let A, B, C be Category; for F being Functor of A,B
for G1, G2 being Functor of B,C
for t being natural_transformation of G1,G2 st G1 is_naturally_transformable_to G2 holds
t * F = t (#) (id F)
let F be Functor of A,B; for G1, G2 being Functor of B,C
for t being natural_transformation of G1,G2 st G1 is_naturally_transformable_to G2 holds
t * F = t (#) (id F)
let G1, G2 be Functor of B,C; for t being natural_transformation of G1,G2 st G1 is_naturally_transformable_to G2 holds
t * F = t (#) (id F)
let t be natural_transformation of G1,G2; ( G1 is_naturally_transformable_to G2 implies t * F = t (#) (id F) )
assume
G1 is_naturally_transformable_to G2
; t * F = t (#) (id F)
then
G1 * F is_naturally_transformable_to G2 * F
by Th20;
hence t * F =
(t * F) `*` (id (G1 * F))
by NATTRA_1:24
.=
t (#) (id F)
by Th31
;
verum