unary_morphism_N : seoidN -> setoidN -> setoidN (was ... -> setoidN+1)

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
index 3aaf2d3d6b34b6da73f52a678e6cfb7d95c5f73b..c15ef844ef169747282a61f232dbba7fd0d754d8 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/subsets.ma
@@ -90,10 +90,10 @@ definition overlaps: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
   [ apply (λA:objs1 SET.λU,V:Ω \sup A.(exT2 ? (λx:A.?(*x*) ∈ U) (λx:A.?(*x*) ∈ V) : CProp0))
   | intros;
     constructor 1; intro; cases e2; exists; [1,4: apply w]
-     [ apply (. #‡e); assumption
-     | apply (. #‡e1); assumption
-     | apply (. #‡(e \sup -1)); assumption;
-     | apply (. #‡(e1 \sup -1)); assumption]]
+     [ apply (. #‡e^-1); assumption
+     | apply (. #‡e1^-1); assumption
+     | apply (. #‡e); assumption;
+     | apply (. #‡e1); assumption]]
 qed.
 
 interpretation "overlaps" 'overlaps U V = (fun21 ___ (overlaps _) U V).
@@ -106,8 +106,8 @@ definition intersects:
     intros; simplify; apply (.= (e‡#)‡(e‡#)); apply refl1;
   | intros;
     split; intros 2; simplify in f ⊢ %;
-    [ apply (. (#‡e)‡(#‡e1)); assumption
-    | apply (. (#‡(e \sup -1))‡(#‡(e1 \sup -1))); assumption]]
+    [ apply (. (#‡e^-1)‡(#‡e1^-1)); assumption
+    | apply (. (#‡e)‡(#‡e1)); assumption]]
 qed.
 
 interpretation "intersects" 'intersects U V = (fun21 ___ (intersects _) U V).
@@ -120,8 +120,8 @@ definition union:
     intros; simplify; apply (.= (e‡#)‡(e‡#)); apply refl1
   | intros;
     split; intros 2; simplify in f ⊢ %;
-    [ apply (. (#‡e)‡(#‡e1)); assumption
-    | apply (. (#‡(e \sup -1))‡(#‡(e1 \sup -1))); assumption]]
+    [ apply (. (#‡e^-1)‡(#‡e1^-1)); assumption
+    | apply (. (#‡e)‡(#‡e1)); assumption]]
 qed.
 
 interpretation "union" 'union U V = (fun21 ___ (union _) U V).
@@ -146,11 +146,11 @@ definition big_intersects:
  intros; constructor 1;
   [ intro; whd; whd in I;
     apply ({x | ∀i:I. x ∈ t i});
-    simplify; intros; split; intros; [ apply (. (e‡#)); | apply (. (e \sup -1‡#)); ]
+    simplify; intros; split; intros; [ apply (. (e^-1‡#)); | apply (. e‡#); ]
     apply f;
   | intros; split; intros 2; simplify in f ⊢ %; intro;
-     [ apply (. (#‡(e i))); apply f;
-     | apply (. (#‡(e i)\sup -1)); apply f]]
+     [ apply (. (#‡(e i)^-1)); apply f;
+     | apply (. (#‡e i)); apply f]]
 qed.
 
 definition big_union:
@@ -159,9 +159,9 @@ definition big_union:
   [ intro; whd; whd in A; whd in I;
     apply ({x | ∃i:carr I. x ∈ t i });
     simplify; intros; split; intros; cases e1; clear e1; exists; [1,3:apply w]
-    [ apply (. (e‡#)); | apply (. (e \sup -1‡#)); ]
+    [ apply (. (e^-1‡#)); | apply (. (e‡#)); ]
     apply x;
   | intros; split; intros 2; simplify in f ⊢ %; cases f; clear f; exists; [1,3:apply w]
-     [ apply (. (#‡(e w))); apply x;
-     | apply (. (#‡(e w)\sup -1)); apply x]]
+     [ apply (. (#‡(e w)^-1)); apply x;
+     | apply (. (#‡e w)); apply x]]
 qed.