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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 swap_equivariance : forall t x y z w,
swap x y (swap z w t) = swap (swap_var x y z) (swap_var x y w) (swap x y t).