the ObjectMap of F is Covariant by Def13;
then consider f being Function of the carrier of C1, the carrier of C2 such that
A1: the ObjectMap of F = [:f,f:] by Def2;
the ObjectMap of G is Covariant by Def13;
then consider g being Function of the carrier of C2, the carrier of C3 such that
A2: the ObjectMap of G = [:g,g:] by Def2;
take g * f ; :: according to FUNCTOR0:def 2,FUNCTOR0:def 13 :: thesis: the ObjectMap of (G * F) = [:(g * f),(g * f):]
thus the ObjectMap of (G * F) = the ObjectMap of G * the ObjectMap of F by Def37
.= [:(g * f),(g * f):] by A1, A2, FUNCT_3:92 ; :: thesis: verum