1) Some reorganization.

[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 e6f816156fe684296548c452f1d03a5583f2cd47..dc3c091bbfe49d75ba005997b44ef38b386db4d6 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -103,11 +103,18 @@ definition full_subset: ∀s:REL. Ω \sup s.
 qed.
 
 coercion full_subset.
+*)
 
 definition setoid1_of_REL: REL → setoid ≝ λS. S.
-
 coercion setoid1_of_REL.
 
+lemma Type_OF_setoid1_of_REL: ∀o1:Type_OF_category1 REL. Type_OF_objs1 o1 → Type_OF_setoid1 ?(*(setoid1_of_SET o1)*).
+ [ apply (setoid1_of_SET o1);
+ | intros; apply t;]
+qed.
+coercion Type_OF_setoid1_of_REL.
+
+(*
 definition comprehension: ∀b:REL. (b ⇒ CPROP) → Ω \sup b.
  apply (λb:REL. λP: b ⇒ CPROP. {x | x ∈ b ∧ P x});
  intros; simplify; apply (.= (H‡#)‡(†H)); apply refl1.
@@ -174,21 +181,11 @@ lemma extS_com: ∀o1,o2,o3,c1,c2,S. extS o1 o3 (c2 ∘ c1) S = extS o1 o2 c1 (e
     assumption]
 qed.
 *)
-(* senza questo exT "fresco", universe inconsistency *)
-inductive exT (A:Type0) (P:A→CProp0) : CProp0 ≝
-  ex_introT: ∀w:A. P w → exT A P.
-
-lemma hint: ∀U. carr U → Type_OF_setoid1 ?(*(setoid1_of_SET U)*).
- [ apply setoid1_of_SET; apply U
- | intros; apply c;]
-qed.
-coercion hint.
 
 (* the same as ⋄ for a basic pair *)
 definition image: ∀U,V:REL. binary_morphism1 (arrows1 ? U V) (Ω \sup U) (Ω \sup V).
  intros; constructor 1;
-  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | (*∃x:U. x ♮r y ∧ x ∈ S*)
-      exT ? (λx:carr U.x ♮r y ∧ x ∈ S) });
+  [ apply (λr: arrows1 ? U V.λS: Ω \sup U. {y | ∃x:carr U. x ♮r y ∧ x ∈ S });
     intros; simplify; split; intro; cases e1; exists [1,3: apply w]
      [ apply (. (#‡e)‡#); assumption
      | apply (. (#‡e ^ -1)‡#); assumption]
@@ -292,43 +289,3 @@ theorem extS_singleton:
   | exists; try assumption; split; try assumption; change with (x = x); apply refl]
 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; 
-     [ apply (λU.image ?? t U);
-     | intros; apply (#‡e); ]
-  | constructor 1;
-     [ apply (λU.minus_star_image ?? t U);
-     | intros; apply (#‡e); ]
-  | constructor 1;
-     [ apply (λU.star_image ?? t U);
-     | intros; apply (#‡e); ]
-  | constructor 1;
-     [ apply (λU.minus_image ?? t U);
-     | intros; apply (#‡e); ]
-  | intros; split; intro;
-     [ change in f with (∀a. a ∈ image ?? t p → a ∈ q);
-       change with (∀a:o1. a ∈ p → a ∈ star_image ?? t q);
-       intros 4; apply f; exists; [apply a] split; assumption;
-     | change in f with (∀a:o1. a ∈ p → a ∈ star_image ?? t q);
-       change with (∀a. a ∈ image ?? t p → a ∈ q);
-       intros; cases f1; cases x; clear f1 x; apply (f ? f3); assumption; ]
-  | intros; split; intro;
-     [ change in f with (∀a. a ∈ minus_image ?? t p → a ∈ q);
-       change with (∀a:o2. a ∈ p → a ∈ minus_star_image ?? t q);
-       intros 4; apply f; exists; [apply a] split; assumption;
-     | change in f with (∀a:o2. a ∈ p → a ∈ minus_star_image ?? t q);
-       change with (∀a. a ∈ minus_image ?? t p → a ∈ q);
-       intros; cases f1; cases x; clear f1 x; apply (f ? f3); assumption; ]
-  | intros; split; intro; cases f; clear f;
-     [ cases x; cases x2; clear x x2; exists; [apply w1]
-        [ assumption;
-        | exists; [apply w] split; assumption]
-     | cases x1; cases x2; clear x1 x2; exists; [apply w1]
-        [ exists; [apply w] split; assumption;
-        | assumption; ]]]
-qed. sistemare anche l'hint da un'altra parte e capire l'exT (doppio!)
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