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 is finite & not M is finite implies N in M & N c= M
proof
  assume that
A1: N is finite and
A2: not M is finite;
A3: N in omega by A1,CARD_1:61;
  omega c= M by A2,Th82;
  hence N in M by A3;
  thus thesis by A1,A2;
end;
