reserve MS for non empty MidStr;
reserve a, b for Element of MS;
reserve M for MidSp;
reserve a,b,c,d,a9,b9,c9,d9,x,y,x9 for Element of M;

theorem Th15:
  ex d st a,b @@ c,d
proof
  consider d such that
A1: d@a =b@c by Def3;
  a,b @@ c,d by A1;
  hence thesis;
end;
