module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 371
values | kind stringclasses 375
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Field.Basic | {
"line": 589,
"column": 4
} | {
"line": 589,
"column": 22
} | {
"line": 590,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ 1 < a / 0 ↔ 0 < 0 ∧ 0 < a ∨ 0 < 0 ∧ a < 0",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Preorder.toLT",
... | [] | simp [zero_le_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Field.Basic | {
"line": 607,
"column": 4
} | {
"line": 607,
"column": 22
} | {
"line": 608,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a / 0 ≤ 1 ↔ 0 < 0 ∧ a ≤ 0 ∨ 0 = 0 ∨ 0 < 0 ∧ 0 ≤ a",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Preorder... | [] | simp [zero_le_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Field.Basic | {
"line": 607,
"column": 4
} | {
"line": 607,
"column": 22
} | {
"line": 608,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a / 0 ≤ 1 ↔ 0 < 0 ∧ a ≤ 0 ∨ 0 = 0 ∨ 0 < 0 ∧ 0 ≤ a",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Preorder... | [] | simp [zero_le_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Field.Basic | {
"line": 607,
"column": 4
} | {
"line": 607,
"column": 22
} | {
"line": 608,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a / 0 ≤ 1 ↔ 0 < 0 ∧ a ≤ 0 ∨ 0 = 0 ∨ 0 < 0 ∧ 0 ≤ a",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Preorder... | [] | simp [zero_le_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 812,
"column": 33
} | {
"line": 812,
"column": 51
} | {
"line": 812,
"column": 52
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β → β\nb : β\nhf : ∀ (a : α), f a b = b\na : α\nl : List α\n⊢ f a (foldr f b l) = b",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"List.foldr",
"Eq"
],
"usedFVars": [
"β",
... | [
"α : Type u\nβ : Type v\nf : α → β → β\nb : β\nhf : ∀ (a : α), f a b = b\na : α\nl : List α\n⊢ f a b = b"
] | foldr_fixed' hf l, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Basic | {
"line": 897,
"column": 17
} | {
"line": 897,
"column": 26
} | {
"line": 899,
"column": 0
} | [
{
"pp": "case cons.none\nα : Type u\nβ : Type v\nf : α → Option β\na : α\nl : List α\nih : filterMap f l = flatMap (fun a ↦ (f a).toList) l\n⊢ (match none with\n | none => filterMap f l\n | some b => b :: filterMap f l) =\n none.toList ++ flatMap (fun a ↦ (f a).toList) l",
"ppTerm": "?cons.none",
... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Basic | {
"line": 897,
"column": 17
} | {
"line": 897,
"column": 26
} | {
"line": 899,
"column": 0
} | [
{
"pp": "case cons.some\nα : Type u\nβ : Type v\nf : α → Option β\na : α\nl : List α\nih : filterMap f l = flatMap (fun a ↦ (f a).toList) l\nval✝ : β\n⊢ (match some val✝ with\n | none => filterMap f l\n | some b => b :: filterMap f l) =\n (some val✝).toList ++ flatMap (fun a ↦ (f a).toList) l",
"pp... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Basic | {
"line": 951,
"column": 2
} | {
"line": 951,
"column": 24
} | {
"line": 953,
"column": 0
} | [
{
"pp": "α : Type u\nl : List α\np q : α → Bool\nh : ∀ (a : α), p a = true → q a = true\n⊢ filter p l <+ filter q l",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right._proof_1_2",
"List.rec",
"List",
"List.f... | [] | induction l with grind | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Data.List.Basic | {
"line": 951,
"column": 2
} | {
"line": 951,
"column": 24
} | {
"line": 953,
"column": 0
} | [
{
"pp": "α : Type u\nl : List α\np q : α → Bool\nh : ∀ (a : α), p a = true → q a = true\n⊢ filter p l <+ filter q l",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right._proof_1_2",
"List.rec",
"List",
"List.f... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 951,
"column": 2
} | {
"line": 951,
"column": 24
} | {
"line": 953,
"column": 0
} | [
{
"pp": "α : Type u\nl : List α\np q : α → Bool\nh : ∀ (a : α), p a = true → q a = true\n⊢ filter p l <+ filter q l",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Basic.0.List.monotone_filter_right._proof_1_2",
"List.rec",
"List",
"List.f... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 977,
"column": 36
} | {
"line": 977,
"column": 71
} | {
"line": 979,
"column": 0
} | [
{
"pp": "α : Type u\nl : List α\n⊢ filter (fun x ↦ true) l = l",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"congrArg",
"List.rec",
"List.cons",
"Bool.true",
"List",
"List.filter",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
... | [] | by induction l <;> simp [*, filter] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Basic | {
"line": 981,
"column": 38
} | {
"line": 981,
"column": 73
} | {
"line": 983,
"column": 0
} | [
{
"pp": "α : Type u\nl : List α\n⊢ filter (fun x ↦ false) l = []",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"congrArg",
"List.rec",
"List.cons",
"List",
"List.filter",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Bool.false"... | [] | by induction l <;> simp [*, filter] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rat.Cast.Defs | {
"line": 169,
"column": 59
} | {
"line": 169,
"column": 74
} | {
"line": 170,
"column": 4
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\nq r : ℚ\nhq : ↑q.den ≠ 0\nhr : ↑r.den ≠ 0\n⊢ ↑(q.num * ↑r.den + r.num * ↑q.den) / ↑(q.den * r.den) = ↑q.num / ↑q.den + ↑r.num / ↑r.den",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemi... | [
"α : Type u_3\ninst✝ : DivisionRing α\nq r : ℚ\nhq : ↑q.den ≠ 0\nhr : ↑r.den ≠ 0\n⊢ ↑(q.num * ↑r.den + ↑q.den * r.num) / ↑(q.den * r.den) = ↑q.num / ↑q.den + ↑r.num / ↑r.den",
"case hb\nα : Type u_3\ninst✝ : DivisionRing α\nq r : ℚ\nhq : ↑q.den ≠ 0\nhr : ↑r.den ≠ 0\n⊢ ↑(q.den * r.den) ≠ 0"
] | mul_comm r.num, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.Ring.Common | {
"line": 896,
"column": 2
} | {
"line": 896,
"column": 44
} | {
"line": 898,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na₂ c₂ : R\nea₁ b c₁ : ℕ\nxa₁ : R\nx✝¹ : ea₁ * b = c₁\nx✝ : a₂ ^ b = c₂\n⊢ (xa₁ ^ ea₁ * a₂) ^ b = xa₁ ^ c₁ * c₂",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiri... | [] | subst_vars; simp [_root_.mul_pow, pow_mul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.Ring.Common | {
"line": 896,
"column": 2
} | {
"line": 896,
"column": 44
} | {
"line": 898,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na₂ c₂ : R\nea₁ b c₁ : ℕ\nxa₁ : R\nx✝¹ : ea₁ * b = c₁\nx✝ : a₂ ^ b = c₂\n⊢ (xa₁ ^ ea₁ * a₂) ^ b = xa₁ ^ c₁ * c₂",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiri... | [] | subst_vars; simp [_root_.mul_pow, pow_mul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.Ring.Common | {
"line": 1224,
"column": 17
} | {
"line": 1226,
"column": 10
} | {
"line": 1228,
"column": 0
} | [
{
"pp": "R : Type u_2\nα : Type u_3\ninst✝¹ : CommSemiring α\ninst✝ : SMul R α\nr : R\na b t c : α\nx✝² : a = b\nx✝¹ : ∀ (x : α), r • x = t * x\nx✝ : t * b = c\n⊢ r • a = c",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"instHSMul",
"HMul.hMul",
"congrArg",
"CommSe... | [] | by
subst_vars
simp [*] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Ring.Canonical | {
"line": 128,
"column": 38
} | {
"line": 128,
"column": 47
} | {
"line": 128,
"column": 48
} | [
{
"pp": "R : Type u\ninst✝⁶ : NonAssocSemiring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : CanonicallyOrderedAdd R\ninst✝³ : Sub R\ninst✝² : OrderedSub R\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : AddLeftReflectLE R\na b : R\n⊢ a * (b - 1) = a * b - a",
"ppTerm": "?m.31",
"assigned": true,
"usedConst... | [
"R : Type u\ninst✝⁶ : NonAssocSemiring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : CanonicallyOrderedAdd R\ninst✝³ : Sub R\ninst✝² : OrderedSub R\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : AddLeftReflectLE R\na b : R\n⊢ a * b - a * 1 = a * b - a"
] | mul_tsub, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Ring.Canonical | {
"line": 142,
"column": 6
} | {
"line": 142,
"column": 15
} | {
"line": 142,
"column": 16
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommSemiring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : CanonicallyOrderedAdd R\ninst✝³ : Sub R\ninst✝² : OrderedSub R\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : AddLeftReflectLE R\na b : R\n⊢ a * a - b * b = (a + b) * (a - b)",
"ppTerm": "?m.37",
"assigned": true,
"use... | [
"R : Type u\ninst✝⁶ : CommSemiring R\ninst✝⁵ : PartialOrder R\ninst✝⁴ : CanonicallyOrderedAdd R\ninst✝³ : Sub R\ninst✝² : OrderedSub R\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : AddLeftReflectLE R\na b : R\n⊢ a * a - b * b = (a + b) * a - (a + b) * b"
] | mul_tsub, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 22
} | {
"line": 408,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\nb : α\nhs : s.Nonempty\nhb : ∀ a ∈ s, a ≤ b\n⊢ sSup s ≤ b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"csSup_le"
],
"used... | [] | exact csSup_le hs hb | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 922,
"column": 2
} | {
"line": 922,
"column": 53
} | {
"line": 922,
"column": 54
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompleteDistribLattice β\ncompleteLattice : CompleteLattice α := e.completeLattice\nbiheytingAlgebra : BiheytingAlgebra α := e.biheytingAlgebra\n⊢ CompleteDistribLattice α",
"ppTerm": "?m.12",
"assigned": true,
"usedCon... | [
"case le\nα : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompleteDistribLattice β\ncompleteLattice : CompleteLattice α := e.completeLattice\nbiheytingAlgebra : BiheytingAlgebra α := e.biheytingAlgebra\nx✝ y✝ : α\n⊢ e x✝ ≤ e y✝ ↔ x✝ ≤ y✝",
"case lt\nα : Type u\nβ : Type v\nι : Sort w\nκ : ... | apply e.injective.completeDistribLattice <;> intros | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Tactic.NormNum.Abs | {
"line": 39,
"column": 2
} | {
"line": 43,
"column": 57
} | {
"line": 45,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : DivisionRing α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\nnum den : ℕ\nra : IsNNRat a num den\n⊢ IsNNRat |a| num den",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"mul_nonneg",
"NonAss... | [] | obtain ⟨ha1, rfl⟩ := ra
refine ⟨ha1, abs_of_nonneg ?_⟩
apply mul_nonneg
· exact Nat.cast_nonneg' num
· simp only [invOf_eq_inv, inv_nonneg, Nat.cast_nonneg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Abs | {
"line": 39,
"column": 2
} | {
"line": 43,
"column": 57
} | {
"line": 45,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : DivisionRing α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\nnum den : ℕ\nra : IsNNRat a num den\n⊢ IsNNRat |a| num den",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"mul_nonneg",
"NonAss... | [] | obtain ⟨ha1, rfl⟩ := ra
refine ⟨ha1, abs_of_nonneg ?_⟩
apply mul_nonneg
· exact Nat.cast_nonneg' num
· simp only [invOf_eq_inv, inv_nonneg, Nat.cast_nonneg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rat.Cast.Order | {
"line": 70,
"column": 26
} | {
"line": 70,
"column": 38
} | {
"line": 70,
"column": 38
} | [
{
"pp": "K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℚ\nn : ℤ\n⊢ ↑m ≤ ↑n ↔ ↑m ≤ ↑↑n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"DivisionRing.toRatCast",
"congrArg",
... | [
"K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℚ\nn : ℤ\n⊢ ↑m ≤ ↑n ↔ ↑m ≤ ↑n"
] | cast_intCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Order | {
"line": 74,
"column": 26
} | {
"line": 74,
"column": 38
} | {
"line": 74,
"column": 38
} | [
{
"pp": "K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℤ\nn : ℚ\n⊢ ↑m ≤ ↑n ↔ ↑↑m ≤ ↑n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"DivisionRing.toRatCast",
"congrArg",
... | [
"K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℤ\nn : ℚ\n⊢ ↑m ≤ ↑n ↔ ↑m ≤ ↑n"
] | cast_intCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Order | {
"line": 86,
"column": 26
} | {
"line": 86,
"column": 38
} | {
"line": 86,
"column": 38
} | [
{
"pp": "K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℚ\nn : ℤ\n⊢ ↑m < ↑n ↔ ↑m < ↑↑n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"Preorder.toLT",
"DivisionRing.toRatCas... | [
"K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℚ\nn : ℤ\n⊢ ↑m < ↑n ↔ ↑m < ↑n"
] | cast_intCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Cast.Order | {
"line": 90,
"column": 26
} | {
"line": 90,
"column": 38
} | {
"line": 90,
"column": 38
} | [
{
"pp": "K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℤ\nn : ℚ\n⊢ ↑m < ↑n ↔ ↑↑m < ↑n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"Preorder.toLT",
"DivisionRing.toRatCas... | [
"K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nm : ℤ\nn : ℚ\n⊢ ↑m < ↑n ↔ ↑m < ↑n"
] | cast_intCast | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 111,
"column": 75
} | {
"line": 112,
"column": 29
} | {
"line": 114,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : Group α\na : α\n⊢ a⁻¹⁻ᵐ = a⁺ᵐ",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"instLeOnePart",
"congrArg",
"Group.toDivisi... | [] | by
simp [oneLePart, leOnePart] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 213,
"column": 63
} | {
"line": 214,
"column": 81
} | {
"line": 216,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : MulLeftMono α\na : α\n⊢ |a|ₘ / a = a⁻ᵐ ^ 2",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"instLeOnePart",
"Monoid.... | [] | by
rw [sq, ← mul_div_div_cancel, oneLePart_mul_leOnePart, oneLePart_div_leOnePart] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.NormNum.Ineq | {
"line": 88,
"column": 4
} | {
"line": 88,
"column": 43
} | {
"line": 89,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nnum✝¹ num✝ da db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝¹ : decide (num✝¹.mul db ≤ num✝.mul da) = true\nh✝ : ↑(num✝¹.mul db) ≤ ↑(num✝.mul da)\nha : 0 ≤ ⅟↑da\nhb : 0 ≤ ⅟↑db\nh : ⅟↑db * (↑(num✝¹.mul d... | [
"α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nnum✝¹ num✝ da db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝¹ : decide (num✝¹.mul db ≤ num✝.mul da) = true\nh✝ : ↑(num✝¹.mul db) ≤ ↑(num✝.mul da)\nha : 0 ≤ ⅟↑da\nhb : 0 ≤ ⅟↑db\nh : ↑(num✝¹.mul db) * ⅟↑db * ⅟↑da ≤ ⅟... | rw [← mul_assoc, Nat.commute_cast] at h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Int.Cast.Field | {
"line": 42,
"column": 33
} | {
"line": 42,
"column": 43
} | {
"line": 43,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionRing α\nk : ℤ\nhn : ↑0 ≠ 0\n⊢ False",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"False",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Int.cast_zero",
"False.elim",... | [] | simp at hn | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.NormNum.Ineq | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 43
} | {
"line": 101,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nnum✝¹ num✝ da db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝¹ : decide (num✝¹ * db < num✝ * da) = true\nh✝ : ↑(num✝¹ * db) < ↑(num✝ * da)\nha : 0 < ⅟↑da\nhb : 0 < ⅟↑db\nh : ⅟↑db * (↑(num✝¹ * db) * ⅟↑da)... | [
"α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nnum✝¹ num✝ da db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝¹ : decide (num✝¹ * db < num✝ * da) = true\nh✝ : ↑(num✝¹ * db) < ↑(num✝ * da)\nha : 0 < ⅟↑da\nhb : 0 < ⅟↑db\nh : ↑(num✝¹ * db) * ⅟↑db * ⅟↑da < ⅟↑db * (↑(n... | rw [← mul_assoc, Nat.commute_cast] at h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 389,
"column": 21
} | {
"line": 389,
"column": 74
} | {
"line": 390,
"column": 2
} | [
{
"pp": "n : ℕ\nx✝ : 0 ≤ n\n⊢ (n - 0)! * n.descFactorial 0 = n !",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Nat.mul_one",
"congrArg",
"HSub.hSub",
"id",
"instSubNat",
"instMulNat",
"instOfNatNat",
"ins... | [] | by rw [descFactorial_zero, Nat.mul_one, Nat.sub_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 515,
"column": 2
} | {
"line": 515,
"column": 9
} | {
"line": 516,
"column": 2
} | [
{
"pp": "⊢ ascFactorial = ascFactorialBinary",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"Nat.ascFactorial",
"funext",
"Nat.ascFactorialBinary",
"Nat"
],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
"kind": ... | [
"n k : ℕ\n⊢ n.ascFactorial k = n.ascFactorialBinary k"
] | ext n k | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 540,
"column": 2
} | {
"line": 540,
"column": 9
} | {
"line": 541,
"column": 2
} | [
{
"pp": "⊢ descFactorial = descFactorialBinary",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"Nat.descFactorialBinary",
"funext",
"Nat",
"Nat.descFactorial"
],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
"kin... | [
"n k : ℕ\n⊢ n.descFactorial k = n.descFactorialBinary k"
] | ext n k | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Data.PNat.Basic | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 24
} | {
"line": 248,
"column": 2
} | [
{
"pp": "case pos\na b : ℕ+\nh : b < a\n⊢ ↑a - ↑b ≤ ↑a",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"PNat.val",
"Nat.sub_le"
],
"usedFVars": [
"a",
"b"
],
"usedGoals": []
},
{
"pp": "case neg\na b : ℕ+\nh : ¬b < a\n⊢ 1 ≤ ↑a",
"ppTerm":... | [
"case neg\na b : ℕ+\nh : ¬b < a\n⊢ 1 ≤ ↑a"
] | · exact Nat.sub_le a b | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.PNat.Basic | {
"line": 297,
"column": 2
} | {
"line": 298,
"column": 23
} | {
"line": 300,
"column": 0
} | [
{
"pp": "m k : ℕ+\n⊢ ↑(m.mod k) + m.div k * ↑k = ↑m",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"PNat.val",
"Eq.mpr",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"PNat.div",
"PNat.mod_add_div",
"id",
"PNat.mod",... | [] | rw [mul_comm]
exact mod_add_div _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.PNat.Basic | {
"line": 297,
"column": 2
} | {
"line": 298,
"column": 23
} | {
"line": 300,
"column": 0
} | [
{
"pp": "m k : ℕ+\n⊢ ↑(m.mod k) + m.div k * ↑k = ↑m",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"PNat.val",
"Eq.mpr",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"PNat.div",
"PNat.mod_add_div",
"id",
"PNat.mod",... | [] | rw [mul_comm]
exact mod_add_div _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.Basic | {
"line": 112,
"column": 2
} | {
"line": 116,
"column": 12
} | {
"line": 118,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_1\ninst✝⁴ : CommGroup α\ninst✝³ : LinearOrder α\ninst✝² : IsOrderedMonoid α\ninst✝¹ : DenselyOrdered α\ninst✝ : Nontrivial α\nh : IsCyclic α\na : α\nha : Surjective fun x ↦ a ^ x\nhlt : 1 < a\n⊢ False",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
... | [] | · rcases exists_between hlt with ⟨b, hb, hba⟩
rcases ha b with ⟨k, rfl⟩
suffices 0 < k ∧ k < 1 by lia
simp_rw [← zpow_lt_zpow_iff_right hlt]
simp_all | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 25
} | {
"line": 254,
"column": 2
} | [
{
"pp": "K : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : y < 1\n⊢ ∃ n, y ^ n < x",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"PartialOrder... | [
"case pos\nK : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : y < 1\ny_pos : y ≤ 0\n⊢ ∃ n, y ^ n < x",
"case neg\nK : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrdered... | by_cases! y_pos : y ≤ 0 | Mathlib.Tactic.ByCases._aux_Mathlib_Tactic_ByCases___macroRules_Mathlib_Tactic_ByCases_byCases!_1 | Mathlib.Tactic.ByCases.byCases! |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 385,
"column": 4
} | {
"line": 385,
"column": 49
} | {
"line": 386,
"column": 4
} | [
{
"pp": "K : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nn : ℕ\nhn : n ≠ 0\nx y : K\nh : x < y\nhy : 0 < y\nδ : K\nδ_pos : δ > 0\ncont : ∀ (q r : K), |r| ≤ max 1 y → |q - r| ≤ δ → |q ^ n - r ^ n| < y - max x 0\n⊢ ∃ m, y ≤ (↑m * δ) ^ n",
"ppTerm"... | [
"K : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nn : ℕ\nhn : n ≠ 0\nx y : K\nh : x < y\nhy : 0 < y\nδ : K\nδ_pos : δ > 0\ncont : ∀ (q r : K), |r| ≤ max 1 y → |q - r| ≤ δ → |q ^ n - r ^ n| < y - max x 0\nm : ℕ\nhm : y / δ + 1 / δ ≤ ↑m\n⊢ ∃ m, y ≤ (↑m * δ... | have ⟨m, hm⟩ := exists_nat_ge (y / δ + 1 / δ) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.Multiset.Replicate | {
"line": 126,
"column": 31
} | {
"line": 128,
"column": 64
} | {
"line": 130,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nn : ℕ\n_l : List α\n⊢ n ≤ count a (Quot.mk (⇑(isSetoid α)) _l) ↔ replicate n a ≤ Quot.mk (⇑(isSetoid α)) _l",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"Multiset.coe_count... | [] | by
simp only [quot_mk_to_coe'', coe_count]
exact replicate_sublist_iff.symm.trans replicate_le_coe.symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Multiset.ZeroCons | {
"line": 381,
"column": 2
} | {
"line": 381,
"column": 17
} | {
"line": 381,
"column": 17
} | [
{
"pp": "α : Type u_1\ns t : Multiset α\na : α\nhs : ¬a ∈ s\n⊢ a ∈ t ∧ s ≤ t → a ::ₘ s ≤ t",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Multiset",
"Multiset.cons",
"LE.le",
"And.case... | [
"α : Type u_1\ns t : Multiset α\na : α\nhs : ¬a ∈ s\nh₁ : a ∈ t\nh₂ : s ≤ t\n⊢ a ::ₘ s ≤ t"
] | rintro ⟨h₁, h₂⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Data.Multiset.AddSub | {
"line": 266,
"column": 34
} | {
"line": 267,
"column": 77
} | {
"line": 269,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nab : a ≠ b\ns : Multiset α\nl : List α\n⊢ count a (erase ⟦l⟧ b) = count a ⟦l⟧",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.coe_count",
"instLawfulBEq",
"congrArg",
"HEq.refl",
... | [] | by
convert! List.count_erase_of_ne ab (l := l) <;> rw [← coe_count] <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Multiset.AddSub | {
"line": 299,
"column": 47
} | {
"line": 299,
"column": 56
} | {
"line": 301,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nt : Multiset α\na : α\ns : Multiset α\nih : 0 - s = 0\n⊢ 0 - a ::ₘ s = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"False",
"Multiset.notMem_zero._simp_1",
"congrArg",
"HSub.hSub",
"Membership.mem",
"Mu... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Multiset.AddSub | {
"line": 299,
"column": 47
} | {
"line": 299,
"column": 56
} | {
"line": 301,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nt : Multiset α\na : α\ns : Multiset α\nih : 0 - s = 0\n⊢ 0 - a ::ₘ s = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"False",
"Multiset.notMem_zero._simp_1",
"congrArg",
"HSub.hSub",
"Membership.mem",
"Mu... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.AddSub | {
"line": 299,
"column": 47
} | {
"line": 299,
"column": 56
} | {
"line": 301,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nt : Multiset α\na : α\ns : Multiset α\nih : 0 - s = 0\n⊢ 0 - a ::ₘ s = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"False",
"Multiset.notMem_zero._simp_1",
"congrArg",
"HSub.hSub",
"Membership.mem",
"Mu... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Lattice | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 24
} | {
"line": 123,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\n⊢ l ∩ [] = []",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"List.rec",
"instBEqOfDecidableEq",
"Inter.inter",
"List",
"List.instInterOfBEq_batteries",
"_private.Mathlib.Data.List.Lattice.0.List.... | [] | induction l with grind | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Data.List.Lattice | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 24
} | {
"line": 123,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\n⊢ l ∩ [] = []",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"List.rec",
"instBEqOfDecidableEq",
"Inter.inter",
"List",
"List.instInterOfBEq_batteries",
"_private.Mathlib.Data.List.Lattice.0.List.... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Lattice | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 24
} | {
"line": 123,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\n⊢ l ∩ [] = []",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"List.rec",
"instBEqOfDecidableEq",
"Inter.inter",
"List",
"List.instInterOfBEq_batteries",
"_private.Mathlib.Data.List.Lattice.0.List.... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Dedup | {
"line": 82,
"column": 17
} | {
"line": 82,
"column": 74
} | {
"line": 84,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.headI = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.headI else (a :: l).headI",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"False",
"eq_false",... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.List.Dedup | {
"line": 82,
"column": 17
} | {
"line": 82,
"column": 74
} | {
"line": 84,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.headI = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.headI else (a :: l).headI",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"False",
"eq_false",... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Dedup | {
"line": 82,
"column": 17
} | {
"line": 82,
"column": 74
} | {
"line": 84,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.headI = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.headI else (a :: l).headI",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"False",
"eq_false",... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Dedup | {
"line": 88,
"column": 17
} | {
"line": 88,
"column": 74
} | {
"line": 90,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.tail = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.tail else (a :: l).tail.dedup",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"False",
"eq_fals... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.List.Dedup | {
"line": 88,
"column": 17
} | {
"line": 88,
"column": 74
} | {
"line": 90,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.tail = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.tail else (a :: l).tail.dedup",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"False",
"eq_fals... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Dedup | {
"line": 88,
"column": 17
} | {
"line": 88,
"column": 74
} | {
"line": 90,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Inhabited α\nl✝ : List α\na : α\nl : List α\n⊢ (a :: l).dedup.tail = if (a :: l).headI ∈ (a :: l).tail then (a :: l).tail.dedup.tail else (a :: l).tail.dedup",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"False",
"eq_fals... | [] | by_cases ha : a ∈ l <;> simp [ha, List.dedup_cons_of_mem] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Lattice | {
"line": 261,
"column": 31
} | {
"line": 261,
"column": 44
} | {
"line": 261,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nhead✝ : α\ntail✝ : List α\nih : ∀ {l₂ : List α}, tail✝.bagInter l₂ <+ tail✝ ∩ l₂\nl₂ : List α\nh✝ : head✝ ∈ l₂\n⊢ head✝ ∈ l₂",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"h✝"
],
"usedGoals": []
}
] | [] | by assumption | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Multiset.UnionInter | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 69
} | {
"line": 131,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\na : α\nx✝ : a ∈ s ∧ a ∈ t\nh₁ : a ∈ s\nh₂ : a ∈ t\n⊢ a ∈ s ∩ t",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.instInter",
"congrArg",
"Membership.mem",
"Multiset",
"Mult... | [] | rw [← cons_erase h₁, cons_inter_of_pos _ h₂]; apply mem_cons_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.UnionInter | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 69
} | {
"line": 131,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\na : α\nx✝ : a ∈ s ∧ a ∈ t\nh₁ : a ∈ s\nh₂ : a ∈ t\n⊢ a ∈ s ∩ t",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.instInter",
"congrArg",
"Membership.mem",
"Multiset",
"Mult... | [] | rw [← cons_erase h₁, cons_inter_of_pos _ h₂]; apply mem_cons_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Filter | {
"line": 429,
"column": 2
} | {
"line": 430,
"column": 67
} | {
"line": 432,
"column": 0
} | [
{
"pp": "α : Type u_1\ns : Multiset α\np : { a // a ∈ s } → Prop\ninst✝¹ : DecidableEq α\ninst✝ : DecidablePred p\n⊢ filter (fun b ↦ ∃ a, p a ∧ ↑a = b) (map val s.attach) =\n map val (map (Subtype.map id ⋯) (filter (fun x ↦ ∃ h, p ⟨x, h⟩) s).attach)",
"ppTerm": "?m.55",
"assigned": true,
"usedCon... | [] | simp only [Function.comp, Subtype.exists, Subtype.map,
exists_and_right, exists_eq_right, attach_map_val, map_map, id] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Finset.Lattice.Basic | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 43
} | {
"line": 242,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ s ∩ (t ∪ s) = s",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.inter_comm",
"id",
"Inter.inter",
"Finset.instInter",
... | [] | rw [inter_comm, union_inter_cancel_right] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Finset.Lattice.Basic | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 43
} | {
"line": 242,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ s ∩ (t ∪ s) = s",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.inter_comm",
"id",
"Inter.inter",
"Finset.instInter",
... | [] | rw [inter_comm, union_inter_cancel_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Lattice.Basic | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 43
} | {
"line": 242,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ s ∩ (t ∪ s) = s",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.inter_comm",
"id",
"Inter.inter",
"Finset.instInter",
... | [] | rw [inter_comm, union_inter_cancel_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Image | {
"line": 665,
"column": 51
} | {
"line": 667,
"column": 11
} | {
"line": 669,
"column": 0
} | [
{
"pp": "α : Type u_1\np : α → Prop\ns : Finset { x // p x }\na : α\nh : a ∈ map (Embedding.subtype fun x ↦ p x) s\n⊢ p a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finset",
"Finset.map",
"Membership.mem",
"Exists",
"Subtype",
"Function.Embedding",... | [] | by
rcases mem_map.1 h with ⟨x, _, rfl⟩
exact x.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.SuccPred | {
"line": 385,
"column": 2
} | {
"line": 385,
"column": 52
} | {
"line": 387,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ i.castPred hi ≤ j ↔ i ≤ j.castSucc",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 385,
"column": 2
} | {
"line": 385,
"column": 52
} | {
"line": 387,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ i.castPred hi ≤ j ↔ i ≤ j.castSucc",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.SuccPred | {
"line": 385,
"column": 2
} | {
"line": 385,
"column": 52
} | {
"line": 387,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ i.castPred hi ≤ j ↔ i ≤ j.castSucc",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 52
} | {
"line": 391,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ j ≤ i.castPred hi ↔ j.castSucc ≤ i",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 52
} | {
"line": 391,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ j ≤ i.castPred hi ↔ j.castSucc ≤ i",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.SuccPred | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 52
} | {
"line": 391,
"column": 0
} | [
{
"pp": "n : ℕ\nj : Fin n\ni : Fin (n + 1)\nhi : i ≠ last n\n⊢ j ≤ i.castPred hi ↔ j.castSucc ≤ i",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
... | [] | rw [← castSucc_le_castSucc_iff, castSucc_castPred] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 184,
"column": 15
} | {
"line": 184,
"column": 37
} | {
"line": 184,
"column": 37
} | [
{
"pp": "m n : ℕ\nα : Fin (n + 1) → Sort u\nx✝ : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α i.succ\ni : Fin n\ny : α i.succ\nz : α 0\nmotive : ((i : Fin n.succ) → α i) → Sort v\ncons : (x₀ : α 0) → (x : (i : Fin n) → α i.succ) → motive (Fin.cons x₀ x)\nx : (i : Fin n.succ) → α i\n⊢ motive (Fin.cons (... | [] | by rw [cons_self_tail] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finset.Card | {
"line": 870,
"column": 4
} | {
"line": 872,
"column": 37
} | {
"line": 873,
"column": 0
} | [
{
"pp": "case inr\nα : Type u_1\np : (s : Finset α) → s.Nonempty → Prop\nh₀ : ∀ (a : α), p {a} ⋯\nh₁ : ∀ ⦃s : Finset α⦄ (hs : s.Nontrivial), (∀ (t : Finset α) (ht : t.Nonempty), t ⊂ s → p t ht) → p s ⋯\ns : Finset α\nhs✝ : s.Nonempty\nhs : s.Nontrivial\n⊢ p s hs✝",
"ppTerm": "?inr",
"assigned": true,
... | [] | · refine h₁ hs fun t ht hts ↦ ?_
have := card_lt_card hts
exact ht.strong_induction h₀ h₁ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Fin.SuccPred | {
"line": 789,
"column": 2
} | {
"line": 789,
"column": 37
} | {
"line": 791,
"column": 0
} | [
{
"pp": "case neg\nn : ℕ\ninst✝ : NeZero n\ni : Fin (n + 1)\nhi : ¬i = 0\n⊢ predAbove 0 i = i.pred hi",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.pred",
"congrArg",
"id",
"Fin.instOfNat",
"Fin.predAbove_zero_of_ne_zero",
"Fin.pre... | [] | · rw [predAbove_zero_of_ne_zero hi] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 630,
"column": 6
} | {
"line": 630,
"column": 20
} | {
"line": 631,
"column": 6
} | [
{
"pp": "case succ.cast\nn : ℕ\nβ : Sort u_2\na : β\nq : Fin n → β\nb : β\nj : Fin n\n⊢ cons a (snoc q b) j.castSucc.succ = snoc (cons a q) b j.castSucc.succ",
"ppTerm": "?succ.cast",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.cons_succ",
"Fin.succ",
"congrArg",
... | [
"case succ.cast\nn : ℕ\nβ : Sort u_2\na : β\nq : Fin n → β\nb : β\nj : Fin n\n⊢ snoc q b j.castSucc = snoc (cons a q) b j.castSucc.succ"
] | rw [cons_succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 759,
"column": 2
} | {
"line": 762,
"column": 45
} | {
"line": 764,
"column": 0
} | [
{
"pp": "case refine_2\nn : ℕ\nα : Type u_2\nx₀ : α\nx : Fin n → α\nh : Injective (snoc x x₀)\n⊢ ¬x₀ ∈ Set.range x",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"False",
"Fin.snoc_castSucc",
"congrArg",
"Function.Injective.eq_iff",
"Membership.mem",
... | [] | · rintro ⟨i, hi⟩
rw [← @snoc_last n (fun i ↦ α) x₀ x, ← @snoc_castSucc n (fun i ↦ α) x₀ x i,
h.eq_iff] at hi
exact ne_last_of_lt i.castSucc_lt_last hi | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Finset.Fold | {
"line": 155,
"column": 6
} | {
"line": 156,
"column": 10
} | {
"line": 158,
"column": 0
} | [
{
"pp": "case insert\nα : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha✝ : Std.Associative op\nf : α → β\nb : β\ns✝ : Finset α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∧ r x z\nc : β\na : α\ns : Finset α\nha : a ∉ s\nIH : r c (fold op b f s) ↔ r c b ∧ ∀ x ∈ s, r c (f x)\... | [] | rw [Finset.fold_insert ha, hr, IH, ← and_assoc, @and_comm (r c (f a)), and_assoc]
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Fold | {
"line": 155,
"column": 6
} | {
"line": 156,
"column": 10
} | {
"line": 158,
"column": 0
} | [
{
"pp": "case insert\nα : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha✝ : Std.Associative op\nf : α → β\nb : β\ns✝ : Finset α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∧ r x z\nc : β\na : α\ns : Finset α\nha : a ∉ s\nIH : r c (fold op b f s) ↔ r c b ∧ ∀ x ∈ s, r c (f x)\... | [] | rw [Finset.fold_insert ha, hr, IH, ← and_assoc, @and_comm (r c (f a)), and_assoc]
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Finite.Basic | {
"line": 940,
"column": 38
} | {
"line": 940,
"column": 49
} | {
"line": 940,
"column": 49
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : DecidableEq β\nf : α → β\ns : Set α\nt : Finset β\nhfs : SurjOn f s ↑t\nu : Set α\nhus : u ⊆ s\nhf : InjOn f u\nhimg : f '' u = ↑t\n⊢ (f '' u).Finite",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.Finite... | [] | simp [himg] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Finite.Basic | {
"line": 940,
"column": 38
} | {
"line": 940,
"column": 49
} | {
"line": 940,
"column": 49
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : DecidableEq β\nf : α → β\ns : Set α\nt : Finset β\nhfs : SurjOn f s ↑t\nu : Set α\nhus : u ⊆ s\nhf : InjOn f u\nhimg : f '' u = ↑t\n⊢ (f '' u).Finite",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.Finite... | [] | simp [himg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Finite.Basic | {
"line": 940,
"column": 38
} | {
"line": 940,
"column": 49
} | {
"line": 940,
"column": 49
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : DecidableEq β\nf : α → β\ns : Set α\nt : Finset β\nhfs : SurjOn f s ↑t\nu : Set α\nhus : u ⊆ s\nhf : InjOn f u\nhimg : f '' u = ↑t\n⊢ (f '' u).Finite",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Set.Finite... | [] | simp [himg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Flatten | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 24
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : List α\nf g : α → List β\nh : ∀ (a : α), a ∈ l → f a <+ g a\n⊢ flatMap f l <+ flatMap g l",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right._proof_1_2",
"Membership.mem",
... | [] | induction l with grind | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Data.List.Flatten | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 24
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : List α\nf g : α → List β\nh : ∀ (a : α), a ∈ l → f a <+ g a\n⊢ flatMap f l <+ flatMap g l",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right._proof_1_2",
"Membership.mem",
... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Flatten | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 24
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : List α\nf g : α → List β\nh : ∀ (a : α), a ∈ l → f a <+ g a\n⊢ flatMap f l <+ flatMap g l",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Flatten.0.List.Sublist.flatMap_right._proof_1_2",
"Membership.mem",
... | [] | induction l with grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Pairwise | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 33
} | {
"line": 51,
"column": 2
} | [
{
"pp": "α : Type u_1\nR : α → α → Prop\nl : List α\ninst✝ : Std.Symm R\nhl : Pairwise R l\nthis : Std.Symm fun x y ↦ x ≠ y → R x y\n⊢ ∀ ⦃a : α⦄, a ∈ l → ∀ ⦃b : α⦄, b ∈ l → a ≠ b → R a b",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Ne",
"List.Pairwise.forall_of_forall"
... | [
"case H₁\nα : Type u_1\nR : α → α → Prop\nl : List α\ninst✝ : Std.Symm R\nhl : Pairwise R l\nthis : Std.Symm fun x y ↦ x ≠ y → R x y\n⊢ ∀ (x : α), x ∈ l → x ≠ x → R x x",
"case H₂\nα : Type u_1\nR : α → α → Prop\nl : List α\ninst✝ : Std.Symm R\nhl : Pairwise R l\nthis : Std.Symm fun x y ↦ x ≠ y → R x y\n⊢ Pairwis... | apply Pairwise.forall_of_forall | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.List.Pairwise | {
"line": 104,
"column": 44
} | {
"line": 104,
"column": 57
} | {
"line": 104,
"column": 57
} | [
{
"pp": "α : Type u_1\nR : α → α → Prop\na : α\ninst✝¹ : Inhabited α\ninst✝ : Std.Refl R\nhead✝ : α\ntail✝ : List α\nh : Pairwise R (head✝ :: tail✝)\na✝ : Mem a tail✝\n⊢ a ∈ tail✝",
"ppTerm": "?m.178",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"a✝"
],
"usedGoals": []
... | [] | by assumption | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 1273,
"column": 4
} | {
"line": 1273,
"column": 61
} | {
"line": 1274,
"column": 4
} | [
{
"pp": "case inr.inr\nn : ℕ\nα : Sort u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nhjk : ↑j ≠ ↑k\nh : ↑j < ↑k\n⊢ j.contractNth op g k = g (j.succAbove k)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove"... | [
"case inr.inr.h\nn : ℕ\nα : Sort u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nhjk : ↑j ≠ ↑k\nh : ↑j < ↑k\n⊢ j ≤ k.castSucc"
] | rwa [j.succAbove_of_le_castSucc, contractNth_apply_of_gt] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Algebra.BigOperators.Group.List.Lemmas | {
"line": 161,
"column": 2
} | {
"line": 163,
"column": 25
} | {
"line": 165,
"column": 0
} | [
{
"pp": "M : Type u_4\ninst✝ : CommMonoid M\nl₁ l₂ : List M\nh : l₁ <+ l₂\n⊢ l₁.prod ∣ l₂.prod",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Dvd.dvd",
"List.prod_append",
"HMul.hMul",
"Semigroup.to_isAssociative",
"Mono... | [] | obtain ⟨l, hl⟩ := h.exists_perm_append
rw [hl.prod_eq, prod_append]
exact dvd_mul_right _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.List.Lemmas | {
"line": 161,
"column": 2
} | {
"line": 163,
"column": 25
} | {
"line": 165,
"column": 0
} | [
{
"pp": "M : Type u_4\ninst✝ : CommMonoid M\nl₁ l₂ : List M\nh : l₁ <+ l₂\n⊢ l₁.prod ∣ l₂.prod",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Dvd.dvd",
"List.prod_append",
"HMul.hMul",
"Semigroup.to_isAssociative",
"Mono... | [] | obtain ⟨l, hl⟩ := h.exists_perm_append
rw [hl.prod_eq, prod_append]
exact dvd_mul_right _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Rotate | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 64
} | {
"line": 137,
"column": 0
} | [
{
"pp": "case inr\nα : Type u\nl : List α\nn : ℕ\nhl : 0 < l.length\n⊢ l.rotate n = drop (n % l.length) l ++ take (n % l.length) l",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.rotate_mod",
"id",
"LT.lt.le",
"Nat.instMod",
... | [] | rw [← rotate_eq_drop_append_take (n.mod_lt hl).le, rotate_mod] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Multiset.Bind | {
"line": 77,
"column": 19
} | {
"line": 77,
"column": 28
} | {
"line": 79,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : map f s✝.join = (map (map f) s✝).join\n⊢ map f (a✝ ::ₘ s✝).join = (map (map f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Multiset.map_cons",
"Mult... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Multiset.Bind | {
"line": 77,
"column": 19
} | {
"line": 77,
"column": 28
} | {
"line": 79,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : map f s✝.join = (map (map f) s✝).join\n⊢ map f (a✝ ::ₘ s✝).join = (map (map f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Multiset.map_cons",
"Mult... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.Bind | {
"line": 77,
"column": 19
} | {
"line": 77,
"column": 28
} | {
"line": 79,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : map f s✝.join = (map (map f) s✝).join\n⊢ map f (a✝ ::ₘ s✝).join = (map (map f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Multiset.map_cons",
"Mult... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Bind | {
"line": 84,
"column": 19
} | {
"line": 84,
"column": 28
} | {
"line": 86,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝ : CommMonoid α\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : s✝.join.prod = (map prod s✝).prod\n⊢ (a✝ ::ₘ s✝).join.prod = (map prod (a✝ ::ₘ s✝)).prod",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Multiset.map_cons",
... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Multiset.Bind | {
"line": 84,
"column": 19
} | {
"line": 84,
"column": 28
} | {
"line": 86,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝ : CommMonoid α\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : s✝.join.prod = (map prod s✝).prod\n⊢ (a✝ ::ₘ s✝).join.prod = (map prod (a✝ ::ₘ s✝)).prod",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Multiset.map_cons",
... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.Bind | {
"line": 84,
"column": 19
} | {
"line": 84,
"column": 28
} | {
"line": 86,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝ : CommMonoid α\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : s✝.join.prod = (map prod s✝).prod\n⊢ (a✝ ::ₘ s✝).join.prod = (map prod (a✝ ::ₘ s✝)).prod",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Multiset.map_cons",
... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Bind | {
"line": 95,
"column": 19
} | {
"line": 95,
"column": 28
} | {
"line": 97,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filter p s✝.join = (map (filter p) s✝).join\n⊢ filter p (a✝ ::ₘ s✝).join = (map (filter p) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Mul... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Multiset.Bind | {
"line": 95,
"column": 19
} | {
"line": 95,
"column": 28
} | {
"line": 97,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filter p s✝.join = (map (filter p) s✝).join\n⊢ filter p (a✝ ::ₘ s✝).join = (map (filter p) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Mul... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.Bind | {
"line": 95,
"column": 19
} | {
"line": 95,
"column": 28
} | {
"line": 97,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filter p s✝.join = (map (filter p) s✝).join\n⊢ filter p (a✝ ::ₘ s✝).join = (map (filter p) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Mul... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Bind | {
"line": 101,
"column": 19
} | {
"line": 101,
"column": 28
} | {
"line": 103,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → Option β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filterMap f s✝.join = (map (filterMap f) s✝).join\n⊢ filterMap f (a✝ ::ₘ s✝).join = (map (filterMap f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"... | [] | simp [ih] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Multiset.Bind | {
"line": 101,
"column": 19
} | {
"line": 101,
"column": 28
} | {
"line": 103,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → Option β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filterMap f s✝.join = (map (filterMap f) s✝).join\n⊢ filterMap f (a✝ ::ₘ s✝).join = (map (filterMap f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.Bind | {
"line": 101,
"column": 19
} | {
"line": 101,
"column": 28
} | {
"line": 103,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nf : α → Option β\na✝ : Multiset α\ns✝ : Multiset (Multiset α)\nih : filterMap f s✝.join = (map (filterMap f) s✝).join\n⊢ filterMap f (a✝ ::ₘ s✝).join = (map (filterMap f) (a✝ ::ₘ s✝)).join",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"... | [] | simp [ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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