
theorem
  for f being Element of the_set_of_ComplexSequences st
    for n being Nat holds (seq_id f).n = 0 holds
  f = CZeroseq
  proof
    let f be Element of the_set_of_ComplexSequences;
    set g = seq_id f;
    assume
A1: for n being Nat holds g.n = 0;
A2: dom g = NAT by FUNCT_2:def 1;
    for z being object st z in dom g holds g.z = 0 by A1;
    hence f = CZeroseq by A2,FUNCOP_1:11;
  end;
