+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
include "sets/sets.ma".
{ objs:> Type[1];
arrows: objs → objs → setoid;
id: ∀o:objs. arrows o o;
- comp: ∀o1,o2,o3. binary_morphism (arrows o2 o3) (arrows o1 o2) (arrows o1 o3);
+ comp: ∀o1,o2,o3. unary_morphism (arrows o2 o3) (unary_morph_setoid (arrows o1 o2) (arrows o1 o3));
comp_assoc: ∀o1,o2,o3,o4. ∀a34,a23,a12.
comp o1 o3 o4 a34 (comp o1 o2 o3 a23 a12) = comp o1 o2 o4 (comp o2 o3 o4 a34 a23) a12;
id_neutral_left: ∀o1,o2. ∀a: arrows o1 o2. comp ??? (id o2) a = a;
##| napply unary_morph_setoid;
##| #o; @ (λx.x); #a; #b; #H; napply H;
##| napply comp_binary_morphisms; (*CSC: why not ∘?*)
-##| #o1; #o2; #o3; #o4; #f; #g; #h; nwhd; #x; napply #;
-##|##6,7: #o1; #o2; #f; nwhd; #x; napply #; ##]
+##| #o1; #o2; #o3; #o4; #f; #g; #h; #x; #x'; #Hx; nnormalize; napply (†(†(†Hx)))
+##|##6,7: #o1; #o2; #f; #x; #x'; #Hx; nnormalize; napply (†Hx) ]
nqed.
unification hint 0 ≔ ;