more work on coercions composition

diff --git a/helm/software/matita/tests/ng_coercions.ma b/helm/software/matita/tests/ng_coercions.ma
index 308697d3c7d1cefd3a73b903755067d217858f13..3e22b3410b426b980396440ed8673c0a8c244cca 100644 (file)
--- a/helm/software/matita/tests/ng_coercions.ma
+++ b/helm/software/matita/tests/ng_coercions.ma
@@ -14,29 +14,49 @@
 
 include "ng_pts.ma".
 
-ninductive list (A : Type) : Type ≝ 
- | nil : list A
- | cons : A → list A → list A. 
-
+(* easy *)
 naxiom T : Type.
 naxiom S : Type.
-naxiom c : list T → list S.
-
-ncoercion foo : ∀_l:list T. list S ≝ c    
-  on _l : list T 
-  to      list ?.
-  
-naxiom P : list S → Prop.  
-  
-ndefinition t1 ≝ ∀x:list T.P x → ?. ##[ napply Prop; ##] nqed.
-  
-ncoercion bar : ∀_l:list T. S → S ≝ λ_.λx.x     
-  on _l : list T 
-  to      Π_.?.
-  
-naxiom Q : (S → S) → Prop.
-
-ndefinition t2 ≝ ∀x:list T.Q x → ?. ##[ napply Prop; ##] nqed.
-
-  
-  
\ No newline at end of file
+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_.?.