
theorem
  for F being Field holds for a being Element of NonZero F holds omf(F).
  (a,ovf(F).(1.F,a)) = 1.F & omf(F).(ovf(F).(1.F,a),a) = 1.F
proof
  let F be Field;
  let a be Element of NonZero F;
  thus
A1: omf(F).(a,ovf(F).(1.F,a)) = ovf(F).(a*1.F,a) by Th21
    .= ovf(F).(a,a) by REALSET2:21
    .= 1.F by Th20;
  thus omf(F).(ovf(F).(1.F,a),a) = ovf(F).(1.F,a)*a .= a*ovf(F).(1.F,a)
    .= 1.F by A1;
end;
