(*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_if_same :
forall (m:Map) (b:bool) (a:ad), MapGet (if b then m else m) a = MapGet m a.