theorem Th17:
  rng (p^'q) c= rng p \/ rng q
proof
  set r = p^'q;
  set qc = (2,len q)-cut q;
  let x be object;
  assume x in rng r;
  then x in rng p \/ rng qc by FINSEQ_1:31;
  then
A1: x in rng p or x in rng qc by XBOOLE_0:def 3;
  rng qc c= rng q by Th11;
  hence thesis by A1,XBOOLE_0:def 3;
end;
