
theorem
  for F being Field holds for a,b,c being Element of F
  holds osf(F).(a,(the addF of F).(b,c)) = osf(F).(osf(F).(a,b),c)
proof
  let F be Field;
  let a,b,c be Element of F;
  thus osf(F).(a,(the addF of F).(b,c)) = (the addF of F).(a,(comp F).((the
  addF of F).(b,c))) by Def1
    .= a-(b+c) by VECTSP_1:def 13
    .= a-b-c by RLVECT_1:27
    .= (the addF of F).((the addF of F).(a,-b),(comp F).c) by VECTSP_1:def 13
    .= (the addF of F).((the addF of F).(a,(comp F).b),(comp F).c) by
VECTSP_1:def 13
    .= (the addF of F).(osf(F).(a,b),(comp F).c) by Def1
    .= osf(F).(osf(F).(a,b),c) by Def1;
end;
