27 lines
677 B
Text
27 lines
677 B
Text
variable f {A : Type} (a b : A) : A.
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check f 10 true
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variable g {A B : Type} (a : A) : A.
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check g 10
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variable h : Pi (A : Type), A -> A.
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check fun x, fun A : Type, h A x
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variable my_eq : Pi A : Type, A -> A -> Bool.
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check fun (A B : Type) (a : _) (b : _) (C : Type), my_eq C a b.
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variable a : Bool
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variable b : Bool
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variable H : a /\ b
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theorem t1 : b := discharge (fun H1, and::intro H1 (and::eliml H)).
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theorem t2 : a = b := trans (refl a) (refl b).
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check f Bool Bool.
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theorem pierce (a b : Bool) : ((a ⇒ b) ⇒ a) ⇒ a :=
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discharge (λ H, or::elim (EM a)
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(λ H_a, H)
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(λ H_na, NotImp1 (MT H H_na)))
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