theorem Th18:
  for M being MonoidalExtension of G holds
    the carrier of M = the carrier of G &
    the multF of M = the multF of G &
    for a,b being Element of M,
        a9,b9 being Element of G st a = a9 & b = b9 holds
      a*b = a9*b9
proof
  let M be MonoidalExtension of G;
A1: the multMagma of M = the multMagma of G by Def22;
  hence carr(M) = carr(G) & op(M) = op(G);
  let a,b be Element of M, a9,b9 be Element of G;
  thus thesis by A1;
end;
