reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;

theorem Th16:
  X,Y are_equipotent implies nextcard X = nextcard Y
proof
  assume X,Y are_equipotent;
  then card X = card Y by Th4;
  hence thesis by Th15;
end;
