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