reserve x,y for set;

theorem
  for F being Field, x,y being Element of NonZero F holds x*y = 1.F
  implies y = revf(F).x
proof
  let F be Field, x,y be Element of NonZero F;
  assume
A1: x*y = 1.F;
  reconsider rx = revf(F).x as Element of F by XBOOLE_0:def 5;
  y = y*1.F
    .= omf(F).(y,1.F)
    .= y*(x*rx) by Def6
    .= 1.F*rx by A1,Th4
    .= revf(F).x;
  hence thesis;
end;
