30 lines
1.2 KiB
Text
30 lines
1.2 KiB
Text
protected def Nat.add : Nat → Nat → Nat :=
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fun x x_1 =>
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Nat.brecOn x_1
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(fun x f x_2 =>
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(match x_2, x with
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| a, Nat.zero => fun x => a
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| a, Nat.succ b => fun x => Nat.succ (PProd.fst x.fst a))
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f)
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x
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protected def Nat.add : Nat → Nat → Nat :=
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fun x x_1 =>
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Nat.brecOn (motive := fun x => Nat → Nat) x_1
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(fun x f x_2 =>
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(match (motive := (x x : Nat) → Nat.below (motive := fun x => Nat → Nat) x → Nat) x_2, x with
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| a, Nat.zero => fun x => a
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| a, Nat.succ b => fun x => Nat.succ (PProd.fst x.fst a))
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f)
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x
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theorem ex.{u} : ∀ {α β : Sort u} (h : α = β) (a : α), HEq (cast h a) a :=
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fun x x_1 x_2 x_3 =>
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match x, x_1, x_2, x_3 with
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| α, .(α), Eq.refl α, a => HEq.refl a
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theorem ex.{u} : ∀ {α β : Sort u} (h : α = β) (a : α), HEq (cast h a) a :=
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fun x x_1 x_2 x_3 =>
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match (motive := ∀ (x x_4 : Sort u) (x_5 : x = x_4) (x_6 : x), HEq (cast x_5 x_6) x_6) x, x_1, x_2, x_3 with
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| α, .(α), Eq.refl α, a => HEq.refl a
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def fact : Nat → Nat :=
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fun n => Nat.recOn n 1 fun n acc => (n + 1) * acc
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def fact : Nat → Nat :=
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fun n => Nat.recOn (motive := fun n => Nat) n 1 fun n acc => (n + 1) * acc
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