
theorem Th21:
  for S1, S2 being non empty RelStr for D being non empty Subset
  of [:S1,S2:] holds proj1 D is non empty & proj2 D is non empty
proof
  let S1, S2 be non empty RelStr, D be non empty Subset of [:S1,S2:];
  reconsider D1 = D as non empty Subset of [:the carrier of S1,the carrier of
  S2:] by Def2;
  proj1 D1 is non empty;
  hence thesis;
end;
