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 x nin rng A holds A <- x = 0
  proof
    let A be FinSequence;
    assume x nin rng A; then
    A"{x} = {} by FUNCT_1:72;
    hence A <- x = 0 by SETFAM_1:def 1;
  end;
