Definition genvs_domain_eq {F1 F2 V1 V2: Type}
(ge1: Genv.t F1 V1) (ge2: Genv.t F2 V2) :=
(forall b, fst (genv2blocks ge1) b <-> fst (genv2blocks ge2) b) /\
(forall b, snd (genv2blocks ge1) b <-> snd (genv2blocks ge2) b) /\
(forall b, (exists f, Genv.find_funct_ptr ge1 b = Some f)
<-> (exists f, Genv.find_funct_ptr ge2 b = Some f)).

Lemma meminj_preserves_globals_ind_compose:
forall {F1 V1 F2 V2} (ge1: Genv.t F1 V1) (ge2: Genv.t F2 V2)
j1 j2 (G: genvs_domain_eq ge1 ge2)
(PG1: meminj_preserves_globals_ind (genv2blocks ge1) j1)
(PG2: meminj_preserves_globals_ind (genv2blocks ge2) j2),
meminj_preserves_globals_ind (genv2blocks ge1) (compose_meminj j1 j2).