Definition mem_respects_readonly {F V} (ge : Genv.t F V) m :=
    forall b gv, Genv.find_var_info ge b = Some gv ->
                 gvar_readonly gv && negb (gvar_volatile gv) = true ->
           Genv.load_store_init_data ge m b 0 (gvar_init gv) /\
           Mem.valid_block m b /\ (forall ofs : Z, ~ Mem.perm m b ofs Max Writable).

(* Specifications: *)
Lemma mem_respects_readonly_fwd {F V} (g : Genv.t F V) m m' (MRR: mem_respects_readonly g m) (FWD: mem_forward m m') (RDO: forall b, Mem.valid_block m b -> readonly m b m'): mem_respects_readonly g m'.
Lemma mem_respects_readonly_forward {F V} (ge : Genv.t F V) m m' (MRR: mem_respects_readonly ge m) (FWD: mem_forward m m') (RDO: forall b gv, Genv.find_var_info ge b = Some gv -> gvar_readonly gv && negb (gvar_volatile gv) = true -> readonly m b m'): mem_respects_readonly ge m'.
Lemma mem_respects_readonly_forward' {F V} (ge : Genv.t F V) m m' (MRR: mem_respects_readonly ge m) (FWD: mem_forward m m') (RDO: RDOnly_fwd m m' (ReadOnlyBlocks ge)): mem_respects_readonly ge m'.
Lemma nextblock_storev: forall chunk m addr v m', Mem.storev chunk m addr v = Some m' -> Mem.nextblock m' = Mem.nextblock m.
Lemma nextblock_freelist: forall fbl m m', Mem.free_list m fbl = Some m' -> Mem.nextblock m' = Mem.nextblock m.
Lemma perm_freelist: forall fbl m m' b ofs k p, Mem.free_list m fbl = Some m' -> Mem.perm m' b ofs k p -> Mem.perm m b ofs k p.
Lemma free_contents: forall m b lo hi m' b' ofs, Mem.free m b lo hi = Some m' -> ~adr_range (b,lo) (hi-lo) (b',ofs) -> ZMap.get ofs (PMap.get b' (Mem.mem_contents m)) = ZMap.get ofs (PMap.get b' (Mem.mem_contents m')).
Lemma alloc_contents: forall b1 ofs, Mem.valid_block m1 b1 -> ZMap.get ofs (PMap.get b1 (Mem.mem_contents m1)) = ZMap.get ofs (PMap.get b1 (Mem.mem_contents m2)).