definition ext: ∀X,S:REL. binary_morphism1 (arrows1 ? X S) S (Ω \sup X).
apply (λX,S.mk_binary_morphism1 ??? (λr:arrows1 REL X S.λf:S.{x ∈ X | x ♮r f}) ?);
[ intros; simplify; apply (.= (e‡#)); apply refl1
| intros; simplify; split; intros; simplify;
[ change with (∀x. x ♮a b → x ♮a' b'); intros;
definition ext: ∀X,S:REL. binary_morphism1 (arrows1 ? X S) S (Ω \sup X).
apply (λX,S.mk_binary_morphism1 ??? (λr:arrows1 REL X S.λf:S.{x ∈ X | x ♮r f}) ?);
[ intros; simplify; apply (.= (e‡#)); apply refl1
| intros; simplify; split; intros; simplify;
[ change with (∀x. x ♮a b → x ♮a' b'); intros;