some minor fixes

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
index b278adfc0541b82b714eb1df4dce3e2f7496c41c..99ea22e91efae5e08f917db5e75a64ce135859a6 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
@@ -65,8 +65,8 @@ record OAlgebra : Type2 := {
   oa_overlap_sym: ∀a,b:oa_P.oa_overlap a b → oa_overlap b a;
   oa_meet_inf: 
     ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.
-      oa_leq p (oa_meet I p_i) = ∀i:I.oa_leq p (p_i i);
-  oa_join_sup: ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.oa_leq (oa_join I p_i) p = ∀i:I.oa_leq (p_i i) p;
+      oa_leq p (oa_meet I p_i) = (∀i:I.oa_leq p (p_i i));
+  oa_join_sup: ∀I:SET.∀p_i:I ⇒ oa_P.∀p:oa_P.oa_leq (oa_join I p_i) p = (∀i:I.oa_leq (p_i i) p);
   oa_zero_bot: ∀p:oa_P.oa_leq oa_zero p;
   oa_one_top: ∀p:oa_P.oa_leq p oa_one;
   oa_overlap_preserves_meet_: 
@@ -74,7 +74,7 @@ record OAlgebra : Type2 := {
        (oa_meet ? { x ∈ BOOL | match x with [ true ⇒ p | false ⇒ q ] | IF_THEN_ELSE_p oa_P p q });
   oa_join_split:
       ∀I:SET.∀p.∀q:I ⇒ oa_P.
-       oa_overlap p (oa_join I q) = ∃i:I.oa_overlap p (q i);
+       oa_overlap p (oa_join I q) = (∃i:I.oa_overlap p (q i));
   (*oa_base : setoid;
   1) enum non e' il nome giusto perche' non e' suriettiva
   2) manca (vedere altro capitolo) la "suriettivita'" come immagine di insiemi di oa_base
@@ -187,10 +187,11 @@ constructor 1;
 | constructor 1;
    (* tenere solo una uguaglianza e usare la proposizione 9.9 per
       le altre (unicita' degli aggiunti e del simmetrico) *)
-   [ apply (λp,q. And42 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
-             (eq2 ? (or_f_minus_ ?? p) (or_f_minus_ ?? q)) 
-             (eq2 ? (or_f_ ?? p) (or_f_ ?? q)) 
-             (eq2 ? (or_f_star_ ?? p) (or_f_star_ ?? q))); 
+   [ apply (λp,q. And42 
+             (or_f_minus_star_ ?? p = or_f_minus_star_ ?? q) 
+             (or_f_minus_ ?? p = or_f_minus_ ?? q) 
+             (or_f_ ?? p = or_f_ ?? q) 
+             (or_f_star_ ?? p = or_f_star_ ?? q)); 
    | whd; simplify; intros; repeat split; intros; apply refl2;
    | whd; simplify; intros; cases a; clear a; split; 
      intro a; apply sym1; generalize in match a;assumption;