+definition setoid_of_REL : objs1 REL → setoid ≝ λx.x.
+coercion setoid_of_REL.
+
+definition binary_relation_setoid_of_arrow1_REL :
+ ∀P,Q. arrows1 REL P Q → binary_relation_setoid P Q ≝ λP,Q,x.x.
+coercion binary_relation_setoid_of_arrow1_REL.
+
+
+notation > "B ⇒_\r1 C" right associative with precedence 72 for @{'arrows1_REL $B $C}.
+notation "B ⇒\sub (\r 1) C" right associative with precedence 72 for @{'arrows1_REL $B $C}.
+interpretation "'arrows1_SET" 'arrows1_REL A B = (arrows1 REL A B).
+
+
+definition full_subset: ∀s:REL. Ω^s.