Definition env_mapsto: forall {key A}{KE: EqDec key} (id: key) (sh: Share.t) (v: A) , pred (env key A) := @_env_mapsto.

Lemma env_mapsto_set_sh{key A}{KE: EqDec key}: forall id (sh: pshare) (v: A), _env_mapsto id (pshare_sh sh) v (env_set_sh id (Some (sh,v)) empty_env).