reserve k,n,m for Nat,
  A,B,C for Ordinal,
  X for set,
  x,y,z for object;
reserve f,g,h,fx for Function,
  K,M,N for Cardinal,
  phi,psi for
  Ordinal-Sequence;

theorem Th1:
  nextcard card X = nextcard X
proof
  card card X in nextcard X & for M st card card X in M holds nextcard X
  c= M by CARD_1:def 3;
  hence thesis by CARD_1:def 3;
end;
