reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;

theorem
  x in rng p implies rng(p -| x) misses {x}
proof
  assume x in rng p;
  then not x in rng(p -| x) by Th37;
  then for y being object st y in rng(p -| x) holds not y in {x}
     by TARSKI:def 1;
  hence thesis by XBOOLE_0:3;
end;
