reserve x,y for set;

theorem
  for F being Field, x being Element of NonZero F holds x =revf(F).(revf (F).x)
proof
  let F be Field, x be Element of NonZero F;
  reconsider rx = revf(F).x as Element of F by XBOOLE_0:def 5;
  reconsider rrx = revf(F).(revf(F).x) as Element of F by XBOOLE_0:def 5;
  x =x*1.F
    .= omf(F).(x,1.F)
    .= x*(rx*rrx) by Def6
    .= x*rx*rrx by Th4
    .= omf(F).(1.F,revf(F).(revf(F).x)) by Def6
    .= 1.F*rrx
    .= revf(F).(revf(F).x);
  hence thesis;
end;
