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[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 88af2926367242ba18372fd91060b8af9e81fe8b..c99239bebf18d663d0f9eb28c368a4d71a750203 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -96,6 +96,7 @@ definition REL: category1.
           first [apply refl | assumption]]]
 qed.
 
+(*
 definition full_subset: ∀s:REL. Ω \sup s.
  apply (λs.{x | True});
  intros; simplify; split; intro; assumption.
@@ -172,21 +173,24 @@ lemma extS_com: ∀o1,o2,o3,c1,c2,S. extS o1 o3 (c2 ∘ c1) S = extS o1 o2 c1 (e
     cases H7; clear H7; exists; [apply w2] split; [assumption] exists [apply w] split;
     assumption]
 qed.
-
+*)
+axiom daemon: False.
 (* the same as ⋄ for a basic pair *)
-definition image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) (Ω \sup V).
+definition image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) ?(*(Ω \sup V)*).
+cases daemon; qed.
  intros; constructor 1;
   [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∃x:U. x ♮r y ∧ x ∈ S});
-    intros; simplify; split; intro; cases H1; exists [1,3: apply w]
-     [ apply (. (#‡H)‡#); assumption
-     | apply (. (#‡H \sup -1)‡#); assumption]
-  | intros; split; simplify; intros; cases H2; exists [1,3: apply w]
-     [ apply (. #‡(#‡H1)); cases x; split; try assumption;
-       apply (if ?? (H ??)); assumption
-     | apply (. #‡(#‡H1 \sup -1)); cases x; split; try assumption;
-       apply (if ?? (H \sup -1 ??)); assumption]]
+    intros; simplify; split; intro; cases H; exists [1,3: apply w]
+     [ apply (. (#‡e)‡#); assumption
+     | apply (. (#‡e ^ -1)‡#); assumption]
+  | intros; split; simplify; intros; cases H; exists [1,3: apply w]
+     [ apply (. #‡(#‡e1)); cases x; split; try assumption;
+       apply (if ?? (e ??)); assumption
+     | apply (. #‡(#‡e1 ^ -1)); cases x; split; try assumption;
+       apply (if ?? (e ^ -1 ??)); assumption]]
 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;
@@ -251,4 +255,20 @@ theorem extS_singleton:
   [ cases H; cases x1; change in f2 with (eq1 ? x w); apply (. #‡f2 \sup -1);
     assumption
   | exists; try assumption; split; try assumption; change with (x = x); apply refl]
+qed.
+*)
+
+include "o-algebra.ma".
+
+definition orelation_of_relation: ∀o1,o2:REL. arrows1 ? o1 o2 → ORelation (SUBSETS o1) (SUBSETS o2).
+ intros;
+ constructor 1;
+  [ 
+  |
+  |
+  |
+  |
+  |
+  |
+  ]
 qed.
\ No newline at end of file