reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem
  succ A c= bool A
proof
  let x be object;
  assume
A1: x in succ A;
  then reconsider B = x as Ordinal;
  x in A or x = A by A1,ORDINAL1:8;
  then B c= A by ORDINAL1:def 2;
  hence thesis;
end;
