End ENVSEC.
End Env.
Export Env.
Module EnvSA.
Existing Instance Join_env.
Existing Instance Perm_env.
Existing Instance Sep_env.
Existing Instance Sing_env.
Existing Instance Canc_env.
Existing Instance Disj_env.
Existing Instance Cross_env.

Lemma env_at_join_sub {key: Type}{A: Type}{KE: EqDec key}:
forall rho1 rho2, (forall id: key, @join_sub _ (@Join_lower (pshare * A) (Join_prod pshare Join_pshare A (Join_equiv _))) (env_get rho1 id) (env_get rho2 id)) -> join_sub rho1 rho2.