Fixing function for integerp-of-svex-extn structures.
(integerp-of-svex-extn-fix x) → new-x
Function:
(defun integerp-of-svex-extn-fix$inline (x) (declare (xargs :guard (integerp-of-svex-extn-p x))) (let ((acl2::__function__ 'integerp-of-svex-extn-fix)) (declare (ignorable acl2::__function__)) (mbe :logic (b* ((fn (svex-foreign-fnsym-fix (car x))) (arg-len (acl2::pos-fix (cdr x)))) (cons fn arg-len)) :exec x)))
Theorem:
(defthm integerp-of-svex-extn-p-of-integerp-of-svex-extn-fix (b* ((new-x (integerp-of-svex-extn-fix$inline x))) (integerp-of-svex-extn-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm integerp-of-svex-extn-fix-when-integerp-of-svex-extn-p (implies (integerp-of-svex-extn-p x) (equal (integerp-of-svex-extn-fix x) x)))
Function:
(defun integerp-of-svex-extn-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (integerp-of-svex-extn-p acl2::x) (integerp-of-svex-extn-p acl2::y)))) (equal (integerp-of-svex-extn-fix acl2::x) (integerp-of-svex-extn-fix acl2::y)))
Theorem:
(defthm integerp-of-svex-extn-equiv-is-an-equivalence (and (booleanp (integerp-of-svex-extn-equiv x y)) (integerp-of-svex-extn-equiv x x) (implies (integerp-of-svex-extn-equiv x y) (integerp-of-svex-extn-equiv y x)) (implies (and (integerp-of-svex-extn-equiv x y) (integerp-of-svex-extn-equiv y z)) (integerp-of-svex-extn-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm integerp-of-svex-extn-equiv-implies-equal-integerp-of-svex-extn-fix-1 (implies (integerp-of-svex-extn-equiv acl2::x x-equiv) (equal (integerp-of-svex-extn-fix acl2::x) (integerp-of-svex-extn-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm integerp-of-svex-extn-fix-under-integerp-of-svex-extn-equiv (integerp-of-svex-extn-equiv (integerp-of-svex-extn-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-integerp-of-svex-extn-fix-1-forward-to-integerp-of-svex-extn-equiv (implies (equal (integerp-of-svex-extn-fix acl2::x) acl2::y) (integerp-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-integerp-of-svex-extn-fix-2-forward-to-integerp-of-svex-extn-equiv (implies (equal acl2::x (integerp-of-svex-extn-fix acl2::y)) (integerp-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm integerp-of-svex-extn-equiv-of-integerp-of-svex-extn-fix-1-forward (implies (integerp-of-svex-extn-equiv (integerp-of-svex-extn-fix acl2::x) acl2::y) (integerp-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm integerp-of-svex-extn-equiv-of-integerp-of-svex-extn-fix-2-forward (implies (integerp-of-svex-extn-equiv acl2::x (integerp-of-svex-extn-fix acl2::y)) (integerp-of-svex-extn-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)