reserve
  a,b,c,d,e for Ordinal,
  m,n for Nat,
  f for Ordinal-Sequence,
  x for object;
reserve S,S1,S2 for Sequence;

theorem Th37:
  for e being epsilon Ordinal holds omega in e
  proof
    let e be epsilon Ordinal;
A1: exp(omega, e) = e by Def5;
A2: exp(omega,0) = 1 & exp(omega,1) = omega & 1 in omega
    by ORDINAL2:43,46; then
A3: e <> 0 & e <> 1 & succ 0 = 1 & succ 1 = 2 by Def5; then
    0 in e by ORDINAL3:8; then
    1 c= e by A3,ORDINAL1:21; then
    1 c< e by A3; then
    1 in e by ORDINAL1:11;
    hence thesis by A1,A2,ORDINAL4:24;
  end;
