reserve a, b, k, n, m for Nat,
  i for Integer,
  r for Real,
  p for Rational,
  c for Complex,
  x for object,
  f for Function;

theorem Th25:
  ex k being Nat st divSeq(m,n).k = 0 & modSeq(m,n).k = 0
proof
  set f = modSeq(m,n);
  consider k such that
A1: f.k = 0 by Lm4;
  take k+1;
A2: k+0 < k+1 by XREAL_1:6;
  hence divSeq(m,n).(k+1) = 0 by A1,Th18;
  thus f.(k+1) = 0 by A1,A2,Th14;
end;
