(*i Lemma MapGet_M2_bit_0_1' : (m,m',m'',m''':Map) (a:ad) (MapGet (if (Nbit0 a) then (M2 m m') else (M2 m'' m''')) a)= (MapGet (if (Nbit0 a) then m' else m'') (Ndiv2 a)). i*)

Lemma MapGet_M2_both_None :
forall (m m':Map) (a:ad),
MapGet m (Ndiv2 a) = None ->
MapGet m' (Ndiv2 a) = None -> MapGet (M2 m m') a = None.