module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | {
"line": 86,
"column": 14
} | [
{
"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)",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝¹ : DecidableEq G\ninst✝ : Group G\nA B C : Finset G\n⊢ #(A / C) * #B ≤ #(A * B) * #(C * B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 13
} | {
"line": 92,
"column": 14
} | [
{
"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)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | {
"line": 98,
"column": 14
} | [
{
"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)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 30
} | {
"line": 105,
"column": 31
} | [
{
"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)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Finset.divisionMonoid",
"Mon... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 30
} | {
"line": 111,
"column": 31
} | [
{
"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)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.PluenneckeRuzsa | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 14
} | [
{
"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)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 88,
"column": 12
} | {
"line": 88,
"column": 23
} | {
"line": 88,
"column": 24
} | [
{
"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)",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"Real... | [
"G : Type u_1\ninst✝¹ : Group G\nK : ℝ\ninst✝ : DecidableEq G\nA : Finset G\nhA : IsApproximateSubgroup K ↑A\n⊢ A.Nonempty"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 101,
"column": 28
} | {
"line": 101,
"column": 44
} | {
"line": 101,
"column": 45
} | [
{
"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)",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 137,
"column": 32
} | {
"line": 137,
"column": 89
} | {
"line": 137,
"column": 90
} | [
{
"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",
"ppTerm": "?m.188",
"assigned": true,
"... | [
"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 * (A * (A * A)) ⊆ F * (A * A)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 95,
"column": 53
} | {
"line": 95,
"column": 64
} | {
"line": 95,
"column": 65
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\na b : ℤ\nf : WithBotTop.coe a ⟶ WithBotTop.coe b\n⊢ a ≤ b",
"ppTerm": "?m.146",
"a... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\na b : ℤ\nf : WithBotTop.coe a ⟶ WithBotTop.coe b\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 43,
"column": 12
} | {
"line": 43,
"column": 23
} | {
"line": 43,
"column": 24
} | [
{
"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)).... | [
"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)).prod) ≤ k * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 48,
"column": 39
} | {
"line": 48,
"column": 54
} | {
"line": 48,
"column": 55
} | [
{
"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 ... | [
"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 ↑(#(List.ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 207,
"column": 6
} | {
"line": 207,
"column": 17
} | {
"line": 207,
"column": 18
} | [
{
"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",
"ppTerm": "?m.195",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 210,
"column": 6
} | {
"line": 210,
"column": 17
} | {
"line": 210,
"column": 18
} | [
{
"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",
"ppTerm": "?m.242",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivI... | [
"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⁻¹ * x⁻¹ ∈ A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ApproximateSubgroup | {
"line": 211,
"column": 9
} | {
"line": 214,
"column": 18
} | {
"line": 215,
"column": 2
} | [] | [] | 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.GroupTheory.Order.Min | {
"line": 65,
"column": 4
} | {
"line": 65,
"column": 15
} | {
"line": 65,
"column": 16
} | [
{
"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)",
"ppTerm": "?refine_2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Order.Min | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 24
} | {
"line": 73,
"column": 25
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : IsMulTorsionFree G\n⊢ minOrder G = ⊤",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"iInf_eq_top._simp_1",
"Eq.mpr",
"ENat.coe_ne_top._simp_1",
"MulOne.toOne",
"False",
"iInf",
"instCompleteLinearOrd... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : IsMulTorsionFree G\n⊢ ∀ (i : G), ¬i = 1 → ¬IsOfFinOrder i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 56
} | {
"line": 132,
"column": 6
} | [
{
"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 + #... | [
"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 + #t ≤ #(s * t)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Convolution | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 13
} | {
"line": 47,
"column": 14
} | [
{
"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",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Convolution | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | {
"line": 51,
"column": 14
} | [
{
"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",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 25
} | {
"line": 91,
"column": 26
} | [
{
"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)",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivI... | [
"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))) ≤ K ^ 2 * ↑(#A)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 13
} | {
"line": 95,
"column": 14
} | [
{
"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)",
"ppTerm": "?m.51",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 25
} | {
"line": 100,
"column": 26
} | [
{
"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)",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivInv... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 109,
"column": 17
} | {
"line": 109,
"column": 28
} | {
"line": 109,
"column": 29
} | [
{
"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)",
"ppTerm": "?m.218",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 25
} | {
"line": 122,
"column": 26
} | [
{
"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)",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Semigroup.toMul",
"Real",
"DivI... | [
"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))) ≤ K ^ 3 * ↑(#A)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 141,
"column": 37
} | {
"line": 141,
"column": 52
} | {
"line": 141,
"column": 53
} | [
{
"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",
"ppTerm": "?m.77",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.Corner.Defs | {
"line": 69,
"column": 32
} | {
"line": 69,
"column": 43
} | {
"line": 69,
"column": 44
} | [
{
"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",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 176,
"column": 4
} | {
"line": 177,
"column": 96
} | {
"line": 178,
"column": 2
} | [
{
"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": 176,
"column": 4
} | {
"line": 177,
"column": 96
} | {
"line": 178,
"column": 2
} | [
{
"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": 176,
"column": 4
} | {
"line": 177,
"column": 96
} | {
"line": 178,
"column": 2
} | [
{
"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": 191,
"column": 2
} | {
"line": 192,
"column": 9
} | {
"line": 192,
"column": 10
} | [
{
"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)",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.CauchyDavenport | {
"line": 200,
"column": 2
} | {
"line": 201,
"column": 9
} | {
"line": 201,
"column": 10
} | [
{
"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)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"ZMod.commRing",
"CommSemiring.toSemiring",
"Finse... | [
"p : ℕ\nhp : Nat.Prime p\ns t : Finset (ZMod p)\nhs : s.Nonempty\nht : t.Nonempty\n⊢ p ≤ #(s + t) ∨ #s + #t - 1 ≤ #(s + t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 184,
"column": 44
} | {
"line": 184,
"column": 82
} | {
"line": 184,
"column": 83
} | [
{
"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)",
"ppT... | [
"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⊢ ↑(#(A * (A * A))) ≤ K * ↑(#A)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.SmallTripling | {
"line": 178,
"column": 35
} | {
"line": 184,
"column": 98
} | {
"line": 186,
"column": 0
} | [
{
"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)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | [] | 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.Maps | {
"line": 567,
"column": 6
} | {
"line": 567,
"column": 36
} | {
"line": 567,
"column": 37
} | [
{
"pp": "case inr\nV : Type u_1\nW : Type u_2\nX : Type u_3\nY : Type u_4\nG : SimpleGraph V\nG' : SimpleGraph W\nu v✝ : V\nH : SimpleGraph W\nf✝ : G ↪g G'\nG'' : SimpleGraph X\nG''' : SimpleGraph Y\nf : Gᶜ ↪g Hᶜ\nv w : V\nhvw : v ≠ w\n⊢ H.Adj (f.toEmbedding v) (f.toEmbedding w) ↔ G.Adj v w",
"ppTerm": "?in... | [
"case inr\nV : Type u_1\nW : Type u_2\nX : Type u_3\nY : Type u_4\nG : SimpleGraph V\nG' : SimpleGraph W\nu v✝ : V\nH : SimpleGraph W\nf✝ : G ↪g G'\nG'' : SimpleGraph X\nG''' : SimpleGraph Y\nf : Gᶜ ↪g Hᶜ\nv w : V\nhvw : v ≠ w\n⊢ H.Adj (f v) (f w) ↔ G.Adj v w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DegreeSum | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 81
} | {
"line": 69,
"column": 4
} | [
{
"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",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"SimpleGraph.dartOfNeighborSet",
"Eq.mpr",
"Finset.univ",
"con... | [
"V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nv : V\n⊢ #(image (G.dartOfNeighborSet v) univ) = G.degree v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Maps | {
"line": 684,
"column": 6
} | {
"line": 684,
"column": 43
} | {
"line": 684,
"column": 44
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nX : Type u_3\nY : Type u_4\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",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Iso",
"S... | [
"V : Type u_1\nW : Type u_2\nX : Type u_3\nY : Type u_4\nG : SimpleGraph V\nG' : SimpleGraph W\nu v✝ : V\nf : G ≃g G'\nv : V\nw : ↑(G'.neighborSet (f v))\n⊢ G.Adj v (f.symm ↑w)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DegreeSum | {
"line": 79,
"column": 26
} | {
"line": 79,
"column": 37
} | {
"line": 79,
"column": 38
} | [
{
"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}",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"Finset.... | [
"V : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nd d' : G.Dart\n⊢ d'.edge = d.edge ↔ d' = d ∨ d' = d.symm"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 453,
"column": 2
} | {
"line": 454,
"column": 18
} | {
"line": 456,
"column": 0
} | [
{
"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",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"SimpleGraph.maxDegree",
"Membership.mem",
"SimpleGr... | [] | · obtain ⟨_, hv⟩ := G.exists_maximal_degree_vertex
exact hv ▸ h _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 581,
"column": 2
} | {
"line": 581,
"column": 13
} | {
"line": 581,
"column": 14
} | [
{
"pp": "V : 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",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Membe... | [
"V : 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⊢ { x // x ∈ G.edgeSet } ≃ { x // x ∈ G'.edgeSet }"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Finite | {
"line": 623,
"column": 2
} | {
"line": 623,
"column": 37
} | {
"line": 623,
"column": 38
} | [
{
"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",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants":... | [
"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⊢ G.edgeFinset ⊆ s.toFinset.sym2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 296,
"column": 6
} | {
"line": 296,
"column": 34
} | {
"line": 296,
"column": 35
} | [
{
"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",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [
"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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 362,
"column": 10
} | {
"line": 362,
"column": 56
} | {
"line": 362,
"column": 57
} | [
{
"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 ... | [
"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 Pr) := Subty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 363,
"column": 10
} | {
"line": 363,
"column": 21
} | {
"line": 363,
"column": 22
} | [
{
"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 ... | [
"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 Pr) := Subty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 364,
"column": 10
} | {
"line": 364,
"column": 34
} | {
"line": 364,
"column": 35
} | [
{
"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 ... | [
"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 Pr) := Subty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 367,
"column": 6
} | {
"line": 367,
"column": 61
} | {
"line": 367,
"column": 62
} | [
{
"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... | [
"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) := Subtype.lattic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 368,
"column": 21
} | {
"line": 368,
"column": 70
} | {
"line": 368,
"column": 71
} | [
{
"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... | [
"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) := Subtype.lattic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 12
} | {
"line": 232,
"column": 13
} | [
{
"pp": "case coe\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nX : C\nn : ℤ\n⊢ (t.eTriangleLTGE.obj (WithBotTop.coe n)).obj X ∈ distinguishedTr... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise | {
"line": 52,
"column": 31
} | {
"line": 52,
"column": 70
} | {
"line": 52,
"column": 71
} | [
{
"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",
"ppTerm": "?m.127",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Finset",
"AddMonoid... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : ℕ\nP : Finpartition s\nhs : a * 0 + b * (0 + 1) = #s\n⊢ #s = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 258,
"column": 33
} | {
"line": 258,
"column": 44
} | {
"line": 258,
"column": 45
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nn : ℤ\nX : C\ni : ℤ\nh : WithBotTop.coe n ≤ WithBotTop.coe i\n⊢ n ≤ ?m.80",
"ppTerm": ... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasZeroObject C\ninst✝² : HasShift C ℤ\ninst✝¹ : ∀ (n : ℤ), (shiftFunctor C n).Additive\ninst✝ : Pretriangulated C\nt : TStructure C\nn : ℤ\nX : C\ni : ℤ\nh : WithBotTop.coe n ≤ WithBotTop.coe i\n⊢ n ≤ ?m.80"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 276,
"column": 35
} | {
"line": 276,
"column": 46
} | {
"line": 276,
"column": 47
} | [
{
"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 ≤ ... | [
"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 ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 442,
"column": 4
} | {
"line": 443,
"column": 11
} | {
"line": 443,
"column": 12
} | [
{
"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)",
"ppTer... | [
"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 (px ⊓ b) (py ⊓ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 298,
"column": 29
} | {
"line": 298,
"column": 40
} | {
"line": 298,
"column": 41
} | [
{
"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 = ⊥",
"ppTerm": "?m.87",
... | [
"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 = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 303,
"column": 62
} | {
"line": 303,
"column": 73
} | {
"line": 303,
"column": 74
} | [
{
"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 ≤ ... | [
"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 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 315,
"column": 53
} | {
"line": 315,
"column": 64
} | {
"line": 315,
"column": 65
} | [
{
"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 ≤ ... | [
"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 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 318,
"column": 29
} | {
"line": 318,
"column": 40
} | {
"line": 318,
"column": 41
} | [
{
"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 = ⊤",
"ppTerm": "?m.163",
... | [
"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 = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | {
"line": 217,
"column": 4
} | {
"line": 217,
"column": 26
} | {
"line": 217,
"column": 27
} | [
{
"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... | [
"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⊢ d ≤ (∑ i ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 414,
"column": 2
} | {
"line": 414,
"column": 13
} | {
"line": 414,
"column": 14
} | [
{
"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... | [
"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.eTruncLTι a).a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 414,
"column": 2
} | {
"line": 414,
"column": 58
} | {
"line": 416,
"column": 0
} | [
{
"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": 414,
"column": 2
} | {
"line": 414,
"column": 58
} | {
"line": 416,
"column": 0
} | [
{
"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": 414,
"column": 2
} | {
"line": 414,
"column": 58
} | {
"line": 416,
"column": 0
} | [
{
"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": 420,
"column": 2
} | {
"line": 420,
"column": 13
} | {
"line": 420,
"column": 14
} | [
{
"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... | [
"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).inv.app X ≫ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 463,
"column": 13
} | {
"line": 463,
"column": 24
} | {
"line": 463,
"column": 25
} | [
{
"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... | [
"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.truncLT b).map ((t.tru... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 615,
"column": 4
} | {
"line": 615,
"column": 69
} | {
"line": 615,
"column": 70
} | [
{
"pp": "case neg\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",
"ppTerm": "?neg✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"case neg\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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 473,
"column": 11
} | {
"line": 473,
"column": 22
} | {
"line": 473,
"column": 23
} | [
{
"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... | [
"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 (𝟙 ((t.eTruncGE.obj a).obj X))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 482,
"column": 11
} | {
"line": 482,
"column": 22
} | {
"line": 482,
"column": 23
} | [
{
"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... | [
"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.eTruncLTι b).app ((t.eTruncL... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 485,
"column": 13
} | {
"line": 485,
"column": 61
} | {
"line": 486,
"column": 8
} | [
{
"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... | [
"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⊢ IsZero ((t.truncGE a).obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | {
"line": 491,
"column": 13
} | {
"line": 491,
"column": 24
} | {
"line": 491,
"column": 25
} | [
{
"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... | [
"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 (𝟙 ((t.truncGE a).o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 99,
"column": 8
} | {
"line": 99,
"column": 19
} | {
"line": 99,
"column": 20
} | [
{
"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 ≤ ↑(#∅)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
... | [
"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 ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 100,
"column": 8
} | {
"line": 100,
"column": 19
} | {
"line": 100,
"column": 20
} | [
{
"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 ≤ ↑(#∅)",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
... | [
"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 ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 106,
"column": 29
} | {
"line": 106,
"column": 40
} | {
"line": 106,
"column": 41
} | [
{
"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",
"ppTerm": "?m.129",
"ass... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 109,
"column": 29
} | {
"line": 109,
"column": 40
} | {
"line": 109,
"column": 41
} | [
{
"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",
"ppTerm": "?m.186",
"assigned": false... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Partition.Finpartition | {
"line": 810,
"column": 4
} | {
"line": 816,
"column": 96
} | {
"line": 817,
"column": 4
} | [
{
"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",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Order... | [
"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⊢ ∀ (a b c d : α), s a d → s b d → (s a c ↔ s b c)"
] | 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": 829,
"column": 2
} | {
"line": 830,
"column": 50
} | {
"line": 831,
"column": 2
} | [
{
"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",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\na : α\ns : Setoid α\nx : Finset α\ninst✝ : DecidableRel ⇑s\nb : α\n⊢ (∃ a₁ ∈ x, (b ∈ x ∧ s a₁ b) ∧ a ∈ x ∧ s a₁ a) ↔ a ∈ x ∧ b ∈ x ∧ s a b"
] | 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.Density | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 96
} | {
"line": 208,
"column": 97
} | [
{
"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)... | [
"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)\nhδ' : 0 ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Density | {
"line": 211,
"column": 4
} | {
"line": 211,
"column": 96
} | {
"line": 211,
"column": 97
} | [
{
"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) ≤ ↑(... | [
"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) ≤ ↑(#s₂)\nhδ' : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 337,
"column": 4
} | {
"line": 337,
"column": 15
} | {
"line": 337,
"column": 16
} | [
{
"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",
"ppTerm": "?inr.calc_1... | [
"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) ≤ ↑(#A) / ↑(#P.parts)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | {
"line": 377,
"column": 4
} | {
"line": 377,
"column": 53
} | {
"line": 379,
"column": 0
} | [
{
"pp": "case 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.IsUniform G ε\... | [] | exact aux (P.parts_nonempty hA.ne_empty).card_pos | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Regularity.Increment | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 75
} | {
"line": 72,
"column": 2
} | [
{
"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... | [
"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.parts\n⊢ ∑ x, ... | 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.Regularity.Equitabilise | {
"line": 127,
"column": 6
} | {
"line": 127,
"column": 17
} | {
"line": 127,
"column": 18
} | [
{
"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... | [
"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.parts | y ⊆ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | {
"line": 107,
"column": 4
} | {
"line": 109,
"column": 10
} | {
"line": 110,
"column": 4
} | [
{
"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... | [
"case refine_2\nα : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nl : ℕ\nhε : 0 < ε\nhl : l ≤ Fintype.card α\nhα : bound ε l ≤ Fintype.card α\nt : ℕ := initialBound ε l\nhtα : t ≤ #univ\ndum : Finpartition univ\nhdum₁ : dum.IsEquipartition\nhdum₂ : #dum.... | · rw [iterate_succ_apply', stepBound, bound]
gcongr
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | {
"line": 118,
"column": 2
} | {
"line": 119,
"column": 69
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Fintype α\ninst✝¹ : DecidableEq α\nP : Finpartition univ\nhP : P.IsEquipartition\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : ℝ\nU : Finset α\nhU : U ∈ P.parts\nV : Finset α\nhV : V ∈ P.parts\nhUV : U ≠ V\nh₂ : ¬G.IsUniform ε U V\nhX : G.nonuniformWitness ε U V ∈ P.nonunif... | [] | grw [sum_const, smul_eq_mul, card_filter_atomise_le_two_pow (s := U) hX,
Finpartition.card_nonuniformWitnesses_le, filter_subset] <;> simp | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 90,
"column": 39
} | {
"line": 90,
"column": 50
} | {
"line": 90,
"column": 51
} | [
{
"pp": "V : 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",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"SimpleGraph.deleteEdges",
"Eq.mpr",
"Sym2.mk",
"congrArg",
"SimpleGraph.Adj",
... | [
"V : Type u_1\ns : Set (Sym2 V)\nG : SimpleGraph V\nhs : s ⊆ Sym2.diagSet\nu v : V\n⊢ G.Adj u v → s(u, v) ∉ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.DeleteEdges | {
"line": 237,
"column": 4
} | {
"line": 238,
"column": 28
} | {
"line": 238,
"column": 29
} | [
{
"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... | [
"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)\ns : Finse... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 28
} | {
"line": 186,
"column": 29
} | [
{
"pp": "case 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)}",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"SimpleGraph.Iso",
"SimpleGraph.Subgraph",
"setOf",
"Membership.mem",
... | [
"case mp\nα : Type u_4\nβ : Type u_5\nA : SimpleGraph α\nB : SimpleGraph β\nf : A.Copy B\n⊢ Nonempty (A ≃g (Subgraph.map f.toHom ⊤).coe)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 28
} | {
"line": 345,
"column": 6
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na b : V\ns : Set G.Subgraph\n⊢ ∀ {v w : V}, (∃ G' ∈ s, G'.Adj v w) → G.Adj v w",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph",
"SimpleGraph.Adj",
"SimpleGraph.Sub... | [] | rintro a b ⟨G', -, hab⟩
exact G'.adj_sub hab | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 28
} | {
"line": 345,
"column": 6
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na b : V\ns : Set G.Subgraph\n⊢ ∀ {v w : V}, (∃ G' ∈ s, G'.Adj v w) → G.Adj v w",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph",
"SimpleGraph.Adj",
"SimpleGraph.Sub... | [] | rintro a b ⟨G', -, hab⟩
exact G'.adj_sub hab | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 348,
"column": 28
} | {
"line": 348,
"column": 50
} | {
"line": 348,
"column": 51
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ns : Set G.Subgraph\na b : V\nh : ∃ G' ∈ s, G'.Adj a b\n⊢ ∃ G' ∈ s, G'.Adj b a",
"ppTerm": "?m.96",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Subgraph",
... | [
"ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ns : Set G.Subgraph\na b : V\nh : ∃ G' ∈ s, G'.Adj a b\n⊢ ∃ G' ∈ s, G'.Adj a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 207,
"column": 44
} | {
"line": 207,
"column": 55
} | {
"line": 207,
"column": 56
} | [
{
"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 : ⊤.Copy G\nv w : α\nh : G.Adj (f.toEmbedding v) (f.toEmbedding w)\n⊢ ⊤.Adj v w",
"ppTerm"... | [
"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 : ⊤.Copy G\nv w : α\nh : G.Adj (f.toEmbedding v) (f.toEmbedding w)\n⊢ ¬v = w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 317,
"column": 2
} | {
"line": 317,
"column": 42
} | {
"line": 318,
"column": 4
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\nf : G.Copy H\nv : V\ninst✝¹ : Fintype ↑(G.neighborSet v)\ninst✝ : Fintype ↑(H.neighborSet (f v))\n⊢ G.degree v ≤ H.degree (f v)",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\nf : G.Copy H\nv : V\ninst✝¹ : Fintype ↑(G.neighborSet v)\ninst✝ : Fintype ↑(H.neighborSet (f v))\n⊢ G.degree v ≤ H.degree (f v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 612,
"column": 32
} | {
"line": 612,
"column": 43
} | {
"line": 612,
"column": 44
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nH₁ H₂ : G.Subgraph\nh : Disjoint H₁ H₂\n⊢ H₁.edgeSet ⊓ H₂.edgeSet ⊆ ⊥",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CompleteLattice.toLattice",
"OrderBot.toBot",
... | [
"V : Type u\nG : SimpleGraph V\nH₁ H₂ : G.Subgraph\nh : Disjoint H₁ H₂\n⊢ H₁.edgeSet ∩ H₂.edgeSet = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Copy | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 38
} | {
"line": 539,
"column": 39
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\ninst✝² : Fintype V\ninst✝¹ : Fintype { f // Injective ⇑f }\ninst✝ : DecidableEq G.Subgraph\n⊢ ↑{G' | Nonempty (H ≃g G'.coe)} = ↑(image Copy.toSubgraph univ)",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Eq.... | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\ninst✝² : Fintype V\ninst✝¹ : Fintype { f // Injective ⇑f }\ninst✝ : DecidableEq G.Subgraph\n⊢ {G' | Nonempty (H ≃g G'.coe)} = Set.range Copy.toSubgraph"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 719,
"column": 66
} | {
"line": 719,
"column": 77
} | {
"line": 719,
"column": 78
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nH : G.Subgraph\na b : V\n⊢ (H.verts.toFinset, fun a b ↦ decide (H.Adj a b)).2 a b = true → G.Adj a b",
"ppTerm": "?m.131",
"assigned": ... | [
"ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nH : G.Subgraph\na b : V\n⊢ H.Adj a b → G.Adj a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 720,
"column": 19
} | {
"line": 720,
"column": 30
} | {
"line": 720,
"column": 31
} | [
{
"pp": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nH : G.Subgraph\na b : V\n⊢ (H.verts.toFinset, fun a b ↦ decide (H.Adj a b)).2 a b = true → a ∈ (H.verts.toFinset, fun a b ↦ decide (H.Adj a b))... | [
"ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : G.Subgraph\na✝ b✝ : V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nH : G.Subgraph\na b : V\n⊢ H.Adj a b → a ∈ H.verts"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 834,
"column": 54
} | {
"line": 839,
"column": 35
} | {
"line": 841,
"column": 0
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nG' : G.Subgraph\nv : V\ninst✝ : Fintype ↑(G'.neighborSet v)\nhG : G'.verts.Subsingleton\n⊢ G'.degree v = 0",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"congrArg",
"SimpleGraph.Subgraph.coe_degree",
... | [] | by
by_cases hv : v ∈ G'.verts
· rw [← G'.coe_degree ⟨v, hv⟩]
have := (Set.subsingleton_coe _).mpr hG
exact G'.coe.degree_eq_zero_of_subsingleton ⟨v, hv⟩
· exact degree_of_notMem_verts hv | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 972,
"column": 28
} | {
"line": 972,
"column": 53
} | {
"line": 972,
"column": 54
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w : V\nhvw : G.Adj v w\nu : V\nthis : w = u ↔ u = w\n⊢ u ∈ (G.subgraphOfAdj hvw).neighborSet v ↔ u ∈ {w}",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph.mem_neighborSet._simp_1",
"Eq.mpr",
"False",
"Sym... | [
"V : Type u\nG : SimpleGraph V\nv w : V\nhvw : G.Adj v w\nu : V\nthis : w = u ↔ u = w\n⊢ w = u ↔ u = w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1045,
"column": 4
} | {
"line": 1045,
"column": 15
} | {
"line": 1045,
"column": 16
} | [
{
"pp": "case Adj\nV : Type u\nG : SimpleGraph V\nG' : G.Subgraph\nG'' : G'.coe.Subgraph\nx✝¹ x✝ : ↑G'.verts\n⊢ (G'.Adj ↑x✝¹ ↑x✝ ∧ ∃ (hv : ↑x✝¹ ∈ G'.verts) (hw : ↑x✝ ∈ G'.verts), G''.Adj ⟨↑x✝¹, hv⟩ ⟨↑x✝, hw⟩) ↔ G''.Adj x✝¹ x✝",
"ppTerm": "?Adj",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case Adj\nV : Type u\nG : SimpleGraph V\nG' : G.Subgraph\nG'' : G'.coe.Subgraph\nx✝¹ x✝ : ↑G'.verts\n⊢ G''.Adj x✝¹ x✝ → G'.Adj ↑x✝¹ ↑x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Subgraph | {
"line": 1200,
"column": 43
} | {
"line": 1203,
"column": 22
} | {
"line": 1205,
"column": 0
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nG' : G.Subgraph\n⊢ G'.IsInduced ↔ ∃ s, G' = ⊤.induce s",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Subgraph",
"SimpleGraph.Adj",
"Membership.mem",
"Exists",
"Eq.rec",
... | [] | by
refine ⟨fun h ↦ ⟨G'.verts, h.induce_top_verts.symm⟩, fun ⟨s, h⟩ _ hu _ hv hadj ↦ ?_⟩
rw [h, (h ▸ rfl : s = G'.verts)]
exact ⟨hu, hv, hadj⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Walk.Basic | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 13
} | {
"line": 229,
"column": 14
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\n⊢ List.map (fun x ↦ x.toProd.2) p.darts = p.support.tail",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u\nG : SimpleGraph V\nu v : V\np : G.Walk u v\n⊢ List.map (fun x ↦ x.toProd.2) p.darts = p.support.tail"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Walk.Traversal | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 13
} | {
"line": 145,
"column": 14
} | [
{
"pp": "V : Type u\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : ¬p.Nil\n⊢ G.Adj v p.snd",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u\nG : SimpleGraph V\nv w : V\np : G.Walk v w\nhp : ¬p.Nil\n⊢ G.Adj v p.snd"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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