definition hole : ∀A:Type.A → A ≝ λA.λx.x.
-inductive pippo (T:Type) (x:T) : Prop ≝ .
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-axiom A: Type.
-axiom B:A.
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-axiom foo : \forall x: (hole ? A).pippo (hole ? A) x.
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-axiom foo: (λx,y:A. pippo (hole ? A) x y)
- (hole ? B) (hole ? B).
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-axiom foo: λx:(hole ? Type).λy:(hole ? Type). pippo (hole ? Type) x y.
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axiom foo: (λx,y.(λz. z x + z (x+y)) (λw:nat.hole ? w)) = λx,y.x. (* KO, delift rels only *)
axiom foo: (λx,y.(λz. z (x+y) + z x) (λw:nat.hole ? w)) = λx,y.x. (* OK *)