
theorem
  for X, Y being RelStr st [:X,Y:] is non empty holds X is non empty & Y
  is non empty
proof
  let X, Y be RelStr;
  assume [:X,Y:] is non empty;
  then
A1: ex x being object st x in the carrier of [:X,Y:] by XBOOLE_0:def 1;
  the carrier of [:X,Y:] = [:the carrier of X, the carrier of Y:] by Def2;
  hence thesis by A1,MCART_1:10;
end;
