
theorem Th9:
  for F being Field holds for a,b,c being Element
  of F holds omf(F).(a,osf(F).(b,c)) = osf(F).(omf(F).(a,b),omf(F).(a,c))
proof
  let F be Field;
  let a,b,c be Element of F;
  thus omf(F).(a,osf(F).(b,c)) = omf(F).(a,(the addF of F).(b,(comp F).c)) by
Def1
    .= a*(b-c) by VECTSP_1:def 13
    .= a*b-a*c by REALSET2:11
    .= (the addF of F).(omf(F).(a,b),(comp F).(a*c)) by VECTSP_1:def 13
    .= osf(F).(omf(F).(a,b),omf(F).(a,c)) by Def1;
end;
