(* Lemma SEPx_super_non_expansive: forall A (R: list (forall ts, functors.MixVariantFunctor._functor (rmaps.dependent_type_functor_rec ts (rmaps.ArrowType A rmaps.Mpred)) mpred)), Forall (fun R0: (forall ts, functors.MixVariantFunctor._functor (rmaps.dependent_type_functor_rec ts (rmaps.ArrowType A rmaps.Mpred)) mpred) => @super_non_expansive A (fun ts (a: functors.MixVariantFunctor._functor (rmaps.dependent_type_functor_rec ts A) mpred) (_: environ) => R0 ts a)) R -> @super_non_expansive A (fun ts (a: functors.MixVariantFunctor._functor (rmaps.dependent_type_functor_rec ts A) mpred) (rho: environ) => SEPx (map (fun R0: forall ts, functors.MixVariantFunctor._functor (rmaps.dependent_type_functor_rec ts (rmaps.ArrowType A rmaps.Mpred)) mpred => R0 ts a) R) rho).*)

Lemma PROP_LOCAL_SEP_nonexpansive: forall P Q R rho,
Forall (fun P0 => nonexpansive (fun S => prop (P0 S))) P ->
Forall (fun R0 => nonexpansive R0) R ->
nonexpansive (fun S => PROPx (map (fun P0 => P0 S) P) (LOCALx Q (SEPx (map (fun R0 => R0 S) R))) rho).