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(* miscellanous                                   *)
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Lemma assoc_add_find_effect :
forall (l0 l1 : assoc) (k k' : K) (v v' : V),
none V = assoc_find l0 k ->
some V v = assoc_find l1 k -> l1 = assoc_add l0 k' v' -> k' = k /\ v' = v.