Hint Resolve match_env_update_temp: rtlg.
(** Matching between environments is preserved by simultaneous assignment to a Cminor local variable (in the Cminor environments) and to the corresponding RTL pseudo-register (in the RTL register environment). *)

Lemma match_env_update_var:
forall j map e le rs id r v tv,
val_inject j v tv ->
map_wf map ->
map.(map_vars)!id = Some r ->
match_env j map e le rs ->
match_env j map (PTree.set id v e) le (rs#r <- tv).