
theorem
  for F being Field holds for a,b,c being Element of F
  holds omf(F).(osf(F).(a,b),c) = osf(F).(omf(F).(a,c),omf(F).(b,c))
proof
  let F be Field;
  let a,b,c be Element of F;
  thus omf(F).(osf(F).(a,b),c) =osf(F).(a,b)*c .= c*osf(F).(a,b)
    .= omf(F).(c,osf(F).(a,b))
    .= osf(F).(c*a,c*b) by Th9
    .= osf(F).(a*c,b*c)
    .= osf(F).(omf(F).(a,c),omf(F).(b,c));
end;
