Basic equivalence relation for width-of-svex-extn structures.
Function:
(defun width-of-svex-extn-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (width-of-svex-extn-p acl2::x) (width-of-svex-extn-p acl2::y)))) (equal (width-of-svex-extn-fix acl2::x) (width-of-svex-extn-fix acl2::y)))
Theorem:
(defthm width-of-svex-extn-equiv-is-an-equivalence (and (booleanp (width-of-svex-extn-equiv x y)) (width-of-svex-extn-equiv x x) (implies (width-of-svex-extn-equiv x y) (width-of-svex-extn-equiv y x)) (implies (and (width-of-svex-extn-equiv x y) (width-of-svex-extn-equiv y z)) (width-of-svex-extn-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm width-of-svex-extn-equiv-implies-equal-width-of-svex-extn-fix-1 (implies (width-of-svex-extn-equiv acl2::x x-equiv) (equal (width-of-svex-extn-fix acl2::x) (width-of-svex-extn-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm width-of-svex-extn-fix-under-width-of-svex-extn-equiv (width-of-svex-extn-equiv (width-of-svex-extn-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-width-of-svex-extn-fix-1-forward-to-width-of-svex-extn-equiv (implies (equal (width-of-svex-extn-fix acl2::x) acl2::y) (width-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-width-of-svex-extn-fix-2-forward-to-width-of-svex-extn-equiv (implies (equal acl2::x (width-of-svex-extn-fix acl2::y)) (width-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm width-of-svex-extn-equiv-of-width-of-svex-extn-fix-1-forward (implies (width-of-svex-extn-equiv (width-of-svex-extn-fix acl2::x) acl2::y) (width-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm width-of-svex-extn-equiv-of-width-of-svex-extn-fix-2-forward (implies (width-of-svex-extn-equiv acl2::x (width-of-svex-extn-fix acl2::y)) (width-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)