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_7: forall m1 m1' m2 j k l j' k' n1' n2'
(HI: mkInjections m1 m1' m2 j k l = (j',k',n1',n2'))
b (HB: (b < n1')%positive),
((Mem.nextblock m1 <= b)%positive -> j' b  <> None) /\
((b < Mem.nextblock m1)%positive -> j' b = j b).