+interpretation "function composition" 'compose f g = (composition ??? f g).
+
+ndefinition comp_unary_morphisms:
+ ∀o1,o2,o3:setoid.
+ unary_morphism o2 o3 → unary_morphism o1 o2 →
+ unary_morphism o1 o3.
+#o1; #o2; #o3; #f; #g; @ (f ∘ g);
+ #a; #a'; #e; nnormalize; napply (.= †(†e)); napply #.
+nqed.
+
+unification hint 0 ≔ o1,o2,o3:setoid,f:unary_morphism o2 o3,g:unary_morphism o1 o2;
+ R ≟ mk_unary_morphism ?? (composition … f g)
+ (prop1 ?? (comp_unary_morphisms o1 o2 o3 f g))
+ (* -------------------------------------------------------------------- *) ⊢
+ fun1 ?? R ≡ (composition … f g).
+
+ndefinition comp_binary_morphisms:
+ ∀o1,o2,o3.
+ unary_morphism (unary_morph_setoid o2 o3)
+ (unary_morph_setoid (unary_morph_setoid o1 o2) (unary_morph_setoid o1 o3)).
+#o1; #o2; #o3; napply mk_binary_morphism
+ [ #f; #g; napply (comp_unary_morphisms … f g) (*CSC: why not ∘?*)
+ | #a; #a'; #b; #b'; #ea; #eb; #x; #x'; #Hx; nnormalize; /3/ ]
+nqed.