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

theorem
  X meets Y & X c= Z implies X meets Y /\ Z
proof
  assume that
A1: X meets Y and
A2: X c= Z;
  now
    assume
A3: X /\ (Y /\ Z) = {};
    X /\ Y = (X /\ Z) /\ Y by A2,Th28
      .= {} by A3,Th16;
    hence contradiction by A1;
  end;
  hence thesis;
end;
