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
  M is finite & (N c= M or N in M) implies N is finite
proof
  assume that
A1: M is finite and
A2: N c= M or N in M;
  N c= M by A2,CARD_1:3;
  hence thesis by A1;
end;
