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_1: forall N n1 n2 j k l j' k' n1' n2' (HI: mkInjectionsN N n1 n2 j k l = (j',k',n1',n2')), forall b1 b2 ofs2 (Jb: j b1 = Some(b2,ofs2)), (b1 < n1)%positive -> j' b1 = Some (b2,ofs2).