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_4Val: forall m1 m1' m2 j k l j' k' n1' n2' (HI: mkInjections m1 m1' m2 j k l = (j',k',n1',n2')) (HK: forall b2 b3 ofs3, k b2 = Some(b3,ofs3) -> (b2 < Mem.nextblock m2)%positive) b2 b3 ofs3, k' b2 = Some(b3,ofs3) -> (k b2 = Some (b3,ofs3) /\ (b2 < Mem.nextblock m2)%positive) \/ (b2 = Mem.nextblock m2 /\ l (Mem.nextblock m1) = Some(b3, ofs3) /\ (b2 < n2')%positive) \/ (exists m, (b2 = Mem.nextblock m2 + m)%positive /\ l ((Mem.nextblock m1+m)%positive) = Some(b3,ofs3) /\ (b2 < n2')%positive).