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_3: forall N n1 n2 j k l j' k' n1' n2' (HI: mkInjectionsN N n1 n2 j k l = (j',k',n1',n2')) b1 b2 ofs2, j' b1 = Some(b2,ofs2) -> (j b1 = Some (b2,ofs2)) \/ (b1 = n1 /\ b2 = n2 /\ ofs2 = 0) \/ (exists m, (b1 = n1 + m /\ b2=n2 + m)%positive /\ ofs2=0).