
theorem Th18:
  for P, Q being pcs holds
  P misses Q implies the InternalRel of pcs-sum(P,Q) is transitive
proof
  let P, Q be pcs;
  assume
A1: the carrier of P misses the carrier of Q;
  pcs-sum(P,Q) = pcsSUM(P,Q) by Th15;
  hence thesis by A1,Th1;
end;
