intros.
apply subtype_in_env with (1 := H).
constructor.
constructor.
red in |- *.
auto with pts.
apply red_incl_le_type.
trivial with pts.
apply wf_var with s; trivial with pts.
Qed.

(* Specifications: *)
Theorem ctxt_sound : rule_sound R -> rule_sound (ctxt R).
red in |- *.