+notation "† c" with precedence 90 for @{'prop1 $c }.
+notation "l ‡ r" with precedence 90 for @{'prop2 $l $r }.
+notation "#" with precedence 90 for @{'refl}.
+interpretation "prop1" 'prop1 c = (prop1 ????? c).
+interpretation "refl" 'refl = (refl ???).
+notation "┼_0 c" with precedence 89 for @{'prop1_x0 $c }.
+notation "l ╪_0 r" with precedence 89 for @{'prop2_x0 $l $r }.
+interpretation "prop1_x0" 'prop1_x0 c = (prop1 ????? c).
+
+ndefinition unary_morph_setoid : setoid → setoid → setoid.
+#S1; #S2; @ (unary_morphism S1 S2); @;
+##[ #f; #g; napply (∀x,x'. x=x' → f x = g x');
+##| #f; #x; #x'; #Hx; napply (.= †Hx); napply #;
+##| #f; #g; #H; #x; #x'; #Hx; napply ((H … Hx^-1)^-1);
+##| #f; #g; #h; #H1; #H2; #x; #x'; #Hx; napply (trans … (H1 …) (H2 …)); //; ##]
+nqed.
+
+alias symbol "hint_decl" (instance 1) = "hint_decl_Type1".
+unification hint 0 ≔ o1,o2 ;
+ X ≟ unary_morph_setoid o1 o2
+ (* ------------------------------ *) ⊢
+ carr X ≡ unary_morphism o1 o2.
+
+interpretation "prop2" 'prop2 l r = (prop1 ? (unary_morph_setoid ??) ? ?? l ?? r).
+interpretation "prop2_x0" 'prop2_x0 l r = (prop1 ? (unary_morph_setoid ??) ? ?? l ?? r).
+
+nlemma unary_morph_eq: ∀A,B.∀f,g: unary_morphism A B. (∀x. f x = g x) → f=g.
+#A B f g H x1 x2 E; napply (.= †E); napply H; nqed.