Stuff moved from old Matita.

[helm.git] / matita / matita / tests / ng_coercions.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ng_pts.ma".
+
+(* easy *)
+naxiom T : Type.
+naxiom S : Type.
+naxiom R : Type.
+naxiom U : Type.
+naxiom c : T → S.
+naxiom c1 : S → R.
+naxiom c2 : R → U.
+
+ncoercion foo1 : ∀_t:T.S ≝ c on _t : T to S.
+ncoercion foo2 : ∀_r:R.U ≝ c2 on _r : R to U.
+ncoercion foo3 : ∀_s:S.R ≝ c1 on _s : S to R.
+
+(* another *)
+
+naxiom nat : Type.
+naxiom A : nat → Type. 
+naxiom B : nat → Type.
+naxiom C : nat → Type.
+naxiom D : nat → Type.
+naxiom a :  ∀n:nat. A n → B n.
+naxiom a1 : ∀n:nat. B n → C n.
+naxiom a2 : ∀n:nat. C n → D n.
+
+ncoercion foo1 : ∀n:nat. ∀_a:A n. B n ≝ a  on _a : A ? to B ?.
+ncoercion foo2 : ∀n:nat. ∀_c:C n. D n ≝ a2 on _c : C ? to D ?.
+ncoercion foo3 : ∀n:nat. ∀_b:B n. C n ≝ a1 on _b : B ? to C ?.
+
+naxiom cx : ∀n,m:nat. B n → C m.
+
+ncoercion foo3 : ∀n,m:nat. ∀_b:B n. C m ≝ cx on _b : B ? to C ?.
+
+naxiom Suc : nat → nat.
+naxiom cs : ∀n:nat. B n → C (Suc n).
+
+ncoercion foo3 : ∀n:nat. ∀_b:B n. C (Suc n) ≝ cs on _b : B ? to C ?.
+
+(* funclass *)
+naxiom Y : Type.
+naxiom W : Type.
+naxiom X : Type.
+naxiom f : Y → W.
+naxiom g : W → X → X → X.
+
+ncoercion foo : ∀_y:Y. W ≝ f on _y : Y to W. 
+ncoercion foo : ∀_w:W. X → X → X ≝ g on _w : W to Π_.Π_.?.