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.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 186,
"column": 2
} | {
"line": 186,
"column": 51
} | [
{
"pp": "ι : Type u_1\nn : ℕ\ns : Finset ι\na : ι → ZMod n\nhs : 2 * n - 1 ≤ #s\n⊢ ∃ t ⊆ s, #t = n ∧ ∑ i ∈ t, a i = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 194,
"column": 83
} | {
"line": 194,
"column": 94
} | [
{
"pp": "n : ℕ\ns : Multiset ℤ\nhs : 2 * n - 1 ≤ s.card\n⊢ 2 * ?m.31 - 1 ≤ #s.toEnumFinset",
"usedConstants": [
"Eq.mpr",
"Nat.instOrderedSub",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"Int.instDecidableEq",
"id",
"instSubNat",
"instMulNat",
"instOfNa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 195,
"column": 78
} | {
"line": 195,
"column": 89
} | [
{
"pp": "n : ℕ\ns : Multiset ℤ\nhs : 2 * n - 1 ≤ s.card\nt : Finset (ℤ × ℕ)\nhts : t ⊆ s.toEnumFinset\nht : #t = n ∧ ↑n ∣ ∑ i ∈ t, i.1\n⊢ (Multiset.map Prod.fst t.val).card = n ∧ ↑n ∣ (Multiset.map Prod.fst t.val).sum",
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"Int.instAddCommMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 227,
"column": 2
} | {
"line": 227,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PartialOrder α\ns t : Finset α\ninst✝ : DecidableEq α\n⊢ toColex (s \\ t) ≤ toColex (t \\ s) ↔ toColex s ≤ toColex t",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PartialOrder α\ns t : Finset α\ninst✝ : DecidableEq α\n⊢ toColex (s \\ t) < toColex (t \\ s) ↔ toColex s < toColex t",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 203,
"column": 84
} | {
"line": 203,
"column": 95
} | [
{
"pp": "n : ℕ\ns : Multiset (ZMod n)\nhs : 2 * n - 1 ≤ s.card\n⊢ 2 * n - 1 ≤ #s.toEnumFinset",
"usedConstants": [
"Eq.mpr",
"Nat.instOrderedSub",
"HMul.hMul",
"congrArg",
"ZMod.decidableEq",
"HSub.hSub",
"id",
"instSubNat",
"instMulNat",
"instOfNa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.ErdosGinzburgZiv | {
"line": 204,
"column": 78
} | {
"line": 204,
"column": 89
} | [
{
"pp": "n : ℕ\ns : Multiset (ZMod n)\nhs : 2 * n - 1 ≤ s.card\nt : Finset (ZMod n × ℕ)\nhts : t ⊆ s.toEnumFinset\nht : #t = n ∧ ∑ i ∈ t, i.1 = 0\n⊢ (Multiset.map Prod.fst t.val).card = n ∧ (Multiset.map Prod.fst t.val).sum = 0",
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"NonUnitalCommR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 307,
"column": 6
} | {
"line": 307,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Finset α\nh : toColex s ≤ toColex t\nhst : s ≠ t\nm : α := (s ∆ t).max' ⋯\nhmt : m ∉ t\n⊢ m ∈ s",
"usedConstants": [
"Finset",
"Membership.mem",
"id",
"Finset.instSetLike",
"SetLike.instMembership"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 37
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : LinearOrder α\ns t : Finset α\nh : ∀ (hst : s ≠ t), (s ∆ t).max' ⋯ ∈ t\na : α\nhas : a ∈ ofColex (toColex s)\nhat : a ∉ ofColex (toColex t)\nhst : s ≠ t\n⊢ (s ∆ t).max' ⋯ ∉ ofColex (toColex s)",
"usedConstants": [
"Iff.mpr",
"Lattice.toSemilatticeSup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Projectivization.Basic | {
"line": 244,
"column": 4
} | {
"line": 244,
"column": 19
} | [
{
"pp": "case pos\nK : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nD D' : ℙ K V\nh : D = D'\n⊢ LinearIndepOn K id {D.rep, D'.rep}",
"usedConstants": [
"Eq.mpr",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"congrArg",
"AddCommGr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Projectivization.Basic | {
"line": 247,
"column": 4
} | {
"line": 247,
"column": 15
} | [
{
"pp": "case neg\nK : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nD D' : ℙ K V\nh : LinearIndepOn K id (Set.range ![D'.rep, D.rep])\n⊢ LinearIndepOn K id {D.rep, D'.rep}",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Projectivization.Basic | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 69
} | [
{
"pp": "case neg\nK : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nD D' : ℙ K V\nh : LinearIndependent K ![D'.rep, D.rep]\n⊢ Function.Injective ![D'.rep, D.rep]",
"usedConstants": [
"Eq.mpr",
"Projectivization.rep",
"id",
"instOfNatNa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 68
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : LinearOrder α\ns : Finset α\na : α\nha : a ∈ s\nhst : toColex s ≤ toColex s\nhcard : #s ≤ #s\nht : s.Nonempty\nm : α := s.min' ht\n⊢ toColex (s.erase a) ≤ toColex (s.erase m)",
"usedConstants": [
"Finset.min'",
"Iff.mpr",
"Equiv.instEquivLike",
... | exact (erase_le_erase ha <| min'_mem _ _).2 <| min'_le _ _ <| ha | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Colex | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 68
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : LinearOrder α\ns : Finset α\na : α\nha : a ∈ s\nhst : toColex s ≤ toColex s\nhcard : #s ≤ #s\nht : s.Nonempty\nm : α := s.min' ht\n⊢ toColex (s.erase a) ≤ toColex (s.erase m)",
"usedConstants": [
"Finset.min'",
"Iff.mpr",
"Equiv.instEquivLike",
... | exact (erase_le_erase ha <| min'_mem _ _).2 <| min'_le _ _ <| ha | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Colex | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 68
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : LinearOrder α\ns : Finset α\na : α\nha : a ∈ s\nhst : toColex s ≤ toColex s\nhcard : #s ≤ #s\nht : s.Nonempty\nm : α := s.min' ht\n⊢ toColex (s.erase a) ≤ toColex (s.erase m)",
"usedConstants": [
"Finset.min'",
"Iff.mpr",
"Equiv.instEquivLike",
... | exact (erase_le_erase ha <| min'_mem _ _).2 <| min'_le _ _ <| ha | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Colex | {
"line": 466,
"column": 19
} | {
"line": 466,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\n𝒜 : Finset (Finset α)\nr : ℕ\ninst✝ : Fintype α\nh𝒜 : IsInitSeg 𝒜 r\nh𝒜₀ : 𝒜.Nonempty\na : Finset α\nha : a ∈ 𝒜\n⊢ toColex a ∈ ⇑ofColex ⁻¹' ↑𝒜",
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"Equiv.instEquivLike",
"Colex... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Derangements.Basic | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 48
} | [
{
"pp": "case refine_2\nα : Type u_1\nβ : Type u_2\np : α → Prop\ninst✝ : DecidablePred p\nf : Perm (Subtype p)\nhf : ∀ a ∈ fixedPoints ⇑↑((Perm.subtypeEquivSubtypePerm p) f), ¬p a\na : α\nha : p a\nhfa : f ⟨a, ha⟩ = ⟨a, ha⟩\n⊢ (Perm.ofSubtype f) a = a",
"usedConstants": [
"Eq.mpr",
"MonoidHom.i... | Perm.ofSubtype_apply_of_mem _ ha, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.Configuration | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 59
} | [
{
"pp": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\np : P\n⊢ 2 < lineCount L p",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Configuration.lineCount",
"id",
"instOfNatNat",
"Configuration.Projectiv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Configuration | {
"line": 434,
"column": 2
} | {
"line": 434,
"column": 60
} | [
{
"pp": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : ProjectivePlane P L\ninst✝¹ : Finite P\ninst✝ : Finite L\nl : L\n⊢ 2 < pointCount P l",
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Combinatorics.Configuration.0.Configuration.ProjectivePlane.two_lt_point... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Digraph.Basic | {
"line": 64,
"column": 4
} | {
"line": 64,
"column": 51
} | [
{
"pp": "case h.h\nV : Type u_1\nadj adj' : V → V → Bool\nh : (fun v w ↦ adj v w = true) = fun v w ↦ adj' v w = true\nv w : V\n⊢ adj v w = adj' v w",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 39
} | [
{
"pp": "case hx\nm : Multiset ℕ\nx : ℕ\nhx : x ∈ m.toFinset.erase 0\n⊢ x ! ^ count x m * ((count x m)! * ∏ j ∈ Finset.range (count x m), (j * x + x - 1).choose (x - 1)) = (x * count x m)!",
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"Nat.choose",
"HMul.hMul",
"Monoid.toMu... | rw [← mul_assoc, bell_mul_eq_lemma] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 65,
"column": 6
} | {
"line": 65,
"column": 41
} | [
{
"pp": "case h.refine_1\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\na✝ : G\nhA : #(A * A) ≤ #A\nha✝ : a✝ ∈ A\nsmul_A : ∀ {a : G}, a ∈ A → a •> A = A * A\nA_smul : ∀ {a : G}, a ∈ A → A <• a = A * A\nsmul_A_eq_A_smul : ∀ {a : G}, a ∈ A → a •> A = A <• a\nmul_mem_A_comm : ∀ {x a : G}, a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Catalan.Tree | {
"line": 36,
"column": 73
} | {
"line": 36,
"column": 84
} | [
{
"pp": "a b : Finset (Tree Unit)\nx✝¹ x✝ : Tree Unit × Tree Unit\nx₁ x₂ y₁ y₂ : Tree Unit\nh : (fun x ↦ node () x.1 x.2) (x₁, x₂) = (fun x ↦ node () x.1 x.2) (y₁, y₂)\n⊢ (x₁, x₂) = (y₁, y₂)",
"usedConstants": [
"Eq.mpr",
"id",
"Prod.mk",
"Tree",
"And",
"Unit",
"Pro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 33
} | [
{
"pp": "m n : ℕ\nhn : n ≠ 0\n⊢ (m * n)! / (n ! ^ m * m !) = m.uniformBell n",
"usedConstants": [
"HMul.hMul",
"Nat.instMonoid",
"instMulNat",
"Monoid.toPow",
"Nat.div_eq_of_eq_mul_left",
"HPow.hPow",
"Nat.factorial",
"Nat",
"instHPow",
"Nat.unifor... | apply Nat.div_eq_of_eq_mul_left | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 36
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA B : Finset G\nhA : ↑(#(B * A)) ≤ K * ↑(#A)\na : G\nha : a ∈ B\nb : G\nhb : b ∈ B\n⊢ (2 - K) * ↑(#A) ≤ ↑(A.convolution A⁻¹ (a⁻¹ * b))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 36
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA B : Finset G\nhA : ↑(#(B * A)) < K * ↑(#A)\na : G\nha : a ∈ B\nb : G\nhb : b ∈ B\n⊢ (2 - K) * ↑(#A) < ↑(A.convolution A⁻¹ (a⁻¹ * b))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 15
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : #(A * A) < 2 * #A\nx : G\nhx : x ∈ A\ny : G\nhy : y ∈ A\n⊢ (x •> A ∩ y •> A).Nonempty",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : #(A * A) < 2 * #A\n⊢ A * A⁻¹ ⊆ A⁻¹ * A",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 142,
"column": 61
} | {
"line": 142,
"column": 88
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : #(A * A) < 2 * #A\n⊢ #(A⁻¹ * A⁻¹) < 2 * #A⁻¹",
"usedConstants": [
"Finset.card_inv",
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Finset.divisionMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 169,
"column": 43
} | {
"line": 169,
"column": 54
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA✝ B S : Finset G\na b c d x✝ y✝ : G\nA : Finset G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\nx : G\nhx : x ∈ A\ny : G\nhy : y ∈ A\n⊢ ↑(#(A * ?m.78)) < ?m.77 * ↑(#?m.78)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 80,
"column": 4
} | {
"line": 81,
"column": 78
} | [
{
"pp": "p q : DyckWord\n⊢ ∀ (i : ℕ), count D (take i (↑p ++ ↑q)) ≤ count U (take i (↑p ++ ↑q))",
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"Nat.instIsOrderedAddMonoid",
"DyckStep.U",
"congrArg",
"covariant_swap_add_of_covariant_add",
"add_le_add",
... | simp only [take_append, count_append]
exact fun _ ↦ add_le_add (p.count_D_le_count_U _) (q.count_D_le_count_U _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 80,
"column": 4
} | {
"line": 81,
"column": 78
} | [
{
"pp": "p q : DyckWord\n⊢ ∀ (i : ℕ), count D (take i (↑p ++ ↑q)) ≤ count U (take i (↑p ++ ↑q))",
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"Nat.instIsOrderedAddMonoid",
"DyckStep.U",
"congrArg",
"covariant_swap_add_of_covariant_add",
"add_le_add",
... | simp only [take_append, count_append]
exact fun _ ↦ add_le_add (p.count_D_le_count_U _) (q.count_D_le_count_U _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 42
} | [
{
"pp": "case cons\ns : DyckStep\ntail✝ : List DyckStep\ncount_U_eq_count_D✝ : count U (s :: tail✝) = count D (s :: tail✝)\nnonneg : ∀ (i : ℕ), count D (take i (s :: tail✝)) ≤ count U (take i (s :: tail✝))\nh : ↑{ toList := s :: tail✝, count_U_eq_count_D := count_U_eq_count_D✝, count_D_le_count_U := nonneg } ≠ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 165,
"column": 19
} | {
"line": 165,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA✝ B S : Finset G\na✝ b✝ c d x y : G\nA : Finset G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\na : G\nha : a⁻¹ ∈ A\nb : G\nhb : b ∈ A\n⊢ b⁻¹⁻¹ ∈ A",
"usedConstants": [
"Eq.mpr",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 213,
"column": 36
} | {
"line": 213,
"column": 47
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\nh₀ : A.Nonempty\na : G\nha : a ∈ A⁻¹ * A\n⊢ ↑(#(A * ?m.103)) < ?m.102 * ↑(#?m.103)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 173,
"column": 75
} | {
"line": 173,
"column": 91
} | [
{
"pp": "case inr\np q : DyckWord\nh : p ≠ 0\ni : ℕ\nhi : i > 0\n⊢ count D (List.take (i - ([U] ++ ↑p).length) [D]) + count D [U] ≤\n count U (List.take (i - ([U] ++ ↑p).length) [D]) + count U [U]",
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"DyckStep.U",
"congrArg",
... | count_singleton' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 15
} | [
{
"pp": "p q : DyckWord\nh : p ≠ 0\nhn : p.IsNested\nthis :\n (count U (↑p).dropLast.tail + if (U == U) = true then 1 else 0) + count U [D] =\n count D (U :: (↑p).dropLast.tail ++ [D])\n⊢ count U (↑p).dropLast.tail = count D (↑p).dropLast.tail",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 32
} | [
{
"pp": "p : DyckWord\nhn : p.IsNested\n⊢ (p.denest hn).nest = p",
"usedConstants": [
"Eq.mpr",
"DyckWord",
"id",
"List",
"DyckWord.nest",
"DyckWord.denest",
"_private.Mathlib.Combinatorics.Enumerative.DyckWord.0.DyckWord.nest_denest._simp_1_1",
"DyckWord.toLi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 35
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\nlp : 0 < (↑p).length\n⊢ p.firstReturn < (range (↑p).length).length",
"usedConstants": [
"instDecidableEqDyckStep",
"DyckStep.U",
"List.findIdx_lt_length_of_exists",
"instOfNatNat",
"List.range",
"instBEqOfDecidableEq",
"instHAdd",
... | apply findIdx_lt_length_of_exists | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 285,
"column": 2
} | {
"line": 285,
"column": 13
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\nthis :\n decide\n (count U\n (List.take\n ((range\n (↑p).length)[findIdx\n (fun i ↦ decide (count U (List.take (i + 1) ↑p) = count D (List.take (i + 1) ↑p)))\n (range (↑p).length)] +\n 1)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 296,
"column": 2
} | {
"line": 313,
"column": 88
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\na : G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\nha : a ∈ A\n⊢ a •> (A⁻¹ * A) = (A⁻¹ * A) <• a",
"usedConstants": [
"Finset.mul_inv_eq_inv_mul_of_doubling_lt_two",
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
... | refine subset_antisymm ?_ ?_
· rw [subset_smul_finset_iff, ← op_inv]
calc
a •> (A⁻¹ * A) <• a⁻¹ ⊆ a •> (A⁻¹ * A) * A⁻¹ := op_smul_finset_subset_mul (by simpa)
_ ⊆ A * (A⁻¹ * A) * A⁻¹ := by grw [smul_finset_subset_mul (by simpa)]
_ = A⁻¹ * A := by
simp_rw [← coe_inj, coe_mul]
rw [... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 296,
"column": 2
} | {
"line": 313,
"column": 88
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\na : G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\nha : a ∈ A\n⊢ a •> (A⁻¹ * A) = (A⁻¹ * A) <• a",
"usedConstants": [
"Finset.mul_inv_eq_inv_mul_of_doubling_lt_two",
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
... | refine subset_antisymm ?_ ?_
· rw [subset_smul_finset_iff, ← op_inv]
calc
a •> (A⁻¹ * A) <• a⁻¹ ⊆ a •> (A⁻¹ * A) * A⁻¹ := op_smul_finset_subset_mul (by simpa)
_ ⊆ A * (A⁻¹ * A) * A⁻¹ := by grw [smul_finset_subset_mul (by simpa)]
_ = A⁻¹ * A := by
simp_rw [← coe_inj, coe_mul]
rw [... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 306,
"column": 6
} | {
"line": 306,
"column": 17
} | [
{
"pp": "case neg.right\np q : DyckWord\nh : ¬p = 0\nu : ↑(p + q) = ↑p ++ ↑q\nv : p.firstReturn < (↑p).length\nj : ℕ\nhj : j < p.firstReturn\n⊢ decide (count U (List.take (j + 1) ↑p) = count D (List.take (j + 1) ↑p)) = false",
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"DyckSt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 334,
"column": 4
} | {
"line": 335,
"column": 11
} | [
{
"pp": "case refine_3\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : ↑(#(A * A)) < 3 / 2 * ↑(#A)\nH : Subgroup G := A.invMulSubgroup h\na : G\nha : a ∈ A\n⊢ a •> ↑H = ↑H <• a",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 56
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nA Z : Finset G\nhZA : ↑Z ⊆ ↑A\nhZinj : Set.InjOn (fun x ↦ ↑H <• x) ↑Z\nhHZA : (fun x ↦ ↑H <• x) '' ↑Z = (fun x ↦ ↑H <• x) '' ↑A\n⊢ ↑H * ↑Z = ↑H * ↑A",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 372,
"column": 4
} | {
"line": 372,
"column": 54
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : DecidableEq G\nH : Subgroup G\ninst✝ : Fintype ↥H\nZ : Finset G\nhZ : Set.InjOn (fun x ↦ ↑H <• x) ↑Z\nh₁ z₁ h₂ z₂ : G\nh : h₁ * z₁ = h₂ * z₂\nhh₁ : h₁ ∈ H\nhz₁ : z₁ ∈ Z\nhh₂ : h₂ ∈ H\nhz₂ : z₂ ∈ Z\n⊢ z₂ * z₁⁻¹ ∈ H",
"usedConstants": [
"Iff.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 318,
"column": 28
} | {
"line": 318,
"column": 43
} | [
{
"pp": "case right\np : DyckWord\nu : ↑p.nest = U :: ↑p ++ [D]\nj : ℕ\nhj : j < (↑p).length + 1\n⊢ decide (count U (List.take (j + 1) (U :: (↑p ++ [D]))) = count D (List.take (j + 1) (U :: (↑p ++ [D])))) = false",
"usedConstants": [
"instDecidableEqDyckStep",
"DyckStep.U",
"id",
"in... | take_succ_cons, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 399,
"column": 24
} | {
"line": 399,
"column": 39
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA : Finset G\nhK₁ : 1 < K\nhKφ : K < φ\nhA₁ : ↑(#(A⁻¹ * A)) ≤ K * ↑(#A)\nhA₂ : ↑(#(A * A⁻¹)) ≤ K * ↑(#A)\nK_pos hK₀ : 0 < K\nhKφ' : 0 < φ - K\nhKψ' : 0 < K - ψ\nhK₂' : 0 < 2 - K\nconst_pos : 0 < K * (2 - K) / ((φ - K) * (K - ψ))\nA_nonempty ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 333,
"column": 36
} | {
"line": 333,
"column": 47
} | [
{
"pp": "p q : DyckWord\nh✝ : p ≠ 0\nh : ¬p = 0\n⊢ ↑{ toList := List.take (p.firstReturn + 1) ↑p, count_U_eq_count_D := ⋯, count_D_le_count_U := ⋯ } ≠ []",
"usedConstants": [
"Eq.mpr",
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"Nat.add_eq_zero_iff._simp_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 408,
"column": 4
} | {
"line": 408,
"column": 61
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA : Finset G\nhK₁ : 1 < K\nhKφ : K < φ\nhA₁ : ↑(#(A⁻¹ * A)) ≤ K * ↑(#A)\nhA₂ : ↑(#(A * A⁻¹)) ≤ K * ↑(#A)\nK_pos hK₀ : 0 < K\nhKφ' : 0 < φ - K\nhKψ' : 0 < K - ψ\nhK₂' : 0 < 2 - K\nconst_pos : 0 < K * (2 - K) / ((φ - K) * (K - ψ))\nA_nonempty ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 19
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congrArg",
"DyckWord",
"id",
"Dy... | rw [← congrArg semilength (nest_insidePart_add_outsidePart h), semilength_add, semilength_nest,
add_right_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 19
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congrArg",
"DyckWord",
"id",
"Dy... | rw [← congrArg semilength (nest_insidePart_add_outsidePart h), semilength_add, semilength_nest,
add_right_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 19
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congrArg",
"DyckWord",
"id",
"Dy... | rw [← congrArg semilength (nest_insidePart_add_outsidePart h), semilength_add, semilength_nest,
add_right_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 114,
"column": 60
} | {
"line": 114,
"column": 71
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs0 : 0 ∉ s\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nx : ℕ\nhx : g x ≠ 0\n⊢ x ∈ g.support",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 128,
"column": 60
} | {
"line": 128,
"column": 71
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nh : g 0 ≠ 0\n⊢ 0 ∈ g.support",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 15
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs0 : 0 ∉ s\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nhgne0 : ∀ (i : ℕ), g i ≠... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 35
} | [
{
"pp": "case refine_4.h\nR : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs0 : 0 ∉ s\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nhgne0 : ∀ (i : ℕ), g i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 139,
"column": 4
} | {
"line": 140,
"column": 97
} | [
{
"pp": "case refine_4\nR : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs0 : 0 ∉ s\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nhgne0 : ∀ (i : ℕ), g i ≠... | ext x
simpa [toFinsuppAntidiag] using Nat.div_mul_cancel <| aux_dvd_of_coeff_ne_zero hs0 hg hprod x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 139,
"column": 4
} | {
"line": 140,
"column": 97
} | [
{
"pp": "case refine_4\nR : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs0 : 0 ∉ s\ng : ℕ →₀ ℕ\nhg : g ∈ s.finsuppAntidiag d\nhprod : ∀ i ∈ s, (coeff (g i)) (1 + ∑' (j : ℕ), f i (j + 1) • X ^ (i * (j + 1))) ≠ 0\nhgne0 : ∀ (i : ℕ), g i ≠... | ext x
simpa [toFinsuppAntidiag] using Nat.div_mul_cancel <| aux_dvd_of_coeff_ne_zero hs0 hg hprod x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 486,
"column": 6
} | {
"line": 486,
"column": 51
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA : Finset G\nhK₁ : 1 < K\nhKφ : K < φ\nhA₁ : ↑(#(A⁻¹ * A)) ≤ K * ↑(#A)\nhA₂ : ↑(#(A * A⁻¹)) ≤ K * ↑(#A)\nK_pos hK₀ : 0 < K\nhKφ' : 0 < φ - K\nhKψ' : 0 < K - ψ\nhK₂' : 0 < 2 - K\nconst_pos : 0 < K * (2 - K) / ((φ - K) * (K - ψ))\nA_nonempty ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 86,
"column": 8
} | {
"line": 86,
"column": 34
} | [
{
"pp": "case h.e'_5.h\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\nm : ℕ\nhm : 0 < m\na✝ : Nontrivial R\ni : ℕ\n⊢ ∑ j ∈ range m, X ^ ((i + 1) * j) = 1 + ∑' (j : ℕ), (if j + 1 < m then 1 else 0) • X ^ ((i + 1) * (j + 1))",
"usedConstants": [
"Eq.mpr",
"... | sum_range_eq_add_Ico _ hm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 93,
"column": 62
} | {
"line": 93,
"column": 73
} | [
{
"pp": "R : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\nm : ℕ\nhm : 0 < m\na✝ : Nontrivial R\ni b : ℕ\nhb : b ∉ range (m - 1)\n⊢ (if b + 1 < m then 1 else 0) = 0",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 85,
"column": 2
} | {
"line": 93,
"column": 86
} | [
{
"pp": "case h.e'_5\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\nm : ℕ\nhm : 0 < m\na✝ : Nontrivial R\n⊢ (fun i ↦ ∑ j ∈ range m, X ^ ((i + 1) * j)) = fun i ↦\n 1 + ∑' (j : ℕ), (if j + 1 < m then 1 else 0) • X ^ ((i + 1) * (j + 1))",
"usedConstants": [
"Eq... | · ext1 i
rw [sum_range_eq_add_Ico _ hm, sum_Ico_eq_sum_range]
congrm $(by simp) + ?_
trans ∑ k ∈ range (m - 1), (if k + 1 < m then (1 : R) else 0) • X ^ ((i + 1) * (k + 1))
· refine sum_congr rfl fun b hn ↦ ?_
rw [add_comm 1 b]
have : b + 1 < m := by grind
simp [this]
· exact (tsum... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 15
} | [
{
"pp": "case inl\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\n⊢ Multipliable fun i ↦ ∑ j ∈ range 0, X ^ ((i + 1) * j)",
"usedConstants": [
"HMul.hMul",
"MvPowerSeries.instCommSemiring",
"CommSemiring.toSemiring",
"id",
"instMulNat",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 501,
"column": 4
} | {
"line": 502,
"column": 11
} | [
{
"pp": "case inr.intro.calc_2.a.a\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA : Finset G\nhK₁ : 1 < K\nhKφ : K < φ\nhA₁ : ↑(#(A⁻¹ * A)) ≤ K * ↑(#A)\nhA₂ : ↑(#(A * A⁻¹)) ≤ K * ↑(#A)\nK_pos hK₀ : 0 < K\nhKφ' : 0 < φ - K\nhKψ' : 0 < K - ψ\nhK₂' : 0 < 2 - K\nconst_pos : 0 < K * (2 - K) / ((φ -... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 518,
"column": 6
} | {
"line": 518,
"column": 18
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA S : Finset G\nhS : S.Nonempty\n⊢ (1 - K) * ↑(#A) ≤ expansion K S A",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Real.instSub",
... | one_sub_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | [
{
"pp": "n m : ℕ\nhm : 0 < m\n⊢ #(restricted n fun x ↦ ¬m ∣ x) = #(countRestricted n m)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Schroder | {
"line": 72,
"column": 6
} | {
"line": 72,
"column": 17
} | [
{
"pp": "case zero\nn : ℕ\nx✝ : n + 2 ≠ 0\nhk : 0 ∈ Iic (n + 1)\n⊢ Even (largeSchroder 0 * (n + 1 - 0).largeSchroder)",
"usedConstants": [
"Eq.mpr",
"Nat.largeSchroder",
"Nat.instOrderedSub",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | {
"line": 516,
"column": 4
} | {
"line": 516,
"column": 40
} | [
{
"pp": "𝕜 : Type u_2\nα : Type u_5\ninst✝³ : Ring 𝕜\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b : α\nthis✝ : DecidableLE α := ⋯\nmud : IncidenceAlgebra 𝕜 αᵒᵈ := ⋯\nthis : mud * zeta 𝕜 * mu 𝕜 = mu 𝕜 * zeta 𝕜 * mu 𝕜\n⊢ mud = mu 𝕜",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 186,
"column": 83
} | {
"line": 186,
"column": 94
} | [
{
"pp": "R : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : TopologicalSpace R\ninst✝ : T2Space R\nf : ℕ → ℕ → R\nd : ℕ\ns : Finset ℕ\nhs✝ : s ≥ range d\nthis :\n ∏ i ∈ s, (1 + ∑' (j : ℕ), f (i + 1) (j + 1) • X ^ ((i + 1) * (j + 1))) =\n ∏ i ∈ Finset.map (addRightEmbedding 1) s, (1 + ∑' (j : ℕ), f i (j + 1) • ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 637,
"column": 31
} | {
"line": 637,
"column": 51
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nH : ∀ (A : Finset G), A.Nonempty → ¬IsFragment K S A\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nκ_add_one_pos : 0 < κ + 1\none_sub_K_pos : 0 < 1 - K\nt : ℕ := ⌊(κ + 1) / (1 - K)... | by norm_cast; gcongr | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 697,
"column": 4
} | {
"line": 697,
"column": 43
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier✝ : 1 ∈ n⁻¹ •> N\nx : G\none_mem_carrier : x •> 1 ∈ x •> n⁻¹ •> N\n⊢ x ∈ x •> n⁻¹ •> N",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 706,
"column": 8
} | {
"line": 706,
"column": 36
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\na b : G\nha : a ∈ n⁻¹ •> N\nhb✝ : b ∈ n⁻¹ •> N\nhb : a * b ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 707,
"column": 6
} | {
"line": 708,
"column": 56
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\na b : G\nha : a ∈ n⁻¹ •> N\nhb✝ : b ∈ n⁻¹ •> N\nhb : a * b ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 713,
"column": 61
} | {
"line": 713,
"column": 72
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\na : G\nha✝ : a ∈ n⁻¹ •> N\nha : 1 ∈ a⁻¹ •> n⁻¹ •> N\n⊢ 1 ∈ n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 714,
"column": 6
} | {
"line": 715,
"column": 58
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\na : G\nha✝ : a ∈ n⁻¹ •> N\nha : 1 ∈ a⁻¹ •> n⁻¹ •> N\nthis : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 718,
"column": 4
} | {
"line": 718,
"column": 49
} | [
{
"pp": "case refine_1\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\nH : Subgroup G := { carrier := n⁻¹ •> ↑N, mul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 719,
"column": 4
} | {
"line": 719,
"column": 56
} | [
{
"pp": "case refine_2\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nS : Finset G\nhK : K < 1\nhS : S.Nonempty\nN : Finset G\nhN : IsAtom K S N\nn : G\nhn : n ∈ N\none_mem_carrier : 1 ∈ n⁻¹ •> N\nself_mem_smul_carrier : ∀ (x : G), x ∈ x •> n⁻¹ •> N\nH : Subgroup G := { carrier := n⁻¹ •> ↑N, mul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 749,
"column": 4
} | {
"line": 749,
"column": 27
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Finset G\nhZS : Z ⊆ S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 769,
"column": 17
} | {
"line": 769,
"column": 28
} | [
{
"pp": "case e_a.e_a.e_s\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nS : Finset G\nε : ℝ\nhε₀ : 0 < ε\nhε₁ : ε ≤ 1\nhS : S.Nonempty\nK : ℝ := 1 - ε / 2\nhK : K < 1\nex : Finset G → ℝ := expansion K S\nκ : ℝ := connectivity K S\nH : Subgroup G\nw✝ : Fintype ↥H\nhH : IsAtom K S (↑H).toFinset\nZ : Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 156,
"column": 4
} | {
"line": 156,
"column": 73
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Fintype α\ninst✝¹ : CommRing α\ns : Finset α\nx : α × α × α\ninst✝ : Fact (IsUnit 2)\na : α\nha : a ∈ s\ny b : α\nhb : b ∈ s\nh : y + 2 * b = y + 2 * a\n⊢ y + a = y + b",
"usedConstants": [
"Eq.mpr",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 73
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Fintype α\ninst✝¹ : CommRing α\ns : Finset α\nx : α × α × α\ninst✝ : Fact (IsUnit 2)\na : α\nha : a ∈ s\ny b : α\nhb : b ∈ s\nh : y + b = y + a\n⊢ y + 2 * a = y + 2 * b",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLef... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 186,
"column": 53
} | {
"line": 186,
"column": 64
} | [
{
"pp": "n : ℕ\nα : Type := Fin (2 * n + 1)\nthis : Coprime 2 (2 * n + 1)\n⊢ IsUnit 2",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 255,
"column": 6
} | {
"line": 255,
"column": 53
} | [
{
"pp": "⊢ (fun n ↦ 2) =o[atTop] fun n ↦ ↑n / 3",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 54
} | [
{
"pp": "case h\nn : ℕ\nhn : 6 ≤ n\nthis : 0 ≤ ↑n / 3 - 2\n⊢ ‖(↑n / 3 - 2) * ↑((n - 3) / 6) * rexp (-4 * √(Real.log ↑((n - 3) / 6)))‖ ≤ ↑(ruzsaSzemerediNumberNat n)",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 192,
"column": 36
} | {
"line": 192,
"column": 51
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nX : Set α\nh : V(G) ⊆ X ∧ E(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ (noEdge X β).IsLink e x y",
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"Membership.mem",
"id",
"G... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 54,
"column": 14
} | {
"line": 54,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nE₀ : Set β\nh : G.restrict E₀ = G\n⊢ E(G) ⊆ E₀",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 393,
"column": 19
} | {
"line": 393,
"column": 35
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nhe : V(G) = ∅\ne : β\nx y : α\nh : G.IsLink e x y\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 17
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nG : Graph α β\nh : V(G) = ∅\ne : β\nx y : α\nhe : G.IsLink e x y\n⊢ ⊥.IsLink e x y",
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 15
} | [
{
"pp": "case refine_1\nα : Type u_1\nβ : Type u_2\nG H : Graph α β\nh : H ≤ G\nF : Set β\n⊢ V(H.restrict F) ⊆ V(G.restrict F)",
"usedConstants": [
"id",
"HasSubset.Subset",
"Graph.vertexSet",
"Set.instHasSubset",
"Graph.restrict",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 11
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Symmetric (G.IsLink e)",
"usedConstants": [
"Eq.mpr",
"Symmetric",
"congrArg",
"Membership.mem",
"Exists",
"id... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Symmetric (G.IsLink e)",
"usedConstants": [
"Eq.mpr",
"Symmetric",
"congrArg",
"Membership.mem",
"Exists",
"id... | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Symmetric (G.IsLink e)",
"usedConstants": [
"Eq.mpr",
"Symmetric",
"congrArg",
"Membership.mem",
"Exists",
"id... | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 25
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nx y z u v w : α\ne f : β\nG✝ H G : Graph α β\nE : Set β\nhE : ∀ (e : β), e ∈ E ↔ ∃ x y, G.IsLink e x y\n⊢ ∀ ⦃e : β⦄, e ∈ E → Symmetric (G.IsLink e)",
"usedConstants": [
"Eq.mpr",
"Symmetric",
"congrArg",
"Membership.mem",
"Exists",
"id... | simpa [show E = E(G) by simp [Set.ext_iff, hE, G.edge_mem_iff_exists_isLink]]
using G.isLink_symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | [
{
"pp": "case idxFun.h.inl.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : α\nhm : m.idxFun i = Sum.inl val✝\n⊢ Sum.inl a = Sum.inl val✝",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | [
{
"pp": "case idxFun.h.inl.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\na : α\nhl : l.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\nval✝ : η\nhm : m.idxFun i = Sum.inr val✝\n⊢ Sum.inl a = Sum.inr val✝",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 42
} | [
{
"pp": "case idxFun.h.inr.inl\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\na : α\nhm : m.idxFun i = Sum.inl a\nb : α\nhba : b ≠ a\n⊢ Sum.inr e = Sum.inl a",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 47
} | [
{
"pp": "case idxFun.h.inr.inr\nη : Type u_5\nα : Type u_6\nι : Type u_7\ninst✝ : Nontrivial α\nl m : Subspace η α ι\ni : ι\nhlm : ∀ (x : η → α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\ne : η\nhl : l.idxFun i = Sum.inr e\nf : η\nhm : m.idxFun i = Sum.inr f\na b : α\nhab : a ≠ b\nhef : e ≠ f\n⊢ False",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | [
{
"pp": "case idxFun.h.a.refine_1.none\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nhi : m.idxFun i = none\n⊢ none = some a",
"usedConstants": [
"Eq.mpr",
"False",
"O... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | [
{
"pp": "case idxFun.h.a.refine_1.some\nα : Type u_2\nι : Type u_3\ninst✝ : Nontrivial α\nl m : Line α ι\ni : ι\na b : α\nhba : b ≠ a\nhlm : ∀ (x : α) (x_1 : ι), ↑l x x_1 = ↑m x x_1\nh : l.idxFun i = some a\nval✝ : α\nhi : m.idxFun i = some val✝\n⊢ some val✝ = some a",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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