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(** ** Exercises                                             *)
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(** *** Recommended Exercise: [swap] properties  Prove the following properties about swapping, either explicitly (by destructing [x == y]) or automatically (using [default_simp]).  *)

Lemma notin_fv_nom_equivariance : forall x0 x y t ,
x0 `notin` fv_nom t ->
swap_var x y x0  `notin` fv_nom (swap x y t).