theorem
  F is having_a_unity implies (F*(id D,u)).(the_unity_wrt F,d) = u.d
proof
  assume
A1: F is having_a_unity;
  set e = the_unity_wrt F;
  thus (F*(id D,u)).(e,d) = F.(e,u.d) by Th81
    .= u.d by A1,SETWISEO:15;
end;
