reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;
reserve D for non empty set;
reserve p, q for FinSequence,
  X, Y, x, y for set,
  D for non empty set,
  i, j, k, l, m, n, r for Nat;

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;
