
theorem Th33:
  for C1 being non empty AltCatStr, C2,C3 being non empty reflexive AltCatStr,
  F be feasible reflexive FunctorStr over C1,C2, G be FunctorStr over C2,C3,
  o be Object of C1 holds (G*F).o = G.(F.o)
proof
  let C1 be non empty AltCatStr, C2,C3 be non empty reflexive AltCatStr,
  F be feasible reflexive FunctorStr over C1,C2, G be FunctorStr over C2,C3,
  o be Object of C1;
  dom the ObjectMap of F = [:the carrier of C1,the carrier of C1:]
  by FUNCT_2:def 1;
  then
A1: [o,o] in dom the ObjectMap of F by ZFMISC_1:87;
  thus (G*F).o = (((the ObjectMap of G)*the ObjectMap of F).(o,o))`1 by Def36
    .= ((the ObjectMap of G).((the ObjectMap of F).[o,o]))`1 by A1,FUNCT_1:13
    .= G.(F.o) by Def10;
end;
