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
  a c= b implies first_epsilon_greater_than a c= first_epsilon_greater_than b
  proof assume
A1: a c= b;
    b in first_epsilon_greater_than b by Def6; then
    a in first_epsilon_greater_than b by A1,ORDINAL1:12;
    hence thesis by Def6;
  end;
