : Fintype ↑G₂.edgeSet\ninst✝ : DecidableEq V\n⊢ (G₁ \\ G₂).edgeFinset = G₁.edgeFinset \\ G₂.edgeFinset",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.toFinset_co... | [] | simp [edgeFinset] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 402,
"column": 2
} | {
"line": 403,
"column": 40
} | {
"line": 405,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Subsingleton V\n⊢ G.minDegree = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finset.univ",
"Finset.image_const",
"congrArg",
"Finset",
"Membership.mem",
... | [] | cases isEmpty_or_nonempty V <;>
simp [minDegree, Finset.image_const] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 402,
"column": 2
} | {
"line": 403,
"column": 40
} | {
"line": 405,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Subsingleton V\n⊢ G.minDegree = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finset.univ",
"Finset.image_const",
"congrArg",
"Finset",
"Membership.mem",
... | [] | cases isEmpty_or_nonempty V <;>
simp [minDegree, Finset.image_const] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 402,
"column": 2
} | {
"line": 403,
"column": 40
} | {
"line": 405,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Subsingleton V\n⊢ G.minDegree = 0",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finset.univ",
"Finset.image_const",
"congrArg",
"Finset",
"Membership.mem",
... | [] | cases isEmpty_or_nonempty V <;>
simp [minDegree, Finset.image_const] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 420,
"column": 2
} | {
"line": 422,
"column": 28
} | {
"line": 424,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Nonempty V\n⊢ G.minDegree < Fintype.card V",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.degree_lt_card_verts",
"congrArg",
"Membership.mem",
... | [] | have ⟨v, hv⟩ := G.exists_minimal_degree_vertex
rw [hv]
apply degree_lt_card_verts | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 420,
"column": 2
} | {
"line": 422,
"column": 28
} | {
"line": 424,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Nonempty V\n⊢ G.minDegree < Fintype.card V",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.degree_lt_card_verts",
"congrArg",
"Membership.mem",
... | [] | have ⟨v, hv⟩ := G.exists_minimal_degree_vertex
rw [hv]
apply degree_lt_card_verts | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Equitable | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 6
} | {
"line": 107,
"column": 2
} | [
{
"pp": "case neg\nα : Type u_1\ns : Finset α\nf : α → ℕ\nb : ℕ\nhb : ∀ a ∈ ↑s, b ≤ f a ∧ f a ≤ b + 1\nx : α\nhx₁ : x ∈ s\nhx₂ : f x ≠ b + 1\n⊢ b = (∑ i ∈ s, f i) / #s",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"instHDiv",
"HDiv.hDiv",
"Nat",
"Nat.instDiv",
... | [
"case neg\nα : Type u_1\ns : Finset α\nf : α → ℕ\nb : ℕ\nhb : ∀ a ∈ ↑s, b ≤ f a ∧ f a ≤ b + 1\nx : α\nhx₁ : x ∈ s\nhx₂ : f x ≠ b + 1\n⊢ (∑ i ∈ s, f i) / #s = b"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.Set.Equitable | {
"line": 124,
"column": 11
} | {
"line": 124,
"column": 41
} | {
"line": 124,
"column": 42
} | [
{
"pp": "α : Type u_1\ns : Finset α\nf : α → ℕ\n⊢ (↑s).EquitableOn f ↔ ∀ a ∈ s, f a = (∑ i ∈ s, f i) / #s ∨ f a = (∑ i ∈ s, f i) / #s + 1",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Set.EquitableOn",
"Eq.mpr",
"instHDiv",
"Nat.instOne",
"congrArg",
... | [
"α : Type u_1\ns : Finset α\nf : α → ℕ\n⊢ (∀ a ∈ s, (∑ i ∈ s, f i) / #s ≤ f a ∧ f a ≤ (∑ i ∈ s, f i) / #s + 1) ↔\n ∀ a ∈ s, f a = (∑ i ∈ s, f i) / #s ∨ f a = (∑ i ∈ s, f i) / #s + 1"
] | equitableOn_iff_le_le_add_one, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 594,
"column": 51
} | {
"line": 594,
"column": 95
} | {
"line": 594,
"column": 95
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nW : Type u_2\nG' : SimpleGraph W\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype W\ninst✝ : DecidableRel G'.Adj\nf : G ≃g G'\nthis : (fun x ↦ G'.degree x) ∘ ⇑f = fun x ↦ G.degree x\n⊢ WithTop.untopD 0 (image (fun x ↦ G'.degree x) (image (⇑f) univ)).mi... | [
"V : Type u_1\nG : SimpleGraph V\nW : Type u_2\nG' : SimpleGraph W\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype W\ninst✝ : DecidableRel G'.Adj\nf : G ≃g G'\nthis : (fun x ↦ G'.degree x) ∘ ⇑f = fun x ↦ G.degree x\n⊢ WithTop.untopD 0 (image (fun x ↦ G'.degree x) univ).min = WithTop.untopD 0 (ima... | Finset.image_univ_of_surjective f.surjective | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 599,
"column": 51
} | {
"line": 599,
"column": 95
} | {
"line": 599,
"column": 95
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nW : Type u_2\nG' : SimpleGraph W\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype W\ninst✝ : DecidableRel G'.Adj\nf : G ≃g G'\nthis : (fun x ↦ G'.degree x) ∘ ⇑f = fun x ↦ G.degree x\n⊢ WithBot.unbotD 0 (image (fun x ↦ G'.degree x) (image (⇑f) univ)).ma... | [
"V : Type u_1\nG : SimpleGraph V\nW : Type u_2\nG' : SimpleGraph W\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype W\ninst✝ : DecidableRel G'.Adj\nf : G ≃g G'\nthis : (fun x ↦ G'.degree x) ∘ ⇑f = fun x ↦ G.degree x\n⊢ WithBot.unbotD 0 (image (fun x ↦ G'.degree x) univ).max = WithBot.unbotD 0 (ima... | Finset.image_univ_of_surjective f.surjective | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Partition.Equipartition | {
"line": 132,
"column": 39
} | {
"line": 140,
"column": 84
} | {
"line": 141,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nP : Finpartition s\nhP : P.IsEquipartition\nf : ↥s ≃ (t : ↥P.parts) × Fin #↑t\nhf : ∀ (a b : ↥s), P.part ↑a = P.part ↑b ↔ (f a).fst = (f b).fst\ng : ↥P.parts ≃ Fin #P.parts\nhg : ∀ (t : ↥P.parts), #↑t = #s / #P.parts + 1 ↔ ↑(g t) < #s % #P.parts\nz : ↥... | [] | by
rcases hP.card_parts_eq_average (f a).1.2 with (c | c)
· calc
_ < #P.parts * ((f a).2 + 1) := by simp only [z, mul_add_one]; gcongr; exact gl a
_ ≤ #P.parts * (#s / #P.parts) := by gcongr; exact c ▸ (f a).2.2
_ ≤ #P.parts * (#s / #P.parts) + #s % #P.parts := Nat.le_add_right ..
... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 48,
"column": 89
} | {
"line": 48,
"column": 95
} | {
"line": 50,
"column": 0
} | [
{
"pp": "case ha\nx✝¹ x✝ : ℕ\nh : x✝¹ ≤ x✝\n⊢ 1 ≤ 4",
"ppTerm": "?ha",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"of_decide_eq_true",
"Preorder.toLE",
"id",
"instOfNatNat",
"LE.le",
"MulZeroOneClass.toMulOneClass",
"Bool.true",
"Nat.in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 73,
"column": 23
} | {
"line": 73,
"column": 29
} | {
"line": 73,
"column": 29
} | [
{
"pp": "ε : ℝ\nn : ℕ\nh : 100 ≤ 4 ^ n * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 73,
"column": 23
} | {
"line": 73,
"column": 29
} | {
"line": 73,
"column": 29
} | [
{
"pp": "ε : ℝ\nn : ℕ\nh : 100 ≤ 4 ^ n * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 73,
"column": 23
} | {
"line": 73,
"column": 29
} | {
"line": 73,
"column": 29
} | [
{
"pp": "ε : ℝ\nn : ℕ\nh : 100 ≤ 4 ^ n * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 120,
"column": 23
} | {
"line": 120,
"column": 29
} | {
"line": 120,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nP : Finpartition univ\nε : ℝ\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 120,
"column": 23
} | {
"line": 120,
"column": 29
} | {
"line": 120,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nP : Finpartition univ\nε : ℝ\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 120,
"column": 23
} | {
"line": 120,
"column": 29
} | {
"line": 120,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nP : Finpartition univ\nε : ℝ\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\n⊢ Odd 5",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Partition.Finpartition | {
"line": 428,
"column": 6
} | {
"line": 428,
"column": 37
} | {
"line": 429,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\na b✝ c✝ : α\nP Q R : Finpartition a\nhPQ : P ≤ Q\nhPR : P ≤ R\nb : α\nhb : b ∈ P.parts\nc : α\nhc : c ∈ Q.parts\nhbc : b ≤ c\nd : α\nhd : d ∈ R.parts\nhbd : b ≤ d\n⊢ ∃ c ∈ (Q ⊓ R).parts, b ≤ c",
"ppTerm": "?m.190",... | [
"α : Type u_1\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\na b✝ c✝ : α\nP Q R : Finpartition a\nhPQ : P ≤ Q\nhPR : P ≤ R\nb : α\nhb : b ∈ P.parts\nc : α\nhc : c ∈ Q.parts\nhbc : b ≤ c\nd : α\nhd : d ∈ R.parts\nhbd : b ≤ d\nh : b ≤ c ⊓ d\n⊢ ∃ c ∈ (Q ⊓ R).parts, b ≤ c"
] | have h := _root_.le_inf hbc hbd | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 277,
"column": 4
} | {
"line": 277,
"column": 42
} | {
"line": 278,
"column": 2
} | [
{
"pp": "case coe\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\nX : C\nn : ℤ\ninst✝ : t.IsGE X n\nj : ℤ\nhj : WithBotTop.coe j ≤ WithBotTop.coe... | [] | exact t.isZero_truncLT_obj_of_isGE _ _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Partition.Finpartition | {
"line": 586,
"column": 2
} | {
"line": 590,
"column": 23
} | {
"line": 592,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\n⊢ c ∈ (P.avoid b).parts ↔ ∃ d ∈ P.parts, ¬d ≤ b ∧ d \\ b = c",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_congr... | [] | simp only [avoid, ofErase, mem_erase, Ne, mem_image, ← exists_and_left,
@and_left_comm (c ≠ ⊥)]
refine exists_congr fun d ↦ and_congr_right' <| and_congr_left ?_
rintro rfl
rw [sdiff_eq_bot_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Partition.Finpartition | {
"line": 586,
"column": 2
} | {
"line": 590,
"column": 23
} | {
"line": 592,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\n⊢ c ∈ (P.avoid b).parts ↔ ∃ d ∈ P.parts, ¬d ≤ b ∧ d \\ b = c",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_congr... | [] | simp only [avoid, ofErase, mem_erase, Ne, mem_image, ← exists_and_left,
@and_left_comm (c ≠ ⊥)]
refine exists_congr fun d ↦ and_congr_right' <| and_congr_left ?_
rintro rfl
rw [sdiff_eq_bot_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Partition.Finpartition | {
"line": 585,
"column": 81
} | {
"line": 590,
"column": 23
} | {
"line": 592,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\n⊢ c ∈ (P.avoid b).parts ↔ ∃ d ∈ P.parts, ¬d ≤ b ∧ d \\ b = c",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_congr... | [] | by
simp only [avoid, ofErase, mem_erase, Ne, mem_image, ← exists_and_left,
@and_left_comm (c ≠ ⊥)]
refine exists_congr fun d ↦ and_congr_right' <| and_congr_left ?_
rintro rfl
rw [sdiff_eq_bot_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Partition.Finpartition | {
"line": 601,
"column": 68
} | {
"line": 602,
"column": 64
} | {
"line": 604,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b : α\nP : Finpartition a\nhab : a < b\n⊢ (P.extendOfLE ⋯).parts = insert (b \\ a) P.parts",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"disjoint_sdiff_self_right",
"of_eq_... | [] | by
simp [extendOfLE, sdiff_eq_bot_iff.not.mpr (not_le_of_gt hab)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 539,
"column": 41
} | {
"line": 539,
"column": 67
} | {
"line": 539,
"column": 68
} | [
{
"pp": "C : 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 : EInt\nhab : a ≤ b\na' b' : EInt\nhab' : a' ≤ b'\nφ : mk₁ ... | [
"C : 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 : EInt\nhab : a ≤ b\na' b' : EInt\nhab' : a' ≤ b'\nφ : mk₁ (homOfLE hab... | NatTrans.naturality_assoc, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 295,
"column": 4
} | {
"line": 296,
"column": 65
} | {
"line": 297,
"column": 2
} | [
{
"pp": "case h\nα : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\nhP : P.IsEquipartition\nhε : 0 ≤ ε\nU V : Finset α\nhUV : U ∈ P.parts ∧ V ∈ ... | [] | exact mul_pos (Nat.cast_pos.2 (P.nonempty_of_mem_parts hUV.1).card_pos)
(Nat.cast_pos.2 (P.nonempty_of_mem_parts hUV.2.1).card_pos) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 303,
"column": 13
} | {
"line": 303,
"column": 44
} | {
"line": 304,
"column": 2
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\nhP : P.IsEquipartition\nhε : 0 ≤ ε\n⊢ (#P.parts * (#A / #P.parts) + #P.parts) ^ 2 ≤ ... | [] | by gcongr; apply Nat.mul_div_le | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Density | {
"line": 346,
"column": 2
} | {
"line": 346,
"column": 64
} | {
"line": 347,
"column": 2
} | [
{
"pp": "α : Type u_4\nG : SimpleGraph α\ninst✝¹ : DecidableRel G.Adj\ns t : Finset α\ninst✝ : DecidableEq α\nhs : s.Nonempty\nht : t.Nonempty\nh : Disjoint s t\n⊢ ↑(#(G.interedges s t)) + ↑(#(Gᶜ.interedges s t)) = ↑(#s) * ↑(#t)",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Nat.ca... | [
"α : Type u_4\nG : SimpleGraph α\ninst✝¹ : DecidableRel G.Adj\ns t : Finset α\ninst✝ : DecidableEq α\nhs : s.Nonempty\nht : t.Nonempty\nh : Disjoint s t\n⊢ ↑(#s) * ↑(#t) ≠ 0"
] | · exact mod_cast card_interedges_add_card_interedges_compl _ h | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 440,
"column": 2
} | {
"line": 440,
"column": 84
} | {
"line": 441,
"column": 2
} | [
{
"pp": "case pos\nα : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\nx y : α\nhx✝ : x ∈ A\nhy✝ : y ∈ A\nh : G.Adj x y\nh' :\n ∀ x_1 ∈ P.parts,\n ∀ x_2 ∈ P.parts, x ∈ x_1 → ... | [
"case neg\nα : Type u_1\n𝕜 : Type u_2\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\nx y : α\nhx✝ : x ∈ A\nhy✝ : y ∈ A\nh : G.Adj x y\nh' :\n ∀ x_1 ∈ P.parts,\n ∀ x_2 ∈ P.parts, x ∈ x_1 → y ∈ x_2 → x_... | · exact Or.inr <| Or.inr ⟨U, V, hU, hV, hUV, h' _ hU _ hV hx hy hUV h₂, hx, hy, h⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 145,
"column": 66
} | {
"line": 145,
"column": 72
} | {
"line": 145,
"column": 72
} | [
{
"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\nhunif : ¬G.IsUniform ε U V\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ :... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 145,
"column": 66
} | {
"line": 145,
"column": 72
} | {
"line": 145,
"column": 72
} | [
{
"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\nhunif : ¬G.IsUniform ε U V\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ :... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 145,
"column": 66
} | {
"line": 145,
"column": 72
} | {
"line": 145,
"column": 72
} | [
{
"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\nhunif : ¬G.IsUniform ε U V\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ :... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 158,
"column": 38
} | {
"line": 158,
"column": 63
} | {
"line": 158,
"column": 64
} | [
{
"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\nhunif : ¬G.IsUniform ε U V\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ :... | [
"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\nhunif : ¬G.IsUniform ε U V\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ : ε ≤ 1\nhP₁ ... | mul_right_comm _ (2 : ℝ), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 21
} | {
"line": 197,
"column": 22
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nx : V\nx✝ : Sym2 V\nh : x✝ ∈ G.edgeFinset\n⊢ x✝ ∉ {e | e ∈ G.edgeSet ∧ x ∈ e} ↔ x ∉ x✝",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"... | [
"V : Type u_1\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nx : V\nx✝ : Sym2 V\nh : x✝ ∈ G.edgeFinset\n⊢ ¬(x✝ ∈ G.edgeSet ∧ x ∈ x✝) ↔ x ∉ x✝"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 170,
"column": 2
} | {
"line": 172,
"column": 100
} | {
"line": 174,
"column": 0
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nX : Type u_3\nα : Type u_4\nβ : Type u_5\nγ : Type u_6\nG G₁ G₂ G₃ : SimpleGraph V\nH : SimpleGraph W\nI : SimpleGraph X\nA : SimpleGraph α\nB : SimpleGraph β\nC : SimpleGraph γ\nf : A.Copy B\nA' : A.Subgraph\n⊢ A'.coe ≃g (Subgraph.map f.toHom A').coe",
"ppTerm": "?m.18"... | [] | use Equiv.Set.image f.toHom _ f.injective
simp_rw [Subgraph.map_verts, Equiv.Set.image_apply, Subgraph.coe_adj, Subgraph.map_adj,
Relation.map_apply, f.injective.eq_iff, exists_eq_right_right, exists_eq_right, forall_true_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 170,
"column": 2
} | {
"line": 172,
"column": 100
} | {
"line": 174,
"column": 0
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nX : Type u_3\nα : Type u_4\nβ : Type u_5\nγ : Type u_6\nG G₁ G₂ G₃ : SimpleGraph V\nH : SimpleGraph W\nI : SimpleGraph X\nA : SimpleGraph α\nB : SimpleGraph β\nC : SimpleGraph γ\nf : A.Copy B\nA' : A.Subgraph\n⊢ A'.coe ≃g (Subgraph.map f.toHom A').coe",
"ppTerm": "?m.18"... | [] | use Equiv.Set.image f.toHom _ f.injective
simp_rw [Subgraph.map_verts, Equiv.Set.image_apply, Subgraph.coe_adj, Subgraph.map_adj,
Relation.map_apply, f.injective.eq_iff, exists_eq_right_right, exists_eq_right, forall_true_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 416,
"column": 27
} | {
"line": 418,
"column": 41
} | {
"line": 420,
"column": 0
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\na b : V\ns : Set G.Subgraph\nhs : s.Nonempty\n⊢ (∀ G' ∈ s, G'.Adj a b) → G.Adj a b",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph",
"SimpleGraph.Adj",
"SimpleGraph.Subgraph.adj_sub",
"Membership.mem",
... | [] | by
obtain ⟨G', hG'⟩ := hs
exact fun h => G'.adj_sub (h _ hG') | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 658,
"column": 4
} | {
"line": 658,
"column": 35
} | {
"line": 660,
"column": 0
} | [
{
"pp": "case right\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nH₁ H₂ : G.Subgraph\nhH : H₁ ≤ H₂\nu v : V\nha : H₁.Adj u v\n⊢ (Subgraph.map f H₂).Adj (f u) (f v)",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"RelHom.instFunLike",
"SimpleGraph... | [] | exact ⟨_, _, hH.2 ha, rfl, rfl⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 990,
"column": 2
} | {
"line": 990,
"column": 26
} | {
"line": 990,
"column": 27
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v w : V\nhvw : G.Adj v w\n⊢ (G.subgraphOfAdj hvw).neighborSet u = (if u = v then {w} else ∅) ∪ if u = w then {v} else ∅",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Adj"... | [
"case pos\nV : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nw : V\nhvw : G.Adj w w\n⊢ (G.subgraphOfAdj hvw).neighborSet w = {w} ∪ {w}",
"case neg\nV : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nv w : V\nhvw : G.Adj v w\nh✝ : ¬v = w\n⊢ (G.subgraphOfAdj hvw).neighborSet v = {w} ∪ ∅",
"case pos\nV : Ty... | split_ifs <;> subst_vars | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 241,
"column": 29
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nε : ℝ\ninst✝ : Nonempty α\nhPα : #P.parts * 16 ^ #P.parts ≤ Fintype.card α\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ : ε ≤ 1\nthis : 0 ≤ ε\n⊢ 1 + ε ^ 5 * 49⁻¹ = 1 + ε ^ 5 / 49",
"ppTerm": "?m.392",
"assigned": true,
... | [] | rw [div_eq_mul_inv] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 241,
"column": 29
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nε : ℝ\ninst✝ : Nonempty α\nhPα : #P.parts * 16 ^ #P.parts ≤ Fintype.card α\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ : ε ≤ 1\nthis : 0 ≤ ε\n⊢ 1 + ε ^ 5 * 49⁻¹ = 1 + ε ^ 5 / 49",
"ppTerm": "?m.392",
"assigned": true,
... | [] | rw [div_eq_mul_inv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 241,
"column": 29
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nε : ℝ\ninst✝ : Nonempty α\nhPα : #P.parts * 16 ^ #P.parts ≤ Fintype.card α\nhPε : 100 ≤ 4 ^ #P.parts * ε ^ 5\nhε₁ : ε ≤ 1\nthis : 0 ≤ ε\n⊢ 1 + ε ^ 5 * 49⁻¹ = 1 + ε ^ 5 / 49",
"ppTerm": "?m.392",
"assigned": true,
... | [] | rw [div_eq_mul_inv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1209,
"column": 4
} | {
"line": 1211,
"column": 33
} | {
"line": 1213,
"column": 0
} | [
{
"pp": "case right\nV : Type u\nG : SimpleGraph V\nG' G'' : G.Subgraph\ns s' : Set V\nhg : G' ≤ G''\nhs : s ⊆ s'\n⊢ ∀ ⦃v w : V⦄, (G'.induce s).Adj v w → (G''.induce s').Adj v w",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Subgraph.induce_adj",
... | [] | simp +contextual only [induce_adj, and_imp]
intro v w hv hw ha
exact ⟨hs hv, hs hw, hg.2 ha⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1209,
"column": 4
} | {
"line": 1211,
"column": 33
} | {
"line": 1213,
"column": 0
} | [
{
"pp": "case right\nV : Type u\nG : SimpleGraph V\nG' G'' : G.Subgraph\ns s' : Set V\nhg : G' ≤ G''\nhs : s ⊆ s'\n⊢ ∀ ⦃v w : V⦄, (G'.induce s).Adj v w → (G''.induce s').Adj v w",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Subgraph.induce_adj",
... | [] | simp +contextual only [induce_adj, and_imp]
intro v w hv hw ha
exact ⟨hs hv, hs hw, hg.2 ha⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 38
} | {
"line": 123,
"column": 39
} | [
{
"pp": "case refine_2.refine_3\nV : Type u_1\nG : SimpleGraph V\nv w v' w' : V\np₁ : G.Walk v w\np₂ : G.Walk v' w'\nx✝ : p₁.support <:+: p₂.support\ns t : List V\nh : s ++ p₁.support ++ t = p₂.support\nthis : s.length + p₁.length ≤ p₂.length\n⊢ s ++ p₁.support ++ t =\n List.take (s.length + 1) s ++ List.tak... | [
"case refine_2.refine_3\nV : Type u_1\nG : SimpleGraph V\nv w v' w' : V\np₁ : G.Walk v w\np₂ : G.Walk v' w'\nx✝ : p₁.support <:+: p₂.support\ns t : List V\nh : s ++ p₁.support ++ t = p₂.support\nthis : s.length + p₁.length ≤ p₂.length\n⊢ s ++ p₁.support ++ t =\n List.take (s.length + 1) s ++ List.take (s.length ... | List.drop_eq_nil_of_le (by lia), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 119,
"column": 41
} | {
"line": 119,
"column": 54
} | {
"line": 119,
"column": 55
} | [
{
"pp": "case neg\nV : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\na v✝ w✝ : V\nh✝ : G.Adj a v✝\np : G.Walk v✝ w✝\nih : ∀ (h : w ∈ p.support), (p.dropUntil w h).support = ((p.drop (List.idxOf w p.support)).copy ⋯ ⋯).support\nh : w ∈ (cons h✝ p).support\nh' : w ≠ a\n⊢ ((cons h✝ p).dropUntil w h)... | [
"case neg\nV : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\na v✝ w✝ : V\nh✝ : G.Adj a v✝\np : G.Walk v✝ w✝\nih : ∀ (h : w ∈ p.support), (p.dropUntil w h).support = ((p.drop (List.idxOf w p.support)).copy ⋯ ⋯).support\nh : w ∈ (cons h✝ p).support\nh' : w ≠ a\n⊢ ((cons h✝ p).dropUntil w h).support = (... | support_copy, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | {
"line": 230,
"column": 39
} | {
"line": 238,
"column": 46
} | {
"line": 240,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nu v : V\nn k : ℕ\np : G.Walk u v\nh : n ≤ k\n⊢ (p.drop k).IsSubwalk (p.drop n)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Nat.recAux",
"SimpleGraph.Walk.drop_zero",
"HEq.refl",
"SimpleGraph.Walk.IsSubwalk.copy",
... | [] | by
induction k, h using Nat.le_induction with
| base => rfl
| succ k h ih =>
apply IsSubwalk.trans ?_ ih
clear h ih
induction k generalizing p u with
| zero => exact p.drop_zero ▸ (p.isSubwalk_rfl.copy rfl rfl p.getVert_zero.symm rfl).tail
| succ _ ih => cases p <;> simp [drop, ih] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 162,
"column": 4
} | {
"line": 172,
"column": 18
} | {
"line": 174,
"column": 0
} | [
{
"pp": "case cons.tail\nV : Type u\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v w x u✝ v✝ w✝ : V\nha : G.Adj u✝ v✝\np' : G.Walk v✝ w✝\nih : ∀ (h : u ∈ p'.support), List.count s(u, x) (p'.takeUntil u h).edges ≤ 1\na✝ : List.Mem u p'.support\n⊢ List.count s(u, x) ((cons ha p').takeUntil u ⋯).edges ≤ 1",
"p... | [] | · simp! only
split_ifs with h'
· subst h'
simp
· rw [edges_cons, List.count_cons]
split_ifs with h''
· simp only [beq_iff_eq, Sym2.eq, Sym2.rel_iff'] at h''
obtain ⟨rfl, rfl⟩ | ⟨rfl, rfl⟩ := h''
· exact (h' rfl).elim
· cases p' <;> simp!
· ... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 39
} | {
"line": 190,
"column": 40
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk v w\nh : u ∈ p.support\n⊢ ((p.take (List.idxOf u p.support)).copy ⋯ ⋯).support <+: p.support",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.getVer... | [
"V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk v w\nh : u ∈ p.support\n⊢ (p.take (List.idxOf u p.support)).support <+: p.support"
] | support_copy, | Mathlib.Tactic.GRewrite.evalGRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 201,
"column": 26
} | {
"line": 201,
"column": 39
} | {
"line": 201,
"column": 40
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk v w\nh : u ∈ p.support\n⊢ ((p.drop (List.idxOf u p.support)).copy ⋯ ⋯).support <:+ p.support",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.getVer... | [
"V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk v w\nh : u ∈ p.support\n⊢ (p.drop (List.idxOf u p.support)).support <:+ p.support"
] | support_copy, | Mathlib.Tactic.GRewrite.evalGRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 6
} | {
"line": 278,
"column": 2
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk u v\nh : w ∈ p.support\nhsu : ¬1 ≤ (p.takeUntil w h).length\n⊢ w = u",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.symm"
],
"usedFVars": [
"V",
"u",
"w"
],
"us... | [
"V : Type u\nG : SimpleGraph V\nv w u : V\ninst✝ : DecidableEq V\np : G.Walk u v\nh : w ∈ p.support\nhsu : ¬1 ≤ (p.takeUntil w h).length\n⊢ u = w"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Combinatorics.SimpleGraph.Walk.Operations | {
"line": 798,
"column": 4
} | {
"line": 798,
"column": 55
} | {
"line": 799,
"column": 4
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : ¬p.Nil\ni : ℕ\nx✝ : i + 1 ≠ 0\n⊢ p.getVert (i + 1) ∈ p.support.tail",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.getVert_tail",
"SimpleGraph.Walk.support... | [
"V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : ¬p.Nil\ni : ℕ\nx✝ : i + 1 ≠ 0\n⊢ p.tail.getVert i ∈ p.tail.support"
] | rw [← getVert_tail, ← p.support_tail_of_not_nil hp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.Clique | {
"line": 535,
"column": 51
} | {
"line": 541,
"column": 31
} | {
"line": 543,
"column": 0
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\n⊢ G.CliqueFree 2 ↔ G = ⊥",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Finset.coe_singleton",
"le_rfl",
"eq_false",
"SimpleGraph.Adj.ne",
"Sym2.mk",
"congrArg",
"Finset",
... | [] | by
classical
constructor
· simp_rw [← edgeSet_eq_empty, Set.eq_empty_iff_forall_notMem, Sym2.forall, mem_edgeSet]
exact fun h a b hab => h _ ⟨by simpa [hab.ne], card_pair hab.ne⟩
· rintro rfl
exact cliqueFree_bot le_rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finset.CastCard | {
"line": 50,
"column": 6
} | {
"line": 50,
"column": 29
} | {
"line": 50,
"column": 30
} | [
{
"pp": "α : Type u_1\nR : Type u_2\ns t : Finset α\ninst✝¹ : DecidableEq α\ninst✝ : AddGroupWithOne R\nh : s ⊆ t\n⊢ ↑(#(t \\ s)) = ↑(#t) - ↑(#s)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Finset",
"Fin... | [
"α : Type u_1\nR : Type u_2\ns t : Finset α\ninst✝¹ : DecidableEq α\ninst✝ : AddGroupWithOne R\nh : s ⊆ t\n⊢ ↑(#t - #s) = ↑(#t) - ↑(#s)"
] | card_sdiff_of_subset h, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.Dissociation | {
"line": 122,
"column": 55
} | {
"line": 123,
"column": 68
} | {
"line": 123,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns t u : Finset α\nht : t ⊆ s\nhu : u ⊆ s\n⊢ ∏ a ∈ s, a ^ ((↑t).indicator 1 - (↑u).indicator 1) a = (∏ a ∈ t, a) / ∏ a ∈ u, a",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",... | [] | simp [prod_div_distrib, zpow_sub,
← div_eq_mul_inv, Set.indicator, pow_ite, inter_eq_right.2, *] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.Additive.Dissociation | {
"line": 122,
"column": 55
} | {
"line": 123,
"column": 68
} | {
"line": 123,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns t u : Finset α\nht : t ⊆ s\nhu : u ⊆ s\n⊢ ∏ a ∈ s, a ^ ((↑t).indicator 1 - (↑u).indicator 1) a = (∏ a ∈ t, a) / ∏ a ∈ u, a",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",... | [] | simp [prod_div_distrib, zpow_sub,
← div_eq_mul_inv, Set.indicator, pow_ite, inter_eq_right.2, *] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.Dissociation | {
"line": 122,
"column": 55
} | {
"line": 123,
"column": 68
} | {
"line": 123,
"column": 68
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns t u : Finset α\nht : t ⊆ s\nhu : u ⊆ s\n⊢ ∏ a ∈ s, a ^ ((↑t).indicator 1 - (↑u).indicator 1) a = (∏ a ∈ t, a) / ∏ a ∈ u, a",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",... | [] | simp [prod_div_distrib, zpow_sub,
← div_eq_mul_inv, Set.indicator, pow_ite, inter_eq_right.2, *] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.DoublingConst | {
"line": 194,
"column": 82
} | {
"line": 195,
"column": 40
} | {
"line": 197,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : DecidableEq G\n𝕜 : Type u_3\ninst✝¹ : Semifield 𝕜\ninst✝ : CharZero 𝕜\nA B : Finset G\n⊢ ↑(#A) * ↑δₘ[A, B] = ↑(#(A / B))",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | [] | by
norm_cast; exact card_mul_divConst _ _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 42
} | {
"line": 87,
"column": 6
} | [
{
"pp": "case refine_2.refine_3\nι : Type u_1\np : ℕ\ninst✝ : Fact (Nat.Prime p)\ns : Finset ι\na : ι → ZMod p\nhs : #s = 2 * p - 1\nthis : NeZero p\nN : ℕ := Fintype.card { x // (eval x) (f₁ s a) = 0 ∧ (eval x) (f₂ s a) = 0 }\nzero_sol : { x // (eval x) (f₁ s a) = 0 ∧ (eval x) (f₂ s a) = 0 } := ⟨0, ⋯⟩\nhN₀ : 0... | [
"case refine_2.refine_3\nι : Type u_1\np : ℕ\ninst✝ : Fact (Nat.Prime p)\ns : Finset ι\na : ι → ZMod p\nhs : #s = 2 * p - 1\nthis : NeZero p\nN : ℕ := Fintype.card { x // (eval x) (f₁ s a) = 0 ∧ (eval x) (f₂ s a) = 0 }\nzero_sol : { x // (eval x) (f₁ s a) = 0 ∧ (eval x) (f₂ s a) = 0 } := ⟨0, ⋯⟩\nhN₀ : 0 < N\nhs' : ... | rw [univ_eq_attach, card_attach, hs] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.Colex | {
"line": 154,
"column": 93
} | {
"line": 159,
"column": 31
} | {
"line": 161,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\ns t : Finset α\na : α\nhst : toColex s ≤ toColex t\nht : ∀ b ∈ t, b ≤ a\n⊢ ∀ b ∈ s, b ≤ a",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Colex",
"ofColex",
"Finset",
"PartialOrder.toPreord... | [] | by
rintro b hb
by_cases b ∈ t
· exact ht _ ‹_›
· obtain ⟨c, hct, -, hbc⟩ := hst hb ‹_›
exact hbc.trans <| ht _ hct | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.CrossProduct | {
"line": 79,
"column": 6
} | {
"line": 79,
"column": 29
} | {
"line": 79,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nv w : Fin 3 → R\n⊢ (crossProduct v) w + (crossProduct w) v = 0",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Pi.Function.module",
"NegZeroClass.toNeg",
"Algebra.to_smulComm... | [
"R : Type u_1\ninst✝ : CommRing R\nv w : Fin 3 → R\n⊢ (crossProduct v) w = -(crossProduct w) v"
] | add_eq_zero_iff_eq_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Configuration | {
"line": 150,
"column": 26
} | {
"line": 150,
"column": 43
} | {
"line": 150,
"column": 44
} | [
{
"pp": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : Nondegenerate P L\ninst✝¹ : Fintype P\ninst✝ : Fintype L\nh : Fintype.card L ≤ Fintype.card P\nt : L → Finset P := fun l ↦ {p | p ∉ l}.toFinset\ns : Finset L\nhs₀ : ¬#s = 0\nhs₁ : ¬#s = 1\np₁ p₂ : P\nhp₁ : ∀ x ∈ s, p₁ ∉ {p | p ∉ x}\nhp₂ : ∀ ... | [
"P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : Nondegenerate P L\ninst✝¹ : Fintype P\ninst✝ : Fintype L\nh : Fintype.card L ≤ Fintype.card P\nt : L → Finset P := fun l ↦ {p | p ∉ l}.toFinset\ns : Finset L\nhs₀ : ¬#s = 0\nhs₁ : ¬#s = 1\np₁ p₂ : P\nhp₁ : ∀ x ∈ s, ¬p₁ ∉ x\nhp₂ : ∀ x ∈ s, ¬p₂ ∉ x\n⊢ p₁ ... | Set.mem_setOf_eq, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.Configuration | {
"line": 405,
"column": 45
} | {
"line": 405,
"column": 93
} | {
"line": 406,
"column": 6
} | [
{
"pp": "case intro\nP : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\np q : P\nl : L\nh : q ∈ l\nval✝ : Fintype { l // q ∈ l }\n⊢ lineCount L q = lineCount L (Classical.choose ⋯) - 1 + 1",
"ppTerm": "?intro",
"assigned": true,
"u... | [
"case intro\nP : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\np q : P\nl : L\nh : q ∈ l\nval✝ : Fintype { l // q ∈ l }\n⊢ lineCount L q = lineCount L q - 1 + 1"
] | lineCount_eq_lineCount L (Classical.choose _) q, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 34
} | {
"line": 261,
"column": 2
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\na : G\nha : a ∈ A\nz b : G\nhb : b ∈ A\nc : G\nhc : c ∈ A\nhz : a * (b⁻¹ * c * a) = z\nl : Finset G := A ∩ (z * a⁻¹) •> (A⁻¹ * A)\nr : Finset G := a •> (A⁻¹ * A) ∩ z •> A⁻¹\nthis : A⁻¹ * A * (A⁻¹ * A) ... | [] | simp [mul_mem_mul, ha, hb, hc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.Configuration | {
"line": 498,
"column": 2
} | {
"line": 498,
"column": 98
} | {
"line": 499,
"column": 2
} | [
{
"pp": "K : Type u_3\ninst✝ : Field K\na b c d : Fin 3 → K\nhac : a ⬝ᵥ c = 0\nhbc : b ⬝ᵥ c = 0\nhad : a ⬝ᵥ d = 0\nhbd : b ⬝ᵥ d = 0\nh : LinearIndependent K (of ![a, b]).row ∧ LinearIndependent K (of ![c, d]).row\nA : Matrix (Fin 2) (Fin 3) K := of ![a, b]\nB : Matrix (Fin 2) (Fin 3) K := of ![c, d]\nhAB : A.ra... | [
"K : Type u_3\ninst✝ : Field K\na b c d : Fin 3 → K\nhac : a ⬝ᵥ c = 0\nhbc : b ⬝ᵥ c = 0\nhad : a ⬝ᵥ d = 0\nhbd : b ⬝ᵥ d = 0\nh : LinearIndependent K (of ![a, b]).row ∧ LinearIndependent K (of ![c, d]).row\nA : Matrix (Fin 2) (Fin 3) K := of ![a, b]\nB : Matrix (Fin 2) (Fin 3) K := of ![c, d]\nhAB : (Nat.succ 0).suc... | rw [rank_transpose, h.1.rank_matrix, h.2.rank_matrix, Fintype.card_fin, Fintype.card_fin] at hAB | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 75,
"column": 8
} | {
"line": 76,
"column": 15
} | {
"line": 78,
"column": 0
} | [
{
"pp": "x : ℕ\nhx : x ≠ 0\nc : ℕ\n⊢ (c + 1) * (c * x + x - 1).choose (x - 1) * (x * c)! * x ! = (x * (c + 1))!",
"ppTerm": "?m.316",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.T... | [] | rw [← Nat.choose_mul_add hx, mul_comm c x, Nat.add_choose_mul_factorial_mul_factorial]
ring_nf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 75,
"column": 8
} | {
"line": 76,
"column": 15
} | {
"line": 78,
"column": 0
} | [
{
"pp": "x : ℕ\nhx : x ≠ 0\nc : ℕ\n⊢ (c + 1) * (c * x + x - 1).choose (x - 1) * (x * c)! * x ! = (x * (c + 1))!",
"ppTerm": "?m.316",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.T... | [] | rw [← Nat.choose_mul_add hx, mul_comm c x, Nat.add_choose_mul_factorial_mul_factorial]
ring_nf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 124,
"column": 6
} | {
"line": 124,
"column": 34
} | {
"line": 124,
"column": 35
} | [
{
"pp": "p : DyckWord\nh : ↑p ≠ []\nf : ¬(↑p).getLast h = D\ns : count U ↑p = count D ↑p\n⊢ False",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"List.getLast",
"instDecidableEqDyckStep",
"DyckStep.U",
"congrArg",
"Eq.mp",
"List.dropLast",
"instBE... | [
"p : DyckWord\nh : ↑p ≠ []\nf : ¬(↑p).getLast h = D\ns : count U ((↑p).dropLast ++ [(↑p).getLast h]) = count D ((↑p).dropLast ++ [(↑p).getLast h])\n⊢ False"
] | ← dropLast_append_getLast h, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 281,
"column": 11
} | {
"line": 284,
"column": 91
} | {
"line": 286,
"column": 0
} | [
{
"pp": "n✝ n : ℕ\nih : ∀ m < n + 1, m.bell = ∑ p, p.parts.bell\n⊢ ∑ p, ∑ a, n.choose (↑a - 1) * (p.parts.erase ↑a).bell = ∑ p, p.parts.bell",
"ppTerm": "?m.228",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"Nat.choose",
"HMul.hMul",
"Finset.univ... | [] | by
congr! with p
rw [bell_eq_sum_erase p]
exact p.parts.toFinset.sum_coe_sort (fun a ↦ choose n (a - 1) * (p.parts.erase a).bell) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 12
} | {
"line": 70,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf : ℕ → ℕ → R\ni n : ℕ\n⊢ ∀ (b : ℕ), n ≤ b → ↑n < (f (i + 1) (b + 1) • X ^ ((i + 1) * (b + 1))).order",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Preorder.toLE",
"LE.le",
"Nat.instPreorder",
"Nat"
],
"usedF... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf : ℕ → ℕ → R\ni n m : ℕ\nhm : n ≤ m\n⊢ ↑n < (f (i + 1) (m + 1) • X ^ ((i + 1) * (m + 1))).order"
] | intro m hm | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
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