reserve i, I for set,
  f, g, h for Function,
  s for ManySortedSet of I;

theorem Th18:
  for G1, G2 being associative non empty multMagma holds
    <*G1,G2*> is associative multMagma-Family of {1,2}
proof
  let G1, G2 be associative non empty multMagma;
  reconsider A = <*G1,G2*> as multMagma-Family of {1,2};
  A is associative
  proof
    let x be Element of {1,2};
    x = 1 or x = 2 by TARSKI:def 2;
    hence thesis;
  end;
  hence thesis;
end;
