Great: some significant progress in fixing universe levels.

[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 f5141a2ed3bf34098ca92ea27126b90d515c2d95..e6f816156fe684296548c452f1d03a5583f2cd47 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -29,10 +29,10 @@ definition binary_relation_setoid: SET → SET → SET1.
      [ apply (λA,B.λr,r': binary_relation A B. ∀x,y. r x y ↔ r' x y)
      | simplify; intros 3; split; intro; assumption
      | simplify; intros 5; split; intro;
-       [ apply (fi ?? (H ??)) | apply (if ?? (H ??))] assumption
+       [ apply (fi ?? (f ??)) | apply (if ?? (f ??))] assumption
      | simplify;  intros 7; split; intro;
-        [ apply (if ?? (H1 ??)) | apply (fi ?? (H ??)) ]
-        [ apply (if ?? (H ??)) | apply (fi ?? (H1 ??)) ]
+        [ apply (if ?? (f1 ??)) | apply (fi ?? (f ??)) ]
+        [ apply (if ?? (f ??)) | apply (fi ?? (f1 ??)) ]
        assumption]]
 qed.
 
@@ -48,7 +48,7 @@ definition composition:
        (* carr to avoid universe inconsistency *)  
        apply (λs1:carr A.λs3:carr C.∃s2:carr B. s1 ♮R12 s2 ∧ s2 ♮R23 s3);
      | intros;
-       split; intro; cases H (w H3); clear H; exists; [1,3: apply w ]
+       split; intro; cases e2 (w H3); clear e2; exists; [1,3: apply w ]
         [ apply (. (e‡#)‡(#‡e1)); assumption
         | apply (. ((e \sup -1)‡#)‡(#‡(e1 \sup -1))); assumption]]
   | intros 8; split; intro H2; simplify in H2 ⊢ %;
@@ -87,7 +87,7 @@ definition REL: category1.
     split; assumption
   |6,7: intros 5; unfold composition; simplify; split; intro;
         unfold setoid1_of_setoid in x y; simplify in x y;
-        [1,3: cases H (w H1); clear H; cases H1; clear H1; unfold;
+        [1,3: cases e (w H1); clear e; cases H1; clear H1; unfold;
           [ apply (. (e ^ -1 : eq1 ? w x)‡#); assumption
           | apply (. #‡(e : eq1 ? w y)); assumption]
         |2,4: exists; try assumption; split;
@@ -210,7 +210,7 @@ definition minus_star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \s
     apply f; [ apply (if ?? (e ^ -1 ??)); | apply (if ?? (e ??)) ] assumption]
 qed.
 
-(* the same as * for a basic pair *)
+(* 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});
@@ -221,7 +221,7 @@ definition star_image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup V)
     apply f; [ apply (if ?? (e ^ -1 ??)); | apply (if ?? (e ??)) ] assumption]
 qed.
 
-(* the same as - for a basic pair *)
+(* the same as Ext for a basic pair *)
 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*)
@@ -294,11 +294,11 @@ qed.
 *)
 
 include "o-algebra.ma".
-
+axiom daemon: False.
 definition orelation_of_relation: ∀o1,o2:REL. arrows1 ? o1 o2 → ORelation (SUBSETS o1) (SUBSETS o2).
  intros;
  constructor 1;
-  [ constructor 1;
+  [ constructor 1; 
      [ apply (λU.image ?? t U);
      | intros; apply (#‡e); ]
   | constructor 1;