reserve f for Function;
reserve n,k,n1 for Element of NAT;
reserve r,p for Complex;
reserve x,y for set;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Complex_Sequence;

theorem Th4:
  seq is non-zero iff for n holds seq.n<>0c
proof
  thus seq is non-zero implies for n holds seq.n<>0c by Th3;
  assume for n holds seq.n<>0c;
  then for x holds x in NAT implies seq.x<>0c;
  hence thesis by Th3;
end;
