theorem
Th84: for a being finite Ordinal, x st x in a
      holds x = 0 or ex b st x = succ b
   proof
     let a be finite Ordinal;
     let x;
     assume
A1:  x in a & x <> 0; then
A2:  {} in x by ORDINAL3:8;
     now assume x is limit_ordinal; then
       omega c= x & x c= a by A1,A2,ORDINAL1:def 2,def 11;
       hence contradiction;
     end;
     hence thesis by A1,ORDINAL1:29;
   end;
