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370 values
Mathlib.Data.List.ReduceOption
{ "line": 137, "column": 2 }
{ "line": 137, "column": 96 }
[ { "pp": "α : Type u_1\nl : List (Option α)\nx : α\n⊢ (l.concat (some x)).reduceOption = l.reduceOption.concat x", "usedConstants": [ "congrArg", "List.concat", "Option.some", "List.concat_eq_append", "List.cons", "instHAppendOfAppend", "List", "congr", "...
simp only [reduceOption_nil, concat_eq_append, reduceOption_append, reduceOption_cons_of_some]
Lean.Elab.Tactic.evalSimp
Lean.Parser.Tactic.simp
Mathlib.Data.List.ReduceOption
{ "line": 137, "column": 2 }
{ "line": 137, "column": 96 }
[ { "pp": "α : Type u_1\nl : List (Option α)\nx : α\n⊢ (l.concat (some x)).reduceOption = l.reduceOption.concat x", "usedConstants": [ "congrArg", "List.concat", "Option.some", "List.concat_eq_append", "List.cons", "instHAppendOfAppend", "List", "congr", "...
simp only [reduceOption_nil, concat_eq_append, reduceOption_append, reduceOption_cons_of_some]
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.ReduceOption
{ "line": 137, "column": 2 }
{ "line": 137, "column": 96 }
[ { "pp": "α : Type u_1\nl : List (Option α)\nx : α\n⊢ (l.concat (some x)).reduceOption = l.reduceOption.concat x", "usedConstants": [ "congrArg", "List.concat", "Option.some", "List.concat_eq_append", "List.cons", "instHAppendOfAppend", "List", "congr", "...
simp only [reduceOption_nil, concat_eq_append, reduceOption_append, reduceOption_cons_of_some]
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.Halting
{ "line": 41, "column": 30 }
{ "line": 41, "column": 38 }
[ { "pp": "case pos\nC : Set (ℕ →. ℕ)\nf g : ℕ →. ℕ\nhf : Nat.Partrec f\nhg : Nat.Partrec g\nfC : f ∈ C\nw✝ : DecidablePred fun c ↦ c.eval ∈ C\nh : Computable fun a ↦ decide ((fun c ↦ c.eval ∈ C) a)\nc : Code\ne : c.eval = fun b ↦ if c.eval ∈ C then g b else f b\nH : c.eval ∈ C\n⊢ g ∈ C", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Computability.Halting
{ "line": 41, "column": 30 }
{ "line": 41, "column": 38 }
[ { "pp": "case neg\nC : Set (ℕ →. ℕ)\nf g : ℕ →. ℕ\nhf : Nat.Partrec f\nhg : Nat.Partrec g\nfC : f ∈ C\nw✝ : DecidablePred fun c ↦ c.eval ∈ C\nh : Computable fun a ↦ decide ((fun c ↦ c.eval ∈ C) a)\nc : Code\ne : c.eval = fun b ↦ if c.eval ∈ C then g b else f b\nH : c.eval ∉ C\n⊢ g ∈ C", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Computability.EpsilonNFA
{ "line": 189, "column": 4 }
{ "line": 189, "column": 53 }
[ { "pp": "α : Type u\nσ : Type v\nM : εNFA α σ\ns u : σ\nx y : List (Option α)\nt : σ\nhx : M.IsPath s t x\nright✝ : M.IsPath t u y\n⊢ M.IsPath s u (x ++ y)", "usedConstants": [ "εNFA.IsPath.nil", "εNFA.IsPath.cons", "HEq.refl", "False.elim", "noConfusion_of_Nat", "Members...
induction x generalizing s <;> cases hx <;> tauto
Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1»
Lean.Parser.Tactic.«tactic_<;>_»
Mathlib.Computability.EpsilonNFA
{ "line": 198, "column": 6 }
{ "line": 198, "column": 22 }
[ { "pp": "case h\nα : Type u\nσ : Type v\nM : εNFA α σ\ns₁ s₂ : σ\n⊢ M.IsPath s₁ s₁ (List.replicate 0 none)", "usedConstants": [ "εNFA.IsPath.nil" ] } ]
apply IsPath.nil
Lean.Elab.Tactic.evalApply
Lean.Parser.Tactic.apply
Mathlib.Data.Num.Lemmas
{ "line": 722, "column": 4 }
{ "line": 722, "column": 71 }
[ { "pp": "p : PosNum\n⊢ castNum <$> (pos p).ppred = (↑(pos p)).ppred", "usedConstants": [ "Iff.mpr", "Eq.mpr", "Nat.instMulZeroClass", "Nat.instOne", "PosNum.pred'", "congrArg", "Option.some", "instFunctorOption", "id", "Nat.ppred_eq_some", "c...
rw [ppred, Option.map_eq_map, Option.map_some, Nat.ppred_eq_some.2]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Computability.RecursiveIn
{ "line": 224, "column": 20 }
{ "line": 224, "column": 69 }
[ { "pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\ns : Part ℕ\nhf : RecursiveIn {fun x ↦ s} f\ng : ℕ →. ℕ\nhg : g ∈ {fun x ↦ s}\n⊢ Partrec g", "usedConstants": [ "Eq.mpr", "PFun", "congrArg", "Primcodable.ofDenumerable", "Membership....
rw [Set.mem_singleton_iff.mp hg]; exact .const' s
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.RecursiveIn
{ "line": 224, "column": 20 }
{ "line": 224, "column": 69 }
[ { "pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\ns : Part ℕ\nhf : RecursiveIn {fun x ↦ s} f\ng : ℕ →. ℕ\nhg : g ∈ {fun x ↦ s}\n⊢ Partrec g", "usedConstants": [ "Eq.mpr", "PFun", "congrArg", "Primcodable.ofDenumerable", "Membership....
rw [Set.mem_singleton_iff.mp hg]; exact .const' s
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.Reduce
{ "line": 385, "column": 2 }
{ "line": 388, "column": 30 }
[ { "pp": "d₁ d₂ d₃ : ManyOneDegree\n⊢ d₁ ≤ d₂ → d₂ ≤ d₃ → d₁ ≤ d₃", "usedConstants": [ "ManyOneDegree.instLE", "Primcodable.ofDenumerable", "ManyOneDegree.ind_on", "ManyOneReducible.trans", "instInhabitedNat", "LE.le", "toNat", "Nat", "ManyOneDegree", ...
induction d₁ using ManyOneDegree.ind_on induction d₂ using ManyOneDegree.ind_on induction d₃ using ManyOneDegree.ind_on apply ManyOneReducible.trans
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.Reduce
{ "line": 385, "column": 2 }
{ "line": 388, "column": 30 }
[ { "pp": "d₁ d₂ d₃ : ManyOneDegree\n⊢ d₁ ≤ d₂ → d₂ ≤ d₃ → d₁ ≤ d₃", "usedConstants": [ "ManyOneDegree.instLE", "Primcodable.ofDenumerable", "ManyOneDegree.ind_on", "ManyOneReducible.trans", "instInhabitedNat", "LE.le", "toNat", "Nat", "ManyOneDegree", ...
induction d₁ using ManyOneDegree.ind_on induction d₂ using ManyOneDegree.ind_on induction d₃ using ManyOneDegree.ind_on apply ManyOneReducible.trans
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.PostTuringMachine
{ "line": 853, "column": 4 }
{ "line": 853, "column": 39 }
[ { "pp": "case some\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\nn : ℕ\nenc : Γ → List.Vector Bool n\ndec : List.Vector Bool n → Γ\nM : Λ → Stmt Γ Λ σ\ninst✝ : Inhabited Γ\nenc0 : enc default = List.Vector.replicate n false\nencdec : ∀ (a : Γ), dec (enc a) = a\nx✝ : Cfg Γ Λ σ\nv : σ\nL : ListBlank Γ\nq : Stmt Γ Λ ...
induction q generalizing v L R with
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction
null
Mathlib.Computability.TuringMachine.Config
{ "line": 284, "column": 6 }
{ "line": 284, "column": 71 }
[ { "pp": "case prim.prec\nn✝¹ : ℕ\nf✝¹ : List.Vector ℕ n✝¹ →. ℕ\nn✝ : ℕ\nf✝ : List.Vector ℕ n✝ → ℕ\nn : ℕ\nf : List.Vector ℕ n → ℕ\ng : List.Vector ℕ (n + 2) → ℕ\na✝¹ : Nat.Primrec' f\na✝ : Nat.Primrec' g\ncf : Code\nhf : ∀ (v : List.Vector ℕ n), cf.eval ↑v = pure <$> ↑f v\ncg : Code\nhg : ∀ (v : List.Vector ℕ (...
simp only [Part.map_eq_map, Part.map_some, PFun.coe_val] at hf hg
Lean.Elab.Tactic.evalSimp
Lean.Parser.Tactic.simp
Mathlib.Computability.TuringMachine.Config
{ "line": 309, "column": 8 }
{ "line": 309, "column": 16 }
[ { "pp": "n✝² : ℕ\nf✝¹ : List.Vector ℕ n✝² →. ℕ\nn✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ → ℕ\nn✝ : ℕ\nf : List.Vector ℕ n✝ → ℕ\ng : List.Vector ℕ (n✝ + 2) → ℕ\na✝² : Nat.Primrec' f\na✝¹ : Nat.Primrec' g\ncf cg : Code\nv : List.Vector ℕ (n✝ + 1)\nhf : cf.eval (↑v).tail = pure (pure (f v.tail))\nhg : ∀ (a b : ℕ), cg.eval ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Computability.TuringMachine.Config
{ "line": 354, "column": 38 }
{ "line": 354, "column": 46 }
[ { "pp": "n✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ →. ℕ\nn✝ : ℕ\nf : List.Vector ℕ (n✝ + 1) → ℕ\na✝ : Nat.Partrec' ↑f\ncf : Code\nv : List.Vector ℕ n✝\nhf : ∀ (a : ℕ), cf.eval (a :: ↑v) = Part.some [f (a ::ᵥ v)]\nv' v₀ : List ℕ\nn : ℕ\nh2 :\n v' ∈\n PFun.fix\n (fun v ↦\n (cf.eval v).bind fun y ↦\n ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Computability.TuringMachine.Config
{ "line": 354, "column": 38 }
{ "line": 354, "column": 46 }
[ { "pp": "n✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ →. ℕ\nn✝ : ℕ\nf : List.Vector ℕ (n✝ + 1) → ℕ\na✝ : Nat.Partrec' ↑f\ncf : Code\nv : List.Vector ℕ n✝\nhf : ∀ (a : ℕ), cf.eval (a :: ↑v) = Part.some [f (a ::ᵥ v)]\nv' v₀ : List ℕ\nn : ℕ\nh2 :\n v' ∈\n PFun.fix\n (fun v ↦\n (cf.eval v).bind fun y ↦\n ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.TuringMachine.Config
{ "line": 354, "column": 38 }
{ "line": 354, "column": 46 }
[ { "pp": "n✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ →. ℕ\nn✝ : ℕ\nf : List.Vector ℕ (n✝ + 1) → ℕ\na✝ : Nat.Partrec' ↑f\ncf : Code\nv : List.Vector ℕ n✝\nhf : ∀ (a : ℕ), cf.eval (a :: ↑v) = Part.some [f (a ::ᵥ v)]\nv' v₀ : List ℕ\nn : ℕ\nh2 :\n v' ∈\n PFun.fix\n (fun v ↦\n (cf.eval v).bind fun y ↦\n ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.StackTuringMachine
{ "line": 593, "column": 12 }
{ "line": 594, "column": 89 }
[ { "pp": "K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nf : σ → Option ...
show (List.cons hd tl).reverse[tl.length]? = some hd by rw [List.reverse_cons, ← List.length_reverse, List.getElem?_concat_length],
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Computability.TuringMachine.Config
{ "line": 617, "column": 10 }
{ "line": 617, "column": 14 }
[ { "pp": "case mp.halt\nf : Code\nk : Cont\nv✝ : List ℕ\nfok : f.Ok\nx c : Cfg\nhe : x ∈ eval step c\nv v' : List ℕ\nh : x ∈ eval step (stepRet (Cont.fix f k) v')\nIH :\n ∀ (a' : Cfg),\n step (stepRet (Cont.fix f k) v') = some a' →\n ∀ (v : List ℕ) (c' : Cfg),\n a' = c'.then (Cont.fix f k) →\n ...
fok,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Computability.TuringMachine.StackTuringMachine
{ "line": 644, "column": 4 }
{ "line": 644, "column": 28 }
[ { "pp": "case succ\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\nk : K\no : StAct K Γ σ k\nq : TM2.Stmt Γ Λ σ\nv : σ\nS : List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ListBlank.map (proj k) L = ListBlank.mk (List.map some S).reverse\nn : ...
rw [iterate_succ_apply']
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Computability.TuringMachine.Config
{ "line": 648, "column": 8 }
{ "line": 648, "column": 12 }
[ { "pp": "case mpr\nf : Code\nk : Cont\nv✝ : List ℕ\nfok : f.Ok\nx : Cfg\nv' : List ℕ\nhe✝ : v' ∈ f.fix.eval v✝\nhr✝ : x ∈ eval step (Cfg.ret k v')\nhr : x ∈ eval step (stepRet k v')\nv : List ℕ\nhe : v' ∈ f.fix.eval v\nIH :\n ∀ (a'' : List ℕ),\n Sum.inr a'' ∈ Part.map (fun v ↦ if v.headI = 0 then Sum.inl v....
fok,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 523, "column": 2 }
{ "line": 523, "column": 27 }
[ { "pp": "a b c d a' : List Γ'\n⊢ update (elim a b c d) main a' = elim a' b c d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'....
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 523, "column": 2 }
{ "line": 523, "column": 27 }
[ { "pp": "a b c d a' : List Γ'\n⊢ update (elim a b c d) main a' = elim a' b c d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'....
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 527, "column": 2 }
{ "line": 527, "column": 27 }
[ { "pp": "a b c d b' : List Γ'\n⊢ update (elim a b c d) rev b' = elim a b' c d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'.c...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 527, "column": 2 }
{ "line": 527, "column": 27 }
[ { "pp": "a b c d b' : List Γ'\n⊢ update (elim a b c d) rev b' = elim a b' c d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'.c...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 531, "column": 2 }
{ "line": 531, "column": 27 }
[ { "pp": "a b c d c' : List Γ'\n⊢ update (elim a b c d) aux c' = elim a b c' d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'.c...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 531, "column": 2 }
{ "line": 531, "column": 27 }
[ { "pp": "a b c d c' : List Γ'\n⊢ update (elim a b c d) aux c' = elim a b c' d", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'.c...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 535, "column": 63 }
{ "line": 535, "column": 88 }
[ { "pp": "a b c d d' : List Γ'\n⊢ update (elim a b c d) stack d' = elim a b c d'", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 535, "column": 63 }
{ "line": 535, "column": 88 }
[ { "pp": "a b c d d' : List Γ'\n⊢ update (elim a b c d) stack d' = elim a b c d'", "usedConstants": [ "Function.update", "Turing.PartrecToTM2.K'.rev", "Turing.PartrecToTM2.instDecidableEqK'", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.K'.stack", "Turing.PartrecToTM2.K'...
funext x; cases x <;> rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 576, "column": 12 }
{ "line": 576, "column": 15 }
[ { "pp": "case some.nil\nα : Type u_1\np : α → Bool\na : α\nL : List α\nIH :\n ∀ (l₁ : List α) (o : Option α) (l₂ : List α),\n (∀ x ∈ l₁, p x = false) →\n Option.elim' (L = l₁ ∧ l₂ = []) (fun a ↦ p a = true ∧ L = l₁ ++ a :: l₂) o → splitAtPred p L = (l₁, o, l₂)\nh₁ : ∀ x ∈ [], p x = false\nh₂ : p a = tr...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Topology.Separation.Profinite
{ "line": 142, "column": 86 }
{ "line": 142, "column": 94 }
[ { "pp": "X : Type u_4\ninst✝³ : TopologicalSpace X\ninst✝² : CompactSpace X\ninst✝¹ : T2Space X\ninst✝ : TotallyDisconnectedSpace X\nZ U : Set X\nhZ : IsClosed[inst✝³] Z\nhU : IsOpen[inst✝³] U\nhZU : Z ⊆ U\nV : ↑Z → Set X\nhV : ∀ (z : ↑Z), IsClopen (V z) ∧ ↑z ∈ V z ∧ V z ⊆ U\nV_cover : Z ⊆ ⋃ z, V z\nI : Finset ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Topology.Separation.Profinite
{ "line": 142, "column": 86 }
{ "line": 142, "column": 94 }
[ { "pp": "X : Type u_4\ninst✝³ : TopologicalSpace X\ninst✝² : CompactSpace X\ninst✝¹ : T2Space X\ninst✝ : TotallyDisconnectedSpace X\nZ U : Set X\nhZ : IsClosed[inst✝³] Z\nhU : IsOpen[inst✝³] U\nhZU : Z ⊆ U\nV : ↑Z → Set X\nhV : ∀ (z : ↑Z), IsClopen (V z) ∧ ↑z ∈ V z ∧ V z ⊆ U\nV_cover : Z ⊆ ⋃ z, V z\nI : Finset ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Topology.Separation.Profinite
{ "line": 142, "column": 86 }
{ "line": 142, "column": 94 }
[ { "pp": "X : Type u_4\ninst✝³ : TopologicalSpace X\ninst✝² : CompactSpace X\ninst✝¹ : T2Space X\ninst✝ : TotallyDisconnectedSpace X\nZ U : Set X\nhZ : IsClosed[inst✝³] Z\nhU : IsOpen[inst✝³] U\nhZU : Z ⊆ U\nV : ↑Z → Set X\nhV : ∀ (z : ↑Z), IsClopen (V z) ∧ ↑z ∈ V z ∧ V z ⊆ U\nV_cover : Z ⊆ ⋃ z, V z\nI : Finset ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Topology.Category.Profinite.Basic
{ "line": 245, "column": 6 }
{ "line": 245, "column": 63 }
[ { "pp": "case mp\nX Y : Profinite\nf : X ⟶ Y\ny : ↑Y.toTop\nhy : ∀ (a : ↑X.toTop), (ConcreteCategory.hom f) a ≠ y\nhf : Epi f\nC : Set ((fun X ↦ ↑X.toTop) Y) := Set.range ⇑(ConcreteCategory.hom f)\nhC : IsClosed C\nU : Set ((fun X ↦ ↑X.toTop) Y) := Cᶜ\nhyU : y ∈ U\nhUy : U ∈ 𝓝 y\nV : Set ↑Y.toTop\nhV : V ∈ {s ...
let h : Y ⟶ Z := ofHom _ ⟨fun _ => ⟨1⟩, continuous_const⟩
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1
Lean.Parser.Tactic.tacticLet__
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 668, "column": 82 }
{ "line": 679, "column": 18 }
[ { "pp": "q : Λ'\ns : Option Γ'\na b c d : List Γ'\n⊢ Reaches₁ (TM2.step tr) { l := some q.copy, var := s, stk := elim a b c d }\n { l := some q, var := none, stk := elim (b.reverseAux a) [] c (b.reverseAux d) }", "usedConstants": [ "List.head?", "cond", "Eq.mpr", "Inhabited.defaul...
by induction b generalizing a d s with | nil => refine TransGen.single ?_ simp | cons x b IH => refine TransGen.head rfl ?_ rw [tr] simp only [TM2.step, Option.mem_def, TM2.stepAux, elim_rev, List.head?_cons, Option.isSome_some, List.tail_cons, elim_update_rev, elim_main, elim_update_mai...
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Topology.Category.Stonean.Basic
{ "line": 159, "column": 4 }
{ "line": 161, "column": 8 }
[ { "pp": "X : Stonean\nB C : CompHaus\nφ : toCompHaus.obj X ⟶ C\nf : B ⟶ C\ninst✝ : Epi f\nthis : ExtremallyDisconnected ↑(toCompHaus.obj X).toTop\nhf : Function.Surjective ⇑(ConcreteCategory.hom f)\n⊢ ∃ f', f' ≫ f = φ", "usedConstants": [ "ContinuousMap.continuous", "TopCat.instCategory", ...
obtain ⟨f', h⟩ := CompactT2.ExtremallyDisconnected.projective φ.hom.hom.continuous f.hom.hom.continuous hf
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain
Lean.Parser.Tactic.obtain
Mathlib.Topology.Category.Stonean.Basic
{ "line": 172, "column": 4 }
{ "line": 174, "column": 8 }
[ { "pp": "X : Stonean\nB C : Profinite\nφ : toProfinite.obj X ⟶ C\nf : B ⟶ C\ninst✝ : Epi f\nthis : ExtremallyDisconnected ↑(toProfinite.obj X).toTop\nhf : Function.Surjective ⇑(ConcreteCategory.hom f)\n⊢ ∃ f', f' ≫ f = φ", "usedConstants": [ "ContinuousMap.continuous", "Stonean.toProfinite", ...
obtain ⟨f', h⟩ := CompactT2.ExtremallyDisconnected.projective φ.hom.hom.continuous f.hom.hom.continuous hf
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain
Lean.Parser.Tactic.obtain
Mathlib.Topology.Category.Stonean.Basic
{ "line": 185, "column": 4 }
{ "line": 187, "column": 8 }
[ { "pp": "X B C : Stonean\nφ : X ⟶ C\nf : B ⟶ C\ninst✝ : Epi f\nthis : ExtremallyDisconnected ↑X.toTop\nhf : Function.Surjective ⇑(ConcreteCategory.hom f)\n⊢ ∃ f', f' ≫ f = φ", "usedConstants": [ "ContinuousMap.continuous", "TopCat.instCategory", "ContinuousMap", "CompHausLike", ...
obtain ⟨f', h⟩ := CompactT2.ExtremallyDisconnected.projective φ.hom.hom.continuous f.hom.hom.continuous hf
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain
Lean.Parser.Tactic.obtain
Mathlib.Topology.ExtremallyDisconnected
{ "line": 318, "column": 6 }
{ "line": 318, "column": 14 }
[ { "pp": "case pos\nX : Type u\ninst✝ : TopologicalSpace X\nh : PreirreducibleSpace X\nU : Set X\nhU : IsOpen U\nUn : U = ∅\n⊢ IsOpen (closure U)", "usedConstants": [ "congrArg", "IsClosed.closure_eq", "IsClosed", "closure", "True", "Set.instEmptyCollection", "of_eq_...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Topology.ExtremallyDisconnected
{ "line": 318, "column": 6 }
{ "line": 318, "column": 14 }
[ { "pp": "case pos\nX : Type u\ninst✝ : TopologicalSpace X\nh : PreirreducibleSpace X\nU : Set X\nhU : IsOpen U\nUn : U = ∅\n⊢ IsOpen (closure U)", "usedConstants": [ "congrArg", "IsClosed.closure_eq", "IsClosed", "closure", "True", "Set.instEmptyCollection", "of_eq_...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Topology.ExtremallyDisconnected
{ "line": 318, "column": 6 }
{ "line": 318, "column": 14 }
[ { "pp": "case pos\nX : Type u\ninst✝ : TopologicalSpace X\nh : PreirreducibleSpace X\nU : Set X\nhU : IsOpen U\nUn : U = ∅\n⊢ IsOpen (closure U)", "usedConstants": [ "congrArg", "IsClosed.closure_eq", "IsClosed", "closure", "True", "Set.instEmptyCollection", "of_eq_...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Topology.ExtremallyDisconnected
{ "line": 328, "column": 4 }
{ "line": 328, "column": 12 }
[ { "pp": "case inl\nX : Type u\ninst✝ : TopologicalSpace X\nh : ExtremallyDisconnected X\nh' : PreconnectedSpace X\ns : Set X\nhs : IsOpen s\nsn : s.Nonempty\nh✝ : closure s = ∅\n⊢ closure s = univ", "usedConstants": [ "Eq.mpr", "False", "congrArg", "Set.univ", "False.elim", ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Topology.ExtremallyDisconnected
{ "line": 328, "column": 4 }
{ "line": 328, "column": 12 }
[ { "pp": "case inl\nX : Type u\ninst✝ : TopologicalSpace X\nh : ExtremallyDisconnected X\nh' : PreconnectedSpace X\ns : Set X\nhs : IsOpen s\nsn : s.Nonempty\nh✝ : closure s = ∅\n⊢ closure s = univ", "usedConstants": [ "Eq.mpr", "False", "congrArg", "Set.univ", "False.elim", ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Topology.ExtremallyDisconnected
{ "line": 328, "column": 4 }
{ "line": 328, "column": 12 }
[ { "pp": "case inl\nX : Type u\ninst✝ : TopologicalSpace X\nh : ExtremallyDisconnected X\nh' : PreconnectedSpace X\ns : Set X\nhs : IsOpen s\nsn : s.Nonempty\nh✝ : closure s = ∅\n⊢ closure s = univ", "usedConstants": [ "Eq.mpr", "False", "congrArg", "Set.univ", "False.elim", ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Computability.TuringMachine.ToPartrec
{ "line": 1019, "column": 74 }
{ "line": 1020, "column": 72 }
[ { "pp": "c : Code\nk : Cont'\n⊢ trStmts₁ (trNormal c k) ⊆ codeSupp' c k", "usedConstants": [ "Turing.PartrecToTM2.trStmts₁", "Finset.instUnion", "Turing.PartrecToTM2.Γ'", "Turing.PartrecToTM2.instDecidableEqΓ'", "Turing.PartrecToTM2.Γ'.consₗ", "Finset", "Finset.unio...
by cases c <;> first | rfl | exact Finset.union_subset_left (fun _ a ↦ a)
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Topology.DiscreteQuotient
{ "line": 232, "column": 8 }
{ "line": 232, "column": 51 }
[ { "pp": "α : Type u_1\nX : Type u_2\nY : Type u_3\nZ : Type u_4\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\nS : DiscreteQuotient X\ninst✝ : LocallyConnectedSpace X\nx : X\n⊢ IsOpen[inst✝³] (setOf ((connectedComponentSetoid X) x))", "usedConstants": [ "Eq.mpr...
convert! isOpen_connectedComponent (x := x)
Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1
Mathlib.Tactic.convert!
Mathlib.Topology.Category.TopCat.Limits.Cofiltered
{ "line": 54, "column": 4 }
{ "line": 54, "column": 26 }
[ { "pp": "case h.e'_3.h.mp\nJ : Type v\ninst✝¹ : Category.{w, v} J\ninst✝ : IsCofiltered J\nF : J ⥤ TopCat\nC : Cone F\nhC : IsLimit C\nT : (j : J) → Set (Set ↑(F.obj j))\nhT : ∀ (j : J), IsTopologicalBasis (T j)\nuniv : ∀ (i : J), Set.univ ∈ T i\ninter : ∀ (i : J) (U1 U2 : Set ↑(F.obj i)), U1 ∈ T i → U2 ∈ T i →...
rintro ⟨j, V, hV, rfl⟩
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro
Lean.Parser.Tactic.rintro
Mathlib.Topology.Category.Profinite.CofilteredLimit
{ "line": 117, "column": 2 }
{ "line": 118, "column": 42 }
[ { "pp": "case h.h\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) (Fin 2)\nU : Set ↑C.pt.toTop := ⋯\nhU : IsClopen U\nj : J\nV : Set ↑(F.obj j).toTop\nhV : IsClopen V\nh : U = ⇑(ConcreteCategory.hom (C.π.app j)) ⁻¹' ...
simp only [Fin.isValue, Functor.const_obj_obj, LocallyConstant.coe_comap, Set.preimage_comp, LocallyConstant.ofIsClopen_fiber_zero]
Lean.Elab.Tactic.evalSimp
Lean.Parser.Tactic.simp
Mathlib.Topology.Category.Profinite.CofilteredLimit
{ "line": 125, "column": 91 }
{ "line": 152, "column": 15 }
[ { "pp": "J : Type v\ninst✝² : SmallCategory J\ninst✝¹ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝ : Finite α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) α\n⊢ ∃ j g,\n LocallyConstant.map (fun a b ↦ if a = b then 0 else 1) f = LocallyConstant.comap (TopCat.Hom.hom (C.π.app j).h...
by cases nonempty_fintype α let ι : α → α → Fin 2 := fun x y => if x = y then 0 else 1 let ff := (f.map ι).flip have hff := fun a : α => exists_locallyConstant_fin_two _ hC (ff a) choose j g h using hff let G : Finset J := Finset.univ.image j obtain ⟨j0, hj0⟩ := IsCofiltered.inf_objs_exists G have hj : ...
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Condensed.TopComparison
{ "line": 55, "column": 10 }
{ "line": 55, "column": 13 }
[ { "pp": "C : Type u\ninst✝³ : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝² : TopologicalSpace X\nZ B : C\nπ : Z ⟶ B\ninst✝¹ : HasPullback π π\ninst✝ : PreservesLimit (cospan π π) G\na : C(↑(G.obj Z), X)\nha : ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.fst π π))) = ⇑a ∘ ⇑(ConcreteCategory.hom (G.map ...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Condensed.TopComparison
{ "line": 68, "column": 49 }
{ "line": 87, "column": 100 }
[ { "pp": "C : Type u\ninst✝² : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝¹ : TopologicalSpace X\ninst✝ : ∀ (Z B : C) (π : Z ⟶ B) [EffectiveEpi π], PreservesLimit (cospan π π) G\nhq : ∀ (Z B : C) (π : Z ⟶ B) [EffectiveEpi π], IsQuotientMap ⇑(ConcreteCategory.hom (G.map π))\n⊢ EqualizerCondition (yoneda...
by apply EqualizerCondition.mk intro Z B π _ _ refine ⟨fun a b h ↦ ?_, fun ⟨a, ha⟩ ↦ ?_⟩ · simp only [yonedaPresheaf, comp, Quiver.Hom.unop_op, TypeCat.Fun.coe_mk, Set.coe_setOf, mapToEqualizer, Set.mem_setOf_eq, ConcreteCategory.hom_ofHom, Subtype.mk.injEq, mk.injEq] at h simp only [yonedaPresh...
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Condensed.Discrete.Module
{ "line": 55, "column": 64 }
{ "line": 59, "column": 70 }
[ { "pp": "P : TopCat → Prop\nR : Type (max u w)\ninst✝² : Ring R\ninst✝¹ : HasExplicitFiniteCoproducts P\ninst✝ : HasExplicitPullbacks P\nhs : ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y), EffectiveEpi f → Function.Surjective ⇑(ConcreteCategory.hom f)\nX : ModuleCat R\n⊢ Presheaf.IsSheaf (coherentTopology (CompHausLike ...
by have := CompHausLike.preregular hs apply Presheaf.isSheaf_coherent_of_hasPullbacks_of_comp (s := CategoryTheory.forget (ModuleCat R)) exact ((CompHausLike.LocallyConstant.functor P hs).obj _).property
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Condensed.Light.TopCatAdjunction
{ "line": 132, "column": 2 }
{ "line": 133, "column": 46 }
[ { "pp": "X✝ Y : LightCondSet\nf : X✝ ⟶ Y\nX : TopCat\n⊢ Epi (topCatAdjunction.counit.app X)", "usedConstants": [ "LightCondensed._proof_1", "Eq.mpr", "lightCondSetToTopCat", "CategoryTheory.Functor", "Opposite", "CategoryTheory.Epi", "congrArg", "CategoryTheor...
rw [TopCat.epi_iff_surjective] exact (topCatAdjunctionCounit_bijective _).2
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Condensed.Light.TopCatAdjunction
{ "line": 132, "column": 2 }
{ "line": 133, "column": 46 }
[ { "pp": "X✝ Y : LightCondSet\nf : X✝ ⟶ Y\nX : TopCat\n⊢ Epi (topCatAdjunction.counit.app X)", "usedConstants": [ "LightCondensed._proof_1", "Eq.mpr", "lightCondSetToTopCat", "CategoryTheory.Functor", "Opposite", "CategoryTheory.Epi", "congrArg", "CategoryTheor...
rw [TopCat.epi_iff_surjective] exact (topCatAdjunctionCounit_bijective _).2
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Topology.Category.LightProfinite.Injective
{ "line": 90, "column": 4 }
{ "line": 90, "column": 12 }
[ { "pp": "X : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : Topo...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Condensed.Discrete.Colimit
{ "line": 301, "column": 2 }
{ "line": 301, "column": 79 }
[ { "pp": "case w.h.w.e_a.h.toFun.h.h\nX : Profiniteᵒᵖ ⥤ Type (u + 1)\ninst✝ : PreservesFiniteProducts X\nhX : (S : Profinite) → IsColimit (X.mapCocone S.asLimitCone.op)\nS : Profiniteᵒᵖ\nY : FintypeCatᵒᵖ\nright✝ : Discrete PUnit.{1}\ng : toProfinite.op.obj Y ⟶ (fromPUnit S).obj right✝\nf :\n LocallyConstant (↑(...
apply injective_of_mono (isoFinYonedaComponents X (fiber.{u, u + 1} f x)).hom
Lean.Elab.Tactic.evalApply
Lean.Parser.Tactic.apply
Mathlib.Condensed.TopCatAdjunction
{ "line": 142, "column": 2 }
{ "line": 143, "column": 46 }
[ { "pp": "X✝ : CondensedSet\nX : TopCat\n⊢ Epi (topCatAdjunction.counit.app X)", "usedConstants": [ "Eq.mpr", "CategoryTheory.Functor", "Opposite", "CategoryTheory.Epi", "Condensed._proof_1", "congrArg", "CategoryTheory.ConcreteCategory.hom", "TopCat.instCatego...
rw [TopCat.epi_iff_surjective] exact (topCatAdjunctionCounit_bijective _).2
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Condensed.TopCatAdjunction
{ "line": 142, "column": 2 }
{ "line": 143, "column": 46 }
[ { "pp": "X✝ : CondensedSet\nX : TopCat\n⊢ Epi (topCatAdjunction.counit.app X)", "usedConstants": [ "Eq.mpr", "CategoryTheory.Functor", "Opposite", "CategoryTheory.Epi", "Condensed._proof_1", "congrArg", "CategoryTheory.ConcreteCategory.hom", "TopCat.instCatego...
rw [TopCat.epi_iff_surjective] exact (topCatAdjunctionCounit_bijective _).2
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Condensed.Light.Sequence
{ "line": 82, "column": 57 }
{ "line": 82, "column": 65 }
[ { "pp": "S : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X), Continuous (σ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Condensed.Light.Sequence
{ "line": 82, "column": 57 }
{ "line": 82, "column": 65 }
[ { "pp": "S : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X), Continuous (σ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Condensed.Light.Sequence
{ "line": 82, "column": 57 }
{ "line": 82, "column": 65 }
[ { "pp": "S : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X), Continuous (σ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Control.Traversable.Equiv
{ "line": 168, "column": 26 }
{ "line": 168, "column": 29 }
[ { "pp": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝² : Traversable t\ninst✝¹ : LawfulTraversable t\ninst✝ : Traversable t'\nh₀ : ∀ {α β : Type u} (f : α → β), map f = Equiv.map eqv f\nh₁ : ∀ {α β : Type u} (f : β), mapConst f = (Equiv.map eqv ∘ Function.const α) f\nh₂ :\n ∀ {F : Type u → Ty...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Control.Traversable.Equiv
{ "line": 169, "column": 32 }
{ "line": 169, "column": 35 }
[ { "pp": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝⁶ : Traversable t\ninst✝⁵ : LawfulTraversable t\ninst✝⁴ : Traversable t'\nh₀ : ∀ {α β : Type u} (f : α → β), map f = Equiv.map eqv f\nh₁ : ∀ {α β : Type u} (f : β), mapConst f = (Equiv.map eqv ∘ Function.const α) f\nh₂ :\n ∀ {F : Type u → T...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Control.Traversable.Equiv
{ "line": 170, "column": 35 }
{ "line": 170, "column": 38 }
[ { "pp": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝² : Traversable t\ninst✝¹ : LawfulTraversable t\ninst✝ : Traversable t'\nh₀ : ∀ {α β : Type u} (f : α → β), map f = Equiv.map eqv f\nh₁ : ∀ {α β : Type u} (f : β), mapConst f = (Equiv.map eqv ∘ Function.const α) f\nh₂ :\n ∀ {F : Type u → Ty...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Control.Traversable.Equiv
{ "line": 171, "column": 33 }
{ "line": 171, "column": 36 }
[ { "pp": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝⁶ : Traversable t\ninst✝⁵ : LawfulTraversable t\ninst✝⁴ : Traversable t'\nh₀ : ∀ {α β : Type u} (f : α → β), map f = Equiv.map eqv f\nh₁ : ∀ {α β : Type u} (f : β), mapConst f = (Equiv.map eqv ∘ Function.const α) f\nh₂ :\n ∀ {F : Type u → T...
h₂,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Data.Semiquot
{ "line": 48, "column": 24 }
{ "line": 48, "column": 44 }
[ { "pp": "α : Type u_1\nq₂ : Semiquot α\ns✝ : Set α\nv₁ : Trunc ↑s✝\nh : { s := s✝, val := v₁ }.s = q₂.s\n⊢ { s := s✝, val := v₁ } = q₂", "usedConstants": [] } ]
obtain ⟨_, v₂⟩ := q₂
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain
Lean.Parser.Tactic.obtain
Mathlib.Data.List.Lookmap
{ "line": 56, "column": 20 }
{ "line": 56, "column": 28 }
[ { "pp": "case none\nα : Type u_1\nf : α → Option α\na : α\nl : List α\nh : f a = none\n⊢ lookmap f (a :: l) =\n match none with\n | none => a :: lookmap f l\n | some b => b :: l", "usedConstants": [ "congrArg", "List.lookmap", "List.cons", "Option.none", "List", ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.List.Lookmap
{ "line": 56, "column": 20 }
{ "line": 56, "column": 28 }
[ { "pp": "case some\nα : Type u_1\nf : α → Option α\na : α\nl : List α\nval✝ : α\nh : f a = some val✝\n⊢ lookmap f (a :: l) =\n match some val✝ with\n | none => a :: lookmap f l\n | some b => b :: l", "usedConstants": [ "Eq.mpr", "congrArg", "Option.some.injEq", "Option.some"...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.FinEnum
{ "line": 238, "column": 4 }
{ "line": 239, "column": 48 }
[ { "pp": "case h.e_3\nα : Type u\nβ : α → Type v\ninst✝ : IsEmpty α\ne : FinEnum α\n⊢ equiv ≍ Equiv.equivOfIsEmpty α (Fin 0)", "usedConstants": [ "congrArg", "Equiv.equivOfIsEmpty", "FinEnum.card", "cast", "IsEmpty.instSubsingleton", "Equiv", "instOfNatNat", "E...
· refine heq_of_cast_eq ?_ (Subsingleton.allEq _ _) exact congrArg (α ≃ Fin ·) <| card_eq_zero
Lean.Elab.Tactic.evalTacticCDot
Lean.cdot
Mathlib.Data.Finset.DenselyOrdered
{ "line": 25, "column": 73 }
{ "line": 25, "column": 81 }
[ { "pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : DenselyOrdered α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\n⊢ s.max' hs < t.min' ht", "usedConstants": [ "Finset.min'", "Preorder.toLT", "Finset", "PartialOrder.toPreorder", "Finset.max'...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.Finset.DenselyOrdered
{ "line": 25, "column": 73 }
{ "line": 25, "column": 81 }
[ { "pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : DenselyOrdered α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\n⊢ s.max' hs < t.min' ht", "usedConstants": [ "Finset.min'", "Preorder.toLT", "Finset", "PartialOrder.toPreorder", "Finset.max'...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.Finset.DenselyOrdered
{ "line": 25, "column": 73 }
{ "line": 25, "column": 81 }
[ { "pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : DenselyOrdered α\ns t : Finset α\nhs : s.Nonempty\nht : t.Nonempty\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\n⊢ s.max' hs < t.min' ht", "usedConstants": [ "Finset.min'", "Preorder.toLT", "Finset", "PartialOrder.toPreorder", "Finset.max'...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Finset.DenselyOrdered
{ "line": 31, "column": 55 }
{ "line": 31, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : s.max' hs < p\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.Finset.DenselyOrdered
{ "line": 31, "column": 55 }
{ "line": 31, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : s.max' hs < p\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.Finset.DenselyOrdered
{ "line": 31, "column": 55 }
{ "line": 31, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : s.max' hs < p\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.List.AList
{ "line": 290, "column": 2 }
{ "line": 292, "column": 33 }
[ { "pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nl : AList β\nk k' : α\nv : β k\n⊢ lookup k' (insert k v l) = none ↔ k' ≠ k ∧ lookup k' l = none", "usedConstants": [ "False", "eq_false", "Option.ctorIdx", "congrArg", "AList.lookup_insert_ne", "False.elim", ...
by_cases h : k' = k · subst h; simp · simp_all [lookup_insert_ne h]
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.AList
{ "line": 290, "column": 2 }
{ "line": 292, "column": 33 }
[ { "pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nl : AList β\nk k' : α\nv : β k\n⊢ lookup k' (insert k v l) = none ↔ k' ≠ k ∧ lookup k' l = none", "usedConstants": [ "False", "eq_false", "Option.ctorIdx", "congrArg", "AList.lookup_insert_ne", "False.elim", ...
by_cases h : k' = k · subst h; simp · simp_all [lookup_insert_ne h]
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Finset.DenselyOrdered
{ "line": 32, "column": 55 }
{ "line": 32, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : p < t.min' ht\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.Finset.DenselyOrdered
{ "line": 32, "column": 55 }
{ "line": 32, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : p < t.min' ht\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.Finset.DenselyOrdered
{ "line": 32, "column": 55 }
{ "line": 32, "column": 63 }
[ { "pp": "α : 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\np : α\nhp : p < t.min' ht\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Finset.DenselyOrdered
{ "line": 33, "column": 43 }
{ "line": 33, "column": 51 }
[ { "pp": "α : 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\np : α\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ "False", "P...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.Finset.DenselyOrdered
{ "line": 33, "column": 43 }
{ "line": 33, "column": 51 }
[ { "pp": "α : 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\np : α\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ "False", "P...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.Finset.DenselyOrdered
{ "line": 33, "column": 43 }
{ "line": 33, "column": 51 }
[ { "pp": "α : 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\np : α\n⊢ (∀ x ∈ s, x < p) ∧ ∀ y ∈ t, p < y", "usedConstants": [ "False", "P...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Multiset.Functor
{ "line": 64, "column": 2 }
{ "line": 64, "column": 12 }
[ { "pp": "case trans\nF : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommApplicative F\nα' β' : Type u\nf : α' → F β'\na b l₁✝ l₂✝ l₃✝ : List α'\na✝¹ : l₁✝ ~ l₂✝\na✝ : l₂✝ ~ l₃✝\na_ih✝¹ : ofList <$> Traversable.traverse f l₁✝ = ofList <$> Traversable.traverse f l₂✝\na_ih✝ : ofList <$> Traversable.traverse ...
| trans =>
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction
null
Mathlib.Data.List.AList
{ "line": 377, "column": 2 }
{ "line": 377, "column": 37 }
[ { "pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : AList β\n⊢ extract a s = (lookup a s, erase a s)", "usedConstants": [ "Eq.mpr", "AList.extract._proof_3", "AList.mk", "congrArg", "id", "Prod.mk", "List.kextract_eq_dlookup_kerase", "List.k...
simp [extract]; constructor <;> rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.AList
{ "line": 377, "column": 2 }
{ "line": 377, "column": 37 }
[ { "pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : AList β\n⊢ extract a s = (lookup a s, erase a s)", "usedConstants": [ "Eq.mpr", "AList.extract._proof_3", "AList.mk", "congrArg", "id", "Prod.mk", "List.kextract_eq_dlookup_kerase", "List.k...
simp [extract]; constructor <;> rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Finset.Functor
{ "line": 100, "column": 30 }
{ "line": 100, "column": 37 }
[ { "pp": "case inl\nα β : Type u\ninst✝ : (P : Prop) → Decidable P\nα✝ β✝ : Type u_1\ns : Finset α✝\n⊢ (if True then ∅ else s) = (image (const β✝) s).sup fun f ↦ ∅", "usedConstants": [ "Eq.mpr", "Lattice.toSemilatticeSup", "if_true", "congrArg", "Finset", "id", "Fins...
if_true
Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1
null
Mathlib.Data.List.Sigma
{ "line": 321, "column": 4 }
{ "line": 322, "column": 29 }
[ { "pp": "case pos\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\na' : α\nb' : β a'\nl : List (Sigma β)\nh : a = a'\n⊢ b ∈ lookupAll a (⟨a', b'⟩ :: l) ↔ ⟨a, b⟩ ∈ ⟨a', b'⟩ :: l", "usedConstants": [ "congrArg", "heq_eq_eq", "Membership.mem", "Sigma.mk.injEq", ...
· subst h simp [*, mem_lookupAll]
Lean.Elab.Tactic.evalTacticCDot
Lean.cdot
Mathlib.Data.List.Sigma
{ "line": 376, "column": 6 }
{ "line": 376, "column": 14 }
[ { "pp": "case neg\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : a = a'\nh✝ : ¬decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "instDecidableTrue", "congrArg...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.List.Sigma
{ "line": 376, "column": 6 }
{ "line": 376, "column": 14 }
[ { "pp": "case neg\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : a = a'\nh✝ : ¬decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "instDecidableTrue", "congrArg...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.Sigma
{ "line": 376, "column": 6 }
{ "line": 376, "column": 14 }
[ { "pp": "case neg\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : a = a'\nh✝ : ¬decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "instDecidableTrue", "congrArg...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.List.Sigma
{ "line": 377, "column": 6 }
{ "line": 377, "column": 14 }
[ { "pp": "case pos\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : ¬a = a'\nh✝ : decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "eq_false", "congrArg", ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.List.Sigma
{ "line": 377, "column": 6 }
{ "line": 377, "column": 14 }
[ { "pp": "case pos\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : ¬a = a'\nh✝ : decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "eq_false", "congrArg", ...
simp_all
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.Sigma
{ "line": 377, "column": 6 }
{ "line": 377, "column": 14 }
[ { "pp": "case pos\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nnd : l.NodupKeys\nh : ⟨a, b⟩ ∈ l\na' : α\nb' : β a'\nh' : ⟨a', b'⟩ ∈ l\nh✝¹ : ¬a = a'\nh✝ : decide (a = a') = true\n⊢ False", "usedConstants": [ "False", "eq_false", "congrArg", ...
simp_all
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.List.Sigma
{ "line": 484, "column": 10 }
{ "line": 484, "column": 18 }
[ { "pp": "case H\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List (Sigma β)\nnd : l₁.NodupKeys\na✝³ b✝ : Sigma β\na✝² : a✝³.fst ≠ b✝.fst\na✝¹ : decide (a = a✝³.fst) = true\na✝ : decide (a = b✝.fst) = true\n⊢ False", "usedConstants": [ "False", "eq_false", "congrArg", ...
simp_all
Lean.Elab.Tactic.evalSimpAll
Lean.Parser.Tactic.simpAll
Mathlib.Data.List.Sigma
{ "line": 653, "column": 11 }
{ "line": 653, "column": 27 }
[ { "pp": "case nil\nα : Type u\nβ : α → Type v\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf (Sigma β)\n⊢ rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) [].dedupKeys ≤\n rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) []", "usedConstants": [ "Lean.Grind.instIsPreorderNat", "Std....
simp [dedupKeys]
Lean.Elab.Tactic.evalSimp
Lean.Parser.Tactic.simp
Mathlib.Data.List.Sigma
{ "line": 653, "column": 11 }
{ "line": 653, "column": 27 }
[ { "pp": "case nil\nα : Type u\nβ : α → Type v\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf (Sigma β)\n⊢ rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) [].dedupKeys ≤\n rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) []", "usedConstants": [ "Lean.Grind.instIsPreorderNat", "Std....
simp [dedupKeys]
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Data.List.Sigma
{ "line": 653, "column": 11 }
{ "line": 653, "column": 27 }
[ { "pp": "case nil\nα : Type u\nβ : α → Type v\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf (Sigma β)\n⊢ rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) [].dedupKeys ≤\n rec 1 (fun head tail tail_ih ↦ 1 + sizeOf head + tail_ih) []", "usedConstants": [ "Lean.Grind.instIsPreorderNat", "Std....
simp [dedupKeys]
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Data.Finsupp.NeLocus
{ "line": 71, "column": 46 }
{ "line": 71, "column": 59 }
[ { "pp": "case h\nα : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf : α →₀ N\na✝ : α\n⊢ f a✝ ≠ 0 a✝ ↔ f a✝ ≠ 0", "usedConstants": [ "Finsupp.instFunLike", "Eq.mpr", "congrArg", "Pi.zero_apply", "id", "Pi.instZero", "Ne", ...
Pi.zero_apply
Lean.Elab.Tactic.evalRewriteSeq
null