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 Th12:
  0 in a & exp(a,b) in exp(a,c) implies b in c proof assume
A1: 0 in a & exp(a,b) in exp(a,c);
    assume not b in c; then
    exp(a,c) c= exp(a,b) by A1,ORDINAL1:16,ORDINAL4:27; then
    exp(a,b) in exp(a,b) by A1;
    hence thesis;
  end;
