Fixpoint mkInjectionsN (N:nat)(n1 n2:block)(j k l: meminj)
:  meminj * meminj * block * block :=
match N with O => (j,k,n1,n2)
| S M => mkInjectionsN M (Pos.succ n1) (Pos.succ n2)
(fun b => if eq_block b n1
then Some (n2,0)
else j b)
(fun b => if eq_block b n2 then l n1 else k b)
l
end.

Lemma mkInjectionsN_9: forall M j' k' l n1' n2'  N j  k n1 n2
(HI: mkInjectionsN N n1 n2 j k l = (j',k',n1',n2'))
(Hj: forall b, j b = None -> (b < n1' -> b < M)%positive) b,
j' b = None -> (b < n1' -> b < M)%positive.