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_splittable {key A}{KE: EqDec key}: forall id (v:A) (sh sh1 sh2: pshare) rho, join (proj1_sig sh1) (proj1_sig sh2) (proj1_sig sh) -> (_env_mapsto id (pshare_sh sh) v rho <-> (_env_mapsto id (pshare_sh sh1) v * _env_mapsto id (pshare_sh sh2) v)%pred rho).