module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Data.Ordmap.Ordset | {
"line": 533,
"column": 4
} | {
"line": 533,
"column": 79
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableLE α\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ insert' x (node size✝ l y r) = insertWith id x (node size✝ l y r)",
"usedConstants": [
"Ordnode.insertWith",
"Ordering.gt",
"Eq.mpr",
"Ordnode.insertWith.eq_def... | unfold insert' insertWith; cases cmpLE x y <;> simp [insert'_eq_insertWith] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Sigma | {
"line": 72,
"column": 16
} | {
"line": 72,
"column": 70
} | [
{
"pp": "n : ℕ\nA : Type u\nF : A → TypeVec.{u} n → Type u\ninst✝ : (α : A) → MvQPF (F α)\nα β : TypeVec.{u} n\nf : α ⟹ β\nx : (Sigma.P F).A\ng : (Sigma.P F).B x ⟹ α\n⊢ ⟨x.fst, abs ⟨x.snd, f ⊚ g⟩⟩ = f <$$> ⟨x.fst, abs ⟨x.snd, g⟩⟩",
"usedConstants": [
"MvQPF.Sigma.instMvFunctor",
"congrArg",
... | simp only [(· <$$> ·), ← abs_map, ← MvPFunctor.map_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 395,
"column": 2
} | {
"line": 396,
"column": 49
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nι : Type u\nR : ι → ι → Prop\nx : F (α ::: ι)\nf : ι → ι\nhh : ∀ (x : ι), R (f x) x\n⊢ LiftR' (α.RelLast' R) ((TypeVec.id ::: f) <$$> x) x",
"usedConstants": [
"congrArg",
"TypeVec.RelLas... | have := liftR_map_last R x f id hh
rwa [appendFun_id_id, MvFunctor.id_map] at this | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 395,
"column": 2
} | {
"line": 396,
"column": 49
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nι : Type u\nR : ι → ι → Prop\nx : F (α ::: ι)\nf : ι → ι\nhh : ∀ (x : ι), R (f x) x\n⊢ LiftR' (α.RelLast' R) ((TypeVec.id ::: f) <$$> x) x",
"usedConstants": [
"congrArg",
"TypeVec.RelLas... | have := liftR_map_last R x f id hh
rwa [appendFun_id_id, MvFunctor.id_map] at this | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 490,
"column": 2
} | {
"line": 490,
"column": 45
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nX Y : Type u\nx₀ : X\nf : X → Y\ng : Y → F (α ::: X)\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦ ∃ x, a = Cofix.corec (g ∘ f) x ∧ b = Cofix.corec (MvFunctor.map (TypeVec.id ::: f) ∘ g) (f x)\na b : Cofix F α\nx : X\nHa : a =... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 503,
"column": 11
} | {
"line": 503,
"column": 54
} | [
{
"pp": "case h.e'_6.h.e'_7.h.inl\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : β → F (α ::: (Cofix F α ⊕ β))\nx✝ : β\ni : Cofix F α\nR : Cofix F α → Cofix F α → Prop :=\n fun a b ↦\n ∃ x,\n a =\n corec\n (MvFunctor.map (TypeVec.id ::: fun... | rw [MvFunctor.map_map, ← appendFun_comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Enumerate | {
"line": 85,
"column": 6
} | {
"line": 85,
"column": 14
} | [
{
"pp": "case zero.succ\nα : Type u_1\nsel : Set α → Option α\na : α\nh_sel : ∀ (s : Set α) (a : α), sel s = some a → a ∈ s\ns : Set α\nh₁ : enumerate sel s 0 = some a\nm : ℕ\nh₂ : enumerate sel s (0 + (m + 1)) = some a\nh' : enumerate sel (s \\ {a}) m = some a\nthis : a ∈ s \\ {a}\n⊢ 0 = 0 + (m + 1)",
"use... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.WSeq.Relation | {
"line": 227,
"column": 28
} | {
"line": 227,
"column": 48
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\ns : WSeq α\nt : WSeq β\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) s.think.destruct t.destruct ↔ LiftRel R s t",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Stream'.WSeq.destruct",
"id",
"Stream'.WSeq.LiftRel",
"Stream'... | liftRel_destruct_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.WSeq.Relation | {
"line": 231,
"column": 28
} | {
"line": 231,
"column": 48
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\ns : WSeq α\nt : WSeq β\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) s.destruct t.think.destruct ↔ LiftRel R s t",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Stream'.WSeq.destruct",
"id",
"Stream'.WSeq.LiftRel",
"Stream'... | liftRel_destruct_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.WSeq.Basic | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 65
} | [
{
"pp": "α : Type u\na a' : α\ns' : WSeq α\nc : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c\n⊢ ∀ {s : WSeq α}, s.destruct = c → (a ∈ s ↔ a = a' ∨ a ∈ s')",
"usedConstants": [
"Computation.memRecOn",
"Stream'.WSeq.destruct",
"Option.some",
"Membership.mem",
"Prod.mk... | apply Computation.memRecOn h <;> [skip; intro c IH] <;> intro s | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h1.nil\nα : Type u\na a' : α\ns' : WSeq α\nc : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c\nm : nil.destruct = Computation.pure (some (a', s'))\n⊢ a ∈ nil ↔ a = a' ∨ a ∈ s'",
"usedConstants": [
"Stream'.WSeq.destruct",
"Option.some",
"Sum",
"Computation.des... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h1.cons\nα : Type u\na a' : α\ns' : WSeq α\nc : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c\nx✝ : α\ns✝ : WSeq α\nm : (cons x✝ s✝).destruct = Computation.pure (some (a', s'))\n⊢ a ∈ cons x✝ s✝ ↔ a = a' ∨ a ∈ s'",
"usedConstants": [
"Stream'.WSeq.destruct",
"Stream'.WSe... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h1.think\nα : Type u\na a' : α\ns' : WSeq α\nc : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c\ns✝ : WSeq α\nm : s✝.think.destruct = Computation.pure (some (a', s'))\n⊢ a ∈ s✝.think ↔ a = a' ∨ a ∈ s'",
"usedConstants": [
"Stream'.WSeq.destruct",
"Option.some",
"Sum... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h2.nil\nα : Type u\na a' : α\ns' : WSeq α\nc✝ : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c✝\nc : Computation (Option (α × WSeq α))\nIH : ∀ {s : WSeq α}, s.destruct = c → (a ∈ s ↔ a = a' ∨ a ∈ s')\nm : nil.destruct = c.think\n⊢ a ∈ nil ↔ a = a' ∨ a ∈ s'",
"usedConstants": [
... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h2.cons\nα : Type u\na a' : α\ns' : WSeq α\nc✝ : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c✝\nc : Computation (Option (α × WSeq α))\nIH : ∀ {s : WSeq α}, s.destruct = c → (a ∈ s ↔ a = a' ∨ a ∈ s')\nx✝ : α\ns✝ : WSeq α\nm : (cons x✝ s✝).destruct = c.think\n⊢ a ∈ cons x✝ s✝ ↔ a = a' ∨ ... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 432,
"column": 4
} | {
"line": 432,
"column": 44
} | [
{
"pp": "case h2.think\nα : Type u\na a' : α\ns' : WSeq α\nc✝ : Computation (Option (α × WSeq α))\nh : some (a', s') ∈ c✝\nc : Computation (Option (α × WSeq α))\nIH : ∀ {s : WSeq α}, s.destruct = c → (a ∈ s ↔ a = a' ∨ a ∈ s')\ns✝ : WSeq α\nm : s✝.think.destruct = c.think\n⊢ a ∈ s✝.think ↔ a = a' ∨ a ∈ s'",
... | have := congr_arg Computation.destruct m | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.WSeq.Basic | {
"line": 534,
"column": 4
} | {
"line": 534,
"column": 21
} | [
{
"pp": "case some\nα : Type u\nβ : Type v\nf : α → β\nb : β\ng : Stream' (Option (Option α))\nal : g.IsSeq\nh : b ∈ map f ⟨g, al⟩\na : α\nom : some a ∈ ⟨g, al⟩\nh' : f a = b\n⊢ ∃ a ∈ ⟨g, al⟩, f a = b",
"usedConstants": [
"Membership.mem",
"Subtype.mk",
"Stream'",
"And",
"Strea... | exact ⟨a, om, h'⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.WSeq.Basic | {
"line": 604,
"column": 2
} | {
"line": 604,
"column": 18
} | [
{
"pp": "case nil\nα : Type u\nl : List α\ns : WSeq α\ns1 s2 : Computation (List α)\nl' : List α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (l, s) =>\n match Seq.destruct s with\n | none => Sum.inl l.reverse\n | some (none, s') =... | case nil => simp | Lean.Elab.Tactic.evalCase | Lean.Parser.Tactic.case |
Mathlib.Data.WSeq.Basic | {
"line": 699,
"column": 4
} | {
"line": 701,
"column": 31
} | [
{
"pp": "case h1\nα : Type u\na : α\nss✝ : WSeq α\nh : a ∈ ss✝\nb : α\nss : WSeq α\no : a = b ∨ ∀ (s : WSeq α) (S : WSeq (WSeq α)), s.append S.join = ss → a ∈ s.append S.join → a ∈ s ∨ ∃ s ∈ S, a ∈ s\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ s.append S.join = cons b ss → a ∈ s.append S.join → a ∈ s ∨ ∃ s ∈ S, a ∈ s",
... | induction s using WSeq.recOn <;>
[induction S using WSeq.recOn; skip; skip] <;>
intro ej m <;> simp at ej | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.WSeq.Basic | {
"line": 711,
"column": 4
} | {
"line": 713,
"column": 31
} | [
{
"pp": "case h2\nα : Type u\na : α\nss✝ : WSeq α\nh : a ∈ ss✝\nss : WSeq α\nIH : ∀ (s : WSeq α) (S : WSeq (WSeq α)), s.append S.join = ss → a ∈ s.append S.join → a ∈ s ∨ ∃ s ∈ S, a ∈ s\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ s.append S.join = ss.think → a ∈ s.append S.join → a ∈ s ∨ ∃ s ∈ S, a ∈ s",
"usedConstan... | induction s using WSeq.recOn <;>
[induction S using WSeq.recOn; skip; skip] <;>
intro ej m <;> simp at ej | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Seq.Parallel | {
"line": 224,
"column": 5
} | {
"line": 224,
"column": 25
} | [
{
"pp": "case h1.inl\nα : Type u\nS✝ : WSeq (Computation α)\na : α\nh : a ∈ parallel S✝\nF : List (Computation α) → α ⊕ List (Computation α) → Prop :=\n fun l a ↦ Sum.casesOn a (fun a ↦ ∃ c ∈ l, a ∈ c) fun l' ↦ ∀ (a' : α), (∃ c ∈ l', a' ∈ c) → ∃ c ∈ l, a' ∈ c\nlem1 : ∀ (l : List (Computation α)), F l (parallel... | injection e' with h' | Lean.Elab.Tactic.evalInjection | Lean.Parser.Tactic.injection |
Mathlib.Data.Seq.Parallel | {
"line": 224,
"column": 55
} | {
"line": 224,
"column": 75
} | [
{
"pp": "case h2.inr\nα : Type u\nS✝ : WSeq (Computation α)\na : α\nh : a ∈ parallel S✝\nF : List (Computation α) → α ⊕ List (Computation α) → Prop :=\n fun l a ↦ Sum.casesOn a (fun a ↦ ∃ c ∈ l, a ∈ c) fun l' ↦ ∀ (a' : α), (∃ c ∈ l', a' ∈ c) → ∃ c ∈ l, a' ∈ c\nlem1 : ∀ (l : List (Computation α)), F l (parallel... | injection e' with h' | Lean.Elab.Tactic.evalInjection | Lean.Parser.Tactic.injection |
Mathlib.Data.Tree.Traversable | {
"line": 46,
"column": 11
} | {
"line": 46,
"column": 29
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nf : α → β\n⊢ traverse (pure ∘ f) nil = pure (map f nil)",
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Tree.map.eq_1",
"Tree.traverse.eq_1",
"Monad.toApplicative",
"Function.comp",
"Tree.nil",
"id"... | rw [traverse, map] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Tree.Traversable | {
"line": 46,
"column": 11
} | {
"line": 46,
"column": 29
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nf : α → β\n⊢ traverse (pure ∘ f) nil = pure (map f nil)",
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Tree.map.eq_1",
"Tree.traverse.eq_1",
"Monad.toApplicative",
"Function.comp",
"Tree.nil",
"id"... | rw [traverse, map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Tree.Traversable | {
"line": 46,
"column": 11
} | {
"line": 46,
"column": 29
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nf : α → β\n⊢ traverse (pure ∘ f) nil = pure (map f nil)",
"usedConstants": [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Tree.map.eq_1",
"Tree.traverse.eq_1",
"Monad.toApplicative",
"Function.comp",
"Tree.nil",
"id"... | rw [traverse, map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.Snoc | {
"line": 128,
"column": 19
} | {
"line": 128,
"column": 27
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nn : ℕ\nx : α\nxs : Vector α n\nf : α → β\n⊢ map f (nil.snoc x) = (map f nil).snoc (f x)",
"usedConstants": [
"List.Vector.map_cons",
"congrArg",
"List.Vector.map",
"List.Vector",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.Snoc | {
"line": 128,
"column": 19
} | {
"line": 128,
"column": 27
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nn : ℕ\nx : α\nxs : Vector α n\nf : α → β\nn✝ : ℕ\nx✝ : α\nw✝ : Vector α n✝\na✝ : map f (w✝.snoc x) = (map f w✝).snoc (f x)\n⊢ map f ((x✝ ::ᵥ w✝).snoc x) = (map f (x✝ ::ᵥ w✝)).snoc (f x)",
"usedConstants": [
"List.Vector.map_cons",
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.Snoc | {
"line": 149,
"column": 49
} | {
"line": 149,
"column": 57
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nσ : Type u_3\nn : ℕ\nx : α\nxs : Vector α n\nys : Vector β n\nf : α → β → σ\ny : β\n⊢ map₂ f (nil.snoc x) (nil.snoc y) = (map₂ f nil nil).snoc (f x y)",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
"of_eq_tru... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.Snoc | {
"line": 149,
"column": 49
} | {
"line": 149,
"column": 57
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nσ : Type u_3\nn : ℕ\nx : α\nxs : Vector α n\nys : Vector β n\nf : α → β → σ\ny : β\nn✝ : ℕ\na✝¹ : α\nb✝ : β\nx✝ : Vector α n✝\ny✝ : Vector β n✝\na✝ : map₂ f (x✝.snoc x) (y✝.snoc y) = (map₂ f x✝ y✝).snoc (f x y)\n⊢ map₂ f ((a✝¹ ::ᵥ x✝).snoc x) ((b✝ ::ᵥ y✝).snoc y) ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.Snoc | {
"line": 162,
"column": 49
} | {
"line": 162,
"column": 57
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nσ : Type u_3\nφ : Type u_4\nn : ℕ\ns : σ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × φ\nx : α\ny : β\n⊢ mapAccumr₂ f (nil.snoc x) (nil.snoc y) s =\n let q := f x y s;\n let r := mapAccumr₂ f nil nil q.1;\n (r.1, r.2.snoc q.2)",
"usedConstant... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.Snoc | {
"line": 162,
"column": 49
} | {
"line": 162,
"column": 57
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nσ : Type u_3\nφ : Type u_4\nn : ℕ\ns : σ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × φ\nx : α\ny : β\nn✝ : ℕ\na✝¹ : α\nb✝ : β\nx✝ : Vector α n✝\ny✝ : Vector β n✝\na✝ :\n mapAccumr₂ f (x✝.snoc x) (y✝.snoc y) s =\n let q := f x y s;\n let r := mapA... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 39,
"column": 66
} | {
"line": 39,
"column": 74
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : β → σ₁ → σ₁ × γ\nf₂ : α → σ₂ → σ₂ × β\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr f₁ (mapAccumr f₂ nil s₂).2 s₁ =\n let m :=\n mapAccumr\n (fun x s ↦\n let r₂ := f₂ x s.2;\n let r₁ := f₁ r₂... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 39,
"column": 66
} | {
"line": 39,
"column": 74
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : β → σ₁ → σ₁ × γ\nf₂ : α → σ₂ → σ₂ × β\nn✝ : ℕ\nxs✝ : Vector α n✝\nx✝ : α\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr f₁ (mapAccumr f₂ xs✝ s₂).2 s₁ =\n let m :=\n mapAccumr\n (fun x s ↦... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 44,
"column": 62
} | {
"line": 44,
"column": 70
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nn : ℕ\nxs : Vector α n\nf₁ : β → σ₁ → σ₁ × γ\nf₂ : α → β\ns : σ₁\n⊢ mapAccumr f₁ (map f₂ nil) s = mapAccumr (fun x s ↦ f₁ (f₂ x) s) nil s",
"usedConstants": [
"List.Vector",
"Prod.mk",
"instOfNatNat",
"Nat",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 44,
"column": 62
} | {
"line": 44,
"column": 70
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nn : ℕ\nxs : Vector α n\nf₁ : β → σ₁ → σ₁ × γ\nf₂ : α → β\nn✝ : ℕ\nxs✝ : Vector α n✝\nx✝ : α\na✝ : ∀ {s : σ₁}, mapAccumr f₁ (map f₂ xs✝) s = mapAccumr (fun x s ↦ f₁ (f₂ x) s) xs✝ s\ns : σ₁\n⊢ mapAccumr f₁ (map f₂ (xs✝.snoc x✝)) s = mapA... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 51,
"column": 62
} | {
"line": 51,
"column": 70
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₂ : Type u_7\nn : ℕ\nxs : Vector α n\nf₂ : α → σ₂ → σ₂ × β\nf₁ : β → γ\ns : σ₂\n⊢ map f₁ (mapAccumr f₂ nil s).2 =\n (mapAccumr\n (fun x s ↦\n let r := f₂ x s;\n (r.1, f₁ r.2))\n nil s).2",
"usedConstants": [
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 51,
"column": 62
} | {
"line": 51,
"column": 70
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₂ : Type u_7\nn : ℕ\nxs : Vector α n\nf₂ : α → σ₂ → σ₂ × β\nf₁ : β → γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nx✝ : α\na✝ :\n ∀ {s : σ₂},\n map f₁ (mapAccumr f₂ xs✝ s).2 =\n (mapAccumr\n (fun x s ↦\n let r := f₂ x s;\n (r... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 56,
"column": 19
} | {
"line": 56,
"column": 27
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\nf₁ : β → γ\nf₂ : α → β\n⊢ map f₁ (map f₂ nil) = map (fun x ↦ f₁ (f₂ x)) nil",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
"of_eq_true",
"List.Vector.nil",
"O... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 56,
"column": 19
} | {
"line": 56,
"column": 27
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\nf₁ : β → γ\nf₂ : α → β\nn✝ : ℕ\nx✝ : α\nw✝ : Vector α n✝\na✝ : map f₁ (map f₂ w✝) = map (fun x ↦ f₁ (f₂ x)) w✝\n⊢ map f₁ (map f₂ (x✝ ::ᵥ w✝)) = map (fun x ↦ f₁ (f₂ x)) (x✝ ::ᵥ w✝)",
"usedConstants": [
"List.Vector.ma... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 60,
"column": 19
} | {
"line": 60,
"column": 27
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\np : α → Prop\nf₁ : β → γ\nf₂ : (a : α) → p a → β\nH : ∀ (x : α), x ∈ nil.toList → p x\n⊢ map f₁ (pmap f₂ nil H) = pmap (fun x hx ↦ f₁ (f₂ x hx)) nil H",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"N... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 60,
"column": 19
} | {
"line": 60,
"column": 27
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\np : α → Prop\nf₁ : β → γ\nf₂ : (a : α) → p a → β\nn✝ : ℕ\nx✝ : α\nw✝ : Vector α n✝\na✝ : ∀ (H : ∀ (x : α), x ∈ w✝.toList → p x), map f₁ (pmap f₂ w✝ H) = pmap (fun x hx ↦ f₁ (f₂ x hx)) w✝ H\nH : ∀ (x : α), x ∈ (x✝ ::ᵥ w✝).toLis... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 65,
"column": 19
} | {
"line": 65,
"column": 27
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nH : ∀ (x : β), x ∈ (map f₂ nil).toList → p x\n⊢ pmap f₁ (map f₂ nil) H = pmap (fun x hx ↦ f₁ (f₂ x) hx) nil ⋯",
"usedConstants": [
"List.Vector",
"instOfNatNat",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 65,
"column": 19
} | {
"line": 65,
"column": 27
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nn✝ : ℕ\nx✝ : α\nw✝ : Vector α n✝\na✝ : ∀ (H : ∀ (x : β), x ∈ (map f₂ w✝).toList → p x), pmap f₁ (map f₂ w✝) H = pmap (fun x hx ↦ f₁ (f₂ x) hx) w✝ ⋯\nH : ∀ (x : β), x ∈ (map f₂ ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 81,
"column": 71
} | {
"line": 81,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : γ → β → σ₁ → σ₁ × ζ\nf₂ : α → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ (mapAccumr f₂ nil s₂).2 nil s₁ =\n let m :=\n mapAccumr₂\n (fun x y s ↦\n let r₂ := f₂ x s.2;\... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 81,
"column": 71
} | {
"line": 81,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : γ → β → σ₁ → σ₁ × ζ\nf₂ : α → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ (mapAccumr f₂ xs✝ s₂).2 ys✝ s₁ =\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 86,
"column": 52
} | {
"line": 86,
"column": 60
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : γ → β → ζ\nf₂ : α → γ\n⊢ map₂ f₁ (map f₂ nil) nil = map₂ (fun x y ↦ f₁ (f₂ x) y) nil nil",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 86,
"column": 52
} | {
"line": 86,
"column": 60
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : γ → β → ζ\nf₂ : α → γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ : map₂ f₁ (map f₂ xs✝) ys✝ = map₂ (fun x y ↦ f₁ (f₂ x) y) xs✝ ys✝\n⊢ map₂ f₁ (map f₂ (xs✝.snoc x✝)) (y... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 97,
"column": 71
} | {
"line": 97,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : α → γ → σ₁ → σ₁ × ζ\nf₂ : β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ nil (mapAccumr f₂ nil s₂).2 s₁ =\n let m :=\n mapAccumr₂\n (fun x y s ↦\n let r₂ := f₂ y s.2;\... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 97,
"column": 71
} | {
"line": 97,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : α → γ → σ₁ → σ₁ × ζ\nf₂ : β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ xs✝ (mapAccumr f₂ ys✝ s₂).2 s₁ =\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 102,
"column": 52
} | {
"line": 102,
"column": 60
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : α → γ → ζ\nf₂ : β → γ\n⊢ map₂ f₁ nil (map f₂ nil) = map₂ (fun x y ↦ f₁ x (f₂ y)) nil nil",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 102,
"column": 52
} | {
"line": 102,
"column": 60
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : α → γ → ζ\nf₂ : β → γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ : map₂ f₁ xs✝ (map f₂ ys✝) = map₂ (fun x y ↦ f₁ x (f₂ y)) xs✝ ys✝\n⊢ map₂ f₁ (xs✝.snoc x✝) (map f₂ (ys... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 113,
"column": 71
} | {
"line": 113,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : γ → σ₁ → σ₁ × ζ\nf₂ : α → β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr f₁ (mapAccumr₂ f₂ nil nil s₂).2 s₁ =\n let m :=\n mapAccumr₂\n (fun x y s ↦\n let r₂ := f₂ x y s.2... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 113,
"column": 71
} | {
"line": 113,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ₁ : Type u_6\nσ₂ : Type u_7\nn : ℕ\nf₁ : γ → σ₁ → σ₁ × ζ\nf₂ : α → β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr f₁ (mapAccumr₂ f₂ xs✝ ys✝ s₂).2 s₁ =\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 118,
"column": 52
} | {
"line": 118,
"column": 60
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : γ → ζ\nf₂ : α → β → γ\n⊢ map f₁ (map₂ f₂ nil nil) = map₂ (fun x y ↦ f₁ (f₂ x y)) nil nil",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 118,
"column": 52
} | {
"line": 118,
"column": 60
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf₁ : γ → ζ\nf₂ : α → β → γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ : map f₁ (map₂ f₂ xs✝ ys✝) = map₂ (fun x y ↦ f₁ (f₂ x y)) xs✝ ys✝\n⊢ map f₁ (map₂ f₂ (xs✝.snoc x✝) (ys... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 130,
"column": 71
} | {
"line": 130,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : γ → α → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ (mapAccumr₂ f₂ nil nil s₂).2 nil s₁ =\n let m :=\n mapAccumr₂\n (fun x y x_1 ↦\n match x_1... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 130,
"column": 71
} | {
"line": 130,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : γ → α → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ (mapAccumr₂ f₂ xs✝ ys✝ s₂).2 xs✝ s₁... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 143,
"column": 71
} | {
"line": 143,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : γ → β → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ (mapAccumr₂ f₂ nil nil s₂).2 nil s₁ =\n let m :=\n mapAccumr₂\n (fun x y x_1 ↦\n match x_1... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 143,
"column": 71
} | {
"line": 143,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : γ → β → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ (mapAccumr₂ f₂ xs✝ ys✝ s₂).2 ys✝ s₁... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 155,
"column": 71
} | {
"line": 155,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : α → γ → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ nil (mapAccumr₂ f₂ nil nil s₂).2 s₁ =\n let m :=\n mapAccumr₂\n (fun x y x_1 ↦\n match x_1... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 155,
"column": 71
} | {
"line": 155,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : α → γ → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ xs✝ (mapAccumr₂ f₂ xs✝ ys✝ s₂).2 s₁... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 167,
"column": 71
} | {
"line": 167,
"column": 79
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : β → γ → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\ns₁ : σ₁\ns₂ : σ₂\n⊢ mapAccumr₂ f₁ nil (mapAccumr₂ f₂ nil nil s₂).2 s₁ =\n let m :=\n mapAccumr₂\n (fun x y x_1 ↦\n match x_1... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 167,
"column": 71
} | {
"line": 167,
"column": 79
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\nf₁ : β → γ → σ₁ → σ₁ × φ\nf₂ : α → β → σ₂ → σ₂ × γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ :\n ∀ {s₁ : σ₁} {s₂ : σ₂},\n mapAccumr₂ f₁ ys✝ (mapAccumr₂ f₂ xs✝ ys✝ s₂).2 s₁... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 47
} | {
"line": 239,
"column": 55
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f nil = (mapAccumr (fun x x_1 ↦ ((), f x)) nil ()).2",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
"of_eq_true",
"List.Vector.nil",
"OfNat.ofNat",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 47
} | {
"line": 239,
"column": 55
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\nn✝ : ℕ\nxs✝ : Vector α n✝\nx✝ : α\na✝ : map f xs✝ = (mapAccumr (fun x x_1 ↦ ((), f x)) xs✝ ()).2\n⊢ map f (xs✝.snoc x✝) = (mapAccumr (fun x x_1 ↦ ((), f x)) (xs✝.snoc x✝) ()).2",
"usedConstants": [
"Unit.unit",
"L... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 257,
"column": 52
} | {
"line": 257,
"column": 60
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → γ\n⊢ map₂ f nil nil = (mapAccumr₂ (fun x y x_1 ↦ ((), f x y)) nil nil ()).2",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
"of_eq_true",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 257,
"column": 52
} | {
"line": 257,
"column": 60
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → γ\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ : map₂ f xs✝ ys✝ = (mapAccumr₂ (fun x y x_1 ↦ ((), f x y)) xs✝ ys✝ ()).2\n⊢ map₂ f (xs✝.snoc x✝) (ys✝.snoc y✝) = (mapAccumr₂ (fun... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 280,
"column": 40
} | {
"line": 280,
"column": 48
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns : σ\nh : ∀ (a : α), (f a s).1 = s\n⊢ mapAccumr f nil s = (s, map (fun x ↦ (f x s).2) nil)",
"usedConstants": [
"List.Vector",
"Prod.mk",
"instOfNatNat",
"Nat",
"eq_self",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 280,
"column": 40
} | {
"line": 280,
"column": 48
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns : σ\nh : ∀ (a : α), (f a s).1 = s\nn✝ : ℕ\nxs✝ : Vector α n✝\nx✝ : α\na✝ : mapAccumr f xs✝ s = (s, map (fun x ↦ (f x s).2) xs✝)\n⊢ mapAccumr f (xs✝.snoc x✝) s = (s, map (fun x ↦ (f x s).2) (xs✝.snoc x✝))",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 290,
"column": 45
} | {
"line": 290,
"column": 53
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns : σ\nh : ∀ (a : α) (b : β), (f a b s).1 = s\n⊢ mapAccumr₂ f nil nil s = (s, map₂ (fun x y ↦ (f x y s).2) nil nil)",
"usedConstants": [
"List.Vector",
"Prod... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 290,
"column": 45
} | {
"line": 290,
"column": 53
} | [
{
"pp": "case snoc\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns : σ\nh : ∀ (a : α) (b : β), (f a b s).1 = s\nn✝ : ℕ\nxs✝ : Vector α n✝\nys✝ : Vector β n✝\nx✝ : α\ny✝ : β\na✝ : mapAccumr₂ f xs✝ ys✝ s = (s, map₂ (fun x y ↦ (f x y s).2) ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 302,
"column": 2
} | {
"line": 302,
"column": 10
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\nf' : α → β\ns : σ\nh : ∀ (a : α) (s : σ), (f a s).2 = f' a\n⊢ map (fun x ↦ (f x s).2) xs = map f' xs",
"usedConstants": [
"congrArg",
"List.Vector.map",
"List.Vector",
"funext",
"True"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 326,
"column": 4
} | {
"line": 326,
"column": 12
} | [
{
"pp": "case h\nα : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\ns : σ\nxs : Vector α n\nf : α → σ × σ → (σ × σ) × β\nh : ∀ (x : α) (s : σ), (f x (s, s)).1.1 = (f x (s, s)).1.2\n⊢ (fun x s ↦\n match x with\n | (s₁, s₂) => s₂ = s ∧ s₁ = s)\n (s, s) s ∧\n ∀ {s : σ × σ} {q : σ} (a : α),\n ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 339,
"column": 4
} | {
"line": 339,
"column": 12
} | [
{
"pp": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\ns : σ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ × σ → (σ × σ) × γ\nh :\n ∀ (x : α) (y : β) (s : σ),\n let s' := (f x y (s, s)).1;\n s'.1 = s'.2\n⊢ (fun x s ↦\n match x with\n | (s₁, s₂) => s₂ = s ∧ s₁ = s... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 383,
"column": 49
} | {
"line": 383,
"column": 57
} | [
{
"pp": "case nil\nα : Type u_1\nβ : Type u_2\nn : ℕ\nxs ys : Vector α n\nf : α → α → β\ncomm : ∀ (a₁ a₂ : α), f a₁ a₂ = f a₂ a₁\n⊢ map₂ f nil nil = map₂ f nil nil",
"usedConstants": [
"List.Vector",
"instOfNatNat",
"Nat",
"eq_self",
"of_eq_true",
"List.Vector.nil",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 383,
"column": 49
} | {
"line": 383,
"column": 57
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nn : ℕ\nxs ys : Vector α n\nf : α → α → β\ncomm : ∀ (a₁ a₂ : α), f a₁ a₂ = f a₂ a₁\nn✝ : ℕ\na✝¹ b✝ : α\nx✝ y✝ : Vector α n✝\na✝ : map₂ f x✝ y✝ = map₂ f y✝ x✝\n⊢ map₂ f (a✝¹ ::ᵥ x✝) (b✝ ::ᵥ y✝) = map₂ f (b✝ ::ᵥ y✝) (a✝¹ ::ᵥ x✝)",
"usedConstants": [
"congrA... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 387,
"column": 64
} | {
"line": 387,
"column": 72
} | [
{
"pp": "case nil\nα : Type u_1\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nf : α → α → σ → σ × γ\ncomm : ∀ (a₁ a₂ : α) (s : σ), f a₁ a₂ s = f a₂ a₁ s\ns : σ\n⊢ mapAccumr₂ f nil nil s = mapAccumr₂ f nil nil s",
"usedConstants": [
"List.Vector",
"Prod.mk",
"instOfNatNat",
"Nat",
"eq_sel... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Vector.MapLemmas | {
"line": 387,
"column": 64
} | {
"line": 387,
"column": 72
} | [
{
"pp": "case cons\nα : Type u_1\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nf : α → α → σ → σ × γ\ncomm : ∀ (a₁ a₂ : α) (s : σ), f a₁ a₂ s = f a₂ a₁ s\nn✝ : ℕ\na✝¹ b✝ : α\nx✝ y✝ : Vector α n✝\na✝ : ∀ {s : σ}, mapAccumr₂ f x✝ y✝ s = mapAccumr₂ f y✝ x✝ s\ns : σ\n⊢ mapAccumr₂ f (a✝¹ ::ᵥ x✝) (b✝ ::ᵥ y✝) s = mapAccumr₂ f (... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.ZMod.Coprime | {
"line": 30,
"column": 55
} | {
"line": 30,
"column": 76
} | [
{
"pp": "n : ℤ\nm : ℕ\n⊢ IsUnit ↑n ↔ n.natAbs.Coprime (↑m).natAbs",
"usedConstants": [
"ZMod.isUnit_iff_coprime",
"Int.cast",
"Eq.mpr",
"Nat.Coprime",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"IsUnit",... | ← isUnit_iff_coprime, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.SemiconjSup | {
"line": 101,
"column": 20
} | {
"line": 101,
"column": 64
} | [
{
"pp": "α : Type u_1\nG : Type u_4\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g') x)) (h x)\ng : G\ny : α\nthis : IsLUB (range (⇑(f₁ g) ∘ fun g' ↦ (f₁ g')⁻¹ ((f₂ g') y))) ((f₁ g) (h y))\n⊢ IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g... | ← (Equiv.mulRight g).surjective.range_comp _ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Group.AEStabilizer | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 10
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G α\nx✝ : MeasurableSpace α\nμ : Measure α\ninst✝ : SMulInvariantMeasure G α μ\ns : Set α\ng : G\nhg : g ∈ stabilizer G s\n⊢ g ∈ aestabilizer G μ s",
"usedConstants": [
"MeasureTheory.ae",
"instHSMul",
"MeasureTheory... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.MeasureTheory.Group.AEStabilizer | {
"line": 74,
"column": 2
} | {
"line": 77,
"column": 40
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G α\nx✝ : MeasurableSpace α\nμ : Measure α\ninst✝ : SMulInvariantMeasure G α μ\ns : Set α\nhs : EventuallyConst s (ae μ)\n⊢ aestabilizer G μ s = ⊤",
"usedConstants": [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"co... | refine top_unique fun g _ ↦ ?_
cases eventuallyConst_set'.mp hs with
| inl h => simp [aestabilizer_congr h]
| inr h => simp [aestabilizer_congr h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Group.AEStabilizer | {
"line": 74,
"column": 2
} | {
"line": 77,
"column": 40
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G α\nx✝ : MeasurableSpace α\nμ : Measure α\ninst✝ : SMulInvariantMeasure G α μ\ns : Set α\nhs : EventuallyConst s (ae μ)\n⊢ aestabilizer G μ s = ⊤",
"usedConstants": [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"co... | refine top_unique fun g _ ↦ ?_
cases eventuallyConst_set'.mp hs with
| inl h => simp [aestabilizer_congr h]
| inr h => simp [aestabilizer_congr h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 193,
"column": 41
} | {
"line": 193,
"column": 91
} | [
{
"pp": "f : CircleDeg1Liftˣ\nx : ℝ\n⊢ ↑f⁻¹ (↑f x) = x",
"usedConstants": [
"Units.val",
"MulOne.toOne",
"Real",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Units.inv_mul",
"CircleDeg1Lift.instFunLikeReal",
"Units",
"MulOne.toMul",
"Mul... | by simp only [← mul_apply, f.inv_mul, coe_one, id] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 83
} | [
{
"pp": "X : Type u_2\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : R1Space X\ninst✝⁸ : MeasurableSpace X\ninst✝⁷ : BorelSpace X\nM : Type u_3\ninst✝⁶ : Monoid M\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : MulAction M X\ninst✝³ : ContinuousSMul M X\ng : M\nhg : DenseRange fun x ↦ g ^ x\nμ : Measure X\ninst✝² : IsFiniteMea... | refine aeconst_of_dense_setOf_preimage_smul_eq hsm.nullMeasurableSet (hg.mono ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 172,
"column": 13
} | {
"line": 172,
"column": 15
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : MeasurableSpace G\ninst✝¹ : OpensMeasurableSpace G\nμ : Measure G\ninst✝ : μ.IsOpenPosMeasure\ng : G\nhg : Ergodic (fun x ↦ g * x) μ\na : G\nh : a ∉ closure[inst✝⁴] (range fun x ↦ g ^ x)\nV : Set G\nhV₁... | s, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 12
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : MeasurableSpace G\ninst✝¹ : OpensMeasurableSpace G\nμ : Measure G\ninst✝ : μ.IsOpenPosMeasure\ng : G\nhg : Ergodic (fun x ↦ g * x) μ\na : G\nh : a ∉ closure[inst✝⁴] (range fun x ↦ g ^ x)\nV : Set G\nhV₁... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Dynamics.Ergodic.Extreme | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 35
} | [
{
"pp": "case inr\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\ninst✝¹ : IsFiniteMeasure μ\nhμ : Ergodic f μ\nc : ℝ≥0∞\ninst✝ : IsFiniteMeasure (c • μ)\nhfν : MeasurePreserving f (c • μ) (c • μ)\nhνμ : c • μ ≪ μ\nhuniv : (c • μ) univ = μ univ\nhμ₀ : μ ≠ 0\n⊢ c • μ = μ",
"usedConstants": [
... | simp_all [ENNReal.mul_eq_right] | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Dynamics.Ergodic.Extreme | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 35
} | [
{
"pp": "case inr\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\ninst✝¹ : IsFiniteMeasure μ\nhμ : Ergodic f μ\nc : ℝ≥0∞\ninst✝ : IsFiniteMeasure (c • μ)\nhfν : MeasurePreserving f (c • μ) (c • μ)\nhνμ : c • μ ≪ μ\nhuniv : (c • μ) univ = μ univ\nhμ₀ : μ ≠ 0\n⊢ c • μ = μ",
"usedConstants": [
... | simp_all [ENNReal.mul_eq_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Dynamics.Ergodic.Extreme | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 35
} | [
{
"pp": "case inr\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\ninst✝¹ : IsFiniteMeasure μ\nhμ : Ergodic f μ\nc : ℝ≥0∞\ninst✝ : IsFiniteMeasure (c • μ)\nhfν : MeasurePreserving f (c • μ) (c • μ)\nhνμ : c • μ ≪ μ\nhuniv : (c • μ) univ = μ univ\nhμ₀ : μ ≠ 0\n⊢ c • μ = μ",
"usedConstants": [
... | simp_all [ENNReal.mul_eq_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 418,
"column": 25
} | {
"line": 418,
"column": 29
} | [
{
"pp": "case h\nα : Type u_1\nm : MeasurableSpace α\nμ ν κ : Measure α\ninst✝² : SigmaFinite μ\ninst✝¹ : SigmaFinite ν\ninst✝ : SigmaFinite κ\nhνκ : ν ≪ κ\nh_meas : Measurable (μ.rnDeriv ν)\nh_sing : μ.singularPart ν ⟂ₘ ν\nhμν : μ = μ.singularPart ν + ν.withDensity (μ.rnDeriv ν)\nx : α\nhx1 :\n (μ.singularPar... | hx2, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage | {
"line": 140,
"column": 59
} | {
"line": 140,
"column": 77
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nS : X → X\nT : Y → Y\nφ : X → Y\nh : Function.Semiconj φ S T\nU : Set (Y × Y)\nn k : ℕ\nx✝ : k < n\n⊢ (map T T)^[k] ∘ map φ φ ⁻¹' U = map φ φ ∘ map S^[k] S^[k] ⁻¹' U",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Prod.map... | map_iterate T T k, | Lean.Elab.Tactic.evalRewriteSeq | null |
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