Definition globals_separate {F V:Type} (ge: Genv.t F V) mu nu :=
    forall b1 b2 d, as_inj mu b1 = None ->
            as_inj nu b1 =Some(b2,d) ->
            isGlobalBlock ge b2 = false.

Lemma gsep_domain_eq: forall {F1 F2 V1 V2} mu mu' (ge1: Genv.t F1 V1) (ge2: Genv.t F2 V2), globals_separate ge1 mu mu' -> genvs_domain_eq ge1 ge2 -> globals_separate ge2 mu mu'.