definition F_comp :
∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.∀o1,o2,o3.
- binary_morphism2 (Fm ?? F o1 o2) (Fm ?? F o2 o3) (Fm ?? F o1 o3).
+ (Fm ?? F o1 o2) × (Fm ?? F o2 o3) ⇒_2 (Fm ?? F o1 o3).
intros; constructor 1;
[ intros (f g); constructor 1;
[ apply (comp2 C2 ??? (ℳ_2 f) (ℳ_2 g));
lapply (FmP ????? a) as H1; lapply (FmP ????? a') as H2;
cut (REW ????? (map_arrows2 ?? F ?? (ℳ_1 a)) =
REW ????? (map_arrows2 ?? F ?? (ℳ_1 a')));[2:
- apply (.= H1); apply (.= e); apply H2^-1;]
+ apply (.= H1); apply (.= e); apply (H2^-1);]
clear H1 H2 e; cases S in a a' Hcut; cases T;
cases H; cases H1; simplify; intros; assumption;]
| intro; apply rule #;