module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Hom.Basic | {
"line": 228,
"column": 2
} | {
"line": 228,
"column": 58
} | {
"line": 228,
"column": 59
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMonoid β\ninst✝¹ : PartialOrder β\ninst✝ : GroupSeminormClass F α β\nf : F\nx y : α\n⊢ f x ≤ f y + f (y / x)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"i... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMonoid β\ninst✝¹ : PartialOrder β\ninst✝ : GroupSeminormClass F α β\nf : F\nx y : α\n⊢ f x ≤ f y + f (x / y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Cast.Lemmas | {
"line": 53,
"column": 14
} | {
"line": 53,
"column": 48
} | {
"line": 53,
"column": 49
} | [
{
"pp": "K : Type u_2\ninst✝ : DivisionRing K\nq : ℚ≥0\n⊢ 0 < ↑q.den",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Data.Rat.Cast.Lemmas.0.Rat.cast_nnratCast._simp_1_1",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.ins... | [
"K : Type u_2\ninst✝ : DivisionRing K\nq : ℚ≥0\n⊢ 0 < q.den"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Round | {
"line": 65,
"column": 37
} | {
"line": 65,
"column": 88
} | {
"line": 65,
"column": 89
} | [
{
"pp": "α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nh : ¬2 * fract x < 1\n⊢ ⌊2 * fract x⌋ = 1",
"ppTerm": "?m.224",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWi... | [
"α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nh : ¬2 * fract x < 1\n⊢ 1 ≤ 2 * fract x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Round | {
"line": 154,
"column": 6
} | {
"line": 154,
"column": 72
} | {
"line": 154,
"column": 73
} | [
{
"pp": "α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nhx : 0 < fract x + fract x\n⊢ 0 < fract x",
"ppTerm": "?m.143",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nhx : 0 < fract x + fract x\n⊢ 0 < fract x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Round | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 67
} | {
"line": 162,
"column": 68
} | [
{
"pp": "case inl\nα : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nz : ℤ\nhx : ↑z ≤ x\n⊢ fract x ≤ fract x + (↑⌊x⌋ - ↑z)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",... | [
"case inl\nα : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\nz : ℤ\nhx : ↑z ≤ x\n⊢ z ≤ ⌊x⌋"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.PNat.Basic | {
"line": 326,
"column": 2
} | {
"line": 336,
"column": 50
} | {
"line": 338,
"column": 0
} | [
{
"pp": "k m : ℕ+\n⊢ k ∣ m ↔ m.mod k = k",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"PNat.mod_coe",
"PNat.val",
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"False.elim",
"semigroupDvd",
"Eq.mp",
"id",
"Nat.instMod",
"instHMod",
... | [] | rw [dvd_iff]
rw [Nat.dvd_iff_mod_eq_zero]; constructor
· intro h
apply PNat.eq
rw [mod_coe, if_pos h]
· intro h
by_cases h' : (m : ℕ) % (k : ℕ) = 0
· exact h'
· replace h : (mod m k : ℕ) = (k : ℕ) := congr_arg _ h
rw [mod_coe, if_neg h'] at h
exact ((Nat.mod_lt (m : ℕ) k.pos).ne h)... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.PNat.Basic | {
"line": 326,
"column": 2
} | {
"line": 336,
"column": 50
} | {
"line": 338,
"column": 0
} | [
{
"pp": "k m : ℕ+\n⊢ k ∣ m ↔ m.mod k = k",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"PNat.mod_coe",
"PNat.val",
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"False.elim",
"semigroupDvd",
"Eq.mp",
"id",
"Nat.instMod",
"instHMod",
... | [] | rw [dvd_iff]
rw [Nat.dvd_iff_mod_eq_zero]; constructor
· intro h
apply PNat.eq
rw [mod_coe, if_pos h]
· intro h
by_cases h' : (m : ℕ) % (k : ℕ) = 0
· exact h'
· replace h : (mod m k : ℕ) = (k : ℕ) := congr_arg _ h
rw [mod_coe, if_neg h'] at h
exact ((Nat.mod_lt (m : ℕ) k.pos).ne h)... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Round | {
"line": 184,
"column": 47
} | {
"line": 184,
"column": 73
} | {
"line": 186,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\n⊢ round 2⁻¹ = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"instHDiv",
... | [] | by norm_num [round_eq_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Round | {
"line": 187,
"column": 52
} | {
"line": 187,
"column": 78
} | {
"line": 189,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝³ : Field α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\n⊢ round (-2⁻¹) = 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Int.cast",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Pre... | [] | by norm_num [round_eq_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 126,
"column": 2
} | {
"line": 126,
"column": 13
} | {
"line": 126,
"column": 14
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ ⌊a⌋ ≤ -1 ↔ a < 0",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ ⌊a⌋ ≤ -1 ↔ a < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 57
} | {
"line": 133,
"column": 58
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ a < ↑⌊a⌋ + 1",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ a < ↑⌊a⌋ + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Basic | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 25
} | {
"line": 111,
"column": 26
} | [
{
"pp": "case inr.inl\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\nha : Surjective fun x ↦ 1 ^ x\nb : α\nhb : b ≠ 1\n⊢ False",
"ppTerm": "?inr.inl",
"assigned": false,
"usedConstants": [],
... | [
"case inr.inl\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\nha : Surjective fun x ↦ 1 ^ x\nb : α\nhb : b ≠ 1\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Pow | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 13
} | {
"line": 61,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\na : R\nHsq : 0 ≤ a ^ 2\nHsq' : 0 ≤ (1 + a) ^ 2\nH : 0 ≤ 2 + a\nn : ℕ\n⊢ 1 + ↑n * a ≤ (1 + a) ^ n",
"ppTerm": "?m.71",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\na : R\nHsq : 0 ≤ a ^ 2\nHsq' : 0 ≤ (1 + a) ^ 2\nH : 0 ≤ 2 + a\nn : ℕ\n⊢ 1 + ↑n * a ≤ (1 + a) ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Pow | {
"line": 62,
"column": 8
} | {
"line": 62,
"column": 19
} | {
"line": 62,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\na : R\nHsq : 0 ≤ a ^ 2\nHsq' : 0 ≤ (1 + a) ^ 2\nH : 0 ≤ 2 + a\nn : ℕ\n⊢ 0 ≤ 2 * 1 + a",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne... | [
"R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\na : R\nHsq : 0 ≤ a ^ 2\nHsq' : 0 ≤ (1 + a) ^ 2\nH : 0 ≤ 2 + a\nn : ℕ\n⊢ 0 ≤ 2 + a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Pow | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 35
} | {
"line": 107,
"column": 36
} | [
{
"pp": "R : Type u_1\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na : R\nH : -1 ≤ a\nn : ℕ\nthis : -2 ≤ a - 1\n⊢ 1 + ↑n * (a - 1) ≤ a ^ n",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na : R\nH : -1 ≤ a\nn : ℕ\nthis : -2 ≤ a - 1\n⊢ 1 + ↑n * (a - 1) ≤ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 207,
"column": 2
} | {
"line": 207,
"column": 29
} | {
"line": 207,
"column": 30
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\nz : ℤ\na : R\n⊢ ⌊↑z + a⌋ = z + ⌊a⌋",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"congrArg",
"id",
"Distri... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\nz : ℤ\na : R\n⊢ ⌊a + ↑z⌋ = z + ⌊a⌋"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 44
} | {
"line": 213,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\nn : ℕ\n⊢ ⌊a + ↑n⌋ = ⌊a⌋ + ↑n",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Int.floor",
"congrArg"... | [] | rw [← Int.cast_natCast, floor_add_intCast] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 44
} | {
"line": 213,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\nn : ℕ\n⊢ ⌊a + ↑n⌋ = ⌊a⌋ + ↑n",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Int.floor",
"congrArg"... | [] | rw [← Int.cast_natCast, floor_add_intCast] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 44
} | {
"line": 213,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\nn : ℕ\n⊢ ⌊a + ↑n⌋ = ⌊a⌋ + ↑n",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Int.floor",
"congrArg"... | [] | rw [← Int.cast_natCast, floor_add_intCast] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 267,
"column": 2
} | {
"line": 267,
"column": 13
} | {
"line": 267,
"column": 14
} | [
{
"pp": "R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℕ\nhn : n ≠ 0\na : R\n⊢ ⌊a * ↑n⌋ / ↑n = ⌊a⌋",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℕ\nhn : n ≠ 0\na : R\n⊢ ⌊a * ↑n⌋ / ↑n = ⌊a⌋"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 13
} | {
"line": 297,
"column": 14
} | [
{
"pp": "k : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\na : k\nn : ℕ\n⊢ ⌊a / ↑n⌋ = ⌊a⌋ / ↑n",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"k : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\na : k\nn : ℕ\n⊢ ⌊a / ↑n⌋ = ⌊a⌋ / ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 328,
"column": 27
} | {
"line": 328,
"column": 39
} | {
"line": 328,
"column": 39
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na b : R\n⊢ fract (a + b) - fract a - fract b = ↑(⌊a⌋ + ⌊b⌋ - ⌊a + b⌋)",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.floor",
"AddGroupWithOne.toAddGroup",
"Int.fra... | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na b : R\n⊢ a + b - ↑⌊a + b⌋ - (a - ↑⌊a⌋) - (b - ↑⌊b⌋) = ↑(⌊a⌋ + ⌊b⌋ - ⌊a + b⌋)"
] | unfold fract | Lean.Elab.Tactic.evalUnfold | Lean.Parser.Tactic.unfold |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 13
} | {
"line": 82,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddMonoid G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n⊢ f (x + n • a) = f x + n • b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": []... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddMonoid G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℕ\n⊢ f (x + n • a) = f x + n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | {
"line": 107,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddZeroClass G\ninst✝¹ : Add H\ninst✝ : AddConstMapClass F G H a b\nf : F\n⊢ f a = f 0 + b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddZeroClass G\ninst✝¹ : Add H\ninst✝ : AddConstMapClass F G H a b\nf : F\n⊢ f a = f 0 + b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 13
} | {
"line": 116,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddMonoid G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H a b\nf : F\nn : ℕ\n⊢ f (n • a) = f 0 + n • b",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddMonoid G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H a b\nf : F\nn : ℕ\n⊢ f (n • a) = f 0 + n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 13
} | {
"line": 121,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddMonoidWithOne G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nn : ℕ\n⊢ f ↑n = f 0 + n • b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddMonoidWithOne G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nn : ℕ\n⊢ f ↑n = f 0 + n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 13
} | {
"line": 151,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddCommMonoidWithOne G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nn : ℕ\nx : G\n⊢ f (↑n + x) = f x + n • b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddCommMonoidWithOne G\ninst✝¹ : AddMonoid H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nn : ℕ\nx : G\n⊢ f (↑n + x) = f x + n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 13
} | {
"line": 174,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\n⊢ f (x - a) = f x - b",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\n⊢ f (x - a) = f x - b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 183,
"column": 2
} | {
"line": 183,
"column": 13
} | {
"line": 183,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddGroupWithOne G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℕ\n⊢ f (x - ↑n) = f x - n • b",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\nb : H\ninst✝² : AddGroupWithOne G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H 1 b\nf : F\nx : G\nn : ℕ\n⊢ f (x - ↑n) = f x - n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 200,
"column": 2
} | {
"line": 200,
"column": 13
} | {
"line": 200,
"column": 14
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nn : ℤ\n⊢ f (n • a) = f 0 + n • b",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nn : ℤ\n⊢ f (n • a) = f 0 + n • b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 414,
"column": 2
} | {
"line": 414,
"column": 14
} | {
"line": 415,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\nz : ℤ\n⊢ fract ↑z = 0",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.fract",
"id",
"AddGroupWithOne.toIntCast",
"Zero.toOfNat0",
... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\nz : ℤ\n⊢ ↑z - ↑⌊↑z⌋ = 0"
] | unfold fract | Lean.Elab.Tactic.evalUnfold | Lean.Parser.Tactic.unfold |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 30
} | {
"line": 213,
"column": 31
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℤ\n⊢ f (x - n • a) = f x - n • b",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"i... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝³ : FunLike F G H\na : G\nb : H\ninst✝² : AddGroup G\ninst✝¹ : AddGroup H\ninst✝ : AddConstMapClass F G H a b\nf : F\nx : G\nn : ℤ\n⊢ f (x + -(n • a)) = f x + -(n • b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 48,
"column": 42
} | {
"line": 48,
"column": 53
} | {
"line": 48,
"column": 54
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝⁴ : CommMonoid G\ninst✝³ : LinearOrder G\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\nf : G →* M\nhf : StrictMono ⇑f\nx x✝ : G\nh : 1 < x✝\n⊢ 1 < ?m.25",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"G : Type u_1\nM : Type u_2\ninst✝⁴ : CommMonoid G\ninst✝³ : LinearOrder G\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\nf : G →* M\nhf : StrictMono ⇑f\nx x✝ : G\nh : 1 < x✝\n⊢ 1 < ?m.25"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 48,
"column": 42
} | {
"line": 48,
"column": 58
} | {
"line": 48,
"column": 58
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝⁴ : CommMonoid G\ninst✝³ : LinearOrder G\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\nf : G →* M\nhf : StrictMono ⇑f\nx x✝ : G\nh : 1 < x✝\n⊢ 1 < ?m.25",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"MonoidHom.i... | [] | simpa using hf h | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 48,
"column": 42
} | {
"line": 48,
"column": 58
} | {
"line": 48,
"column": 58
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝⁴ : CommMonoid G\ninst✝³ : LinearOrder G\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\nf : G →* M\nhf : StrictMono ⇑f\nx x✝ : G\nh : 1 < x✝\n⊢ 1 < ?m.25",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"MonoidHom.i... | [] | simpa using hf h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 48,
"column": 42
} | {
"line": 48,
"column": 58
} | {
"line": 48,
"column": 58
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝⁴ : CommMonoid G\ninst✝³ : LinearOrder G\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\nf : G →* M\nhf : StrictMono ⇑f\nx x✝ : G\nh : 1 < x✝\n⊢ 1 < ?m.25",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"MonoidHom.i... | [] | simpa using hf h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 80,
"column": 36
} | {
"line": 80,
"column": 51
} | {
"line": 80,
"column": 52
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\ng : G\ns : Set ℤ := {n | a ^ n ≤ g}\nk : ℕ\nhk : g⁻¹ ≤ a ^ k\n⊢ -↑k ∈ s",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"zpow_natCast",
... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\ng : G\ns : Set ℤ := {n | a ^ n ≤ g}\nk : ℕ\nhk : g⁻¹ ≤ a ^ k\n⊢ (a ^ k)⁻¹ ≤ g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Floor | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 46
} | {
"line": 378,
"column": 0
} | [
{
"pp": "q : ℚ\nthis : 0 < 1 - fract q\n⊢ 0 < (1 - fract q) * ↑q.den",
"ppTerm": "?m.288",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"Rat.instSub",
"Preorder.toLT",
"Rat.pos",
"congrArg",
"Nat.cast_lt._simp_1",
"Int.fract",
"AddMonoid.toAdd... | [] | exact mul_pos this (by exact mod_cast q.pos) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 255,
"column": 50
} | {
"line": 255,
"column": 61
} | {
"line": 255,
"column": 62
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl :... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl : G\nhf : ∀ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 66
} | {
"line": 99,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\ng : G\n⊢ ∃! k, 1 ≤ g / a ^ k ∧ g / a ^ k < a",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Algebra.Order.A... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\ng : G\n⊢ ∃! k, a ^ k ≤ g ∧ g < a ^ k * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 104,
"column": 2
} | {
"line": 104,
"column": 98
} | {
"line": 105,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! m, b / a ^ m ∈ Ico c (c * a)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"instIsRightCancelMulOfMulRightReflectLE",
"I... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! m, a ^ m * c ≤ b ∧ b < a * (a ^ m * c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 111,
"column": 4
} | {
"line": 112,
"column": 53
} | {
"line": 112,
"column": 54
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, b * a ^ (Equiv.neg ℤ) x ∈ Ico c (c * a)",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"instIsRightCancelMulOfMulRightReflec... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, a ^ x * c ≤ b ∧ b < a * (a ^ x * c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 118,
"column": 4
} | {
"line": 119,
"column": 62
} | {
"line": 120,
"column": 6
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, b * a ^ (Equiv.addRight 1) x ∈ Ioc c (c * a)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Equiv.addRight",
"Eq.mpr"... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, b * a ^ x ≤ c ∧ c < b * a ^ x * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 126,
"column": 4
} | {
"line": 126,
"column": 64
} | {
"line": 127,
"column": 6
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, b / a ^ (Equiv.neg ℤ) x ∈ Ioc c (c * a)",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"ins... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na : G\nha : 1 < a\nb c : G\n⊢ ∃! x, b * a ^ x ∈ Ioc c (c * a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 266,
"column": 20
} | {
"line": 266,
"column": 31
} | {
"line": 266,
"column": 32
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl :... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl : G\nhf : ∀ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 268,
"column": 48
} | {
"line": 268,
"column": 59
} | {
"line": 268,
"column": 60
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl :... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl : G\nhf : ∀ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 538,
"column": 4
} | {
"line": 538,
"column": 50
} | {
"line": 538,
"column": 51
} | [
{
"pp": "case inr.refine_2\nk : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\nm n : ℕ\nhn : n > 0\nhn' : 0 < ↑n\n⊢ ↑(m % n) / ↑n < 1",
"ppTerm": "?inr.refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCom... | [
"case inr.refine_2\nk : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\nm n : ℕ\nhn : n > 0\nhn' : 0 < ↑n\n⊢ m % n < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Action.Basic | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 33
} | {
"line": 105,
"column": 2
} | [
{
"pp": "G✝ : Type u_1\nM : Type u_2\nA✝ : Type u_3\nB✝ : Type u_4\nα : Type u_5\nβ : Type u_6\nG : Type u_7\nA : Type u_8\nB : Type u_9\ninst✝¹ : DivisionMonoid G\ninst✝ : MulAction G A\nf : A → B\n⊢ (fun x ↦ f (1⁻¹ • x)) = f",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"instHSMu... | [] | simp only [inv_one, one_smul] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Group.Action.Basic | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 23
} | {
"line": 128,
"column": 2
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\ninst✝¹ : Monoid α\ninst✝ : MulAction α β\nm : α\nhm : IsUnit m\n⊢ Function.Bijective fun a ↦ m • a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Units.val",
"instHSMul",
"IsUnit",
"Exists",
"Units",
"Exists.casesOn... | [
"α : Type u_5\nβ : Type u_6\ninst✝¹ : Monoid α\ninst✝ : MulAction α β\nm : αˣ\n⊢ Function.Bijective fun a ↦ ↑m • a"
] | lift m to αˣ using hm | Mathlib.Tactic._aux_Mathlib_Tactic_Lift___elabRules_Mathlib_Tactic_lift_1 | Mathlib.Tactic.lift |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 560,
"column": 4
} | {
"line": 560,
"column": 52
} | {
"line": 560,
"column": 53
} | [
{
"pp": "k : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\nn : ℕ\nhn : 0 < ↑n\nthis : ∀ {l : ℤ}, 0 ≤ l → fract (↑l / ↑n) = ↑(l % ↑n) / ↑n\nm₀ : ℕ\nq : ℤ := ⌈↑m₀ / ↑n⌉\nm₁ : ℤ := q * ↑n - ↑m₀\n⊢ 0 ≤ m₁",
"ppTerm": "?m.222",
"assigned": true,
"usedC... | [
"k : Type u_4\ninst✝³ : Field k\ninst✝² : LinearOrder k\ninst✝¹ : IsOrderedRing k\ninst✝ : FloorRing k\nn : ℕ\nhn : 0 < ↑n\nthis : ∀ {l : ℤ}, 0 ≤ l → fract (↑l / ↑n) = ↑(l % ↑n) / ↑n\nm₀ : ℕ\nq : ℤ := ⌈↑m₀ / ↑n⌉\nm₁ : ℤ := q * ↑n - ↑m₀\n⊢ ↑m₀ / ↑n ≤ ↑q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 586,
"column": 2
} | {
"line": 586,
"column": 13
} | {
"line": 586,
"column": 14
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ 1 ≤ ⌈a⌉ ↔ 0 < a",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ 1 ≤ ⌈a⌉ ↔ 0 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 606,
"column": 62
} | {
"line": 606,
"column": 80
} | {
"line": 608,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ ⌈a⌉ = 0 ↔ a ∈ Ioc (-1) 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Set.Ioc",
"NegZeroClass.toNeg",
"Preorder.toLT",... | [] | simp [ceil_eq_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 606,
"column": 62
} | {
"line": 606,
"column": 80
} | {
"line": 608,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ ⌈a⌉ = 0 ↔ a ∈ Ioc (-1) 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Set.Ioc",
"NegZeroClass.toNeg",
"Preorder.toLT",... | [] | simp [ceil_eq_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 606,
"column": 62
} | {
"line": 606,
"column": 80
} | {
"line": 608,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na : R\n⊢ ⌈a⌉ = 0 ↔ a ∈ Ioc (-1) 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Set.Ioc",
"NegZeroClass.toNeg",
"Preorder.toLT",... | [] | simp [ceil_eq_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 390,
"column": 51
} | {
"line": 390,
"column": 76
} | {
"line": 390,
"column": 77
} | [
{
"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\nex : ∃ m, y ≤ (↑m * δ) ^ n\nm : ℕ := N... | [
"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\nex : ∃ m, y ≤ (↑m * δ) ^ n\nm : ℕ := Nat.find ex\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 441,
"column": 2
} | {
"line": 441,
"column": 33
} | {
"line": 441,
"column": 34
} | [
{
"pp": "K : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nx : K\nx0 : 0 < x\n⊢ ∃ q, 0 < q ∧ ↑q < x",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nx : K\nx0 : 0 < x\n⊢ ∃ q, 0 < q ∧ ↑q < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 459,
"column": 8
} | {
"line": 459,
"column": 58
} | {
"line": 460,
"column": 10
} | [
{
"pp": "G : Type u_1\nM : Type u_2\nR : Type u_3\nK : Type u_4\nn m : ℤ\nm0 : 0 < m\n⊢ ↑n.toNat ≤ n.toNat • m",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"HMul.hMul... | [
"G : Type u_1\nM : Type u_2\nR : Type u_3\nK : Type u_4\nn m : ℤ\nm0 : 0 < m\n⊢ ↑n.toNat ≤ ↑n.toNat * m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 506,
"column": 15
} | {
"line": 506,
"column": 48
} | {
"line": 506,
"column": 49
} | [
{
"pp": "case coe.coe\nG : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : AddCommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : Archimedean M\ny : M\nhxy : 0 < ↑y\nx : M\n⊢ ∃ n, ↑x ≤ n • ↑y",
"ppTerm": "?coe.coe",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"W... | [
"case coe.coe\nG : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : AddCommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : Archimedean M\ny : M\nhxy : 0 < ↑y\nx : M\n⊢ ∃ n, x ≤ n • y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 506,
"column": 73
} | {
"line": 506,
"column": 84
} | {
"line": 506,
"column": 85
} | [
{
"pp": "G : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : AddCommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : Archimedean M\ny : M\nhxy : 0 < ↑y\nx : M\n⊢ 0 < y",
"ppTerm": "?m.103",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : AddCommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : Archimedean M\ny : M\nhxy : 0 < ↑y\nx : M\n⊢ 0 < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 517,
"column": 15
} | {
"line": 517,
"column": 47
} | {
"line": 517,
"column": 48
} | [
{
"pp": "case coe.coe\nG : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\ny : M\nhxy : 1 < ↑y\nx : M\n⊢ ∃ n, ↑x ≤ ↑y ^ n",
"ppTerm": "?coe.coe",
"assigned": true,
"usedConstants": [
"CommMonoidWithZer... | [
"case coe.coe\nG : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\ny : M\nhxy : 1 < ↑y\nx : M\n⊢ ∃ n, x ≤ y ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 517,
"column": 75
} | {
"line": 517,
"column": 86
} | {
"line": 517,
"column": 87
} | [
{
"pp": "G : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\ny : M\nhxy : 1 < ↑y\nx : M\n⊢ 1 < y",
"ppTerm": "?m.111",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\nM✝ : Type u_2\nR : Type u_3\nK : Type u_4\nM : Type u_5\ninst✝² : CommMonoid M\ninst✝¹ : PartialOrder M\ninst✝ : MulArchimedean M\ny : M\nhxy : 1 < ↑y\nx : M\n⊢ 1 < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Count | {
"line": 54,
"column": 27
} | {
"line": 54,
"column": 38
} | {
"line": 54,
"column": 39
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\n⊢ ∀ (a_1 : List α), p a → countP p (a ::ₘ Quot.mk (⇑(isSetoid α)) a_1) = countP p (Quot.mk (⇑(isSetoid α)) a_1) + 1",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Multiset.cons",
"id",
... | [
"α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\n⊢ ∀ (a_1 : List α), p a → List.countP (fun b ↦ decide (p b)) (a :: a_1) = List.countP (fun b ↦ decide (p b)) a_1 + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Count | {
"line": 58,
"column": 27
} | {
"line": 58,
"column": 38
} | {
"line": 58,
"column": 39
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\n⊢ ∀ (a_1 : List α), ¬p a → countP p (a ::ₘ Quot.mk (⇑(isSetoid α)) a_1) = countP p (Quot.mk (⇑(isSetoid α)) a_1)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Multiset.cons",
"id",
"Li... | [
"α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\n⊢ ∀ (a_1 : List α), ¬p a → List.countP (fun b ↦ decide (p b)) (a :: a_1) = List.countP (fun b ↦ decide (p b)) a_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Count | {
"line": 111,
"column": 6
} | {
"line": 111,
"column": 17
} | {
"line": 111,
"column": 18
} | [
{
"pp": "α : Type u_1\ns s' : Multiset α\np p' : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred p'\nl l' : List α\nhp : ∀ (x : α), x ∈ Quot.mk (⇑(isSetoid α)) l → p x = p' x\nhs : l ~ l'\n⊢ ∀ (x : α), x ∈ l → decide (p x) = decide (p' x)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstan... | [
"α : Type u_1\ns s' : Multiset α\np p' : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred p'\nl l' : List α\nhp : ∀ (x : α), x ∈ Quot.mk (⇑(isSetoid α)) l → p x = p' x\nhs : l ~ l'\n⊢ ∀ (x : α), x ∈ l → (p x ↔ p' x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Count | {
"line": 228,
"column": 35
} | {
"line": 228,
"column": 46
} | {
"line": 228,
"column": 47
} | [
{
"pp": "α : Type u_1\ns : Multiset α\ninst✝ : DecidableEq α\n_l : List α\n⊢ Nodup (Quot.mk (⇑(isSetoid α)) _l) ↔\n ∀ (a : α), a ∈ Quot.mk (⇑(isSetoid α)) _l → count a (Quot.mk (⇑(isSetoid α)) _l) = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.coe_co... | [
"α : Type u_1\ns : Multiset α\ninst✝ : DecidableEq α\n_l : List α\n⊢ _l.Nodup ↔ ∀ (a : α), a ∈ _l → List.count a _l = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Nodup | {
"line": 35,
"column": 4
} | {
"line": 35,
"column": 33
} | {
"line": 36,
"column": 6
} | [
{
"pp": "α : Type u\nβ : Type v\nr : α → β → Prop\nhr : Relator.BiUnique r\na✝ : α\nb✝ : β\nl₁✝ : List α\nl₂✝ : List β\nhab : r a✝ b✝\nh : Forall₂ r l₁✝ l₂✝\n⊢ (fun x1 x2 ↦ x1 ↔ x2) (a✝ :: l₁✝).Nodup (b✝ :: l₂✝).Nodup",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_... | [
"α : Type u\nβ : Type v\nr : α → β → Prop\nhr : Relator.BiUnique r\na✝ : α\nb✝ : β\nl₁✝ : List α\nl₂✝ : List β\nhab : r a✝ b✝\nh : Forall₂ r l₁✝ l₂✝\n⊢ ¬a✝ ∈ l₁✝ ∧ l₁✝.Nodup ↔ ¬b✝ ∈ l₂✝ ∧ l₂✝.Nodup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Nodup | {
"line": 112,
"column": 6
} | {
"line": 112,
"column": 45
} | {
"line": 112,
"column": 46
} | [
{
"pp": "case pos\nα : Type u\nx hd : α\ntl : List α\nhl : tl ≠ [x] ↔ tl = [] ∨ ∃ y, y ∈ tl ∧ y ≠ x\nh : (hd :: tl).Nodup\nhx : tl = [x]\n⊢ hd :: tl ≠ [x] ↔ hd :: tl = [] ∨ ∃ y, y ∈ hd :: tl ∧ y ≠ x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Nodup.0.L... | [
"case pos\nα : Type u\nx hd : α\ntl : List α\nhl : tl ≠ [x] ↔ tl = [] ∨ ∃ y, y ∈ tl ∧ y ≠ x\nh : (hd :: tl).Nodup\nhx : tl = [x]\n⊢ ¬hd = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.ZeroCons | {
"line": 234,
"column": 6
} | {
"line": 234,
"column": 17
} | {
"line": 234,
"column": 18
} | [
{
"pp": "case neg\nα : Type u_1\na b : α\nas bs : Multiset α\nthis✝³ : DecidableEq α\neq : a ::ₘ as = b ::ₘ bs\nh : ¬a = b\nthis✝² : a ∈ b ::ₘ bs\nthis✝¹ : a ∈ bs\ncs : Multiset α\nhcs : bs = a ::ₘ cs\nthis✝ : a ::ₘ as = b ::ₘ a ::ₘ cs\nthis : a ::ₘ as = a ::ₘ b ::ₘ cs\n⊢ as = b ::ₘ cs",
"ppTerm": "?neg✝",
... | [
"case neg\nα : Type u_1\na b : α\nas bs : Multiset α\nthis✝³ : DecidableEq α\neq : a ::ₘ as = b ::ₘ bs\nh : ¬a = b\nthis✝² : a ∈ b ::ₘ bs\nthis✝¹ : a ∈ bs\ncs : Multiset α\nhcs : bs = a ::ₘ cs\nthis✝ : a ::ₘ as = b ::ₘ a ::ₘ cs\nthis : a ::ₘ as = a ::ₘ b ::ₘ cs\n⊢ as = b ::ₘ cs"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.ZeroCons | {
"line": 264,
"column": 2
} | {
"line": 264,
"column": 18
} | {
"line": 265,
"column": 2
} | [
{
"pp": "α : Type u_1\na : α\n⊢ a ∈ {a}",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Multiset",
"Multiset.cons",
"id",
"Multiset.instSingleton",
"Multiset.instMembership",
"Zero.toOfNat0",
... | [
"α : Type u_1\na : α\n⊢ a ∈ a ::ₘ 0"
] | rw [← cons_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Multiset.AddSub | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 13
} | {
"line": 88,
"column": 14
} | [
{
"pp": "α : Type u_1\ns t : Multiset α\n⊢ s ≤ s + t",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns t : Multiset α\n⊢ s ≤ s + t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.AddSub | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 13
} | {
"line": 91,
"column": 14
} | [
{
"pp": "α : Type u_1\ns t : Multiset α\n⊢ s ≤ t + s",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns t : Multiset α\n⊢ s ≤ t + s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Nodup | {
"line": 365,
"column": 8
} | {
"line": 365,
"column": 23
} | {
"line": 365,
"column": 24
} | [
{
"pp": "α : Type u\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\nb : α\nl : List α\nn : ℕ\nhl : (b :: l).Nodup\n⊢ take (n + 1) (b :: l) = List.filter (fun a ↦ elem a (take (n + 1) (b :: l))) (b :: l)",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.take_succ_cons",
... | [
"α : Type u\ninst✝¹ : BEq α\ninst✝ : LawfulBEq α\nb : α\nl : List α\nn : ℕ\nhl : (b :: l).Nodup\n⊢ b :: take n l = List.filter (fun a ↦ elem a (b :: take n l)) (b :: l)"
] | take_succ_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Multiset.AddSub | {
"line": 213,
"column": 4
} | {
"line": 213,
"column": 19
} | {
"line": 213,
"column": 20
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nh : a ∈ s\n⊢ s.erase a < s",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nh : a ∈ s\n⊢ s.erase a < s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.AddSub | {
"line": 374,
"column": 12
} | {
"line": 374,
"column": 23
} | {
"line": 374,
"column": 24
} | [
{
"pp": "case zero\nα : Type u_1\nβ : Type v\nr : α → β → Prop\ns : Multiset α\nt : Multiset β\nu : Multiset α\nv : Multiset β\nhuv : Rel r u v\n⊢ Rel r (0 + u) (0 + v)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Multiset",
"id",
"Mu... | [
"case zero\nα : Type u_1\nβ : Type v\nr : α → β → Prop\ns : Multiset α\nt : Multiset β\nu : Multiset α\nv : Multiset β\nhuv : Rel r u v\n⊢ Rel r u v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.AddSub | {
"line": 375,
"column": 23
} | {
"line": 375,
"column": 34
} | {
"line": 375,
"column": 35
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type v\nr : α → β → Prop\ns : Multiset α\nt : Multiset β\nu : Multiset α\nv : Multiset β\nhuv : Rel r u v\na✝ : α\nb✝ : β\nas✝ : Multiset α\nbs✝ : Multiset β\nhab : r a✝ b✝\nhst : Rel r as✝ bs✝\nih : Rel r (as✝ + u) (bs✝ + v)\n⊢ Rel r (a✝ ::ₘ as✝ + u) (b✝ ::ₘ bs✝ + v)",
... | [
"case cons\nα : Type u_1\nβ : Type v\nr : α → β → Prop\ns : Multiset α\nt : Multiset β\nu : Multiset α\nv : Multiset β\nhuv : Rel r u v\na✝ : α\nb✝ : β\nas✝ : Multiset α\nbs✝ : Multiset β\nhab : r a✝ b✝\nhst : Rel r as✝ bs✝\nih : Rel r (as✝ + u) (bs✝ + v)\n⊢ Rel r (a✝ ::ₘ (as✝ + u)) (b✝ ::ₘ (bs✝ + v))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.ZeroCons | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 17
} | {
"line": 592,
"column": 18
} | [
{
"pp": "case refine_2.refine_2\nα : Type u_1\nm2 : Multiset α\nr : α → α → Prop\na : α\nt : Multiset α\nih : ∀ {m1 : Multiset α}, (∀ (a b : α), a ∈ m1 → b ∈ t → r a b) → m1.card = t.card → Rel r m1 t\nb : α\nm' : Multiset α\nh : ∀ (a_1 b_1 : α), a_1 ∈ b ::ₘ m' → b_1 ∈ a ::ₘ t → r a_1 b_1\nhc : (b ::ₘ m').card ... | [
"case refine_2.refine_2\nα : Type u_1\nm2 : Multiset α\nr : α → α → Prop\na : α\nt : Multiset α\nih : ∀ {m1 : Multiset α}, (∀ (a b : α), a ∈ m1 → b ∈ t → r a b) → m1.card = t.card → Rel r m1 t\nb : α\nm' : Multiset α\nh : ∀ (a_1 b_1 : α), a_1 ∈ b ::ₘ m' → b_1 ∈ a ::ₘ t → r a_1 b_1\nhc : (b ::ₘ m').card = t.card + 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Dedup | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 52
} | {
"line": 51,
"column": 53
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nthis : (¬∀ (b : α), b ∈ pwFilter (fun x1 x2 ↦ x1 ≠ x2) l → a ≠ b) ↔ ¬∀ (b : α), b ∈ l → a ≠ b\n⊢ a ∈ l.dedup ↔ a ∈ l",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"List.dedup",
"Membership.mem... | [
"case refine_2\nα : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nthis : (¬∀ (b : α), b ∈ pwFilter (fun x1 x2 ↦ x1 ≠ x2) l → a ≠ b) ↔ ¬∀ (b : α), b ∈ l → a ≠ b\n⊢ a ∈ pwFilter (fun x1 x2 ↦ x1 ≠ x2) l ↔ a ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Dedup | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 13
} | {
"line": 65,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\n⊢ (a :: l).dedup = if a ∈ l then l.dedup else a :: l.dedup",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\n⊢ (a :: l).dedup = if a ∈ l then l.dedup else a :: l.dedup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lattice | {
"line": 126,
"column": 64
} | {
"line": 126,
"column": 75
} | {
"line": 126,
"column": 76
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\na : α\ninst✝ : DecidableEq α\nh : a ∈ l₁ ∩ l₂\n⊢ a ∈ l₂",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nl₁ l₂ : List α\na : α\ninst✝ : DecidableEq α\nh : a ∈ l₁ ∩ l₂\n⊢ a ∈ l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lattice | {
"line": 129,
"column": 29
} | {
"line": 129,
"column": 40
} | {
"line": 129,
"column": 41
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\na : α\ninst✝ : DecidableEq α\nh₁ : a ∈ l₁\nh₂ : a ∈ l₂\n⊢ elem a l₂ = true",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instLawfulBEq",
"congrArg",
"List.elem",
"List.contains",
"List.elem_eq_contains"... | [
"α : Type u_1\nl₁ l₂ : List α\na : α\ninst✝ : DecidableEq α\nh₁ : a ∈ l₁\nh₂ : a ∈ l₂\n⊢ a ∈ l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lattice | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 21
} | {
"line": 243,
"column": 22
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : DecidableEq α\nb : α\nl₁ l₂ : List α\nh : ¬b ∈ l₂\n⊢ (b :: l₁).bagInter l₂ = [] ↔ (b :: l₁) ∩ l₂ = []",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.inter_cons_of_notMem",
"False",
"eq_false",
"congrArg... | [
"case neg\nα : Type u_1\ninst✝ : DecidableEq α\nb : α\nl₁ l₂ : List α\nh : ¬b ∈ l₂\n⊢ l₁.bagInter l₂ = [] ↔ l₁ ∩ l₂ = []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.MapFold | {
"line": 206,
"column": 26
} | {
"line": 206,
"column": 48
} | {
"line": 206,
"column": 49
} | [
{
"pp": "α : Type u_1\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nx y : α\ns : Multiset α\nih : x ∈ s → map f (s.erase x) = (map f s).erase (f x)\nh : x ∈ y ::ₘ s\nhxy : y ≠ x\n⊢ x ∈ s",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"α : Type u_1\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nx y : α\ns : Multiset α\nih : x ∈ s → map f (s.erase x) = (map f s).erase (f x)\nh : x ∈ y ::ₘ s\nhxy : y ≠ x\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Dedup | {
"line": 127,
"column": 80
} | {
"line": 127,
"column": 91
} | {
"line": 127,
"column": 92
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na✝ b✝ : List α\nh : _root_.Disjoint (Quot.mk (⇑(isSetoid α)) a✝) (Quot.mk (⇑(isSetoid α)) b✝)\n⊢ a✝.Disjoint b✝",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\na✝ b✝ : List α\nh : _root_.Disjoint (Quot.mk (⇑(isSetoid α)) a✝) (Quot.mk (⇑(isSetoid α)) b✝)\n⊢ a✝.Disjoint b✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Basic | {
"line": 106,
"column": 87
} | {
"line": 107,
"column": 30
} | {
"line": 109,
"column": 0
} | [
{
"pp": "α : Type u_1\np : Multiset α → Sort u_3\nn : ℕ\nH : (t₁ : Multiset α) → ({t₂ : Multiset α} → t₂.card ≤ n → t₁ < t₂ → p t₂) → t₁.card ≤ n → p t₁\ns : Multiset α\n⊢ strongDownwardInduction H s = H s fun {t₂} ht _hst ↦ strongDownwardInduction H t₂ ht",
"ppTerm": "?m.20",
"assigned": true,
"use... | [] | by
rw [strongDownwardInduction] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Multiset.UnionInter | {
"line": 116,
"column": 6
} | {
"line": 116,
"column": 21
} | {
"line": 116,
"column": 22
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nIH : ∀ {t : Multiset α}, s ∩ t ≤ t\nt : Multiset α\nh : a ∈ t\n⊢ (a ::ₘ s) ∩ t ≤ t",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.instInter",
"congrArg",
"PartialOrde... | [
"case pos\nα : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nIH : ∀ {t : Multiset α}, s ∩ t ≤ t\nt : Multiset α\nh : a ∈ t\n⊢ a ::ₘ s ∩ t.erase a ≤ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.UnionInter | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 33
} | {
"line": 121,
"column": 34
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝ : DecidableEq α\nt s u : Multiset α\nh₁ : s ≤ 0\nh₂ : s ≤ u\n⊢ s ≤ 0 ∩ u",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.instInter",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [
"case refine_1\nα : Type u_1\ninst✝ : DecidableEq α\nt s u : Multiset α\nh₁ : s ≤ 0\nh₂ : s ≤ u\n⊢ s ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.UnionInter | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 82
} | {
"line": 160,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t u : Multiset α\n⊢ s ∪ t + u = s + u ∪ (t + u)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Multiset",
"id",
"Multiset.add_assoc",
"instHAdd",
"instHSub",... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns t u : Multiset α\n⊢ s - t = s + u - (t + u)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.UnionInter | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 13
} | {
"line": 167,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\ns t : Multiset α\n⊢ a ::ₘ (s ∪ t) = a ::ₘ s ∪ a ::ₘ t",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\na : α\ns t : Multiset α\n⊢ a ::ₘ (s ∪ t) = a ::ₘ s ∪ a ::ₘ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Dedup | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 51
} | {
"line": 62,
"column": 52
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : Multiset α\nhl : l.Nodup\nhl' : l'.Nodup\nh : l.toFinset = l'.toFinset\n⊢ l = l'",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\nl l' : Multiset α\nhl : l.Nodup\nhl' : l'.Nodup\nh : l.toFinset = l'.toFinset\n⊢ l = l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 55,
"column": 77
} | {
"line": 55,
"column": 88
} | {
"line": 55,
"column": 89
} | [
{
"pp": "α : Type u_1\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Multiset α\n_l : List α\nh : ∀ (x : α), x ∈ Quot.mk (⇑(isSetoid α)) _l → (p x ↔ q x)\n⊢ ∀ (x : α), x ∈ _l → decide (p x) = decide (q x)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mp... | [
"α : Type u_1\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Multiset α\n_l : List α\nh : ∀ (x : α), x ∈ Quot.mk (⇑(isSetoid α)) _l → (p x ↔ q x)\n⊢ ∀ (x : α), x ∈ _l → (p x ↔ q x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 78,
"column": 65
} | {
"line": 78,
"column": 76
} | {
"line": 78,
"column": 77
} | [
{
"pp": "α : Type u_1\ns : Multiset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∀ (b : α), p b → q b\nl : List α\n⊢ ∀ (a : α), decide (p a) = true → decide (q a) = true",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Bool.tru... | [
"α : Type u_1\ns : Multiset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∀ (b : α), p b → q b\nl : List α\n⊢ ∀ (a : α), p a → q a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 84,
"column": 82
} | {
"line": 84,
"column": 93
} | {
"line": 84,
"column": 94
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nx✝ : List α\nh : p a\n⊢ decide (p a) = true",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Bool.true",
"Bool",
"decide_eq_true_eq",
"Decidable.decide",... | [
"α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nx✝ : List α\nh : p a\n⊢ p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 88,
"column": 82
} | {
"line": 88,
"column": 93
} | {
"line": 88,
"column": 94
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nx✝ : List α\nh : ¬p a\n⊢ ¬decide (p a) = true",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Bool.true",
"Bool",
"decide_eq_true_eq",
... | [
"α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nx✝ : List α\nh : ¬p a\n⊢ ¬p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Empty | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 13
} | {
"line": 164,
"column": 14
} | [
{
"pp": "α : Type u_1\ns : Finset α\n⊢ IsEmpty ↥s ↔ s = ∅",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns : Finset α\n⊢ IsEmpty ↥s ↔ s = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.UnionInter | {
"line": 253,
"column": 4
} | {
"line": 253,
"column": 15
} | {
"line": 253,
"column": 16
} | [
{
"pp": "case refine_1\nα : Type u_1\ns t : Multiset α\nh : _root_.Disjoint s t\na : α\nhs : a ∈ s\nht : a ∈ t\n⊢ False",
"ppTerm": "?refine_1",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case refine_1\nα : Type u_1\ns t : Multiset α\nh : _root_.Disjoint s t\na : α\nhs : a ∈ s\nht : a ∈ t\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 15
} | {
"line": 240,
"column": 16
} | [
{
"pp": "α : Type u_1\nβ : Type v\np : α → Prop\ninst✝ : DecidablePred p\nf : α → Option β\ns : Multiset α\nl : List α\n⊢ List.filterMap f (List.filter (fun b ↦ decide (p b)) l) = List.filterMap (fun x ↦ if p x then f x else none) l",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"u... | [
"α : Type u_1\nβ : Type v\np : α → Prop\ninst✝ : DecidablePred p\nf : α → Option β\ns : Multiset α\nl : List α\n⊢ List.filterMap f (List.filter (fun b ↦ decide (p b)) l) = List.filterMap (fun x ↦ if p x then f x else none) l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.FinsetOps | {
"line": 182,
"column": 78
} | {
"line": 182,
"column": 89
} | {
"line": 182,
"column": 90
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na✝ b✝ : List α\nh : _root_.Disjoint (Quot.mk (⇑(isSetoid α)) a✝) (Quot.mk (⇑(isSetoid α)) b✝)\n⊢ a✝.Disjoint b✝",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\na✝ b✝ : List α\nh : _root_.Disjoint (Quot.mk (⇑(isSetoid α)) a✝) (Quot.mk (⇑(isSetoid α)) b✝)\n⊢ a✝.Disjoint b✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 310,
"column": 4
} | {
"line": 310,
"column": 15
} | {
"line": 310,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nh : p a\n_l : List α\n⊢ decide (p a) = true",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Bool.true",
"Bool",
"decide_eq_true_eq",
... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nh : p a\n_l : List α\n⊢ p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Infix | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 48
} | {
"line": 47,
"column": 49
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\nh : l₁ <+: l₂\nn : ℕ\n⊢ List.take n l₁ <+: List.take n l₂",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"and_true",
"congrArg",
"id",
"LE.le",
"instLENat",
"List.length_take",
"And",
"_p... | [
"α : Type u_1\nl₁ l₂ : List α\nh : l₁ <+: l₂\nn : ℕ\n⊢ List.take n l₁ <+: l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.UnionInter | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 29
} | {
"line": 338,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nx y z : Multiset α\nh : z ≤ y\n⊢ x + y = x ∪ z ↔ y = z ∧ _root_.Disjoint x y",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Data.Multiset.UnionInter.0.Multiset.add_eq_union_right_of_le.... | [
"α : Type u_1\ninst✝ : DecidableEq α\nx y z : Multiset α\nh : z ≤ y\n⊢ x + y = x ∪ z ↔ _root_.Disjoint x y ∧ y = z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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