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 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Fin.Pigeonhole | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | {
"line": 51,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Surjective f\n⊢ n ≤ m",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Surjective f\n⊢ n ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | {
"line": 59,
"column": 14
} | [
{
"pp": "m : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Fin m → α\n⊢ Fintype.card ↑(Set.range f) ≤ m",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fintype.card_ofFinset",
"Finset.univ",
"Finset.univ_filter_exists",
"Iff.of_eq",... | [
"m : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Fin m → α\n⊢ (Finset.image f Finset.univ).card ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 260,
"column": 28
} | {
"line": 295,
"column": 42
} | {
"line": 297,
"column": 0
} | [
{
"pp": "S T : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ninst✝ : Epi π\n⊢ ∃ S' T' y' π' g',\n Epi π' ∧\n Epi y' ∧\n π' ≫ y' ▷ ℕ∪{∞} = g' ≫ π ∧\n IsSplitEpi (LightProfinite.fibreIncl ∞ (π' ≫ snd S' ℕ∪{∞}) ≫ π' ≫ fst S' ℕ∪{∞}) ∧ Epi (cover π')",
"ppTerm": "?m.89",
"assigned": true,
"u... | [] | by
-- Construct the space `S'` space which has functions `σ'` we can plug into
-- `fibres`.
have := S'_compactSpace π (by fun_prop)
let S'π (n : ℕ∪{∞}) : LightProfinite.of (S' π) ⟶ LightProfinite.fibre n (π ≫ snd _ _) :=
⟨TopCat.ofHom {
toFun x := x.val n,
continuous_toFun := by refine (continuo... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Condensed.Light.Sequence | {
"line": 326,
"column": 19
} | {
"line": 326,
"column": 30
} | {
"line": 326,
"column": 31
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | [
"R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : LightProfinit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 83,
"column": 39
} | {
"line": 83,
"column": 50
} | {
"line": 83,
"column": 51
} | [
{
"pp": "α : Type u\nβ✝ : α → Type v\nβ : Type ?u.19\nf : β → α\ninst✝¹ : DecidableEq α\ninst✝ : FinEnum β\nh : Surjective f\nx✝ : α\n⊢ x✝ ∈ List.map f (toList β)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"congrArg",
"List.map",
... | [
"α : Type u\nβ✝ : α → Type v\nβ : Type ?u.19\nf : β → α\ninst✝¹ : DecidableEq α\ninst✝ : FinEnum β\nh : Surjective f\nx✝ : α\n⊢ ∃ a, f a = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 328,
"column": 24
} | {
"line": 328,
"column": 45
} | {
"line": 328,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝¹ : FinEnum α\nβ : α → Type u_2\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ f ∈ enum β",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"Membership.mem",
"Exists",
"id",
"FinEnum.mem_toList... | [
"α : Type u_1\ninst✝¹ : FinEnum α\nβ : α → Type u_2\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ ∃ a ∈ (FinEnum.toList α).pi fun x ↦ FinEnum.toList (β x), (fun x ↦ a x ⋯) = f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 70
} | {
"line": 336,
"column": 71
} | [
{
"pp": "α✝ : Type u_1\ninst✝³ : FinEnum α✝\nβ : α✝ → Type u_2\ninst✝² : (a : α✝) → FinEnum (β a)\np : Prop\ninst✝¹ : Decidable p\nα : p → Type\ninst✝ : (hp : p) → FinEnum (α hp)\nhp : p\nx : (hp : p) → α hp\n⊢ x ∈ map (fun x x_1 ↦ x) (FinEnum.toList (α hp))",
"ppTerm": "?m.30",
"assigned": true,
"u... | [
"α✝ : Type u_1\ninst✝³ : FinEnum α✝\nβ : α✝ → Type u_2\ninst✝² : (a : α✝) → FinEnum (β a)\np : Prop\ninst✝¹ : Decidable p\nα : p → Type\ninst✝ : (hp : p) → FinEnum (α hp)\nhp : p\nx : (hp : p) → α hp\n⊢ ∃ a, (fun x ↦ a) = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 25
} | {
"line": 49,
"column": 26
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\nhα : Nat.card α ≤ 2\n⊢ Nat.card (Perm α) ∣ 2",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"Nat.card_perm",
"id",
"Nat.card",
"instOfNatNat",
"Nat.instDvd",
"Na... | [
"α : Type u_1\ninst✝ : Finite α\nhα : Nat.card α ≤ 2\n⊢ (Nat.card α)! ∣ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 46
} | {
"line": 60,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\na b c : α\nleft✝² : a ∈ _root_.Set.univ\nleft✝¹ : b ∈ _root_.Set.univ\nleft✝ : c ∈ _root_.Set.univ\nhab : a ≠ b\nhac : a ≠ c\nhbc : b ≠ c\nh : ∀ (a b : Perm α) (x : α), (a * b) x = (b * a) x\n⊢ b = c",
"ppTerm": "?m.108",
"assigned": false,
"usedConstants": [... | [
"α : Type u_1\ninst✝ : Finite α\na b c : α\nleft✝² : a ∈ _root_.Set.univ\nleft✝¹ : b ∈ _root_.Set.univ\nleft✝ : c ∈ _root_.Set.univ\nhab : a ≠ b\nhac : a ≠ c\nhbc : b ≠ c\nh : ∀ (a b : Perm α) (x : α), (a * b) x = (b * a) x\n⊢ b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 22
} | {
"line": 81,
"column": 23
} | [
{
"pp": "case none\nα : Type u_1\nβ : Type u_2\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f (a :: l)) = map g (a :: l)",
"ppTerm": "?none",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.map_cons",
... | [
"case none\nα : Type u_1\nβ : Type u_2\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f l) = map g l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 99,
"column": 6
} | {
"line": 99,
"column": 21
} | {
"line": 99,
"column": 22
} | [
{
"pp": "case cons.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na : α\nl₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\nIH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) l₁✝ → lookmap f l₁✝ ~ lookmap f l₂✝\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d)... | [
"case cons.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na : α\nl₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\nIH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) l₁✝ → lookmap f l₁✝ ~ lookmap f l₂✝\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (a :: l₁✝)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 103,
"column": 6
} | {
"line": 103,
"column": 26
} | {
"line": 103,
"column": 27
} | [
{
"pp": "case swap.none.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap.none.non... | [
"case swap.none.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nh₂ : f b = none\n⊢ b :: a :: lookmap f l ~ a :: b :: lookmap f l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 104,
"column": 6
} | {
"line": 104,
"column": 48
} | {
"line": 104,
"column": 49
} | [
{
"pp": "case swap.none.some\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nd : α\nh₂ : f b = some d\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap... | [
"case swap.none.some\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nd : α\nh₂ : f b = some d\n⊢ d :: a :: l ~ a :: d :: l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.AList | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 22
} | {
"line": 323,
"column": 23
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : (c :: l).NodupKeys\n⊢ { entries := c :: l, nodupKeys := h } = insert c.fst c.snd { entries := l, nodupKeys := ⋯ }",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AList.mk... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : (c :: l).NodupKeys\n⊢ l = kerase c.fst l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 48
} | {
"line": 105,
"column": 49
} | [
{
"pp": "case swap.some.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nc : α\nh₁ : f a = some c\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap... | [
"case swap.some.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nc : α\nh₁ : f a = some c\nh₂ : f b = none\n⊢ b :: c :: l ~ c :: b :: l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | [] | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | [] | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Condensed.Light.Sequence | {
"line": 360,
"column": 70
} | {
"line": 360,
"column": 81
} | {
"line": 360,
"column": 82
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | [
"R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : LightProfinit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finmap | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 15
} | {
"line": 307,
"column": 16
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nf : { f // ∀ (i : α), (f.2 i).isSome = true ↔ i ∈ f.1 }\ni : α\nx : β i\nleft✝¹ : ⟨i, x⟩.fst ∈ (↑f).1\nhx : (↑f).2 ⟨i, x⟩.fst = some ⟨i, x⟩.snd\ny : β i\nleft✝ : ⟨i, y⟩.fst ∈ (↑f).1\nhy : (↑f).2 ⟨i, y⟩.fst = some ⟨i, y⟩.snd\n⊢ ⟨i, x⟩ = ⟨i, y⟩",
"pp... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nf : { f // ∀ (i : α), (f.2 i).isSome = true ↔ i ∈ f.1 }\ni : α\nx : β i\nleft✝¹ : ⟨i, x⟩.fst ∈ (↑f).1\nhx : (↑f).2 ⟨i, x⟩.fst = some ⟨i, x⟩.snd\ny : β i\nleft✝ : ⟨i, y⟩.fst ∈ (↑f).1\nhy : (↑f).2 ⟨i, y⟩.fst = some ⟨i, y⟩.snd\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Sigma | {
"line": 455,
"column": 46
} | {
"line": 455,
"column": 67
} | {
"line": 455,
"column": 68
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na₁ a₂ : α\nl : List (Sigma β)\nh : a₁ ≠ a₂\np✝ : a₁ ∈ l.keys\nw✝² : β a₂\nw✝¹ w✝ : List (Sigma β)\nleft✝ : ¬a₂ ∈ w✝¹.keys\np : a₁ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\nq : a₂ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\n⊢ a₁ ∈ (w✝¹ ++ w✝).keys",
"ppTerm": "?m.75",
... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na₁ a₂ : α\nl : List (Sigma β)\nh : a₁ ≠ a₂\np✝ : a₁ ∈ l.keys\nw✝² : β a₂\nw✝¹ w✝ : List (Sigma β)\nleft✝ : ¬a₂ ∈ w✝¹.keys\np : a₁ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\nq : a₂ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\n⊢ (∃ x, ⟨a₁, x⟩ ∈ w✝¹) ∨ ∃ x, ⟨a₁, x⟩ ∈ w✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.PiInduction | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 28
} | {
"line": 52,
"column": 29
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : Finite ι\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nr : (i : ι) → α i → Finset (α i) → Prop\nH_ex : ∀ (i : ι) (s : Finset (α i)), s.Nonempty → ∃ x ∈ s, r i x (s.erase x)\np : ((i : ι) → Finset (α i)) → Prop\nh0 : p fun x ↦ ∅\nstep : ∀ (g : (i ... | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝² : Finite ι\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nr : (i : ι) → α i → Finset (α i) → Prop\nH_ex : ∀ (i : ι) (s : Finset (α i)), s.Nonempty → ∃ x ∈ s, r i x (s.erase x)\np : ((i : ι) → Finset (α i)) → Prop\nh0 : p fun x ↦ ∅\nstep : ∀ (g : (i : ι) → Finse... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 749,
"column": 4
} | {
"line": 753,
"column": 35
} | {
"line": 755,
"column": 0
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | [] | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 749,
"column": 4
} | {
"line": 753,
"column": 35
} | {
"line": 755,
"column": 0
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | [] | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.AList | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 28
} | {
"line": 83,
"column": 2
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x ↦ M\n⊢ l.lookupFinsupp.support = (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [
"α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x ↦ M\n⊢ (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset =\n (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset"
] | dsimp only [lookupFinsupp] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Data.Finsupp.AList | {
"line": 91,
"column": 60
} | {
"line": 93,
"column": 39
} | {
"line": 95,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x ↦ M\na : α\n⊢ l.lookupFinsupp a = 0 ↔ a ∉ l ∨ 0 ∈ lookup a l",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"False",
"Option.ctorIdx",
... | [] | by
rw [lookupFinsupp_apply, ← lookup_eq_none]
rcases lookup a l with - | m <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finsupp.AList | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 17
} | {
"line": 119,
"column": 18
} | [
{
"pp": "case neg\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\nf : α →₀ M\na : α\nh : ¬f a = 0\n⊢ ⟨a, f a⟩ ∈ f.toAList.entries",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Prod.toSigma",
"congrArg",
"Finset",
"List.ma... | [
"case neg\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\nf : α →₀ M\na : α\nh : ¬f a = 0\n⊢ ¬f a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 44,
"column": 2
} | {
"line": 45,
"column": 32
} | {
"line": 45,
"column": 33
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\na : α\n⊢ a ∈ f.neLocus g ↔ f a ≠ g a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"instDecidableNot",
"Finset.instU... | [
"α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\na : α\n⊢ f a ≠ g a → f a ≠ 0 ∨ g a ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 83,
"column": 14
} | {
"line": 83,
"column": 73
} | {
"line": 83,
"column": 74
} | [
{
"pp": "α : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ x ∈ (mapRange F F0 f).neLocus (mapRange F F0 g) → x ∈ f.neLocus g",
"ppTerm": "?m.31",
"assigned": t... | [
"α : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ f x = g x → F (f x) = F (g x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 35
} | {
"line": 138,
"column": 36
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf₁ f₂ g : α →₀ N\n⊢ (f₁ - g).neLocus (f₂ - g) = f₁.neLocus f₂",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"congrArg",
... | [
"α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf₁ f₂ g : α →₀ N\n⊢ (f₁ + -g).neLocus (f₂ + -g) = f₁.neLocus f₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.Sigma | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 13
} | {
"line": 90,
"column": 14
} | [
{
"pp": "κ : Type u_1\nι : κ → Type u_2\nM : Type u_3\ninst✝ : Zero M\nk : κ\nf g : ι k →₀ M\nh : f.embSigma = g.embSigma\ni : ι k\nthis : f.embSigma ⟨k, i⟩ = g.embSigma ⟨k, i⟩\n⊢ f i = g i",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"κ : Type u_1\nι : κ → Type u_2\nM : Type u_3\ninst✝ : Zero M\nk : κ\nf g : ι k →₀ M\nh : f.embSigma = g.embSigma\ni : ι k\nthis : f.embSigma ⟨k, i⟩ = g.embSigma ⟨k, i⟩\n⊢ f i = g i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 152,
"column": 4
} | {
"line": 152,
"column": 14
} | {
"line": 153,
"column": 4
} | [
{
"pp": "α : Type\nds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ (x ⊗ y ⊗ z) t = cast ⋯ (x ⊗ (y ⊗ z)) t",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Semigroup.toMul",
"cast",
"id",
... | [
"α : Type\nds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ x t.take.take * y t.take.drop * z t.drop = cast ⋯ (fun t ↦ x t.take * (y t.drop.take * z t.drop.drop)) t"
] | unfold mul | Lean.Elab.Tactic.evalUnfold | Lean.Parser.Tactic.unfold |
Mathlib.Data.Holor | {
"line": 245,
"column": 28
} | {
"line": 245,
"column": 82
} | {
"line": 245,
"column": 83
} | [
{
"pp": "α : Type\nd : ℕ\nds : List ℕ\ninst✝ : Semiring α\nx : Holor α (d :: ds)\ni : ℕ\nhid : i < d\nb : ↥(Finset.range d)\na✝ : b ∈ (Finset.range d).attach\nhbi : b ≠ ⟨i, ⋯⟩\n⊢ i ≠ ↑b",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"Finset",
"Membership.mem",
"id",
... | [
"α : Type\nd : ℕ\nds : List ℕ\ninst✝ : Semiring α\nx : Holor α (d :: ds)\ni : ℕ\nhid : i < d\nb : ↥(Finset.range d)\na✝ : b ∈ (Finset.range d).attach\nhbi : b ≠ ⟨i, ⋯⟩\n⊢ ¬i = ↑b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 283,
"column": 6
} | {
"line": 283,
"column": 59
} | {
"line": 283,
"column": 60
} | [
{
"pp": "α : Type\nds : List ℕ\ninst✝¹ : Mul α\ninst✝ : AddMonoid α\nm n : ℕ\ny x₁ x₂ : Holor α ds\nhx₁ : x₁.CPRankMax1\nhx₂ : CPRankMax m x₂\nhy : CPRankMax n y\nthis : CPRankMax (m + n + 1) (x₁ + (x₂ + y))\n⊢ CPRankMax (m + 1 + n) (x₁ + x₂ + y)",
"ppTerm": "?m.245",
"assigned": true,
"usedConstant... | [
"α : Type\nds : List ℕ\ninst✝¹ : Mul α\ninst✝ : AddMonoid α\nm n : ℕ\ny x₁ x₂ : Holor α ds\nhx₁ : x₁.CPRankMax1\nhx₂ : CPRankMax m x₂\nhy : CPRankMax n y\nthis : CPRankMax (m + n + 1) (x₁ + (x₂ + y))\n⊢ CPRankMax (m + (n + 1)) (x₁ + (x₂ + y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 44
} | {
"line": 57,
"column": 4
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 35
} | {
"line": 61,
"column": 36
} | [
{
"pp": "a b : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = -b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = -b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 35
} | {
"line": 65,
"column": 36
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a.natAbs = b.natAbs ↔ -a = b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a.natAbs = b.natAbs ↔ -a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 30
} | {
"line": 92,
"column": 4
} | [
{
"pp": "a : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ b.natAbs < a.natAbs",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ b.natAbs < a.natAbs"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 330,
"column": 4
} | {
"line": 330,
"column": 19
} | {
"line": 331,
"column": 4
} | [
{
"pp": "α : Type\ninst✝ : Semiring α\nd : ℕ\nds : List ℕ\nx : Holor α (d :: ds)\nh_summands : ∀ (i : ↥(Finset.range d)), CPRankMax ds.prod (unitVec d ↑i ⊗ x.slice ↑i ⋯)\nh_dds_prod : (d :: ds).prod = (Finset.range d).card * ds.prod\nthis : CPRankMax ((Finset.range d).attach.card * ds.prod) (∑ i ∈ (Finset.range... | [
"α : Type\ninst✝ : Semiring α\nd : ℕ\nds : List ℕ\nx : Holor α (d :: ds)\nh_summands : ∀ (i : ↥(Finset.range d)), CPRankMax ds.prod (unitVec d ↑i ⊗ x.slice ↑i ⋯)\nh_dds_prod : (d :: ds).prod = (Finset.range d).card * ds.prod\nthis : CPRankMax ((Finset.range d).attach.card * ds.prod) (∑ i ∈ (Finset.range d).attach, ... | rw [h_dds_prod] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Int.CardIntervalMod | {
"line": 61,
"column": 2
} | {
"line": 62,
"column": 76
} | {
"line": 63,
"column": 2
} | [
{
"pp": "a b r : ℤ\nhr : 0 < r\nx : ℤ\n⊢ x ∈ {x ∈ Ioc a b | r ∣ x} ↔ x ∈ map { toFun := fun x ↦ x * r, inj' := ⋯ } (Ioc ⌊↑a / ↑r⌋ ⌊↑b / ↑r⌋)",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Int.decidableDvd",
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toM... | [
"a b r : ℤ\nhr : 0 < r\nx : ℤ\n⊢ ((a < x ∧ x ≤ b) ∧ ∃ c, x = c * r) ↔\n ∃ a_1, (a < a_1 * r ∧ a_1 * r ≤ b) ∧ { toFun := fun x ↦ x * r, inj' := ⋯ } a_1 = x"
] | simp only [mem_map, mem_filter, mem_Ioc, floor_lt, le_floor, div_lt_iff₀, le_div_iff₀,
dvd_iff_exists_eq_mul_left, cast_pos.2 hr, ← cast_mul, cast_lt, cast_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.TakeWhile | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 19
} | {
"line": 110,
"column": 20
} | [
{
"pp": "case false\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : false = p head\nphh' : ¬p head = true\n⊢ (!p head) = true",
"ppTerm": "?false✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not... | [
"case false\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : false = p head\nphh' : ¬p head = true\n⊢ p head = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 113,
"column": 8
} | {
"line": 113,
"column": 19
} | {
"line": 113,
"column": 20
} | [
{
"pp": "case true\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : true = p head\n⊢ ¬(!p head) = true",
"ppTerm": "?true✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not",
"Bool.not_eq_fal... | [
"case true\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : true = p head\n⊢ p head = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 123,
"column": 62
} | {
"line": 123,
"column": 73
} | {
"line": 123,
"column": 74
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ p x = true\n⊢ dropWhile (fun x ↦ !p x) l ≠ []",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"Bool.not",
"Bool.not_eq_false",
"congrArg",
"M... | [
"α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ p x = true\n⊢ ∃ x, x ∈ l ∧ p x = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 127,
"column": 62
} | {
"line": 127,
"column": 73
} | {
"line": 127,
"column": 74
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ dropWhile p l ≠ []",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Ne",
... | [
"α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ p x = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 15
} | {
"line": 130,
"column": 16
} | [
{
"pp": "case convert_2\nα : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ (!p x) = true",
"ppTerm": "?convert_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Bo... | [
"case convert_2\nα : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ p x = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Intervals | {
"line": 69,
"column": 59
} | {
"line": 69,
"column": 75
} | {
"line": 69,
"column": 75
} | [
{
"pp": "n m k : ℕ\n⊢ range' (k + n) (m - n) = range' (n + k) (m - n)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.range'",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"List",
"instHAdd",
"instH... | [
"n m k : ℕ\n⊢ range' (k + n) (m - n) = range' (k + n) (m - n)"
] | Nat.add_comm n k | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.ModifyLast | {
"line": 41,
"column": 30
} | {
"line": 41,
"column": 52
} | {
"line": 41,
"column": 53
} | [
{
"pp": "case cons\nα : Type u_1\nf : α → α\na head✝ : α\ntl : List α\n⊢ (#[].push head✝).toListAppend (modifyLast.go f (tl ++ [a]) #[]) = head✝ :: (tl ++ [f a])",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Array.toListAppend_eq",
"Array.push",
"congrA... | [
"case cons\nα : Type u_1\nf : α → α\na head✝ : α\ntl : List α\n⊢ (#[].push head✝).toList ++ modifyLast.go f (tl ++ [a]) #[] = head✝ :: (tl ++ [f a])"
] | Array.toListAppend_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Palindrome | {
"line": 66,
"column": 69
} | {
"line": 68,
"column": 38
} | {
"line": 70,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\n⊢ (l ++ l.reverse).Palindrome",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"List.Palindrome.of_reverse_eq",
"Eq.mpr",
"congrArg",
"id",
"instHAppendOfAppend",
"List",
"List.reverse_reverse",
"List.reverse"... | [] | by
apply of_reverse_eq
rw [reverse_append, reverse_reverse] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Lemmas | {
"line": 44,
"column": 8
} | {
"line": 44,
"column": 42
} | {
"line": 44,
"column": 43
} | [
{
"pp": "case cons.succ.succ.refine_1\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | [
"case cons.succ.succ.refine_1\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.length + 1\nn✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lemmas | {
"line": 45,
"column": 8
} | {
"line": 45,
"column": 42
} | {
"line": 45,
"column": 43
} | [
{
"pp": "case cons.succ.succ.refine_2\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | [
"case cons.succ.succ.refine_2\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.length + 1\nn✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Intervals | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 15
} | {
"line": 189,
"column": 16
} | [
{
"pp": "n m : ℕ\nhnm : n < m\nx✝¹ : ℕ\nx✝ : x✝¹ ∈ Ico n m\n⊢ decide (x✝¹ ≤ n) = decide (x✝¹ < n + 1)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Iff",
"HAdd.hAdd",
... | [
"n m : ℕ\nhnm : n < m\nx✝¹ : ℕ\nx✝ : x✝¹ ∈ Ico n m\n⊢ x✝¹ ≤ n ↔ x✝¹ < n + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 53,
"column": 46
} | {
"line": 53,
"column": 57
} | {
"line": 53,
"column": 58
} | [
{
"pp": "α : Type u_1\nl : List α\nsz : List ℕ\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nl : List α\nsz : List ℕ\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 26
} | {
"line": 68,
"column": 27
} | [
{
"pp": "case h\nα : Type u_1\nhead : ℕ\ntail : List ℕ\nih : ∀ (l : List α), l.length ≤ tail.sum → (tail.splitLengths l).flatten = l\nl : List α\nh : l.length ≤ (head :: tail).sum\n⊢ (drop head l).length ≤ tail.sum",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrAr... | [
"case h\nα : Type u_1\nhead : ℕ\ntail : List ℕ\nih : ∀ (l : List α), l.length ≤ tail.sum → (tail.splitLengths l).flatten = l\nl : List α\nh : l.length ≤ (head :: tail).sum\n⊢ l.length ≤ head + tail.sum"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 93,
"column": 46
} | {
"line": 93,
"column": 57
} | {
"line": 93,
"column": 58
} | [
{
"pp": "α✝ : Type u_1\nl✝ : List α✝\nsz✝ : List ℕ\nα : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α✝ : Type u_1\nl✝ : List α✝\nsz✝ : List ℕ\nα : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 15
} | {
"line": 97,
"column": 16
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : map length (sz.splitLengths l) = sz\n⊢ i < (map length (sz.splitLengths l)).length",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"α : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : map length (sz.splitLengths l) = sz\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 104,
"column": 23
} | {
"line": 104,
"column": 34
} | {
"line": 104,
"column": 35
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nb : ℕ\nh : ∀ (n : ℕ), n ∈ sz → n ≤ b\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : (sz.splitLengths l)[i].length ≤ sz[i]\n⊢ i < sz.length",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nl : List α\nsz : List ℕ\nb : ℕ\nh : ∀ (n : ℕ), n ∈ sz → n ≤ b\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : (sz.splitLengths l)[i].length ≤ sz[i]\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 29
} | {
"line": 62,
"column": 2
} | [
{
"pp": "α : Type u_1\nr : α → α → Bool\nl : List α\n⊢ splitBy r l = [] ↔ l = []",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"List.splitBy",
"List",
"List.flatten_splitBy",
"Eq",
"List.flatten"
],
"usedFVars": [
"α",
"r",
"l"
]... | [
"α : Type u_1\nr : α → α → Bool\nl : List α\nthis : (splitBy r l).flatten = l\n⊢ splitBy r l = [] ↔ l = []"
] | have := flatten_splitBy r l | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.List.SplitBy | {
"line": 76,
"column": 6
} | {
"line": 76,
"column": 17
} | {
"line": 76,
"column": 18
} | [
{
"pp": "case h_2\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH : ∀ {a : α} {g : List α}, ¬[] ∈ splitBy.loop r l a g []\na : α\ng : List α\nx✝ : Bool\nheq✝ : r a b = false\n⊢ ¬([] ∈ [(a :: g).reverse].reverse ∨ [] ∈ splitBy.loop r l b [] [])",
"ppTerm": "?h_2",
"assigned": true,
"usedConsta... | [
"case h_2\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH : ∀ {a : α} {g : List α}, ¬[] ∈ splitBy.loop r l a g []\na : α\ng : List α\nx✝ : Bool\nheq✝ : r a b = false\n⊢ ¬[] ∈ splitBy.loop r l b [] []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | {
"line": 134,
"column": 16
} | [
{
"pp": "case nil\nα : Type u_1\nr : α → α → Bool\na : α\ng : List α\ngs : List (List α)\nhgs' : ¬[] ∈ gs\nhgs : IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs\nhga : ∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = false\n⊢ IsChain (fun b a ↦ ∃ ha hb... | [
"case nil\nα : Type u_1\nr : α → α → Bool\na : α\ng : List α\ngs : List (List α)\nhgs' : ¬[] ∈ gs\nhgs : IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs\nhga : ∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = false\n⊢ IsChain (fun b a ↦ ∃ h hb, r (a.getLas... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 143,
"column": 8
} | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 20
} | [
{
"pp": "case h_2.hgs'\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH :\n ∀ {a : α} {g : List α} {gs : List (List α)},\n ¬[] ∈ gs →\n IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs →\n (∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).hea... | [
"case h_2.hgs'\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH :\n ∀ {a : α} {g : List α} {gs : List (List α)},\n ¬[] ∈ gs →\n IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs →\n (∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = fals... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 15
} | {
"line": 148,
"column": 16
} | [
{
"pp": "case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : Nonempty n\na : Matrix l m A\ninhabited_h : Inhabited n\ni : l\nj : m\nh : (mulLeftLinearMap n R a) (Ma... | [
"case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : Nonempty n\na : Matrix l m A\ninhabited_h : Inhabited n\ni : l\nj : m\nh : (mulLeftLinearMap n R a) (Matrix.single ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 159,
"column": 50
} | {
"line": 159,
"column": 73
} | {
"line": 159,
"column": 74
} | [
{
"pp": "m : Type u_2\nn✝ : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : SMulCommClass R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulLeftLinearMap n✝ R a ^ n * mulLeftLinearMap n✝ R a = mulLeftLinearMap n✝ R (a ... | [
"m : Type u_2\nn✝ : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : SMulCommClass R A A\na : Matrix m m A\nk n : ℕ\n⊢ (mulLeftLinearMap n✝ R a ^ n) ∘ₗ mulLeftLinearMap n✝ R a = mulLeftLinearMap n✝ R (a ^ n) ∘ₗ m... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 15
} | {
"line": 181,
"column": 16
} | [
{
"pp": "case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\na : Matrix m n A\ninst✝ : Nonempty l\ninhabited_h : Inhabited l\ni : m\nj : n\nh : (mulRightLinearMap l R a) (M... | [
"case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\na : Matrix m n A\ninst✝ : Nonempty l\ninhabited_h : Inhabited l\ni : m\nj : n\nh : (mulRightLinearMap l R a) (Matrix.single... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 192,
"column": 52
} | {
"line": 192,
"column": 75
} | {
"line": 192,
"column": 76
} | [
{
"pp": "l : Type u_1\nm : Type u_2\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulRightLinearMap l R a ^ n * mulRightLinearMap l R a = mulRightLinearMap l R (a ^... | [
"l : Type u_1\nm : Type u_2\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R A A\na : Matrix m m A\nk n : ℕ\n⊢ (mulRightLinearMap l R a ^ n) ∘ₗ mulRightLinearMap l R a = mulRightLinearMap l R (a ^ n) ∘ₗ mu... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 38
} | {
"line": 60,
"column": 39
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝ : Preorder α\nX₁ Y₁ Z₁ : Multiset α\nhYZ₁ : ∀ (y : α), y ∈ Y₁ → ∃ z, z ∈ Z₁ ∧ y < z\nX₂ Y₂ Z₂ : Multiset α\nhZ₂ : Z₂ ≠ ∅\nhXZXY : Z₁ + X₁ = Y₂ + X₂\nhYZ₂ : ∀ (y : α), y ∈ Y₂ → ∃ z, z ∈ Z₂ ∧ y < z\n⊢ Z₂ + (Z₁ - Y₂) ≠ ∅",
"ppTerm": "?refine_1",
"assigned": true,... | [
"case refine_1\nα : Type u_1\ninst✝ : Preorder α\nX₁ Y₁ Z₁ : Multiset α\nhYZ₁ : ∀ (y : α), y ∈ Y₁ → ∃ z, z ∈ Z₁ ∧ y < z\nX₂ Y₂ Z₂ : Multiset α\nhZ₂ : Z₂ ≠ ∅\nhXZXY : Z₁ + X₁ = Y₂ + X₂\nhYZ₂ : ∀ (y : α), y ∈ Y₂ → ∃ z, z ∈ Z₂ ∧ y < z\n⊢ ¬Z₂ = 0 ∨ ¬Z₁ - Y₂ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 93,
"column": 4
} | {
"line": 93,
"column": 56
} | {
"line": 93,
"column": 57
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nh0 : a ::ₘ M = X + {a}\nh2 : ∀ (y : α), y ∈ Y → y < a\n⊢ X + Y = M + Y",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PartialOrder.toPreorder",
"instIsRightCancelAddOf... | [
"case inl\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nh0 : a ::ₘ M = X + {a}\nh2 : ∀ (y : α), y ∈ Y → y < a\n⊢ M = X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 21
} | {
"line": 99,
"column": 22
} | [
{
"pp": "case inr.refine_1\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : M + {a} = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : a ∈ X + {b}\n⊢ {a} ≤ X",
"ppTerm": "?inr.refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Par... | [
"case inr.refine_1\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : M + {a} = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : a ∈ X + {b}\n⊢ a ∈ X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 102,
"column": 4
} | {
"line": 102,
"column": 26
} | {
"line": 102,
"column": 27
} | [
{
"pp": "case inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : a ::ₘ M = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : b ∈ a ::ₘ M\n⊢ {b} ≤ M",
"ppTerm": "?inr.refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Par... | [
"case inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : a ::ₘ M = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : b ∈ a ::ₘ M\n⊢ b ∈ M"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 15
} | {
"line": 115,
"column": 16
} | [
{
"pp": "case intro.intro.inr.empty\nα : Type u_1\ninst✝ : Preorder α\na✝ a : α\nh✝ : ∀ (y : α), y < a → Acc LT.lt y\nha : ∀ (y : α), y < a → ∀ {M : Multiset α}, Acc OneStep M → Acc OneStep (y ::ₘ M)\nM✝ M : Multiset α\nhM : ∀ (y : Multiset α), y.OneStep M → Acc OneStep y\nihM : ∀ (y : Multiset α), y.OneStep M ... | [
"case intro.intro.inr.empty\nα : Type u_1\ninst✝ : Preorder α\na✝ a : α\nh✝ : ∀ (y : α), y < a → Acc LT.lt y\nha : ∀ (y : α), y < a → ∀ {M : Multiset α}, Acc OneStep M → Acc OneStep (y ::ₘ M)\nM✝ M : Multiset α\nhM : ∀ (y : Multiset α), y.OneStep M → Acc OneStep y\nihM : ∀ (y : Multiset α), y.OneStep M → Acc OneSte... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 145,
"column": 39
} | {
"line": 145,
"column": 50
} | {
"line": 145,
"column": 51
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nz : α\nM N X Y : Multiset α\nhM : M = X + Y\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n 0 ≠ ∅ → M = X + Y → N = X + 0 → (∀ (y : α), y ∈ Y → ∃ z, z ∈ 0 ∧ y < z) → TransGen OneStep M N\nhZ : z ::ₘ 0 ≠ ∅\nhN : N = X + z ::ₘ 0\nhYZ : ∀ (y : α), y ∈ Y → ∃ z_1, z_... | [
"α : Type u_1\ninst✝ : Preorder α\nz : α\nM N X Y : Multiset α\nhM : M = X + Y\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n 0 ≠ ∅ → M = X + Y → N = X + 0 → (∀ (y : α), y ∈ Y → ∃ z, z ∈ 0 ∧ y < z) → TransGen OneStep M N\nhZ : z ::ₘ 0 ≠ ∅\nhN : N = X + z ::ₘ 0\nhYZ : ∀ (y : α), y ∈ Y → ∃ z_1, z_1 ∈ z ::ₘ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 41
} | {
"line": 147,
"column": 2
} | [
{
"pp": "case cons.inr\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhY... | [
"case cons.inr\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhYZ : ∀ (y : α... | let Y' : Multiset α := Y.filter (· < z) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 22
} | {
"line": 151,
"column": 23
} | [
{
"pp": "case cons.inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ... | [
"case cons.inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhYZ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Floor | {
"line": 37,
"column": 23
} | {
"line": 37,
"column": 34
} | {
"line": 37,
"column": 35
} | [
{
"pp": "a✝ : ℚ≥0\nh : a✝ < 0\n⊢ ⌊↑a✝⌋₊ = 0",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"Nat.floor_eq_zero._simp_1",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"FloorRing.toFloorSemiring",
"NNRat.inst... | [
"a✝ : ℚ≥0\nh : a✝ < 0\n⊢ a✝ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 35,
"column": 12
} | {
"line": 35,
"column": 23
} | {
"line": 35,
"column": 24
} | [
{
"pp": "case zero\nA : Type u_1\ninst✝ : Semiring A\nm : ℕ\nhn_fac : IsUnit ↑(m + 0)!\n⊢ IsUnit ↑m !",
"ppTerm": "?zero",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case zero\nA : Type u_1\ninst✝ : Semiring A\nm : ℕ\nhn_fac : IsUnit ↑(m + 0)!\n⊢ IsUnit ↑m !"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 50,
"column": 4
} | {
"line": 50,
"column": 15
} | {
"line": 50,
"column": 16
} | [
{
"pp": "A : Type u_1\ninst✝³ : Semiring A\nK : Type u_2\ninst✝² : Semifield K\ninst✝¹ : CharZero K\ninst✝ : Algebra K A\nn : ℕ\nthis : IsUnit ↑n !\n⊢ IsUnit ↑n !",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\ninst✝³ : Semiring A\nK : Type u_2\ninst✝² : Semifield K\ninst✝¹ : CharZero K\ninst✝ : Algebra K A\nn : ℕ\nthis : IsUnit ↑n !\n⊢ IsUnit ↑n !"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 20
} | {
"line": 83,
"column": 21
} | [
{
"pp": "A : Type u_1\ninst✝ : CommRing A\nn p : ℕ\nh✝ : p.Coprime n\nm : ℕ\nhm : ↑p ^ m = 0\na b : A\nh : ↑p ^ m * a + ↑n * b = 1\n⊢ ↑n * b = 1",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\ninst✝ : CommRing A\nn p : ℕ\nh✝ : p.Coprime n\nm : ℕ\nhm : ↑p ^ m = 0\na b : A\nh : ↑p ^ m * a + ↑n * b = 1\n⊢ ↑n * b = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 128,
"column": 16
} | {
"line": 128,
"column": 55
} | {
"line": 128,
"column": 56
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nl l' : List ι\nhl : l.Perm l'\nhs : ∀ i ∈ l, s i ≠ 0\nco : List.Pairwise (Coprime on s) l\nz : { k // ∀ i ∈ l', k ≡ a i [MOD s i] } := chineseRemainderOfList a s l' ⋯\nhlp : (List.map s l).prod = (List.map s l').prod\n⊢ ∀ i ∈ l', s i ≠ 0",
"ppTerm": "?m.90",
"assigned... | [
"ι : Type u_1\na s : ι → ℕ\nl l' : List ι\nhl : l.Perm l'\nhs : ∀ i ∈ l, s i ≠ 0\nco : List.Pairwise (Coprime on s) l\nz : { k // ∀ i ∈ l', k ≡ a i [MOD s i] } := chineseRemainderOfList a s l' ⋯\nhlp : (List.map s l).prod = (List.map s l').prod\n⊢ ∀ i ∈ l, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 142,
"column": 39
} | {
"line": 142,
"column": 73
} | {
"line": 142,
"column": 74
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\n⊢ ∀ i ∈ l, s i ≠ 0",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"id",
"Ne",
"instOfNatNa... | [
"ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\n⊢ ∀ i ∈ l', ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 144,
"column": 62
} | {
"line": 144,
"column": 96
} | {
"line": 144,
"column": 97
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\n⊢ {x | x ∈ l}.Pairwise (Coprime on s)",
"ppTerm": "?m.178",
"assigned": true,
"usedConstants"... | [
"ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\n⊢ {x | x ∈ l'}.Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 151,
"column": 50
} | {
"line": 152,
"column": 33
} | {
"line": 153,
"column": 6
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\nco : {x | x ∈ l}.Pairwise (Coprime on s)\nlco : List.Pairwise (Coprime on s) l\n⊢ ∀ {m' : Multiset ι} {e ... | [] | by
rintro _ rfl _ _ _; rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 42,
"column": 4
} | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 16
} | [
{
"pp": "n k p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ (X + 1) ^ n = (X + 1) ^ (n % p) * (X ^ p + 1) ^ (n / p)",
"ppTerm": "?m.84",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n k p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ (X + 1) ^ n = (X + 1) ^ (n % p) * (X ^ p + 1) ^ (n / p)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 13
} | {
"line": 168,
"column": 14
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ { k // ∀ i ∈ t, k ≡ a i [MOD s i] }",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ { k // ∀ i ∈ t, k ≡ a i [MOD s i] }"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 57
} | {
"line": 168,
"column": 68
} | {
"line": 168,
"column": 69
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t.val, s i ≠ 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Membership.mem",
"Multiset",
"id",
"Ne",
"instOfNatNat",
"Finset.val",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 77
} | {
"line": 168,
"column": 88
} | {
"line": 168,
"column": 89
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ {x | x ∈ t.val}.Pairwise (Coprime on s)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"Function.onFun",
"Set.ofPred",
"Membership.mem",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ (↑t).Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 40
} | {
"line": 174,
"column": 4
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ↑(chineseRemainderOfFinset a s t hs pp) < ∏ i ∈ t, s i",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Finset",
"Membership.mem",
"id",
"Finset.prod",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ↑(chineseRemainderOfMultiset a s ⋯ ⋯ ⋯) < ∏ i ∈ t, s i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 174,
"column": 55
} | {
"line": 174,
"column": 66
} | {
"line": 174,
"column": 67
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t.val, s i ≠ 0",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Membership.mem",
"Multiset",
"id",
"Ne",
"instOfNatNat",
"Finset.val",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 174,
"column": 75
} | {
"line": 174,
"column": 86
} | {
"line": 174,
"column": 87
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ {x | x ∈ t.val}.Pairwise (Coprime on s)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"Function.onFun",
"Set.ofPred",
"Membership.mem",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ (↑t).Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.Root | {
"line": 69,
"column": 83
} | {
"line": 70,
"column": 69
} | {
"line": 72,
"column": 0
} | [
{
"pp": "n : ℕ\nhn : n ≠ 0\na : ℕ\n⊢ n.floorRoot (a ^ n) = a",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"instPowNat",
"Finsupp.instPosSMulReflectLE",
"Eq.mpr",
"Finsupp.smulZeroClass",
"Finsupp.instFloorDiv",
"False",
"Nat.inst... | [] | by
simp [floorRoot_def, pos_iff_ne_zero.2, hn]; split_ifs <;> simp [*] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Factorization.Root | {
"line": 145,
"column": 40
} | {
"line": 145,
"column": 51
} | {
"line": 145,
"column": 52
} | [
{
"pp": "n a : ℕ\nh : ¬(n = 0 ∨ a = 0)\np : ℕ\nhp : p ∈ (a.factorization ⌈/⌉ n).support\n⊢ Prime p ∧ p ∣ a ∧ ¬a = 0",
"ppTerm": "?m.60",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n a : ℕ\nh : ¬(n = 0 ∨ a = 0)\np : ℕ\nhp : p ∈ (a.factorization ⌈/⌉ n).support\n⊢ Prime p ∧ p ∣ a ∧ ¬a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 69,
"column": 22
} | {
"line": 69,
"column": 70
} | {
"line": 69,
"column": 70
} | [
{
"pp": "n a : ℕ\nl : List ℕ\nhn : ∀ a_1 ∈ (a :: l ++ [0]).head?, a_1 < n\nthis : ∀ b ∈ (l ++ [0]).head?, b < a - 1\nhl : ((∀ x ∈ l, x + 2 ≤ a) ∧ 2 ≤ a) ∧ IsChain (fun a b ↦ b + 2 ≤ a) (l ++ [0])\n⊢ fib (a - 1) + fib a ≤ fib n",
"ppTerm": "?m.179",
"assigned": true,
"usedConstants": [
"Eq.mpr"... | [
"n a : ℕ\nl : List ℕ\nhn : ∀ a_1 ∈ (a :: l ++ [0]).head?, a_1 < n\nthis : ∀ b ∈ (l ++ [0]).head?, b < a - 1\nhl : ((∀ x ∈ l, x + 2 ≤ a) ∧ 2 ≤ a) ∧ IsChain (fun a b ↦ b + 2 ≤ a) (l ++ [0])\n⊢ fib (a + 1) ≤ fib n"
] | ← fib_add_one (hl.1.2.trans_lt' zero_lt_two).ne' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 101,
"column": 14
} | {
"line": 101,
"column": 25
} | {
"line": 101,
"column": 26
} | [
{
"pp": "n : ℕ\nh : n.greatestFib = 0\n⊢ n = 0",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nh : n.greatestFib = 0\n⊢ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 52
} | {
"line": 113,
"column": 53
} | [
{
"pp": "n : ℕ\nhn : n ≠ 0\n⊢ n.greatestFib - 1 ≠ 0",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instOrderedSub",
"Preorder.toLT",
"congrArg",
"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_... | [
"n : ℕ\nhn : n ≠ 0\n⊢ 1 ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 25
} | {
"line": 148,
"column": 26
} | [
{
"pp": "n p : ℕ\nhp : Fact (Nat.Prime p)\nhn : 0 < n\nhn₀ : n ≠ p ^ multiplicity p n\nm : ℕ\nh : ↑m ≡ 0 [ZMOD ↑p]\nhm : n = p ^ multiplicity p n * m\n⊢ p ^ (multiplicity p n + 1) ∣ p ^ multiplicity p n * m",
"ppTerm": "?m.151",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.t... | [
"n p : ℕ\nhp : Fact (Nat.Prime p)\nhn : 0 < n\nhn₀ : n ≠ p ^ multiplicity p n\nm : ℕ\nh : ↑m ≡ 0 [ZMOD ↑p]\nhm : n = p ^ multiplicity p n * m\n⊢ p ^ multiplicity p n * p ∣ p ^ multiplicity p n * m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 15
} | {
"line": 210,
"column": 16
} | [
{
"pp": "n : ℕ\nh : IsPrimePow n\nne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0\nisPrime : Nat.Prime n.minFac\n⊢ n.minFac ^ 1 ∣ (Icc 1 (n - 1)).gcd n.choose",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"Nat.choose",
"congrArg",
"Nat.instMo... | [
"n : ℕ\nh : IsPrimePow n\nne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0\nisPrime : Nat.Prime n.minFac\n⊢ n.minFac ∣ (Icc 1 (n - 1)).gcd n.choose"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 204,
"column": 47
} | {
"line": 212,
"column": 66
} | {
"line": 214,
"column": 0
} | [
{
"pp": "n : ℕ\nh : IsPrimePow n\n⊢ (Icc 1 (n - 1)).gcd n.choose = n.minFac",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finsupp.instFunLike",
"Nat.multiplicity_eq_factorization",
"Eq.mpr",
"Inhabited.default",
"Nat.instMulZeroClass",
... | [] | by
have ne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0 :=
gcd_ne_zero_iff.mpr ⟨1, by simp; grind [IsPrimePow.two_le h]⟩
have isPrime := minFac_prime_iff.mpr (IsPrimePow.ne_one h)
have : multiplicity n.minFac ((Icc 1 (n - 1)).gcd n.choose) = 1 := by
refine multiplicity_eq_of_dvd_of_not_dvd ?_ (minFac_sq_ndvd_g... | [anonymous] | Lean.Parser.Term.byTactic |
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