Definition mkInjections (m1 m1' m2:mem) (j k l: meminj)
                     :  meminj * meminj * block * block :=
  if plt (Mem.nextblock m1) (Mem.nextblock m1')
  then mkInjectionsN (Pos.to_nat (Mem.nextblock m1') - Pos.to_nat(Mem.nextblock m1))
                (Mem.nextblock m1)
                (Mem.nextblock m2) j k l
  else (j,k,Mem.nextblock m1,Mem.nextblock m2).

Lemma mkInjections_5: forall m1 m1' m2 j k l j' k' n1' n2' (HI: mkInjections m1 m1' m2 j k l = (j',k',n1',n2')) (VBj1: forall b1 b2 ofs2, j b1 = Some(b2,ofs2) -> Mem.valid_block m1 b1) (VBj2: forall b1 b2 ofs2, j b1 = Some(b2,ofs2) -> Mem.valid_block m2 b2) (VBk2: forall b1 b2 ofs2, k b1 = Some(b2,ofs2) -> Mem.valid_block m2 b1) (VBl1: forall b1 b2 ofs2, l b1 = Some(b2,ofs2) -> (b1 < n1')%positive) b2 (HB: (b2 < n2')%positive), k' b2 = None -> (Mem.valid_block m2 b2 /\ k b2 = None) \/ (b2 = Mem.nextblock m2 /\ l (Mem.nextblock m1) = None) \/ (exists m, b2 = ((Mem.nextblock m2) + m)%positive /\ l ((Mem.nextblock m1+m)%positive) = None).