Module VSF := FSetFacts.Facts(VSet).Module VSP := FSetProperties.Properties(VSet).Definition match_prog (p tp: program) : Prop :=
    match_program (fun ctx f tf => transf_fundef f = OK tf) eq p tp
 /\ prog_types tp = prog_types p.

Lemma match_envs_invariant: forall f cenv e le m lo hi te tle tlo thi f' m', match_envs f cenv e le m lo hi te tle tlo thi -> (forall b chunk v, f b = None -> Ple lo b /\ Plt b hi -> Mem.load chunk m b 0 = Some v -> Mem.load chunk m' b 0 = Some v) -> inject_incr f f' -> (forall b, Ple lo b /\ Plt b hi -> f' b = f b) -> (forall b b' delta, f' b = Some(b', delta) -> Ple tlo b' /\ Plt b' thi -> f' b = f b) -> match_envs f' cenv e le m' lo hi te tle tlo thi.