
theorem Th13:
  for F being Field holds for a,b,c,d being Element
  of F holds osf(F).(a,b) = osf(F).(c,d) iff a+d = b+c
proof
  let F be Field;
  let a,b,c,d be Element of F;
A1: osf(F).(c,d) = (the addF of F).(c,(comp F).d) by Def1
    .= c-d by VECTSP_1:def 13;
  osf(F).(a,b) = (the addF of F).(a,(comp F).b) by Def1
    .= a-b by VECTSP_1:def 13;
  hence thesis by A1,Th4;
end;
