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 T is TargetCat of I * F
let F be Functor of C,D; :: thesis: for I being Indexing of D
for T being TargetCat of I holds T is TargetCat of I * F
let I be Indexing of D; :: thesis: for T being TargetCat of I holds T is TargetCat of I * F
let T be TargetCat of I; :: thesis: T is TargetCat of I * F
consider T' being TargetCat of I * F;
A1: rng (I * F) = Image ((I * F) -functor C,T') by Def12;
I * F = ((I -functor D,T) * F) -indexing_of C by Th23;
then rng (I * F) = Image ((I -functor D,T) * F) by A1, Th18, CAT_5:22;
hence T is TargetCat of I * F by Th14; :: thesis: verum