reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem
  for f being Function, A,B being set st A misses B holds f"A misses f"B
proof
  let f be Function, A,B be set;
  assume A misses B;
  then A /\ B = {};
  then {} = f"(A /\ B)
    .= f"A /\ f"B by Th67;
  hence thesis;
end;
