Basic equivalence relation for wirelist structures.
Function:
(defun wirelist-equiv$inline (x y) (declare (xargs :guard (and (wirelist-p x) (wirelist-p y)))) (equal (wirelist-fix x) (wirelist-fix y)))
Theorem:
(defthm wirelist-equiv-is-an-equivalence (and (booleanp (wirelist-equiv x y)) (wirelist-equiv x x) (implies (wirelist-equiv x y) (wirelist-equiv y x)) (implies (and (wirelist-equiv x y) (wirelist-equiv y z)) (wirelist-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm wirelist-equiv-implies-equal-wirelist-fix-1 (implies (wirelist-equiv x x-equiv) (equal (wirelist-fix x) (wirelist-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm wirelist-fix-under-wirelist-equiv (wirelist-equiv (wirelist-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-wirelist-fix-1-forward-to-wirelist-equiv (implies (equal (wirelist-fix x) y) (wirelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-wirelist-fix-2-forward-to-wirelist-equiv (implies (equal x (wirelist-fix y)) (wirelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm wirelist-equiv-of-wirelist-fix-1-forward (implies (wirelist-equiv (wirelist-fix x) y) (wirelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm wirelist-equiv-of-wirelist-fix-2-forward (implies (wirelist-equiv x (wirelist-fix y)) (wirelist-equiv x y)) :rule-classes :forward-chaining)