lean2/tests/lean/elab1.lean
Leonardo de Moura 048151487e feat(kernel): use Pi as forall/implication
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-08 00:38:39 -08:00

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