helm/software/matita/tests/ng_coercions.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 axiom A : Type.
  16 axiom B : Type.
  17 axiom C : Type.
  18
  19 axiom f : A → B.
  20 axiom g : B → C.
  21
  22 (* nlemma xxx : ∀P:C → Prop. ∀x:A. P x. *)
  23
  24 coercion f. coercion g.
  25
  26 axiom T : Type.
  27
  28 axiom h : A → T. coercion h.
  29
  30 nlemma xxx : ∀P:C → Prop. ∀x:A. P x.