theorem
  (<*x*> qua Element of product <*G1*>)" = <*x"*>
proof
  reconsider G = <*G1*> as associative Group-like multMagma-Family of {1};
  reconsider lF = <*x*>, p = <*x"*> as Element of product Carrier G by Def2;
 for i being set st i in {1} ex H being Group, z being Element of H st H
  = G.i & p.i = z" & z = lF.i
  proof
    reconsider H = G.1 as Group;
    reconsider z = p.1 as Element of H;
    let i be set;
    assume
A3: i in {1};
    take H, z";
    thus H = G.i by A3,TARSKI:def 1;
    thus p.i = z"" by A3,TARSKI:def 1;
    i = 1 by A3,TARSKI:def 1;
    hence thesis;
  end;
  hence thesis by Th7;
end;
