
theorem Th2:
  for F being Field holds for a,b being Element of NonZero F holds
  revf(F).(omf(F).(a,revf(F).b)) = omf(F).(b,revf(F).a)
proof
  let F be Field;
  let a,b be Element of NonZero F;
  reconsider revfa = revf(F).a, revfb = revf(F).b as Element of NonZero F;
A1: omf(F).(a,revf(F).b) is Element of NonZero F by REALSET2:24;
A2: omf(F).(b,revf(F).a) is Element of NonZero F by REALSET2:24;
  revfb*(b*revfa) = revfa*(b*revfb) by REALSET2:4
    .= revfa*(omf F).(b,revfb)
    .= revfa*1.F by REALSET2:def 6
    .= revf(F).a by REALSET2:6;
  then a*revfb*(b*revfa) = a*revfa by A2,REALSET2:4
    .= (omf F).(a,revfa)
    .= 1.F by REALSET2:def 6;
  hence thesis by A1,A2,REALSET2:22;
end;
