reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X misses Y implies X misses Y \ Z
proof
  assume
A1: X misses Y;
  assume X meets Y \ Z;
  then consider x being object such that
A2: x in X and
A3: x in Y \ Z by XBOOLE_0:3;
  x in Y by A3,XBOOLE_0:def 5;
  hence thesis by A1,A2,XBOOLE_0:3;
end;
