
theorem
  for F being Field holds for a,b being Element of F
  holds osf(F).((comp F).a,b) = (comp F).((the addF of F).(a,b))
proof
  let F be Field;
  let a,b be Element of F;
  thus osf(F).((comp F).a,b) = (the addF of F).((comp F).a,(comp F).b) by Def1
    .= (the addF of F).(-a,(comp F).b) by VECTSP_1:def 13
    .= -a+-b by VECTSP_1:def 13
    .= -(a+b) by RLVECT_1:31
    .= (comp F).((the addF of F).(a,b)) by VECTSP_1:def 13;
end;
