Hint Resolve apply_stack_lc : lngen.
(* /SOLUTION *)

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(** ** Properties of apply_heap *)
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(** Since the heap is just an iterated substitution, it inherits properties from [subst_exp].  Below, [alist induction] is a tactic from the metatheory library for induction over association lists (such as the heap).  *)
Lemma apply_heap_abs : forall h e,
apply_heap h (abs e) = abs (apply_heap h e).