End Properties.
Hint Rewrite @subst0_id : open.
Hint Rewrite @substl_subst1 : open.
Hint Rewrite @substl_trunc_notin using assumption : open.
Section MoreLemmas.
Context {A val : Type} {Heq : RelDec (@eq A)} {HeqOk : RelDec_Correct Heq}.
Context {R : ValNull val}.
Open Scope open_scope.

Lemma subst_singleton {B} :
forall x e (P : @open A val B), P[{e//x}] = P // (cons (x, e) nil).