theorem
  H is conjunctive implies (M,v |= H iff M,v |= the_left_argument_of H &
  M,v |= the_right_argument_of H)
proof
  assume H is conjunctive;
  then H = (the_left_argument_of H) '&' (the_right_argument_of H)
  by ZF_LANG:40;
  hence thesis by ZF_MODEL:15;
end;
