The new coercion from SET to Type0 with higher priority really helps a lot:

[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 ec7db6df4899b3b49de18c8ccb4ab711994e76e9..5678b6a892bbc75c2f5f97852dd3c820566349e5 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -44,9 +44,7 @@ definition composition:
   [ intros (R12 R23);
     constructor 1;
     constructor 1;
-     [ alias symbol "and" = "and_morphism".
-       (* carr to avoid universe inconsistency *)  
-       apply (λs1:carr A.λs3:carr C.∃s2:carr B. s1 ♮R12 s2 ∧ s2 ♮R23 s3);
+     [ apply (λs1:A.λs3:C.∃s2:B. s1 ♮R12 s2 ∧ s2 ♮R23 s3);
      | intros;
        split; intro; cases e2 (w H3); clear e2; exists; [1,3: apply w ]
         [ apply (. (e^-1‡#)‡(#‡e1^-1)); assumption
@@ -107,7 +105,7 @@ 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 (setoid1_of_SET o1);
+ [ apply rule o1;
  | intros; apply t;]
 qed.
 coercion Type_OF_setoid1_of_REL.
@@ -187,7 +185,7 @@ qed.
 (* the same as ⋄ for a basic pair *)
 definition image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) (Ω \sup V).
  intros; constructor 1;
-  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∃x:carr U. x ♮r y ∧ x ∈ S });
+  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∃x:U. x ♮r y ∧ x ∈ S });
     intros; simplify; split; intro; cases e1; exists [1,3: apply w]
      [ apply (. (#‡e^-1)‡#); assumption
      | apply (. (#‡e)‡#); assumption]
@@ -201,7 +199,7 @@ qed.
 (* the same as □ for a basic pair *)
 definition minus_star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) (Ω \sup V).
  intros; constructor 1;
-  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∀x:carr U. x ♮r y → x ∈ S});
+  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∀x:U. x ♮r y → x ∈ S});
     intros; simplify; split; intros; apply f;
      [ apply (. #‡e); assumption
      | apply (. #‡e ^ -1); assumption]
@@ -212,7 +210,7 @@ qed.
 (* the same as Rest for a basic pair *)
 definition star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V) (Ω \sup U).
  intros; constructor 1;
-  [ apply (λr: arrows1 ? U V.λS: Ω \sup V. {x | ∀y:carr V. x ♮r y → y ∈ S});
+  [ apply (λr: arrows1 ? U V.λS: Ω \sup V. {x | ∀y:V. x ♮r y → y ∈ S});
     intros; simplify; split; intros; apply f;
      [ apply (. e ‡#); assumption
      | apply (. e^ -1‡#); assumption]
@@ -224,7 +222,7 @@ qed.
 definition minus_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V) (Ω \sup U).
  intros; constructor 1;
   [ apply (λr: arrows1 ? U V.λS: Ω \sup V. {x | (*∃x:U. x ♮r y ∧ x ∈ S*)
-      exT ? (λy:carr V.x ♮r y ∧ y ∈ S) });
+      exT ? (λy:V.x ♮r y ∧ y ∈ S) });
     intros; simplify; split; intro; cases e1; exists [1,3: apply w]
      [ apply (. (e ^ -1‡#)‡#); assumption
      | apply (. (e‡#)‡#); assumption]