theorem
  q<>p & LSeg(q,p) /\ L~f = {q} implies not p in L~f
proof
  assume that
A1: q<>p and
A2: LSeg(q,p) /\ L~f = {q} & p in L~f;
  p in LSeg(q,p) by RLTOPSP1:68;
  then p in {q} by A2,XBOOLE_0:def 4;
  hence contradiction by A1,TARSKI:def 1;
end;
