 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;

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;
