theorem
  K+`M in K+`N implies M in N
proof
  assume that
A1: K+`M in K+`N and
A2: not M in N;
  N c= M by A2,CARD_1:4;
  then K+`N c= K+`M by Th82;
  hence thesis by A1,CARD_1:4;
end;
