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(* 02110-1301 USA                                                     *)
Unset Standard Proposition Elimination Names.

Theorem swap_under_out :
forall (P : proc) (n1 n2 : name) (p q : PP),
swap_proc (out n1 n2 P) p q =
out (swap_name n1 p q) (swap_name n2 p q) (swap_proc P p q).