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.