reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;
reserve A,B for Ordinal;

theorem
  N in nextcard M iff N c= M
proof
A1: not N c= M iff M in N by CARD_1:4;
  N in nextcard M iff not nextcard M c= N by CARD_1:4;
  hence thesis by A1,Th87;
end;
