reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  p in rng f implies f-:p is non empty
proof
  assume
A1: p in rng f;
  then 1 <= p..f by FINSEQ_4:21;
  then 1 <= len(f-:p) by A1,Th42;
  hence thesis;
end;
