reserve
  I for non empty set,
  F for associative Group-like multMagma-Family of I,
  i, j for Element of I;

theorem Th6:
  for g be Element of product F st g in ProjSet(F,i)
  holds g" in ProjSet(F,i)
  proof
    let g be Element of product F;
    assume A1: g in ProjSet(F,i);
    consider z be Element of (F.i) such that
    A2: g = 1_product F +* (i,z) by Def1,A1;
    g" = (1_product F)+* (i,z") by Th4,A2;
    hence g" in ProjSet(F,i) by Def1;
  end;
