let C, D be Category; :: thesis: for F being Functor of C,D
for I being Indexing of D
for T being TargetCat of I holds I * F = ((I -functor D,T) * F) -indexing_of C
let F be Functor of C,D; :: thesis: for I being Indexing of D
for T being TargetCat of I holds I * F = ((I -functor D,T) * F) -indexing_of C
let I be Indexing of D; :: thesis: for T being TargetCat of I holds I * F = ((I -functor D,T) * F) -indexing_of C
let T be TargetCat of I; :: thesis: I * F = ((I -functor D,T) * F) -indexing_of C
Image F is Subcategory of D ;
then A1: I * F = ((I -functor D,(rng I)) * F) -indexing_of C by Def16;
(I -functor D,(rng I)) * F = (I -functor D,T) * F by Th11;
hence I * F = ((I -functor D,T) * F) -indexing_of C by A1, Th2; :: thesis: verum