theorem Th3:
  seq is non-zero iff for n holds seq.n<>0.TOP-REAL N
proof
  thus seq is non-zero implies for n holds seq.n<>0.TOP-REAL N
    by ORDINAL1:def 12,Th2;
  assume for n holds seq.n<>0.TOP-REAL N;
  then for x holds x in NAT implies seq.x<>0.TOP-REAL N;
  hence thesis by Th2;
end;
