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
  X misses Y & f is one-to-one implies f.:X misses f.:Y
proof
  assume X /\ Y = {} & f is one-to-one;
  then f.:(X /\ Y) = {} & f.:(X /\ Y) = f.:X /\ f.:Y by Th61;
  hence thesis;
end;
