theorem Th3:
  for r ex n st r<n
proof
  let r;
  for r st r in NAT holds r+1 in NAT by AXIOMS:2;
  then consider p such that
A1: p in NAT and
A2: r<p by Th2, NUMBERS:19;
  consider n1 such that
A3: n1=p by A1;
  take n1;
  thus thesis by A2,A3;
end;
