the new coercion behaviour (variants + composition with ID) and the new

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / relations.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/relations.ma b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
index 5678b6a892bbc75c2f5f97852dd3c820566349e5..74a7c7d7839bb26fee44529654fc3cc5ff653bb2 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -21,7 +21,7 @@ notation < "hvbox (x \nbsp \natur term 90 r \nbsp y)"  with precedence 45 for @{
 notation > "hvbox (x \natur term 90 r y)"  with precedence 45 for @{'satisfy $r $x $y}.
 interpretation "relation applied" 'satisfy r x y = (fun21 ___ (satisfy __ r) x y).
 
-definition binary_relation_setoid: SET → SET → SET1.
+definition binary_relation_setoid: SET → SET → setoid1.
  intros (A B);
  constructor 1;
   [ apply (binary_relation A B)
@@ -36,6 +36,10 @@ definition binary_relation_setoid: SET → SET → SET1.
        assumption]]
 qed.
 
+definition binary_relation_of_binary_relation_setoid : 
+  ∀A,B.binary_relation_setoid A B → binary_relation A B ≝ λA,B,c.c.
+coercion binary_relation_of_binary_relation_setoid.
+
 definition composition:
  ∀A,B,C.
   binary_morphism1 (binary_relation_setoid A B) (binary_relation_setoid B C) (binary_relation_setoid A C).
@@ -94,6 +98,15 @@ definition REL: category1.
           first [apply refl | assumption]]]
 qed.
 
+(* 
+definition setoid_of_REL : objs1 REL → setoid ≝ λx.x.
+coercion setoid_of_REL.
+*)
+
+definition binary_relation_setoid_of_arrow1_REL : 
+  ∀P,Q. arrows1 REL P Q → binary_relation_setoid P Q ≝ λP,Q,x.x.
+coercion binary_relation_setoid_of_arrow1_REL.
+
 definition full_subset: ∀s:REL. Ω \sup s.
  apply (λs.{x | True});
  intros; simplify; split; intro; assumption.
@@ -101,15 +114,6 @@ qed.
 
 coercion full_subset.
 
-definition setoid1_of_REL: REL → setoid ≝ λS. S.
-coercion setoid1_of_REL.
-
-lemma Type_OF_setoid1_of_REL: ∀o1:Type_OF_category1 REL. Type_OF_objs1 o1 → Type_OF_setoid1 ?(*(setoid1_of_SET o1)*).
- [ apply rule o1;
- | intros; apply t;]
-qed.
-coercion Type_OF_setoid1_of_REL.
-
 definition comprehension: ∀b:REL. (unary_morphism1 b CPROP) → Ω \sup b.
  apply (λb:REL. λP: b ⇒ CPROP. {x | P x});
  intros; simplify;