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(* This is proved in the preservation file. Lemma reduction_erasure : forall G a a', head_reduction G a a' -> reduction_in_one (erase a) (erase a') \/ erase a = erase a'. *)
(* ------------------------------------- *)

Lemma multi_trans : forall r a b, multi r a b -> forall c, multi r b c -> multi r a c.