some work

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / o-concrete_spaces.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma b/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
index cbdf68fdd99c93c3620ee020e63e28a15bea8ef2..633f0b89e01591db6d5c73c75800fa608ed50385 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
@@ -17,34 +17,37 @@ include "o-saturations.ma".
 
 notation "□ \sub b" non associative with precedence 90 for @{'box $b}.
 notation > "□_term 90 b" non associative with precedence 90 for @{'box $b}.
-interpretation "Universal image ⊩⎻*" 'box x = (or_f_minus_star _ _ (rel x)).
+interpretation "Universal image ⊩⎻*" 'box x = (fun_1 _ _ (or_f_minus_star _ _) (rel x)).
  
 notation "◊ \sub b" non associative with precedence 90 for @{'diamond $b}.
 notation > "◊_term 90 b" non associative with precedence 90 for @{'diamond $b}.
-interpretation "Existential image ⊩" 'diamond x = (or_f _ _ (rel x)).
+interpretation "Existential image ⊩" 'diamond x = (fun_1 _ _ (or_f _ _) (rel x)).
 
 notation "'Rest' \sub b" non associative with precedence 90 for @{'rest $b}.
 notation > "'Rest'⎽term 90 b" non associative with precedence 90 for @{'rest $b}.
-interpretation "Universal pre-image ⊩*" 'rest x = (or_f_star _ _ (rel x)).
+interpretation "Universal pre-image ⊩*" 'rest x = (fun_1 _ _ (or_f_star _ _) (rel x)).
 
 notation "'Ext' \sub b" non associative with precedence 90 for @{'ext $b}.
 notation > "'Ext'⎽term 90 b" non associative with precedence 90 for @{'ext $b}.
-interpretation "Existential pre-image ⊩⎻" 'ext x = (or_f_minus _ _ (rel x)).
+interpretation "Existential pre-image ⊩⎻" 'ext x = (fun_1 _ _ (or_f_minus _ _) (rel x)).
+
+lemma hint : ∀p,q.arrows1 OA p q → ORelation_setoid p q.
+intros; assumption;
+qed.
+
+coercion hint nocomposites.
 
 definition A : ∀b:BP. unary_morphism (oa_P (form b)) (oa_P (form b)).
 intros; constructor 1;
  [ apply (λx.□_b (Ext⎽b x));
- | do 2 unfold FunClass_1_OF_carr1; intros; apply  (†(†H));]
+ | do 2 unfold uncurry_arrows; intros; apply  (†(†H));]
 qed.
 
 lemma xxx : ∀x.carr x → carr1 (setoid1_of_setoid x). intros; assumption; qed.
-coercion xxx.
+coercion xxx nocomposites.
 
-definition d_p_i : 
-  ∀S,I:SET.∀d:unary_morphism S S.∀p:arrows1 SET I S.arrows1 SET I S.
-intros; constructor 1;
- [ apply (λi:I. u (c i));
- | unfold FunClass_1_OF_carr1; intros; apply (†(†H));].
+lemma down_p : ∀S,I:SET.∀u:S⇒S.∀c:arrows1 SET I S.∀a:I.∀a':I.a=a'→u (c a)=u (c a').
+intros; unfold uncurry_arrows; apply (†(†H));
 qed.
 
 alias symbol "eq" = "setoid eq".
@@ -58,12 +61,13 @@ record concrete_space : Type ≝
      (Ext⎽bp q1 ∧ (Ext⎽bp q2)) = (Ext⎽bp ((downarrow q1) ∧ (downarrow q2)));
    all_covered: Ext⎽bp (oa_one (form bp)) = oa_one (concr bp);
    il2: ∀I:SET.∀p:arrows1 SET I (oa_P (form bp)).
-     downarrow (oa_join ? I (d_p_i ?? downarrow p)) =
-     oa_join ? I (d_p_i ?? downarrow p);
+     downarrow (∨ { x ∈ I | downarrow (p x) | down_p ???? }) =
+     ∨ { x ∈ I | downarrow (p x) | down_p ???? };
    il1: ∀q.downarrow (A ? q) = A ? q
  }.
 
-interpretation "o-concrete space downarrow" 'downarrow x = (fun_1 __ (downarrow _) x).
+interpretation "o-concrete space downarrow" 'downarrow x = 
+  (fun_1 __ (downarrow _) x).
 
 definition bp': concrete_space → basic_pair ≝ λc.bp c.
 coercion bp'.