1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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17 ninductive list (A : Type) : Type ≝
19 | cons : A → list A → list A.
23 naxiom c : list T → list S.
25 ncoercion foo : ∀_l:list T. list S ≝ c
29 naxiom P : list S → Prop.
31 ndefinition t1 ≝ ∀x:list T.P x → ?. ##[ napply Prop; ##] nqed.
33 ncoercion bar : ∀_l:list T. S → S ≝ λ_.λx.x
37 naxiom Q : (S → S) → Prop.
39 ndefinition t2 ≝ ∀x:list T.Q x → ?. ##[ napply Prop; ##] nqed.