Definition removeUndefs (j l j':meminj):meminj :=
fun b => match j b with
None => match l b with
None => None | Some (b1,delta1) => j' b
end
| Some(b2,delta2) => Some(b2, delta2)
end.

Lemma RU_composememinj: forall m1 m1' m2 j k l j' k' n1' n2'
(HI: mkInjections m1 m1' m2 j k l = (j',k',n1',n2'))
(InjIncr: inject_incr (compose_meminj j k) l) m3
(InjSep: inject_separated (compose_meminj j k) l m1 m3)
(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 b3 ofs3, l b1 = Some (b3, ofs3) -> (b1 < n1')%positive),
l = compose_meminj (removeUndefs j l j') k'.