90a79a0b06
Now, `universe` may declare many universes. The goal is to make it consistent with the `variable` command
43 lines
936 B
Text
43 lines
936 B
Text
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def g : List Nat → List Nat → Nat
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| [], y::ys => y
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| [], ys => 0
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| x1::x2::xs, ys => g xs ys
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| x::xs, y::ys => g xs ys + y
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| x::xs, [] => g xs []
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universe u v
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inductive Imf {α : Type u} {β : Type v} (f : α → β) : β → Type (max u v)
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| mk : (a : α) → Imf f (f a)
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def h {α β} {f : α → β} : {b : β} → Imf f b → α
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| _, Imf.mk a => a
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theorem ex1 {α β} (f : α → β) (a : α) : h (Imf.mk (f := f) a) = a :=
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rfl
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def v₁ : Imf Nat.succ 1 :=
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Imf.mk 0
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def v₂ : Imf (fun x => 1 + x) 1 :=
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Imf.mk 0
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theorem ex2 : h v₁ = 0 :=
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rfl
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theorem ex3 : h v₂ = 0 :=
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rfl
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theorem ex4 {α} : {a b : α} → a = b → b = a
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| _, _, rfl => rfl
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theorem ex5 {α} : {a b : α} → a = b → b = a
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| a, .(a), rfl => rfl
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theorem ex6 {α} : {a b : α} → a = b → b = a
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| a, .(a), Eq.refl .(a) => rfl
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theorem ex7 {α} : {a b : α} → a = b → b = a
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| .(a), a, Eq.refl .(a) => rfl
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