
theorem
  for F being Field holds for a,c being Element of F
holds for b being Element of NonZero F holds omf(F).(a,b) = c iff ovf(F).(c,b)
  = a
proof
  let F be Field;
  let a,c be Element of F;
  let b be Element of NonZero F;
  set d=1.F;
A1: omf(F).(c,d) = c*1.F .= c by REALSET2:21;
A2: omf(F).(b,a) = b*a .= a*b
    .= omf(F).(a,b);
  ovf(F).(a,d) = a & 1.F is Element of NonZero F by Th27,STRUCT_0:2;
  hence thesis by A1,A2,Th25;
end;
