update in groud_2 and models

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

diff --git a/helm/software/matita/library/formal_topology/o-algebra.ma b/helm/software/matita/library/formal_topology/o-algebra.ma
index ed363cd2d6045a41ab4e90a35a6a03c4ae09637e..fb508aa92b23c61b90dc280ab72297416ca177d9 100644 (file)
--- a/helm/software/matita/library/formal_topology/o-algebra.ma
+++ b/helm/software/matita/library/formal_topology/o-algebra.ma
@@ -80,7 +80,7 @@ record OAlgebra : Type2 := {
   oa_zero_bot: ∀p:oa_P.𝟘 ≤ p;
   oa_one_top: ∀p:oa_P.p ≤ 𝟙;
   oa_overlap_preserves_meet_: ∀p,q:oa_P.p >< q → 
-        p >< (⋀ { x ∈ BOOL | If x then p else q(*match x with [ true ⇒ p | false ⇒ q ]*) | IF_THEN_ELSE_p oa_P p q });
+        p >< (⋀ { x ∈ BOOL | If x then p else q | IF_THEN_ELSE_p oa_P p q });
   oa_join_split: ∀I:SET.∀p.∀q:I ⇒_2 oa_P.p >< (⋁ q) = (∃i:I.p >< (q i));
   (*oa_base : setoid;
   1) enum non e' il nome giusto perche' non e' suriettiva
@@ -241,21 +241,12 @@ intros; apply (or_f ?? c);
 qed.
 coercion arrows1_of_ORelation_setoid.
 
-notation "r \sup *" non associative with precedence 90 for @{'OR_f_star $r}.
-notation > "r *" non associative with precedence 90 for @{'OR_f_star $r}.
-
-notation "r \sup (⎻* )" non associative with precedence 90 for @{'OR_f_minus_star $r}.
-notation > "r⎻*" non associative with precedence 90 for @{'OR_f_minus_star $r}.
-
-notation "r \sup ⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
-notation > "r⎻" non associative with precedence 90 for @{'OR_f_minus $r}.
-
 interpretation "o-relation f⎻*" 'OR_f_minus_star r = (fun12 ?? (or_f_minus_star ? ?) r).
 interpretation "o-relation f⎻" 'OR_f_minus r = (fun12 ?? (or_f_minus ? ?) r).
 interpretation "o-relation f*" 'OR_f_star r = (fun12 ?? (or_f_star ? ?) r).
 
 definition or_prop1 : ∀P,Q:OAlgebra.∀F:ORelation_setoid P Q.∀p,q.
-   (F p ≤ q) = (p ≤ F* q).
+   (F p ≤ q) =_1 (p ≤ F* q).
 intros; apply (or_prop1_ ?? F p q);
 qed.