let C be Category; :: thesis: for I being Indexing of C
for T being TargetCat of I
for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of D,E holds (G * F) * I = G * (F * I)
let I be Indexing of C; :: thesis: for T being TargetCat of I
for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of D,E holds (G * F) * I = G * (F * I)
let T be TargetCat of I; :: thesis: for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of D,E holds (G * F) * I = G * (F * I)
let D, E be Categorial Category; :: thesis: for F being Functor of T,D
for G being Functor of D,E holds (G * F) * I = G * (F * I)
let F be Functor of T,D; :: thesis: for G being Functor of D,E holds (G * F) * I = G * (F * I)
reconsider D9 = D as TargetCat of F * I by Th29;
let G be Functor of D,E; :: thesis: (G * F) * I = G * (F * I)
reconsider G9 = G as Functor of D9,E ;
F * I = (F * (I -functor (C,T))) -indexing_of C by Def17;
then A1: (F * I) -functor (C,D9) = F * (I -functor (C,T)) by Th18;
thus (G * F) * I = ((G * F) * (I -functor (C,T))) -indexing_of C by Def17
.= (G9 * ((F * I) -functor (C,D9))) -indexing_of C by A1, RELAT_1:36
.= G * (F * I) by Def17 ; :: thesis: verum