reserve X for set, R,R1,R2 for Relation;
reserve x,y,z for set;
reserve n,m,k for Nat;

theorem
  for A being FinSequence st A <- x = 0 holds x nin rng A
  proof
    let A be FinSequence;
    assume A <- x = 0 & x in rng A; then
    0 in dom A by Th16;
    hence thesis by FINSEQ_3:24;
  end;
