module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.Projectivization.Basic | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 69
} | {
"line": 248,
"column": 70
} | [
{
"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]",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Projecti... | [
"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⊢ ¬D'.rep = D.rep"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Colex | {
"line": 464,
"column": 19
} | {
"line": 464,
"column": 30
} | {
"line": 464,
"column": 31
} | [
{
"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",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_... | [
"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⊢ a ∈ 𝒜"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Derangements.Basic | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 48
} | {
"line": 68,
"column": 49
} | [
{
"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",
"ppTerm": "?refine_2",
"assigned": true,
"use... | [
"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⊢ ↑(f ⟨a, ha⟩) = a"
] | Perm.ofSubtype_apply_of_mem _ ha, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 36
} | {
"line": 108,
"column": 37
} | [
{
"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))",
"ppTerm": "?m.106",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"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))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 36
} | {
"line": 115,
"column": 37
} | [
{
"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))",
"ppTerm": "?m.106",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"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))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 15
} | {
"line": 124,
"column": 16
} | [
{
"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",
"ppTerm": "?m.60",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Digraph.Basic | {
"line": 64,
"column": 4
} | {
"line": 64,
"column": 51
} | {
"line": 64,
"column": 52
} | [
{
"pp": "V : 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",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 13
} | {
"line": 142,
"column": 4
} | [
{
"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",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 142,
"column": 61
} | {
"line": 142,
"column": 88
} | {
"line": 142,
"column": 89
} | [
{
"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",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Finset.card_inv",
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toIn... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nA : Finset G\nh : #(A * A) < 2 * #A\n⊢ #(A * A) < 2 * #A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 169,
"column": 43
} | {
"line": 169,
"column": 54
} | {
"line": 169,
"column": 55
} | [
{
"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)",
"ppTerm": "?m.82",
"assigned": false,
"usedConstants": [],
"us... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Configuration | {
"line": 430,
"column": 2
} | {
"line": 430,
"column": 59
} | {
"line": 430,
"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\np : P\n⊢ 2 < lineCount L p",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Configuration.lineCount",
"id",
"i... | [
"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⊢ 1 < order P L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Configuration | {
"line": 435,
"column": 2
} | {
"line": 435,
"column": 60
} | {
"line": 435,
"column": 61
} | [
{
"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",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Combinatorics.Configuration.... | [
"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⊢ 1 < order P L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 165,
"column": 19
} | {
"line": 165,
"column": 30
} | {
"line": 165,
"column": 31
} | [
{
"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",
"ppTerm": "?m.581",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvOneM... | [
"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 ∈ A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 213,
"column": 36
} | {
"line": 213,
"column": 47
} | {
"line": 213,
"column": 48
} | [
{
"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)",
"ppTerm": "?m.106",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Catalan.Tree | {
"line": 36,
"column": 73
} | {
"line": 36,
"column": 84
} | {
"line": 36,
"column": 85
} | [
{
"pp": "a b : Finset (BinaryTree Unit)\nx✝¹ x✝ : BinaryTree Unit × BinaryTree Unit\nx₁ x₂ y₁ y₂ : BinaryTree 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)",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bina... | [
"a b : Finset (BinaryTree Unit)\nx✝¹ x✝ : BinaryTree Unit × BinaryTree Unit\nx₁ x₂ y₁ y₂ : BinaryTree Unit\nh : (fun x ↦ node () x.1 x.2) (x₁, x₂) = (fun x ↦ node () x.1 x.2) (y₁, y₂)\n⊢ x₁ = y₁ ∧ x₂ = y₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 80,
"column": 4
} | {
"line": 81,
"column": 78
} | {
"line": 81,
"column": 78
} | [
{
"pp": "p q : DyckWord\n⊢ ∀ (i : ℕ), count D (take i (↑p ++ ↑q)) ≤ count U (take i (↑p ++ ↑q))",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"Nat.instIsOrderedAddMonoid",
"DyckStep.U",
"congrArg",
"covariant_swap_a... | [] | 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
} | {
"line": 81,
"column": 78
} | [
{
"pp": "p q : DyckWord\n⊢ ∀ (i : ℕ), count D (take i (↑p ++ ↑q)) ≤ count U (take i (↑p ++ ↑q))",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckStep",
"Nat.instIsOrderedAddMonoid",
"DyckStep.U",
"congrArg",
"covariant_swap_a... | [] | 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.Bell | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 39
} | {
"line": 98,
"column": 4
} | [
{
"pp": "case e_a.a\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)!",
"ppTerm": "?e_a.a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"... | [
"case e_a.a.hx\nm : Multiset ℕ\nx : ℕ\nhx : x ∈ m.toFinset.erase 0\n⊢ x ≠ 0"
] | 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.Enumerative.DyckWord | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 43
} | [
{
"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 } ≠ ... | [
"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 } ≠ []\nf : ¬s =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 38
} | {
"line": 128,
"column": 39
} | [
{
"pp": "m : Multiset ℕ\na : ℕ\nha : a ≠ 0\nrest : ℕ := ∏ j ∈ (m.toFinset.erase 0).erase a, (count j m)!\nhrest : rest = ∏ j ∈ ((a ::ₘ m).toFinset.erase 0).erase a, (count j (a ::ₘ m))!\nc : ℕ := (map (fun x ↦ x !) m).prod * (count a m)! * rest\nhsplit : (count a m)! * rest = ∏ j ∈ m.toFinset.erase 0, (count j ... | [
"m : Multiset ℕ\na : ℕ\nha : a ≠ 0\nrest : ℕ := ∏ j ∈ (m.toFinset.erase 0).erase a, (count j m)!\nhrest : rest = ∏ j ∈ ((a ::ₘ m).toFinset.erase 0).erase a, (count j (a ::ₘ m))!\nc : ℕ := (map (fun x ↦ x !) m).prod * (count a m)! * rest\nhsplit : (count a m)! * rest = ∏ j ∈ m.toFinset.erase 0, (count j m)!\n⊢ m.bel... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 296,
"column": 2
} | {
"line": 313,
"column": 88
} | {
"line": 315,
"column": 0
} | [
{
"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",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Finset.mul_inv_eq_inv_mul_of_doubling_lt_two",
"Eq.mpr",
"l... | [] | 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
} | {
"line": 315,
"column": 0
} | [
{
"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",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Finset.mul_inv_eq_inv_mul_of_doubling_lt_two",
"Eq.mpr",
"l... | [] | 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.Bell | {
"line": 137,
"column": 6
} | {
"line": 137,
"column": 77
} | {
"line": 137,
"column": 78
} | [
{
"pp": "m : Multiset ℕ\na : ℕ\nha : a ≠ 0\nrest : ℕ := ∏ j ∈ (m.toFinset.erase 0).erase a, (count j m)!\nhrest : rest = ∏ j ∈ ((a ::ₘ m).toFinset.erase 0).erase a, (count j (a ::ₘ m))!\nc : ℕ := (map (fun x ↦ x !) m).prod * (count a m)! * rest\nhm0 : m.bell * c = m.sum !\nhm : m.sum ! * a ! = m.bell * a ! * c\... | [
"m : Multiset ℕ\na : ℕ\nha : a ≠ 0\nrest : ℕ := ∏ j ∈ (m.toFinset.erase 0).erase a, (count j m)!\nhrest : rest = ∏ j ∈ ((a ::ₘ m).toFinset.erase 0).erase a, (count j (a ::ₘ m))!\nc : ℕ := (map (fun x ↦ x !) m).prod * (count a m)! * rest\nhm0 : m.bell * c = m.sum !\nhm : m.sum ! * a ! = m.bell * a ! * c\nhc : 0 < a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 334,
"column": 4
} | {
"line": 335,
"column": 11
} | {
"line": 335,
"column": 12
} | [
{
"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",
"ppTerm": "?refine_3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
... | [
"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 •> (A⁻¹ * A) = (A⁻¹ * A) <• a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 33
} | {
"line": 194,
"column": 2
} | [
{
"pp": "m n : ℕ\nhn : n ≠ 0\n⊢ (m * n)! / (n ! ^ m * m !) = m.uniformBell n",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Nat.instMonoid",
"instMulNat",
"NPow.toPow",
"Nat.div_eq_of_eq_mul_left",
"HPow.hPow",
"Nat.factorial",
... | [
"case H1\nm n : ℕ\nhn : n ≠ 0\n⊢ 0 < n ! ^ m * m !",
"case H2\nm n : ℕ\nhn : n ≠ 0\n⊢ (m * n)! = m.uniformBell n * (n ! ^ m * m !)"
] | apply Nat.div_eq_of_eq_mul_left | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 56
} | {
"line": 362,
"column": 57
} | [
{
"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",
"ppTerm": "?m.95",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 42
} | {
"line": 236,
"column": 43
} | [
{
"pp": "n : ℕ\np : (n + 1).Partition\n⊢ n + 1 = ∑ a ∈ p.parts.toFinset, count a p.parts * a",
"ppTerm": "?m.139",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\np : (n + 1).Partition\n⊢ n + 1 = ∑ a ∈ p.parts.toFinset, count a p.parts * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 41
} | {
"line": 242,
"column": 42
} | [
{
"pp": "n : ℕ\np : (n + 1).Partition\na : ℕ\nha : a ∈ p.parts.toFinset\nha0 : a ≠ 0\n⊢ (p.parts.erase a).sum + a = n + 1",
"ppTerm": "?m.195",
"assigned": true,
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"congrArg",
"Nat.Partition.parts",
"id",
"instOfNatNat",
... | [
"n : ℕ\np : (n + 1).Partition\na : ℕ\nha : a ∈ p.parts.toFinset\nha0 : a ≠ 0\n⊢ a + (p.parts.erase a).sum = n + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 249,
"column": 40
} | {
"line": 249,
"column": 51
} | {
"line": 249,
"column": 52
} | [
{
"pp": "n : ℕ\nx : (i : Fin n.succ) × { p // ↑i + 1 ∈ p.parts }\n⊢ ↑x.fst + 1 ∈ (↑x.snd).parts.toFinset",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"Finset",
"Nat.Partition.parts",
"Membership.mem",
"Multiset",
"... | [
"n : ℕ\nx : (i : Fin n.succ) × { p // ↑i + 1 ∈ p.parts }\n⊢ ↑x.fst + 1 ∈ (↑x.snd).parts"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 372,
"column": 4
} | {
"line": 372,
"column": 54
} | {
"line": 372,
"column": 55
} | [
{
"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",
"ppTerm": "?m.93",
"assigned": true,
... | [
"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⊢ h₂⁻¹ * h₁ ∈ H"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Bell | {
"line": 275,
"column": 51
} | {
"line": 275,
"column": 71
} | {
"line": 275,
"column": 71
} | [
{
"pp": "n✝ n : ℕ\nih : ∀ m < n + 1, m.bell = ∑ p, p.parts.bell\n⊢ ∑ i, ∑ p, n.choose ↑i * ((↑p).parts.erase (↑i + 1)).bell =\n ∑ x, n.choose (↑x.snd - 1) * (x.fst.parts.erase ↑x.snd).bell",
"ppTerm": "?m.357",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
... | [
"n✝ n : ℕ\nih : ∀ m < n + 1, m.bell = ∑ p, p.parts.bell\n⊢ ∑ x, n.choose ↑x.fst * ((↑x.snd).parts.erase (↑x.fst + 1)).bell =\n ∑ x, n.choose (↑x.snd - 1) * (x.fst.parts.erase ↑x.snd).bell"
] | ← Fintype.sum_sigma' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 173,
"column": 75
} | {
"line": 173,
"column": 91
} | {
"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]",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableEqDyckS... | [
"case inr\np q : DyckWord\nh : p ≠ 0\ni : ℕ\nhi : i > 0\n⊢ (count D (List.take (i - ([U] ++ ↑p).length) [D]) + if U = D then 1 else 0) ≤\n count U (List.take (i - ([U] ++ ↑p).length) [D]) + count U [U]"
] | count_singleton' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 15
} | {
"line": 201,
"column": 16
} | [
{
"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",
"ppTerm": "?m.38",
"assigned": false,
"usedConstan... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 35
} | {
"line": 275,
"column": 2
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\nlp : 0 < (↑p).length\n⊢ p.firstReturn < (range (↑p).length).length",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instDecidableEqDyckStep",
"DyckStep.U",
"List.findIdx_lt_length_of_exists",
"instOfNatNat",
"List.range",
... | [
"p : DyckWord\nh : p ≠ 0\nlp : 0 < (↑p).length\n⊢ ∃ x ∈ range (↑p).length, decide (count U (List.take (x + 1) ↑p) = count D (List.take (x + 1) ↑p)) = true"
] | apply findIdx_lt_length_of_exists | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 114,
"column": 60
} | {
"line": 114,
"column": 71
} | {
"line": 114,
"column": 72
} | [
{
"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",
... | [
"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⊢ ¬g x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 128,
"column": 60
} | {
"line": 128,
"column": 71
} | {
"line": 128,
"column": 72
} | [
{
"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",
"ppTerm": "?m.253... | [
"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⊢ ¬g 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 306,
"column": 6
} | {
"line": 306,
"column": 17
} | {
"line": 306,
"column": 18
} | [
{
"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",
"ppTerm": "?neg.right✝",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"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⊢ ¬count U (List.take (j + 1) ↑p) = count D (List.take (j + 1) ↑p)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 15
} | {
"line": 131,
"column": 16
} | [
{
"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 ≠... | [
"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 ≠ 0 ↔ i ≠ 0 ∧... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 318,
"column": 28
} | {
"line": 318,
"column": 43
} | {
"line": 318,
"column": 44
} | [
{
"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",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"instDecidableEqDyckSt... | [
"case right\np : DyckWord\nu : ↑p.nest = U :: ↑p ++ [D]\nj : ℕ\nhj : j < (↑p).length + 1\n⊢ decide (count U (U :: List.take j (↑p ++ [D])) = count D (U :: List.take j (↑p ++ [D]))) = false"
] | take_succ_cons, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 35
} | {
"line": 140,
"column": 36
} | [
{
"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 ≠... | [
"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 ≠ 0 ↔ i ≠ 0 ∧... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.GenFun | {
"line": 139,
"column": 4
} | {
"line": 140,
"column": 97
} | {
"line": 142,
"column": 0
} | [
{
"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
} | {
"line": 142,
"column": 0
} | [
{
"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.Enumerative.DyckWord | {
"line": 333,
"column": 36
} | {
"line": 333,
"column": 47
} | {
"line": 333,
"column": 48
} | [
{
"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 := ⋯ } ≠ []",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
... | [
"p q : DyckWord\nh✝ : p ≠ 0\nh : ¬p = 0\n⊢ ¬↑p = []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.DyckWord | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 19
} | {
"line": 389,
"column": 0
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congr... | [] | 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
} | {
"line": 389,
"column": 0
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congr... | [] | 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
} | {
"line": 389,
"column": 0
} | [
{
"pp": "p : DyckWord\nh : p ≠ 0\n⊢ p.insidePart.semilength + p.outsidePart.semilength + 1 = p.semilength",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DyckWord.semilength_add",
"DyckWord.nest_insidePart_add_outsidePart",
"instAddDyckWord",
"congr... | [] | 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.IncidenceAlgebra | {
"line": 513,
"column": 4
} | {
"line": 513,
"column": 40
} | {
"line": 513,
"column": 41
} | [
{
"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",
"ppTerm": "?m.189",
"ass... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 518,
"column": 6
} | {
"line": 518,
"column": 18
} | {
"line": 518,
"column": 19
} | [
{
"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",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGrou... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : DecidableEq G\nK : ℝ\nA S : Finset G\nhS : S.Nonempty\n⊢ ↑(#A) - K * ↑(#A) ≤ expansion K S A"
] | one_sub_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 86,
"column": 8
} | {
"line": 86,
"column": 34
} | {
"line": 86,
"column": 35
} | [
{
"pp": "case 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\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))",
"ppTerm": "?e'_5",
"assigned": true,
"... | [
"case 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\ni : ℕ\n⊢ X ^ ((i + 1) * 0) + ∑ x ∈ Ico 1 m, X ^ ((i + 1) * x) =\n 1 + ∑' (j : ℕ), (if j + 1 < m then 1 else 0) • X ^ ((i + 1) * (j + 1))"
] | sum_range_eq_add_Ico _ hm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 93,
"column": 62
} | {
"line": 93,
"column": 73
} | {
"line": 93,
"column": 74
} | [
{
"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",
"ppTerm": "?m.334",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring... | [
"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⊢ m ≤ b + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 85,
"column": 2
} | {
"line": 93,
"column": 86
} | {
"line": 94,
"column": 2
} | [
{
"pp": "case 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))",
"ppTerm": "?e'_5",
"assign... | [
"case e'_6\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\nm : ℕ\nhm : 0 < m\na✝ : Nontrivial R\n⊢ (PowerSeries.mk fun n ↦ ↑(#(countRestricted n m))) = genFun fun i c ↦ if c < m then 1 else 0"
] | · 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
} | {
"line": 100,
"column": 16
} | [
{
"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)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"MvPowerSeries.instCommSemiring",
"CommSemiring.to... | [
"case inl\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : T2Space R\ninst✝ : CommSemiring R\n⊢ Multipliable fun i ↦ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 637,
"column": 31
} | {
"line": 637,
"column": 51
} | {
"line": 638,
"column": 6
} | [
{
"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.Enumerative.Partition.GenFun | {
"line": 186,
"column": 83
} | {
"line": 186,
"column": 94
} | {
"line": 186,
"column": 95
} | [
{
"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) • ... | [
"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) • X ^ (i * (j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Schroder | {
"line": 72,
"column": 6
} | {
"line": 72,
"column": 17
} | {
"line": 72,
"column": 18
} | [
{
"pp": "case zero\nn : ℕ\nx✝ : n + 2 ≠ 0\nhk : 0 ∈ Iic (n + 1)\n⊢ Even (largeSchroder 0 * (n + 1 - 0).largeSchroder)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.largeSchroder",
"Nat.instOrderedSub",
"HMul.hMul",
"congrArg",
"AddMonoid... | [
"case zero\nn : ℕ\nx✝ : n + 2 ≠ 0\nhk : 0 ∈ Iic (n + 1)\n⊢ Even (n + 1).largeSchroder"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Partition.Glaisher | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | {
"line": 155,
"column": 14
} | [
{
"pp": "n m : ℕ\nhm : 0 < m\n⊢ #(restricted n fun x ↦ ¬m ∣ x) = #(countRestricted n m)",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n m : ℕ\nhm : 0 < m\n⊢ #(restricted n fun x ↦ ¬m ∣ x) = #(countRestricted n m)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 749,
"column": 4
} | {
"line": 749,
"column": 27
} | {
"line": 749,
"column": 28
} | [
{
"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... | [
"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\nhHZS : ↑H ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Additive.VerySmallDoubling | {
"line": 769,
"column": 17
} | {
"line": 769,
"column": 28
} | {
"line": 769,
"column": 29
} | [
{
"pp": "case e_a\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 : Finset G\nh... | [
"case e_a\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 : Finset G\nhZS : Z ⊆ S\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 73
} | {
"line": 157,
"column": 74
} | [
{
"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",
"ppTerm": "?m.173",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Add... | [
"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⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 192,
"column": 36
} | {
"line": 192,
"column": 51
} | {
"line": 192,
"column": 52
} | [
{
"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",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",... | [
"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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 73
} | {
"line": 161,
"column": 74
} | [
{
"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",
"ppTerm": "?m.247",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMu... | [
"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⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 393,
"column": 19
} | {
"line": 393,
"column": 35
} | {
"line": 393,
"column": 36
} | [
{
"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",
"ppTerm": "?m.40",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Subgraph | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 17
} | {
"line": 397,
"column": 18
} | [
{
"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",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"OrderBot.toBot",
"P... | [
"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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 54,
"column": 14
} | {
"line": 54,
"column": 25
} | {
"line": 54,
"column": 26
} | [
{
"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",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nG : Graph α β\nE₀ : Set β\nh : G.restrict E₀ = G\n⊢ E(G) ⊆ E₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Delete | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 15
} | {
"line": 73,
"column": 16
} | [
{
"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)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"LE.le",
"Set.instLE",
"congr",
"Graph.ve... | [
"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) ⊆ V(G)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 257,
"column": 6
} | {
"line": 257,
"column": 53
} | {
"line": 258,
"column": 8
} | [
{
"pp": "⊢ (fun n ↦ 2) =o[atTop] fun n ↦ ↑n / 3",
"ppTerm": "?m.167",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real.partialOrder",
"Real",
"instHDiv",
"GroupWithZero.toDivisionMonoid",... | [
"⊢ Tendsto (fun x ↦ 3⁻¹ * ↑x) atTop atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 54
} | {
"line": 275,
"column": 55
} | [
{
"pp": "n : 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)",
"ppTerm": "?m.307",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
"instHDi... | [
"n : 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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 72
} | [
{
"pp": "case 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✝",
"ppTerm": "?i... | [
"case 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⊢ a = val✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 121,
"column": 30
} | {
"line": 121,
"column": 71
} | {
"line": 121,
"column": 72
} | [
{
"pp": "case 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✝",
"ppTerm": "?i... | [
"case 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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 42
} | {
"line": 126,
"column": 43
} | [
{
"pp": "case 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",
"ppTerm": "?inr.inl",
... | [
"case 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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 47
} | {
"line": 131,
"column": 48
} | [
{
"pp": "case 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",
"ppTerm": "?inr.inr",
... | [
"case 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | {
"line": 201,
"column": 69
} | [
{
"pp": "case 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",
"ppTerm": "?refine_1.none",
"assigned": true,
"usedConstants"... | [
"case 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⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 201,
"column": 30
} | {
"line": 201,
"column": 68
} | {
"line": 201,
"column": 69
} | [
{
"pp": "case 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",
"ppTerm": "?refine_1.some",
"assigned": true,... | [
"case 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⊢ val✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 202,
"column": 30
} | {
"line": 202,
"column": 68
} | {
"line": 202,
"column": 69
} | [
{
"pp": "case refine_2.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 : m.idxFun i = some a\nhi : l.idxFun i = none\n⊢ none = some a",
"ppTerm": "?refine_2.none",
"assigned": true,
"usedConstants"... | [
"case refine_2.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 : m.idxFun i = some a\nhi : l.idxFun i = none\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 202,
"column": 30
} | {
"line": 202,
"column": 68
} | {
"line": 202,
"column": 69
} | [
{
"pp": "case refine_2.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 : m.idxFun i = some a\nval✝ : α\nhi : l.idxFun i = some val✝\n⊢ some val✝ = some a",
"ppTerm": "?refine_2.some",
"assigned": true,... | [
"case refine_2.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 : m.idxFun i = some a\nval✝ : α\nhi : l.idxFun i = some val✝\n⊢ val✝ = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 11
} | {
"line": 344,
"column": 12
} | [
{
"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 → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [
"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(G) → Std.Symm (G.IsLink e)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Graph.Basic | {
"line": 343,
"column": 8
} | {
"line": 344,
"column": 25
} | {
"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 → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | 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
} | {
"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 → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | 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
} | {
"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 → Std.Symm (G.IsLink e)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Std.Symm",
"congrArg",
... | [] | 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.Hindman | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 50
} | {
"line": 174,
"column": 51
} | [
{
"pp": "M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\nS : Set (Ultrafilter M) := ⋯\nU : Ultrafilter M\nhU : ∀ (i : ℕ), U ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nV : Ultrafilter M\nhV : ∀ (i : ℕ), V ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nn : ℕ\nm : M\nhm : m ∈ FP (Stream'.drop n a... | [
"M : Type u_1\ninst✝ : Semigroup M\na : Stream' M\nS : Set (Ultrafilter M) := ⋂ n, {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop n a)}\nU : Ultrafilter M\nhU : ∀ (i : ℕ), U ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nV : Ultrafilter M\nhV : ∀ (i : ℕ), V ∈ {U | ∀ᶠ (m : M) in ↑U, m ∈ FP (Stream'.drop i a)}\nn ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 58,
"column": 41
} | {
"line": 58,
"column": 52
} | {
"line": 58,
"column": 53
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ Fintype.card ↥s ≤ Fintype.card X",
"ppTerm": "?m.273",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Fins... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ #s ≤ Fintype.card X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 59,
"column": 35
} | {
"line": 59,
"column": 46
} | {
"line": 59,
"column": 47
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ ↑(↑f ((Equiv.symm ↑f) ⟨↑n, ⋯⟩)) < #s",
"ppTerm": "?m.293",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.apply_symm_a... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥s)\n⊢ ↑n < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 67,
"column": 54
} | {
"line": 67,
"column": 65
} | {
"line": 67,
"column": 66
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥sᶜ)\n⊢ ↑n < Fintype.card X - #s",
"ppTerm": "?m.344",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝¹ : Fintype X\nf✝ : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nf : ↥(prefixed s)\nn : Fin (Fintype.card ↥sᶜ)\n⊢ ↑n < Fintype.card X - #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 82,
"column": 24
} | {
"line": 82,
"column": 35
} | {
"line": 82,
"column": 36
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nn : Fin (Fintype.card X)\nhn : ↑n < #s\n⊢ ↑n < Fintype.card ↥s",
"ppTerm": "?m.424",
"assigned": true,
"usedConst... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nn : Fin (Fintype.card X)\nhn : ↑n < #s\n⊢ ↑n < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 87,
"column": 38
} | {
"line": 87,
"column": 49
} | {
"line": 87,
"column": 50
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, hx⟩) < #s",
"ppTerm": "?m.458",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"X : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, hx⟩) < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Hindman | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 51
} | {
"line": 210,
"column": 4
} | [
{
"pp": "case h.cons'\nM : Type u_1\ninst✝ : Semigroup M\nU : Ultrafilter M\nU_idem : U * U = U\nexists_elem : ∀ {s : Set M}, s ∈ U → (s ∩ {m | ∀ᶠ (m' : M) in ↑U, m * m' ∈ s}).Nonempty\nelem : { s // s ∈ U } → M := fun p ↦ ⋯.some\nsucc : { s // s ∈ U } → { s // s ∈ U } := fun p ↦ ⟨↑p ∩ {m | elem p * m ∈ ↑p}, ⋯⟩... | [
"case h.cons'.refine_2\nM : Type u_1\ninst✝ : Semigroup M\nU : Ultrafilter M\nU_idem : U * U = U\nexists_elem : ∀ {s : Set M}, s ∈ U → (s ∩ {m | ∀ᶠ (m' : M) in ↑U, m * m' ∈ s}).Nonempty\nelem : { s // s ∈ U } → M := fun p ↦ ⋯.some\nsucc : { s // s ∈ U } → { s // s ∈ U } := fun p ↦ ⟨↑p ∩ {m | elem p * m ∈ ↑p}, ⋯⟩\na... | have := Set.inter_subset_right (ih (succ p) ?_) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.KatonaCircle | {
"line": 97,
"column": 10
} | {
"line": 97,
"column": 38
} | {
"line": 97,
"column": 39
} | [
{
"pp": "case mp\nX : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑({ toFun := fun x ↦ if hx : x ∈ s then Fin.castLE ⋯ (g ⟨x, hx⟩) else Fin.cast ⋯ ((g' ⟨x, ⋯⟩).a... | [
"case mp\nX : Type u_1\ninst✝¹ : Fintype X\nf : Numbering X\ns✝ t : Finset X\ninst✝ : DecidableEq X\ns : Finset X\nx✝ : Numbering ↥s × Numbering ↥sᶜ\ng : Numbering ↥s\ng' : Numbering ↥sᶜ\nx : X\nhx : x ∈ s\n⊢ ↑(g ⟨x, ⋯⟩) < #s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.HalesJewett | {
"line": 512,
"column": 2
} | {
"line": 512,
"column": 13
} | {
"line": 512,
"column": 14
} | [
{
"pp": "case h\nα : Type u_5\nκ : Type u_6\nη : Type u_7\ninst✝² : Finite α\ninst✝¹ : Finite κ\ninst✝ : Finite η\nι : Type\nιfin : Fintype ι\nhι : ∀ (C : (ι → α) → κ), ∃ l, IsMono C l\nC : (Fin (Fintype.card ι) → α) → κ\nl : Subspace η α ι\nc : κ\ncl : ∀ (x : η → α), (fun v ↦ C (v ∘ ⇑(Fintype.equivFin ι).symm)... | [
"case h\nα : Type u_5\nκ : Type u_6\nη : Type u_7\ninst✝² : Finite α\ninst✝¹ : Finite κ\ninst✝ : Finite η\nι : Type\nιfin : Fintype ι\nhι : ∀ (C : (ι → α) → κ), ∃ l, IsMono C l\nC : (Fin (Fintype.card ι) → α) → κ\nl : Subspace η α ι\nc : κ\ncl : ∀ (x : η → α), (fun v ↦ C (v ∘ ⇑(Fintype.equivFin ι).symm)) (↑l x) = c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 95,
"column": 26
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 38
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nC : Set α\n⊢ (M✶ ＼ C)✶ = M ↔ Disjoint C M.E",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Matro... | [
"α : Type u_1\nM : Matroid α\nC : Set α\n⊢ (M✶ ＼ C)✶✶ = M✶ ↔ Disjoint C M.E"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.KatonaCircle | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 29
} | {
"line": 108,
"column": 30
} | [
{
"pp": "X : Type u_1\ninst✝¹ : Fintype X\ninst✝ : DecidableEq X\ns : Finset X\n⊢ #(prefixed s) = (#s)! * (Fintype.card X - #s)!",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝¹ : Fintype X\ninst✝ : DecidableEq X\ns : Finset X\n⊢ #(prefixed s) = (#s)! * (Fintype.card X - #s)!"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 173,
"column": 47
} | {
"line": 173,
"column": 58
} | {
"line": 173,
"column": 59
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\n⊢ M ／ (X \\ I ∪ I) = M ／ I ＼ (X \\ I)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Matroid.dual",
"Set.instUnion",
"id",
"SDiff.sdiff",
"propext",
... | [
"α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\n⊢ (M ／ (X \\ I ∪ I))✶ = (M ／ I ＼ (X \\ I))✶"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 178,
"column": 41
} | {
"line": 178,
"column": 52
} | {
"line": 178,
"column": 53
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\nJ : Set α\nhJ : J ⊆ (M✶ ＼ I ＼ (X \\ I)).E\ne : α\nhe : e ∈ X \\ I\n⊢ Disjoint {e} I",
"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Complet... | [
"α : Type u_1\nM : Matroid α\nI X : Set α\nhI : M.IsBasis I X\nJ : Set α\nhJ : J ⊆ (M✶ ＼ I ＼ (X \\ I)).E\ne : α\nhe : e ∈ X \\ I\n⊢ e ∉ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 202,
"column": 2
} | {
"line": 203,
"column": 85
} | {
"line": 205,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ ∀ ⦃K : Set α⦄, Disjoint K J → M.Indep (K ∪ J) → K ⊆ X → I ⊆ K ∪ J → K ⊆ I",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBoolea... | [] | exact fun K hJK hKJi hKX hIJK ↦ by
simp [hIX.eq_of_subset_indep hKJi hIJK (union_subset hKX (hJI.trans hIX.subset))] | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 97
} | {
"line": 212,
"column": 4
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ (M ／ J).IsBasis' (I \\ J) X",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.Matroid.Minor.Contract.0.Matroid.IsBasis'.contract_isBasis'_sdiff_of_subset._simp_1_1",... | [
"α : Type u_1\nM : Matroid α\nI J X : Set α\nhIX : M.IsBasis' I X\nhJI : J ⊆ I\n⊢ (M ／ J).IsBasis (I \\ J) (X ∩ (M.E \\ J))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 52
} | {
"line": 240,
"column": 4
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nI J X : Set α\nh : M.IsBasis' (J ∪ I) (X ∪ I)\nhJI : Disjoint J I\nhXI : Disjoint X I\n⊢ (M ／ I).IsBasis' J X",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nM : Matroid α\nI J X : Set α\nh : M.IsBasis' (J ∪ I) (X ∪ I)\nhJI : Disjoint J I\nhXI : Disjoint X I\n⊢ (M ／ I).IsBasis' J X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Sum | {
"line": 67,
"column": 38
} | {
"line": 67,
"column": 49
} | {
"line": 67,
"column": 50
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nM✝ M : (i : ι) → Matroid (α i)\nI : Set ((i : ι) × α i)\nh : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nBs : (i : ι) → Set (α i)\nhBs : ∀ (i : ι), (M i).IsBase (Bs i) ∧ Sigma.mk i ⁻¹' I ⊆ Bs i\ni : ι\n⊢ (M i).IsBase (Sigma.mk i ⁻¹' univ.sigma Bs)",
"ppTerm": "?m.102"... | [
"ι : Type u_1\nα : ι → Type u_2\nM✝ M : (i : ι) → Matroid (α i)\nI : Set ((i : ι) × α i)\nh : ∀ (i : ι), (M i).Indep (Sigma.mk i ⁻¹' I)\nBs : (i : ι) → Set (α i)\nhBs : ∀ (i : ι), (M i).IsBase (Bs i) ∧ Sigma.mk i ⁻¹' I ⊆ Bs i\ni : ι\n⊢ (M i).IsBase (Bs i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 367,
"column": 6
} | {
"line": 367,
"column": 17
} | {
"line": 367,
"column": 18
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nX : Set α\nhX : X ⊆ M.coloops\n⊢ M ／ X = M ＼ X",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Matroid.dual",
"id",
"propext",
"Eq.symm",
"Eq",
"Matroid",
"Matroid.contract",
... | [
"α : Type u_1\nM : Matroid α\nX : Set α\nhX : X ⊆ M.coloops\n⊢ (M ／ X)✶ = (M ＼ X)✶"
] | ← dual_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 490,
"column": 2
} | {
"line": 490,
"column": 49
} | {
"line": 490,
"column": 50
} | [
{
"pp": "α : Type u_1\nM : Matroid α\nK C : Set α\nhC : M.IsCircuit C\nhK : K.Nonempty\nhKC : K ⊆ C\n⊢ (M ／ (C \\ K)).IsCircuit K",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nM : Matroid α\nK C : Set α\nhC : M.IsCircuit C\nhK : K.Nonempty\nhKC : K ⊆ C\n⊢ (M ／ (C \\ K)).IsCircuit K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 541,
"column": 2
} | {
"line": 541,
"column": 51
} | {
"line": 542,
"column": 2
} | [
{
"pp": "α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\n⊢ (M ／ C ↾ R).Indep I ↔ ((M ↾ (R ∪ C)) ／ C).Indep I",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Matroid.IsBasis'",
"Exists",
"Set.instUnion",
"Matroid.Indep",
"Iff... | [
"α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ (M ／ C ↾ R).Indep I ↔ ((M ↾ (R ∪ C)) ／ C).Indep I"
] | obtain ⟨J, hJ⟩ := (M ↾ (R ∪ C)).exists_isBasis' C | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Combinatorics.Matroid.Minor.Contract | {
"line": 543,
"column": 4
} | {
"line": 543,
"column": 65
} | {
"line": 543,
"column": 66
} | [
{
"pp": "α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ M.IsBasis' J C",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nR C : Set α\nM : Matroid α\nh : Disjoint C R\nI : Set α\nhI : I ⊆ R\nJ : Set α\nhJ : (M ↾ (R ∪ C)).IsBasis' J C\n⊢ M.IsBasis' J C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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