Some work on concrete spaces.

[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 97e386c1545e1b3b8af6122a94843f7ed2e418ef..d0e4ffd4a67607650efe5cbc7127fc1dbc333b2d 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs.ma
@@ -139,49 +139,50 @@ definition BP: category1.
     apply ((id_neutral_left1 ????)‡#);]
 qed.
 
-(*
 definition BPext: ∀o: BP. form o ⇒ Ω \sup (concr o).
  intros; constructor 1;
   [ apply (ext ? ? (rel o));
   | intros;
-    apply (.= #‡H);
+    apply (.= #‡e);
     apply refl1]
 qed.
 
-definition BPextS: ∀o: BP. Ω \sup (form o) ⇒ Ω \sup (concr o) ≝
- λo.extS ?? (rel o).
+definition BPextS: ∀o: BP. Ω \sup (form o) ⇒ Ω \sup (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)).
  intros (o); constructor 1;
   [ apply (λa,b: form o.{c | BPext o c ⊆ BPext o a ∩ BPext o b });
-    intros; simplify; apply (.= (†H)‡#); apply refl1
+    intros; simplify; apply (.= (†e)‡#); apply refl1
   | intros; split; simplify; intros;
-     [ apply (. #‡((†H)‡(†H1))); assumption
-     | apply (. #‡((†H\sup -1)‡(†H1\sup -1))); assumption]]
+     [ apply (. #‡((†e)‡(†e1))); assumption
+     | apply (. #‡((†e\sup -1)‡(†e1\sup -1))); assumption]]
 qed.
 
-interpretation "fintersects" 'fintersects U V = (fun1 ___ (fintersects _) U V).
+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)).
  intros (o); constructor 1;
   [ apply (λo: basic_pair.λa,b: Ω \sup (form o).{c | BPext o c ⊆ BPextS o a ∩ BPextS o b });
-    intros; simplify; apply (.= (†H)‡#); apply refl1
+    intros; simplify; apply (.= (†e)‡#); apply refl1
   | intros; split; simplify; intros;
-     [ apply (. #‡((†H)‡(†H1))); assumption
-     | apply (. #‡((†H\sup -1)‡(†H1\sup -1))); assumption]]
+     [ apply (. #‡((†e)‡(†e1))); assumption
+     | apply (. #‡((†e\sup -1)‡(†e1\sup -1))); assumption]]
 qed.
 
-interpretation "fintersectsS" 'fintersects U V = (fun1 ___ (fintersectsS _) U V).
+interpretation "fintersectsS" 'fintersects U V = (fun21 ___ (fintersectsS _) U V).
 
 definition relS: ∀o: BP. binary_morphism1 (concr o) (Ω \sup (form o)) CPROP.
  intros (o); constructor 1;
-  [ apply (λx:concr o.λS: Ω \sup (form o).∃y: form o.y ∈ S ∧ x ⊩ y);
-  | intros; split; intros; cases H2; exists [1,3: apply w]
-     [ apply (. (#‡H1)‡(H‡#)); assumption
-     | apply (. (#‡H1 \sup -1)‡(H \sup -1‡#)); assumption]]
+  [ apply (λx:concr o.λS: Ω \sup (form o).∃y:carr (form o).y ∈ S ∧ x ⊩ y);
+  | intros; split; intros; cases e2; exists [1,3: apply w]
+     [ apply (. (#‡e1)‡(e‡#)); assumption
+     | apply (. (#‡e1 \sup -1)‡(e \sup -1‡#)); assumption]]
 qed.
 
-interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun1 (concr _) __ (relS _) x y).
-interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun1 ___ (relS _)).
-*)
+interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun21 (concr _) __ (relS _) x y).
+interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun21 ___ (relS _)).