Section EVAL_EXPR.
Variables e te: env.
Variables le tle: temp_env.
Variables m tm: mem.
Variable f: meminj.
Variable cenv: compilenv.
Variables lo hi tlo thi: block.
Hypothesis MATCH: match_envs f cenv e le m lo hi te tle tlo thi.
Hypothesis MEMINJ: Mem.inject f m tm.
Hypothesis GLOB: exists bound, match_globalenvs f bound.

Lemma eval_simpl_expr:
forall a v,
eval_expr ge e le m a v ->
compat_cenv (addr_taken_expr a) cenv ->
exists tv, eval_expr tge te tle tm (simpl_expr cenv a) tv /\ Val.inject f v tv
with eval_simpl_lvalue:
forall a b ofs,
eval_lvalue ge e le m a b ofs ->
compat_cenv (addr_taken_expr a) cenv ->
match a with Evar id ty => VSet.mem id cenv = false | _ => True end ->
exists b', exists ofs', eval_lvalue tge te tle tm (simpl_expr cenv a) b' ofs' /\ Val.inject f (Vptr b ofs) (Vptr b' ofs').