311 lines
14 KiB
Text
311 lines
14 KiB
Text
[Elab.info] command @ ⟨13, 0⟩-⟨15, 6⟩
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Nat : Type @ ⟨13, 11⟩-⟨13, 14⟩
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[.] `Nat : some Sort.{?_uniq.535} @ ⟨13, 11⟩-⟨13, 14⟩
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Nat : Type @ ⟨13, 11⟩-⟨13, 14⟩
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x : Nat @ ⟨13, 7⟩-⟨13, 8⟩
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Nat × Nat : Type @ ⟨13, 18⟩-⟨13, 27⟩
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Macro expansion
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Nat × Nat
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===>
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Prod✝ Nat Nat
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Prod : Type → Type → Type @ ⟨13, 18⟩†-⟨13, 22⟩†
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Nat : Type @ ⟨13, 18⟩-⟨13, 21⟩
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[.] `Nat : some Type.{?_uniq.539} @ ⟨13, 18⟩-⟨13, 21⟩
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Nat : Type @ ⟨13, 18⟩-⟨13, 21⟩
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Nat : Type @ ⟨13, 24⟩-⟨13, 27⟩
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[.] `Nat : some Type.{?_uniq.538} @ ⟨13, 24⟩-⟨13, 27⟩
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Nat : Type @ ⟨13, 24⟩-⟨13, 27⟩
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let y : Nat × Nat := (x, x);
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id y : Nat × Nat @ ⟨14, 2⟩-⟨15, 6⟩
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Nat × Nat : Type @ ⟨14, 6⟩-⟨14, 7⟩
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(x, x) : Nat × Nat @ ⟨14, 11⟩-⟨14, 17⟩
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Macro expansion
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⟨x, x⟩
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===>
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Prod.mk✝ x x
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(x, x) : Nat × Nat @ ⟨14, 11⟩†-⟨14, 16⟩
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Prod.mk : {α β : Type} → α → β → α × β @ ⟨14, 11⟩†-⟨17, 8⟩†
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x : Nat @ ⟨14, 12⟩-⟨14, 13⟩
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x : Nat @ ⟨14, 12⟩-⟨14, 13⟩
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x : Nat @ ⟨14, 15⟩-⟨14, 16⟩
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x : Nat @ ⟨14, 15⟩-⟨14, 16⟩
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y : Nat × Nat @ ⟨14, 6⟩-⟨14, 7⟩
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id y : Nat × Nat @ ⟨15, 2⟩-⟨15, 6⟩
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[.] `id : some Prod.{0 0} Nat Nat @ ⟨15, 2⟩-⟨15, 4⟩
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id : {α : Type} → α → α @ ⟨15, 2⟩-⟨15, 4⟩
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y : Nat × Nat @ ⟨15, 5⟩-⟨15, 6⟩
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y : Nat × Nat @ ⟨15, 5⟩-⟨15, 6⟩
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[Elab.info] command @ ⟨17, 0⟩-⟨19, 8⟩
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∀ (x y : Nat), Bool → x + 0 = x : Prop @ ⟨17, 8⟩-⟨17, 44⟩
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Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
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[.] `Nat : some Sort.{?_uniq.568} @ ⟨17, 15⟩-⟨17, 18⟩
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Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
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x : Nat @ ⟨17, 9⟩-⟨17, 10⟩
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Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
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[.] `Nat : some Sort.{?_uniq.570} @ ⟨17, 15⟩-⟨17, 18⟩
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Nat : Type @ ⟨17, 15⟩-⟨17, 18⟩
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y : Nat @ ⟨17, 11⟩-⟨17, 12⟩
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Bool → x + 0 = x : Prop @ ⟨17, 22⟩-⟨17, 44⟩
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Bool : Type @ ⟨17, 27⟩-⟨17, 31⟩
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[.] `Bool : some Sort.{?_uniq.573} @ ⟨17, 27⟩-⟨17, 31⟩
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Bool : Type @ ⟨17, 27⟩-⟨17, 31⟩
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b : Bool @ ⟨17, 23⟩-⟨17, 24⟩
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x + 0 = x : Prop @ ⟨17, 35⟩-⟨17, 44⟩
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Macro expansion
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x + 0 = x
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===>
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binrel% Eq✝ (x + 0)x
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x + 0 : Nat @ ⟨17, 35⟩-⟨17, 40⟩
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Macro expansion
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x + 0
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===>
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binop% HAdd.hAdd✝ x 0
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Macro expansion
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binop% HAdd.hAdd✝ x 0
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===>
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HAdd.hAdd✝ x 0
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x + 0 : Nat @ ⟨17, 35⟩†-⟨17, 40⟩
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HAdd.hAdd : {α β γ : Type} → [self : HAdd α β γ] → α → β → γ @ ⟨17, 35⟩†-⟨17, 44⟩†
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x : Nat @ ⟨17, 35⟩-⟨17, 36⟩
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x : Nat @ ⟨17, 35⟩-⟨17, 36⟩
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0 : Nat @ ⟨17, 39⟩-⟨17, 40⟩
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x : Nat @ ⟨17, 43⟩-⟨17, 44⟩
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x : Nat @ ⟨17, 43⟩-⟨17, 44⟩
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fun (x y : Nat) (b : Bool) =>
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ofEqTrue
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(Eq.trans (congrFun (congrArg Eq (Nat.add_zero x)) x)
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(eqSelf x)) : ∀ (x y : Nat), Bool → x + 0 = x @ ⟨18, 2⟩-⟨19, 8⟩
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Nat : Type @ ⟨18, 6⟩-⟨18, 7⟩
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x : Nat @ ⟨18, 6⟩-⟨18, 7⟩
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Nat : Type @ ⟨18, 8⟩-⟨18, 9⟩
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y : Nat @ ⟨18, 8⟩-⟨18, 9⟩
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Bool : Type @ ⟨18, 10⟩-⟨18, 11⟩
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b : Bool @ ⟨18, 10⟩-⟨18, 11⟩
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Tactic @ ⟨18, 15⟩-⟨19, 8⟩
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(Term.byTactic "by" (Tactic.tacticSeq (Tactic.tacticSeq1Indented [(group (Tactic.simp "simp" [] [] [] []) [])])))
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before
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x y : Nat
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b : Bool
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⊢ x + 0 = x
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after no goals
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Tactic @ ⟨19, 4⟩-⟨19, 8⟩
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(Tactic.tacticSeq (Tactic.tacticSeq1Indented [(group (Tactic.simp "simp" [] [] [] []) [])]))
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before
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x y : Nat
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b : Bool
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⊢ x + 0 = x
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after no goals
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Tactic @ ⟨19, 4⟩-⟨19, 8⟩
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(Tactic.tacticSeq1Indented [(group (Tactic.simp "simp" [] [] [] []) [])])
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before
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x y : Nat
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b : Bool
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⊢ x + 0 = x
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after no goals
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Tactic @ ⟨19, 4⟩-⟨19, 8⟩
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(Tactic.simp "simp" [] [] [] [])
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before
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x y : Nat
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b : Bool
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⊢ x + 0 = x
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after no goals
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[Elab.info] command @ ⟨21, 0⟩-⟨25, 10⟩
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Nat → Nat → Bool → Nat : Type @ ⟨21, 9⟩-⟨21, 39⟩
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Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
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[.] `Nat : some Sort.{?_uniq.890} @ ⟨21, 16⟩-⟨21, 19⟩
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Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
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x : Nat @ ⟨21, 10⟩-⟨21, 11⟩
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Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
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[.] `Nat : some Sort.{?_uniq.892} @ ⟨21, 16⟩-⟨21, 19⟩
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Nat : Type @ ⟨21, 16⟩-⟨21, 19⟩
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y : Nat @ ⟨21, 12⟩-⟨21, 13⟩
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Bool → Nat : Type @ ⟨21, 23⟩-⟨21, 39⟩
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Bool : Type @ ⟨21, 28⟩-⟨21, 32⟩
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[.] `Bool : some Sort.{?_uniq.895} @ ⟨21, 28⟩-⟨21, 32⟩
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Bool : Type @ ⟨21, 28⟩-⟨21, 32⟩
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b : Bool @ ⟨21, 24⟩-⟨21, 25⟩
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Nat : Type @ ⟨21, 36⟩-⟨21, 39⟩
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[.] `Nat : some Sort.{?_uniq.897} @ ⟨21, 36⟩-⟨21, 39⟩
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Nat : Type @ ⟨21, 36⟩-⟨21, 39⟩
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fun (x y : Nat) (b : Bool) =>
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let x : Nat × Nat := (x + y, x - y);
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match x with
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let z1 : Nat := z + w;
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z + z1 : Nat → Nat → Bool → Nat @ ⟨22, 2⟩-⟨25, 10⟩
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Nat : Type @ ⟨22, 6⟩-⟨22, 7⟩
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x : Nat @ ⟨22, 6⟩-⟨22, 7⟩
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Nat : Type @ ⟨22, 8⟩-⟨22, 9⟩
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y : Nat @ ⟨22, 8⟩-⟨22, 9⟩
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Bool : Type @ ⟨22, 10⟩-⟨22, 11⟩
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b : Bool @ ⟨22, 10⟩-⟨22, 11⟩
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let x : Nat × Nat := (x + y, x - y);
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match x with
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let z1 : Nat := z + w;
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z + z1 : Nat @ ⟨23, 4⟩-⟨25, 10⟩
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Macro expansion
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let (z, w) := (x + y, x - y)
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let z1 := z + w
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z + z1
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===>
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let x✝ : _ := (x + y, x - y);
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match x✝ with
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let z1 := z + w
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z + z1
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let x : Nat × Nat := (x + y, x - y);
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match x with
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let z1 : Nat := z + w;
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z + z1 : Nat @ ⟨23, 4⟩†-⟨25, 10⟩
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Nat × Nat : Type @ ⟨23, 4⟩-⟨23, 5⟩
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(x + y, x - y) : Nat × Nat @ ⟨23, 18⟩-⟨23, 32⟩
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Macro expansion
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(x + y, x - y)
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===>
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Prod.mk✝ (x + y) (x - y)
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Prod.mk : {α β : Type} → α → β → α × β @ ⟨23, 18⟩†-⟨23, 25⟩†
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x + y : Nat @ ⟨23, 19⟩-⟨23, 24⟩
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Macro expansion
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x + y
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===>
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binop% HAdd.hAdd✝ x y
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x : Nat @ ⟨23, 19⟩-⟨23, 20⟩
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x : Nat @ ⟨23, 19⟩-⟨23, 20⟩
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y : Nat @ ⟨23, 23⟩-⟨23, 24⟩
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y : Nat @ ⟨23, 23⟩-⟨23, 24⟩
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x - y : Nat @ ⟨23, 26⟩-⟨23, 31⟩
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Macro expansion
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x - y
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===>
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binop% HSub.hSub✝ x y
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x : Nat @ ⟨23, 26⟩-⟨23, 27⟩
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x : Nat @ ⟨23, 26⟩-⟨23, 27⟩
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y : Nat @ ⟨23, 30⟩-⟨23, 31⟩
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y : Nat @ ⟨23, 30⟩-⟨23, 31⟩
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x✝ : Nat × Nat @ ⟨23, 4⟩†-⟨25, 10⟩†
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match x✝ with
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| (z, w) =>
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let z1 : Nat := z + w;
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z + z1 : Nat @ ⟨23, 4⟩†-⟨25, 10⟩
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Prod.mk : {α : Type ?u} → {β : Type ?u} → α → β → α × β @ ⟨23, 4⟩†-⟨25, 10⟩†
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[.] `z : none @ ⟨23, 9⟩-⟨23, 10⟩
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[.] `w : none @ ⟨23, 12⟩-⟨23, 13⟩
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(z, w) : Nat × Nat @ ⟨23, 4⟩†-⟨23, 13⟩
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Prod.mk : {α β : Type} → α → β → α × β @ ⟨23, 4⟩†-⟨23, 11⟩†
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Nat : Type @ ⟨23, 4⟩†-⟨23, 13⟩†
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Nat : Type @ ⟨23, 4⟩†-⟨23, 13⟩†
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z : Nat @ ⟨23, 9⟩-⟨23, 10⟩
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z : Nat @ ⟨23, 9⟩-⟨23, 10⟩
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w : Nat @ ⟨23, 12⟩-⟨23, 13⟩
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w : Nat @ ⟨23, 12⟩-⟨23, 13⟩
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let z1 : Nat := z + w;
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z + z1 : Nat @ ⟨24, 4⟩-⟨25, 10⟩
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Nat : Type @ ⟨24, 8⟩-⟨24, 9⟩
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z + w : Nat @ ⟨24, 14⟩-⟨24, 19⟩
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Macro expansion
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z + w
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===>
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binop% HAdd.hAdd✝ z w
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z : Nat @ ⟨24, 14⟩-⟨24, 15⟩
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z : Nat @ ⟨24, 14⟩-⟨24, 15⟩
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w : Nat @ ⟨24, 18⟩-⟨24, 19⟩
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w : Nat @ ⟨24, 18⟩-⟨24, 19⟩
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z1 : Nat @ ⟨24, 8⟩-⟨24, 10⟩
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z + z1 : Nat @ ⟨25, 4⟩-⟨25, 10⟩
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Macro expansion
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z + z1
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===>
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binop% HAdd.hAdd✝ z z1
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z : Nat @ ⟨25, 4⟩-⟨25, 5⟩
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z : Nat @ ⟨25, 4⟩-⟨25, 5⟩
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z1 : Nat @ ⟨25, 8⟩-⟨25, 10⟩
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z1 : Nat @ ⟨25, 8⟩-⟨25, 10⟩
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[Elab.info] command @ ⟨27, 0⟩-⟨28, 17⟩
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Nat × Array (Array Nat) : Type @ ⟨27, 12⟩-⟨27, 35⟩
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Macro expansion
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Nat × Array (Array Nat)
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===>
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Prod✝ Nat (Array (Array Nat))
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Prod : Type → Type → Type @ ⟨27, 12⟩†-⟨27, 16⟩†
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Nat : Type @ ⟨27, 12⟩-⟨27, 15⟩
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[.] `Nat : some Type.{?_uniq.1900} @ ⟨27, 12⟩-⟨27, 15⟩
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Nat : Type @ ⟨27, 12⟩-⟨27, 15⟩
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Array (Array Nat) : Type @ ⟨27, 18⟩-⟨27, 35⟩
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[.] `Array : some Type.{?_uniq.1899} @ ⟨27, 18⟩-⟨27, 23⟩
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Array : Type → Type @ ⟨27, 18⟩-⟨27, 23⟩
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Array Nat : Type @ ⟨27, 24⟩-⟨27, 35⟩
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Macro expansion
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(Array Nat)
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===>
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Array Nat
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[.] `Array : some Type.{?_uniq.1901} @ ⟨27, 25⟩-⟨27, 30⟩
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Array : Type → Type @ ⟨27, 25⟩-⟨27, 30⟩
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Nat : Type @ ⟨27, 31⟩-⟨27, 34⟩
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[.] `Nat : some Type.{?_uniq.1902} @ ⟨27, 31⟩-⟨27, 34⟩
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Nat : Type @ ⟨27, 31⟩-⟨27, 34⟩
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s : Nat × Array (Array Nat) @ ⟨27, 8⟩-⟨27, 9⟩
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Array Nat : Type @ ⟨27, 39⟩-⟨27, 48⟩
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[.] `Array : some Sort.{?_uniq.1904} @ ⟨27, 39⟩-⟨27, 44⟩
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Array : Type → Type @ ⟨27, 39⟩-⟨27, 44⟩
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Nat : Type @ ⟨27, 45⟩-⟨27, 48⟩
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[.] `Nat : some Type.{?_uniq.1905} @ ⟨27, 45⟩-⟨27, 48⟩
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Nat : Type @ ⟨27, 45⟩-⟨27, 48⟩
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Array.push (Array.getOp s.snd 1) s.fst : Array Nat @ ⟨28, 2⟩-⟨28, 17⟩
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s : Nat × Array (Array Nat) @ ⟨28, 2⟩-⟨28, 3⟩
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Prod.snd : {α β : Type} → α × β → β @ ⟨28, 4⟩-⟨28, 5⟩
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Array.getOp : {α : Type} → [inst : Inhabited α] → Array α → Nat → α @ ⟨28, 5⟩-⟨28, 6⟩
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1 : Nat @ ⟨28, 6⟩-⟨28, 7⟩
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[.] Array.getOp s.snd 1 : Array Nat @ ⟨28, 2⟩-⟨28, 8⟩ : some Array.{0} Nat
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Array.push : {α : Type} → Array α → α → Array α @ ⟨28, 9⟩-⟨28, 13⟩
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s.fst : Nat @ ⟨28, 14⟩-⟨28, 17⟩
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s : Nat × Array (Array Nat) @ ⟨28, 14⟩-⟨28, 15⟩
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Prod.fst : {α β : Type} → α × β → α @ ⟨28, 16⟩-⟨28, 17⟩
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[Elab.info] command @ ⟨30, 0⟩-⟨31, 20⟩
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B : Type @ ⟨30, 14⟩-⟨30, 15⟩
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[.] `B : some Sort.{?_uniq.1946} @ ⟨30, 14⟩-⟨30, 15⟩
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B : Type @ ⟨30, 14⟩-⟨30, 15⟩
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arg : B @ ⟨30, 8⟩-⟨30, 11⟩
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Nat : Type @ ⟨30, 19⟩-⟨30, 22⟩
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[.] `Nat : some Sort.{?_uniq.1948} @ ⟨30, 19⟩-⟨30, 22⟩
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Nat : Type @ ⟨30, 19⟩-⟨30, 22⟩
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A.val arg.pair.fst 0 : Nat @ ⟨31, 2⟩-⟨31, 20⟩
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arg : B @ ⟨31, 2⟩-⟨31, 5⟩
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[.] arg : B @ ⟨31, 2⟩-⟨31, 18⟩ : some Nat
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B.pair : B → A × A @ ⟨31, 6⟩-⟨31, 10⟩
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[.] arg.pair : A × A @ ⟨31, 2⟩-⟨31, 18⟩ : some Nat
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Prod.fst : {α β : Type} → α × β → α @ ⟨31, 11⟩-⟨31, 14⟩
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[.] arg.pair.fst : A @ ⟨31, 2⟩-⟨31, 18⟩ : some Nat
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A.val : A → Nat → Nat @ ⟨31, 15⟩-⟨31, 18⟩
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0 : Nat @ ⟨31, 19⟩-⟨31, 20⟩
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[Elab.info] command @ ⟨33, 0⟩-⟨35, 1⟩
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Nat : Type @ ⟨33, 12⟩-⟨33, 15⟩
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[.] `Nat : some Sort.{?_uniq.1968} @ ⟨33, 12⟩-⟨33, 15⟩
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Nat : Type @ ⟨33, 12⟩-⟨33, 15⟩
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x : Nat @ ⟨33, 8⟩-⟨33, 9⟩
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B : Type @ ⟨33, 19⟩-⟨33, 20⟩
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[.] `B : some Sort.{?_uniq.1970} @ ⟨33, 19⟩-⟨33, 20⟩
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B : Type @ ⟨33, 19⟩-⟨33, 20⟩
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{ pair := ({ val := id }, { val := id }) } : B @ ⟨33, 24⟩-⟨35, 1⟩
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({ val := id }, { val := id }) : A × A @ ⟨34, 10⟩-⟨34, 40⟩
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Macro expansion
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({ val := id }, { val := id })
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===>
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Prod.mk✝ { val := id } { val := id }
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Prod.mk : {α β : Type} → α → β → α × β @ ⟨34, 10⟩†-⟨34, 17⟩†
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{ val := id } : A @ ⟨34, 11⟩-⟨34, 24⟩
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id : Nat → Nat @ ⟨34, 20⟩-⟨34, 22⟩
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[.] `id : some Nat -> Nat @ ⟨34, 20⟩-⟨34, 22⟩
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id : {α : Type} → α → α @ ⟨34, 20⟩-⟨34, 22⟩
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val : Nat → Nat := id @ ⟨34, 13⟩-⟨34, 16⟩
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{ val := id } : A @ ⟨34, 26⟩-⟨34, 39⟩
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id : Nat → Nat @ ⟨34, 35⟩-⟨34, 37⟩
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[.] `id : some Nat -> Nat @ ⟨34, 35⟩-⟨34, 37⟩
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id : {α : Type} → α → α @ ⟨34, 35⟩-⟨34, 37⟩
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val : Nat → Nat := id @ ⟨34, 28⟩-⟨34, 31⟩
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pair : A × A := ({ val := id }, { val := id }) @ ⟨34, 2⟩-⟨34, 6⟩
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def id.{u} : {α : Sort u} → α → α :=
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||
fun {α : Sort u} (a : α) => a
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[Elab.info] command @ ⟨37, 0⟩-⟨37, 9⟩
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||
id : {α : Sort u} → α → α @ ⟨37, 7⟩-⟨37, 9⟩
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