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.Triangulated.TStructure.ETrunc | {
"line": 274,
"column": 35
} | {
"line": 274,
"column": 46
} | [
{
"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\nX : C\nn : ℤ\ninst✝ : t.IsGE X n\nj : ℤ\nhj : WithBotTop.coe j ≤ WithBotTop.coe n\n⊢ j ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 219,
"column": 43
} | {
"line": 219,
"column": 54
} | [
{
"pp": "α : Type u_2\ninst✝ : CommMonoid α\nA₁ A₂ : Set α\nn : ℕ\nhA : A₁ ⊆ A₂\ns t : Multiset α\nx✝³ : ∀ ⦃x : α⦄, x ∈ s → x ∈ A₁\nx✝² : ∀ ⦃x : α⦄, x ∈ t → x ∈ A₁\nx✝¹ : s.card = n\nx✝ : t.card = n\nh : s.prod = t.prod\n⊢ (map id s).prod = (map id t).prod",
"usedConstants": [
"Eq.mpr",
"Multise... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 296,
"column": 29
} | {
"line": 296,
"column": 40
} | [
{
"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 : EInt\nX : C\nh : a ≤ ⊥\n⊢ a = ⊥",
"usedConstants": []
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 232,
"column": 6
} | {
"line": 232,
"column": 17
} | [
{
"pp": "case refine_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 301,
"column": 62
} | {
"line": 301,
"column": 73
} | [
{
"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\nX : C\nb a : ℤ\nh : WithBotTop.coe a ≤ WithBotTop.coe b\n⊢ a ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 233,
"column": 6
} | {
"line": 233,
"column": 17
} | [
{
"pp": "case refine_2\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanHom n B C g\nhf : IsMulFreimanHom n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 313,
"column": 53
} | {
"line": 313,
"column": 64
} | [
{
"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\nX : C\na b : ℤ\nh : WithBotTop.coe a ≤ WithBotTop.coe b\n⊢ a ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 17
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 51
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | simpa using fun a h ↦ hf.bijOn.mapsTo (hsA h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 17
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nA : Set α\nB : Set β\nC : Set γ\nf : α → β\ng : β → γ\nn : ℕ\nhg : IsMulFreimanIso n B C g\nhf : IsMulFreimanIso n A B f\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 316,
"column": 29
} | {
"line": 316,
"column": 40
} | [
{
"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\nb : EInt\nX : C\nh : ⊤ ≤ b\n⊢ b = ⊤",
"usedConstants": []
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 13
} | [
{
"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\nX : C\n⊢ (t.eTruncGE.obj b).map ((t.eT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 13
} | [
{
"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\nX : C\n⊢ (t.eTruncGEIsoGEGE a b hab).i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | [
{
"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 : b ≤ a\nX : C\n⊢ (t.eTruncLT.obj b).map ((t.eT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 58
} | [
{
"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 : b ≤ a\nX : C\n⊢ (t.eTruncLT.obj b).map ((t.eT... | simpa using (t.eTruncLTLTIsoLT a b hab).hom_inv_id_app X | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 58
} | [
{
"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 : b ≤ a\nX : C\n⊢ (t.eTruncLT.obj b).map ((t.eT... | simpa using (t.eTruncLTLTIsoLT a b hab).hom_inv_id_app X | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 58
} | [
{
"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 : b ≤ a\nX : C\n⊢ (t.eTruncLT.obj b).map ((t.eT... | simpa using (t.eTruncLTLTIsoLT a b hab).hom_inv_id_app X | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 417,
"column": 2
} | {
"line": 417,
"column": 13
} | [
{
"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 : b ≤ a\nX : C\n⊢ (t.eTruncLTLTIsoLT a b hab).i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 460,
"column": 13
} | {
"line": 460,
"column": 24
} | [
{
"pp": "case coe.bot\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✝ : EInt\nX : C\nb : ℤ\n⊢ IsIso ((t.eTruncLTGE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 336,
"column": 8
} | {
"line": 336,
"column": 23
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CommMonoid α\ninst✝ : CancelCommMonoid β\nA : Set α\nB : Set β\nf : α → β\nn✝ : ℕ\ns t : Multiset α\nhsA : ∀ ⦃x : α⦄, x ∈ s → x ∈ A\nhtA : ∀ ⦃x : α⦄, x ∈ t → x ∈ A\nh : s.prod = t.prod\nn : ℕ\nhf : IsMulFreimanHom (n + 1 + 1) A B f\nhs : s.card = n + 1\nx✝ : t.card ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 470,
"column": 11
} | {
"line": 470,
"column": 22
} | [
{
"pp": "case top\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 : EInt\nX : C\n⊢ IsIso ((t.eTruncLTGELTSelfToLTGE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 370,
"column": 20
} | {
"line": 370,
"column": 33
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\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... | prod_map_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 370,
"column": 34
} | {
"line": 370,
"column": 47
} | [
{
"pp": "α : Type u_2\ninst✝¹ : CommMonoid α\nA : Set α\nn : ℕ\nβ : Type u_5\ninst✝ : DivisionCommMonoid β\nB₁ B₂ : Set β\nf₁ f₂ : α → β\nh₁ : IsMulFreimanHom n A B₁ f₁\nh₂ : IsMulFreimanHom n A B₂ f₂\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... | prod_map_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 479,
"column": 11
} | {
"line": 479,
"column": 22
} | [
{
"pp": "case bot\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✝ b : EInt\nX✝ X : C\n⊢ IsIso ((t.eTruncLTGELTSelf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 482,
"column": 13
} | {
"line": 482,
"column": 61
} | [
{
"pp": "case coe.bot\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✝ b : EInt\nX✝ X : C\na : ℤ\n⊢ IsIso ((t.eTru... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 488,
"column": 13
} | {
"line": 488,
"column": 24
} | [
{
"pp": "case coe.top\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✝ b : EInt\nX✝ X : C\na : ℤ\n⊢ IsIso ((t.eTru... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.FreimanHom | {
"line": 448,
"column": 6
} | {
"line": 448,
"column": 81
} | [
{
"pp": "k m n : ℕ\nhm : m ≠ 0\nhkmn : m * k ≤ n\ns t : Multiset (Fin (n + 1))\nhsA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ s → x ∈ Iic ↑k\nhtA : ∀ ⦃x : Fin (n + 1)⦄, x ∈ t → x ∈ Iic ↑k\nhs : s.card = m\nht : t.card = m\nthis : ∀ (u : Multiset (Fin (n + 1))), (Nat.castRingHom (Fin (n + 1))) (map val u).sum = u.sum\nu : Mult... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 88,
"column": 12
} | {
"line": 88,
"column": 23
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA : IsApproximateSubgroup K ↑A\n⊢ ↑(#(A ^ 0)) ≤ K ^ (0 - 1) * ↑(#A)",
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"Real.partialOrder",
"Real.instLE",
"N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 101,
"column": 28
} | {
"line": 101,
"column": 44
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA : IsApproximateSubgroup K ↑A\n⊢ ↑(#(A * A)) ≤ K * ↑(#A)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 137,
"column": 32
} | {
"line": 137,
"column": 89
} | [
{
"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 ^ 4 * A)) ≤ K ^ 3 * ↑(#A)\nhA₀ : A.Nonempty\nF : Finset G\nhF : ↑(#F) ≤ K ^ 3\nhAF : A ^ 4 ⊆ F * (A / A)\n⊢ (A ^ 2) ^ 2 ≤ F • A ^ 2",
"usedConstants": [
"Eq.mpr",
"MulOn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Order.Min | {
"line": 65,
"column": 4
} | {
"line": 65,
"column": 15
} | [
{
"pp": "case refine_2\nG : Type u_1\ninst✝ : Group G\nn : ℕ∞\nh : ∀ ⦃s : Subgroup G⦄, s ≠ ⊥ → (↑s).Finite → n ≤ ↑(Nat.card ↥s)\na : G\nha : a ≠ 1\nha' : IsOfFinOrder a\n⊢ n ≤ ↑(orderOf a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Order.Min | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 24
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : IsMulTorsionFree G\n⊢ minOrder G = ⊤",
"usedConstants": [
"iInf_eq_top._simp_1",
"Eq.mpr",
"ENat.coe_ne_top._simp_1",
"MulOne.toOne",
"False",
"iInf",
"instCompleteLinearOrderENat",
"ENat.instNatCast",
"Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 56
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nih :\n ∀ (a b : Finset α),\n a.Nonempty → b.Nonempty → DevosMulRel (a, b) (s, t) → minOrder α ≤ ↑(#(a * b)) ∨ #a + #b ≤ #(a * b) + 1\nhts : #t < #s\n⊢ minOrder α ≤ ↑(#(s * t)) ∨ #s + #... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 207,
"column": 6
} | {
"line": 207,
"column": 17
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nA : Set G\nhA : IsApproximateSubgroup 1 A\nx : G\nhx : A * A ⊆ x • A\nhx' : x⁻¹ • (A * A) ⊆ A\n⊢ x⁻¹ ∈ A",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 210,
"column": 6
} | {
"line": 210,
"column": 17
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nA : Set G\nhA : IsApproximateSubgroup 1 A\nx : G\nhx : A * A ⊆ x • A\nhx' : x⁻¹ • (A * A) ⊆ A\nhx_inv : x⁻¹ ∈ A\n⊢ x * x ∈ A⁻¹",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 211,
"column": 9
} | {
"line": 214,
"column": 18
} | [] | A * A ⊆ x • A := by assumption
_ = x⁻¹ • (x * x) • A := by simp [smul_smul]
_ ⊆ x⁻¹ • (A • A) := smul_set_mono (smul_set_subset_smul hx_sq)
_ ⊆ A := hx' | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 177,
"column": 4
} | {
"line": 178,
"column": 96
} | [
{
"pp": "case inr.inr.inr.inr.inl\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nih :\n ∀ (a b : Finset α),\n a.Nonempty → b.Nonempty → DevosMulRel (a, b) (s, t) → minOrder α ≤ ↑(#(a * b)) ∨ #a + #b ≤ #(a * b) + 1\nhst : #s ≤ #t\na : α\nha : a ∈ ↑s\... | exact (ih _ _ hgs (hgt.mono inter_subset_union) <| devosMulRel_of_le_of_le aux1 hstg hsg).imp
(WithTop.coe_le_coe.2 aux1).trans' fun h ↦ hstg.trans <| h.trans <| add_le_add_left aux1 _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 177,
"column": 4
} | {
"line": 178,
"column": 96
} | [
{
"pp": "case inr.inr.inr.inr.inl\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nih :\n ∀ (a b : Finset α),\n a.Nonempty → b.Nonempty → DevosMulRel (a, b) (s, t) → minOrder α ≤ ↑(#(a * b)) ∨ #a + #b ≤ #(a * b) + 1\nhst : #s ≤ #t\na : α\nha : a ∈ ↑s\... | exact (ih _ _ hgs (hgt.mono inter_subset_union) <| devosMulRel_of_le_of_le aux1 hstg hsg).imp
(WithTop.coe_le_coe.2 aux1).trans' fun h ↦ hstg.trans <| h.trans <| add_le_add_left aux1 _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 177,
"column": 4
} | {
"line": 178,
"column": 96
} | [
{
"pp": "case inr.inr.inr.inr.inl\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nih :\n ∀ (a b : Finset α),\n a.Nonempty → b.Nonempty → DevosMulRel (a, b) (s, t) → minOrder α ≤ ↑(#(a * b)) ∨ #a + #b ≤ #(a * b) + 1\nhst : #s ≤ #t\na : α\nha : a ∈ ↑s\... | exact (ih _ _ hgs (hgt.mono inter_subset_union) <| devosMulRel_of_le_of_le aux1 hstg hsg).imp
(WithTop.coe_le_coe.2 aux1).trans' fun h ↦ hstg.trans <| h.trans <| add_le_add_left aux1 _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 192,
"column": 2
} | {
"line": 193,
"column": 9
} | [
{
"pp": "G : Type u_1\ninst✝² : DecidableEq G\ninst✝¹ : Group G\ninst✝ : IsMulTorsionFree G\ns t : Finset G\nhs : s.Nonempty\nht : t.Nonempty\n⊢ #s + #t - 1 ≤ #(s * t)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 201,
"column": 2
} | {
"line": 202,
"column": 9
} | [
{
"pp": "p : ℕ\nhp : Nat.Prime p\ns t : Finset (ZMod p)\nhs : s.Nonempty\nht : t.Nonempty\n⊢ min p (#s + #t - 1) ≤ #(s + t)",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"ZMod.commRing",
"CommSemiring.toSemiring",
"Finset",
"PartialOrder.toPreorder",
"Z... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A * C⁻¹) * #B ≤ #(A * B⁻¹) * #(C * B⁻¹)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 68
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A⁻¹ * C) ≤ #(B⁻¹ * A) * #(B⁻¹ * C)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A / C) * #B ≤ #(A * B) * #(C * B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A * C⁻¹) * #B ≤ #(A * B) * #(C * B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A⁻¹ * C) ≤ #(B * A) * #(B * C)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A * C) ≤ #(B / A) * #(B * C)",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Finset.divisionMonoid",
"Monoid.toMulOneClass",
"congrArg",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #B * #(A * C) ≤ #(B * A⁻¹) * #(B * C)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A * C) * #B ≤ #(A * B) * #(C⁻¹ * B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Corner.Defs | {
"line": 69,
"column": 32
} | {
"line": 69,
"column": 43
} | [
{
"pp": "G : Type u_1\ninst✝ : AddCommMonoid G\nA : Set (G × G)\nhA : A.Subsingleton\n_x₁ _y₁ _x₂ _y₂ : G\nhxyd : IsCorner A _x₁ _y₁ _x₂ _y₂\n⊢ _x₁ = _x₂",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 43,
"column": 12
} | {
"line": 43,
"column": 23
} | [
{
"pp": "case base\nG : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nk : ℝ\nm : ℕ\nh : ∀ (ε : Fin 3 → ℤ), (∀ (i : Fin 3), |ε i| = 1) → ↑(#(List.map (fun i ↦ A ^ ε i) (finRange 3)).prod) ≤ k * ↑(#A)\nε : Fin 3 → ℤ\nhε : ∀ (i : Fin 3), |ε i| = 1\n⊢ ↑(#(List.map (fun i ↦ A ^ ε i) (finRange 3)).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 48,
"column": 39
} | {
"line": 48,
"column": 54
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nk : ℝ\nm✝ : ℕ\nh✝ : ∀ (ε : Fin 3 → ℤ), (∀ (i : Fin 3), |ε i| = 1) → ↑(#(List.map (fun i ↦ A ^ ε i) (finRange 3)).prod) ≤ k * ↑(#A)\nm : ℕ\nhm : 3 ≤ m + 1\nih :\n ∀ (ε : Fin (m + 1) → ℤ),\n (∀ (i : Fin (m + 1)), |ε i| = 1) →\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 264,
"column": 2
} | {
"line": 264,
"column": 45
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : CommGroup G\nA : Finset G\nhA : A.Nonempty\nB : Finset G\nn : ℕ\n⊢ ↑(#(B ^ n)) ≤ (↑(#(A * B)) / ↑(#A)) ^ n * ↑(#A)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 270,
"column": 2
} | {
"line": 270,
"column": 45
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : CommGroup G\nA : Finset G\nhA : A.Nonempty\nB : Finset G\nn : ℕ\n⊢ ↑(#(B ^ n)) ≤ (↑(#(A / B)) / ↑(#A)) ^ n * ↑(#A)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Convolution | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA B : Finset G\nx : G\n⊢ #(A ∩ x •> B) = A.convolution B⁻¹ x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Convolution | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA B : Finset G\nx : G\n⊢ #(x •> A ∩ B) = A.convolution B⁻¹ x⁻¹",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 25
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\n⊢ ↑(#(A⁻¹ * A⁻¹ * A)⁻¹) ≤ K ^ 2 * ↑(#A)",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"Di... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\n⊢ ↑(#(A * A⁻¹ * A⁻¹)) ≤ K ^ 2 * ↑(#A)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 25
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\n⊢ ↑(#(A * A * A⁻¹)⁻¹) ≤ K ^ 2 * ↑(#A)",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 109,
"column": 17
} | {
"line": 109,
"column": 28
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\nhA₀ : A.Nonempty\n⊢ #A * #(A * A⁻¹ * A) ≤ #(A * (A * A⁻¹)) * #(A * A)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 25
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\n⊢ ↑(#(A⁻¹ * A * A⁻¹)⁻¹) ≤ K ^ 3 * ↑(#A)",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"Di... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 141,
"column": 37
} | {
"line": 141,
"column": 52
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nm : ℕ\nhm : 3 ≤ m\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\nε : Fin m → ℤ\nhε : ∀ (i : Fin m), |ε i| = 1\nhm₀ : m ≠ 0\ni : Fin m\nh : ε i = 0\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Maps | {
"line": 552,
"column": 6
} | {
"line": 552,
"column": 36
} | [
{
"pp": "case inr\nV : Type u_1\nW : Type u_2\nX : Type u_3\nG : SimpleGraph V\nG' : SimpleGraph W\nu v✝ : V\nH : SimpleGraph W\nf✝ : G ↪g G'\nG'' : SimpleGraph X\nf : Gᶜ ↪g Hᶜ\nv w : V\nhvw : v ≠ w\n⊢ H.Adj (f.toEmbedding v) (f.toEmbedding w) ↔ G.Adj v w",
"usedConstants": [
"Compl.compl",
"Sim... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DegreeSum | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 81
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nv : V\n⊢ #{d | d.toProd.1 = v} = G.degree v",
"usedConstants": [
"SimpleGraph.dartOfNeighborSet",
"Eq.mpr",
"Finset.univ",
"congrArg",
"Finset",
"Membership.mem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DegreeSum | {
"line": 79,
"column": 26
} | {
"line": 79,
"column": 37
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nd d' : G.Dart\n⊢ d' ∈ {d' | d'.edge = d.edge} ↔ d' ∈ {d, d.symm}",
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"Finset.univ",
"congrArg",
"Finset",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Maps | {
"line": 669,
"column": 6
} | {
"line": 669,
"column": 43
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nX : Type u_3\nG : SimpleGraph V\nG' : SimpleGraph W\nu v✝ : V\nf : G ≃g G'\nv : V\nw : ↑(G'.neighborSet (f v))\n⊢ f.symm ↑w ∈ G.neighborSet v",
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Iso",
"SimpleGraph.Adj",
"Membership.mem",
"SimpleGraph... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Equitable | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 37
} | [
{
"pp": "α : Type u_1\ns : Set α\nf : α → ℕ\n⊢ s.EquitableOn f ↔ ∃ b, f '' s ⊆ Icc b (b + 1)",
"usedConstants": [
"Set.EquitableOn",
"Eq.mpr",
"Nat.instOne",
"congrArg",
"Exists",
"id",
"HasSubset.Subset",
"instOfNatNat",
"instLENat",
"funext",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 184,
"column": 44
} | {
"line": 184,
"column": 82
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nm : ℕ\nhm : 3 ≤ m\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\nhAsymm : A⁻¹ = A\nthis : ∀ (ε : ℤ), |ε| = 1 → A ^ ε = A\nδ : Fin 3 → ℤ\nhδ : ∀ (i : Fin 3), |δ i| = 1\n⊢ ↑(#(List.map (fun i ↦ A ^ δ i) (finRange 3)).prod) ≤ K * ↑(#A)",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 178,
"column": 35
} | {
"line": 184,
"column": 98
} | [
{
"pp": "G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA : Finset G\nK : ℝ\nm : ℕ\nhm : 3 ≤ m\nhA : ↑(#(A ^ 3)) ≤ K * ↑(#A)\nhAsymm : A⁻¹ = A\n⊢ ↑(#(A ^ m)) ≤ K ^ (m - 2) * ↑(#A)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"List.repli... | by
have (ε : ℤ) (hε : |ε| = 1) : A ^ ε = A := by
obtain rfl | rfl := eq_or_eq_neg_of_abs_eq hε <;> simp [hAsymm]
calc
(#(A ^ m) : ℝ) = #((finRange m).map fun i ↦ A ^ 1).prod := by simp
_ ≤ K ^ (m - 2) * #A :=
inductive_claim_mul hm (fun δ hδ ↦ by simpa [this _ (hδ _), pow_succ'] using hA) _ (by si... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 455,
"column": 2
} | {
"line": 456,
"column": 18
} | [
{
"pp": "case inr\nV : Type u_1\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nk : ℕ\nh : ∀ (v : V), G.degree v ≤ k\nh✝ : Nonempty V\n⊢ G.maxDegree ≤ k",
"usedConstants": [
"SimpleGraph.maxDegree",
"Membership.mem",
"SimpleGraph.neighborSet",
"Exists",
"Sub... | · obtain ⟨_, hv⟩ := G.exists_maximal_degree_vertex
exact hv ▸ h _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 13
} | [
{
"pp": "case i\nV : Type u_1\nG : SimpleGraph V\nW : Type u_2\nG' : SimpleGraph W\nf : G ≃g G'\ninst✝¹ : Fintype ↑G.edgeSet\ninst✝ : Fintype ↑G'.edgeSet\n⊢ ↥G.edgeFinset ≃ ↥G'.edgeFinset",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Membership.mem",
"id",
"Equiv"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 581,
"column": 2
} | {
"line": 581,
"column": 37
} | [
{
"pp": "V : Type u_1\ns : Set V\ninst✝² : DecidablePred fun x ↦ x ∈ s\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nh : G.support ⊆ s\n⊢ map (Embedding.subtype fun x ↦ x ∈ s).sym2Map (induce s G).edgeFinset = G.edgeFinset",
"usedConstants": [
"Eq.mpr",
"congrArg",
"F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 278,
"column": 6
} | {
"line": 278,
"column": 34
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝² : Lattice α\ninst✝¹ : OrderBot α\na : α\nP✝ : Finpartition a\ninst✝ : Decidable (a = ⊥)\nP : Finpartition a\nh : a = ⊥\nx : α\nhx : x ∈ P.parts\n⊢ ∃ c ∈ ((Finpartition.empty α).copy ⋯).parts, x ≤ c",
"usedConstants": [
"Eq.mpr",
"bot_nonempty",
"Fals... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 344,
"column": 10
} | {
"line": 344,
"column": 56
} | [
{
"pp": "case a\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\na : α\nP✝ : Finpartition a\ns : α\nP : Finpartition s\nPr : α → Prop\nPrsup : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊔ t)\nPrinf : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊓ t)\nPrbot : Pr ⊥\nhs : Pr s\nhP : ∀ p ∈ P.parts, Pr p\nthis✝¹ : Lattice (Subtype ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 345,
"column": 10
} | {
"line": 345,
"column": 21
} | [
{
"pp": "case a\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\na : α\nP✝ : Finpartition a\ns : α\nP : Finpartition s\nPr : α → Prop\nPrsup : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊔ t)\nPrinf : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊓ t)\nPrbot : Pr ⊥\nhs : Pr s\nhP : ∀ p ∈ P.parts, Pr p\nthis✝¹ : Lattice (Subtype ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 346,
"column": 10
} | {
"line": 346,
"column": 34
} | [
{
"pp": "case a\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\na : α\nP✝ : Finpartition a\ns : α\nP : Finpartition s\nPr : α → Prop\nPrsup : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊔ t)\nPrinf : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊓ t)\nPrbot : Pr ⊥\nhs : Pr s\nhP : ∀ p ∈ P.parts, Pr p\nthis✝¹ : Lattice (Subtype ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 349,
"column": 6
} | {
"line": 349,
"column": 61
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\na : α\nP✝ : Finpartition a\ns : α\nP : Finpartition s\nPr : α → Prop\nPrsup : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊔ t)\nPrinf : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊓ t)\nPrbot : Pr ⊥\nhs : Pr s\nhP : ∀ p ∈ P.parts, Pr p\nthis✝ : Lattice (Subtype Pr) := Su... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 350,
"column": 21
} | {
"line": 350,
"column": 70
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\na : α\nP✝ : Finpartition a\ns : α\nP : Finpartition s\nPr : α → Prop\nPrsup : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊔ t)\nPrinf : ∀ ⦃s t : α⦄, Pr s → Pr t → Pr (s ⊓ t)\nPrbot : Pr ⊥\nhs : Pr s\nhP : ∀ p ∈ P.parts, Pr p\nthis✝ : Lattice (Subtype Pr) := Su... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise | {
"line": 52,
"column": 31
} | {
"line": 52,
"column": 70
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : ℕ\nP : Finpartition s\nhs : a * 0 + b * (0 + 1) = #s\n⊢ #({i ∈ ⊥.parts | #i = 0 + 1}) = b",
"usedConstants": [
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Finset.card_map",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 424,
"column": 4
} | {
"line": 425,
"column": 11
} | [
{
"pp": "α : Type u_1\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\na b c : α\nP : Finpartition a\nhb : b ≤ a\npx : α\nhpx : px ∈ ↑P.parts\nright✝¹ : ¬px ⊓ b = ⊥\npy : α\nhpy : py ∈ ↑P.parts\nhxy : px ⊓ b ≠ py ⊓ b\nright✝ : ¬py ⊓ b = ⊥\n⊢ (Disjoint on id) (px ⊓ b) (py ⊓ b)",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Density | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 96
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nα : Type u_4\nβ : Type u_5\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns₁ : Finset α\nt₁ t₂ : Finset β\nδ : 𝕜\nht : t₂ ⊆ t₁\nhδ₀ : 0 ≤ δ\nhδ₁ : 0 < 1 - δ\nht₂ : (1 - δ) * ↑(#t₁) ≤ ↑(#t₂)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 597,
"column": 4
} | {
"line": 597,
"column": 69
} | [
{
"pp": "case neg.h\nα : Type u_1\ninst✝¹ : GeneralizedBooleanAlgebra α\ninst✝ : DecidableEq α\na b : α\nP : Finpartition a\nhab : a ≤ b\np : α\nhp : p ∈ (P.extendOfLE hab).parts\nh : ¬a < b\n⊢ p ∈ P.parts",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Density | {
"line": 211,
"column": 4
} | {
"line": 211,
"column": 96
} | [
{
"pp": "case inr.inl\n𝕜 : Type u_1\nα : Type u_4\nβ : Type u_5\ninst✝³ : Field 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsStrictOrderedRing 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns₁ s₂ : Finset α\nt₁ : Finset β\nδ : 𝕜\nhs : s₂ ⊆ s₁\nhδ₀ : 0 ≤ δ\nhδ₁ : 0 < 1 - δ\nhs₂ : (1 - δ) * ↑(#s₁) ≤ ↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 217,
"column": 4
} | {
"line": 217,
"column": 26
} | [
{
"pp": "case inl\nι : Type u_2\n𝕜 : Type u_3\ninst✝² : Field 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\ns t : Finset ι\nx : 𝕜\nhst : s ⊆ t\nf : ι → 𝕜\nd : 𝕜\nhx : 0 ≤ x\nhs : x ≤ |(∑ i ∈ s, f i) / ↑(#s) - (∑ i ∈ t, f i) / ↑(#t)|\nht : d ≤ ((∑ i ∈ t, f i) / ↑(#t)) ^ 2\nhscard : 0 = ↑(#s)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 792,
"column": 4
} | {
"line": 798,
"column": 96
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ns✝ t u : Finset α\nP : Finpartition s✝\na : α\ns : Setoid α\nx : Finset α\ninst✝ : DecidableRel ⇑s\n⊢ (image (fun a ↦ {b ∈ x | s a b}) x).SupIndep id",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Order.Partition.Finpartition.0.Finpartition.ofSetS... | suffices ∀ (a b c d : α), s a d → s b d → (s a c ↔ s b c) by
simp only [supIndep_iff_pairwiseDisjoint, Set.PairwiseDisjoint, Set.Pairwise, coe_image,
Set.mem_image, mem_coe, ne_eq, onFun, id_eq, disjoint_iff_ne, forall_mem_not_eq,
forall_exists_index, and_imp, forall_apply_eq_imp_iff₂, mem_filter,... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Order.Partition.Finpartition | {
"line": 811,
"column": 2
} | {
"line": 812,
"column": 50
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\na : α\ns : Setoid α\nx : Finset α\ninst✝ : DecidableRel ⇑s\nb : α\n⊢ b ∈ (ofSetSetoid s x).part a ↔ a ∈ x ∧ b ∈ x ∧ s a b",
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"Finset",
"exists_exists_and_eq_and._... | suffices (∃ a₁ ∈ x, (b ∈ x ∧ s a₁ b) ∧ a ∈ x ∧ s a₁ a) ↔ a ∈ x ∧ b ∈ x ∧ s a b by
simpa [mem_part_iff_exists, ofSetSetoid_parts] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 19
} | [
{
"pp": "α : 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\nhG : G.IsUniform ε s t\nhε : ε ≤ 0\n⊢ ↑(#s) * ε ≤ ↑(#∅)",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 95,
"column": 8
} | {
"line": 95,
"column": 19
} | [
{
"pp": "α : 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\nhG : G.IsUniform ε s t\nhε : ε ≤ 0\n⊢ ↑(#t) * ε ≤ ↑(#∅)",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 101,
"column": 29
} | {
"line": 101,
"column": 40
} | [
{
"pp": "α : 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\na b : α\nhε : 0 < ε\nt' : Finset α\nht' : t' ⊆ {b}\nht : ε ≤ ↑(#t')\nhs' : ∅ ⊆ {a}\nhs : ε ≤ ↑(#∅)\n⊢ ε ≤ 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 104,
"column": 29
} | {
"line": 104,
"column": 40
} | [
{
"pp": "α : 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\na b : α\nhε : 0 < ε\nhs' : {a} ⊆ {a}\nhs : ε ≤ ↑(#{a})\nht' : ∅ ⊆ {b}\nht : ε ≤ ↑(#∅)\n⊢ ε ≤ 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise | {
"line": 127,
"column": 6
} | {
"line": 127,
"column": 17
} | [
{
"pp": "case neg.refine_2.refine_1.inr\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.p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 15
} | [
{
"pp": "case inr.calc_1\nα : 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\n⊢ ↑(#A / #P.parts + 1) ≤ ↑(#A) / ↑(#P.parts) + 1",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 372,
"column": 4
} | {
"line": 372,
"column": 53
} | [
{
"pp": "case calc_2.hbc\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\nhA : A.Nonempty\nhε : 0 < ε\nhP : P.IsEquipartition\nhG : P.IsUnifo... | exact aux (P.parts_nonempty hA.ne_empty).card_pos | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 89,
"column": 39
} | {
"line": 89,
"column": 50
} | [
{
"pp": "case Adj.h.h.a\nV : Type u_1\ns : Set (Sym2 V)\nG : SimpleGraph V\nhs : s ⊆ Sym2.diagSet\nu v : V\n⊢ (G.deleteEdges s).Adj u v ↔ G.Adj u v",
"usedConstants": [
"SimpleGraph.deleteEdges",
"Eq.mpr",
"Sym2.mk",
"congrArg",
"SimpleGraph.Adj",
"SimpleGraph.deleteEdges... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 236,
"column": 4
} | {
"line": 237,
"column": 28
} | [
{
"pp": "case refine_2\nV : Type u_1\nG : SimpleGraph V\n𝕜 : Type u_2\ninst✝³ : Ring 𝕜\ninst✝² : PartialOrder 𝕜\ninst✝¹ : Fintype ↑G.edgeSet\np : SimpleGraph V → Prop\nr : 𝕜\ninst✝ : Fintype (Sym2 V)\nh : ∀ ⦃H : SimpleGraph V⦄ [inst : DecidableRel H.Adj], H ≤ G → p H → r ≤ ↑(#G.edgeFinset) - ↑(#H.edgeFinset... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | {
"line": 107,
"column": 4
} | {
"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.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Regularity.Increment | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 75
} | [
{
"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\nhPα : #P.parts * 16 ^ #P.parts ≤ Fintype.card α\nhPG : ¬P.IsUniform G ε\nhPα' : stepBound #P.parts ≤ Fintype.card α\nhPpos : 0 < stepBound #P.pa... | simp_rw [chunk, apply_dite Finpartition.parts, apply_dite card, sum_dite] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 28
} | [
{
"pp": "case h.mp\nα : Type u_4\nβ : Type u_5\nA : SimpleGraph α\nB : SimpleGraph β\nf : A.Copy B\n⊢ f.toSubgraph ∈ {B' | Nonempty (A ≃g B'.coe)}",
"usedConstants": [
"SimpleGraph.Iso",
"SimpleGraph.Subgraph",
"setOf",
"Membership.mem",
"Set.Elem",
"id",
"SimpleGra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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