lean2/examples/ex16.lean

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Variable f : Pi (A : Type), A -> Bool
Show fun (A B : Type) (a : _), f B a
(* The following one should produce an error *)
(* Show fun (A : Type) (a : _) (B : Type), f B a *)
Variable myeq : Pi (A : Type u), A -> A -> Bool
Show myeq _ (fun (A : Type) (a : _), a) (fun (B : Type) (b : B), b)
Check myeq _ (fun (A : Type) (a : _), a) (fun (B : Type) (b : B), b)
Variable R : Type -> Bool
Variable h : (Pi (A : Type), R A) -> Bool
Check (fun (H : Bool)
(f1 : Pi (A : Type), R _)
(g1 : Pi (A : Type), R A)
(G : Pi (A : Type), myeq _ (f1 _) (g1 A)),
h f1)