
theorem Th6:
  for I being non empty set, i being Element of I
  for F being Group-Family of I
  st I is trivial holds F.i,product F are_isomorphic
proof
  let I be non empty set, i be Element of I;
  let F be Group-Family of I;
  assume I is trivial;
  then reconsider I as 1-element set;
  set h = proj(F,i);
  h is onto by GROUP_23:33;
  then A1: rng h = the carrier of F.i by FUNCT_2:def 3;
  reconsider i as Element of I;
  h = proj(Carrier F,i) by GROUP_23:36;
  then h is bijective by A1, GROUP_6:60;
  hence thesis by GROUP_6:def 11;
end;
