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;
