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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "nat/plus.ma".
17 definition hole : ∀A:Type.A → A ≝ λA.λx.x.
19 inductive pippo (T:Type) (x:T) : Prop ≝ .
24 axiom foo : \forall x: (hole ? A).pippo (hole ? A) x.
26 axiom foo: (λx,y:A. pippo (hole ? A) x y)
27 (hole ? B) (hole ? B).
29 axiom foo: λx:(hole ? Type).λy:(hole ? Type). pippo (hole ? Type) x y.
31 axiom foo: (λx,y.(λz. z x + z (x+y)) (λw:nat.hole ? w)) = λx,y.x. (* KO, delift rels only *)
32 axiom foo: (λx,y.(λz. z (x+y) + z x) (λw:nat.hole ? w)) = λx,y.x. (* OK *)
35 axiom foo: (λx,y.(λz. z x + z y) (λw:nat.hole ? w)) = λx,y.x. (* OK *)