notation made half decent

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
index 1ce789ed3b86e184ae9b050e7410dc1f354f8ab3..9d4cbbed0d44b3c5ed71afbaaecfba9d1e13002c 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
@@ -192,7 +192,7 @@ definition relation_pair_setoid_of_arrows1_BP :
   ∀P,Q. arrows1 BP P Q → relation_pair_setoid P Q ≝ λP,Q,x.x.
 coercion relation_pair_setoid_of_arrows1_BP.
 
-definition BPext: ∀o: BP. form o ⇒ Ω \sup (concr o).
+definition BPext: ∀o: BP. (form o) ⇒_1 Ω^(concr o).
  intros; constructor 1;
   [ apply (ext ? ? (rel o));
   | intros;
@@ -200,13 +200,13 @@ definition BPext: ∀o: BP. form o ⇒ Ω \sup (concr o).
     apply refl1]
 qed.
 
-definition BPextS: ∀o: BP. Ω \sup (form o) ⇒ Ω \sup (concr o).
+definition BPextS: ∀o: BP. Ω^(form o) ⇒_1 Ω^(concr o).
  intros; constructor 1;
   [ apply (minus_image ?? (rel o));
   | intros; apply (#‡e); ]
 qed.
 
-definition fintersects: ∀o: BP. binary_morphism1 (form o) (form o) (Ω \sup (form o)).
+definition fintersects: ∀o: BP. (form o) × (form o) ⇒_1 Ω^(form o).
  intros (o); constructor 1;
   [ apply (λa,b: form o.{c | BPext o c ⊆ BPext o a ∩ BPext o b });
     intros; simplify; apply (.= (†e)‡#); apply refl1
@@ -218,9 +218,9 @@ qed.
 interpretation "fintersects" 'fintersects U V = (fun21 ??? (fintersects ?) U V).
 
 definition fintersectsS:
- ∀o:BP. binary_morphism1 (Ω \sup (form o)) (Ω \sup (form o)) (Ω \sup (form o)).
+ ∀o:BP. Ω^(form o) × Ω^(form o) ⇒_1 Ω^(form o).
  intros (o); constructor 1;
-  [ apply (λo: basic_pair.λa,b: Ω \sup (form o).{c | BPext o c ⊆ BPextS o a ∩ BPextS o b });
+  [ apply (λo: basic_pair.λa,b: Ω^(form o).{c | BPext o c ⊆ BPextS o a ∩ BPextS o b });
     intros; simplify; apply (.= (†e)‡#); apply refl1
   | intros; split; simplify; intros;
      [ apply (. #‡((†e^-1)‡(†e1^-1))); assumption
@@ -229,9 +229,9 @@ qed.
 
 interpretation "fintersectsS" 'fintersects U V = (fun21 ??? (fintersectsS ?) U V).
 
-definition relS: ∀o: BP. binary_morphism1 (concr o) (Ω \sup (form o)) CPROP.
+definition relS: ∀o: BP. (concr o) × Ω^(form o) ⇒_1 CPROP.
  intros (o); constructor 1;
-  [ apply (λx:concr o.λS: Ω \sup (form o).∃y:form o.y ∈ S ∧ x ⊩⎽o y);
+  [ apply (λx:concr o.λS: Ω^(form o).∃y:form o.y ∈ S ∧ x ⊩⎽o y);
   | intros; split; intros; cases e2; exists [1,3: apply w]
      [ apply (. (#‡e1^-1)‡(e^-1‡#)); assumption
      | apply (. (#‡e1)‡(e‡#)); assumption]]