(* 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 SEPx_nonexpansive: forall R rho,
Forall (fun R0 => predicates_rec.nonexpansive R0) R ->
nonexpansive (fun S => SEPx (map (fun R0 => R0 S) R) rho).