theorem Th17:
  A c= C & B c= D implies A ^^ B c= C ^^ D
proof
  assume
A1: A c= C & B c= D;
  thus thesis
  proof
    let x be object;
    assume x in A ^^ B;
    then ex a, b st a in A & b in B & x = a ^ b by Def1;
    hence thesis by A1,Def1;
  end;
end;
