theorem
  H is conjunctive implies the_left_argument_of (H/(x,y)) = (
  the_left_argument_of H)/(x,y) & the_right_argument_of (H/(x,y)) = (
  the_right_argument_of H)/(x,y)
proof
  assume
A1: H is conjunctive;
  then H/(x,y) is conjunctive by Th169;
  then
A2: H/(x,y) = (the_left_argument_of (H/(x,y))) '&' (the_right_argument_of (H
  /(x,y))) by ZF_LANG:40;
  H = (the_left_argument_of H) '&' (the_right_argument_of H) by A1,ZF_LANG:40;
  hence thesis by A2,Th158;
end;
