Fixing function for g-map-tag structures.
(g-map-tag-fix x) → new-x
Function:
(defun g-map-tag-fix$inline (x) (declare (xargs :guard (g-map-tag-p x))) (let ((__function__ 'g-map-tag-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((index (acl2::maybe-natp-fix (cdr x)))) (cons :g-map index)) :exec x)))
Theorem:
(defthm g-map-tag-p-of-g-map-tag-fix (b* ((new-x (g-map-tag-fix$inline x))) (g-map-tag-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm g-map-tag-fix-when-g-map-tag-p (implies (g-map-tag-p x) (equal (g-map-tag-fix x) x)))
Function:
(defun g-map-tag-equiv$inline (x y) (declare (xargs :guard (and (g-map-tag-p x) (g-map-tag-p y)))) (equal (g-map-tag-fix x) (g-map-tag-fix y)))
Theorem:
(defthm g-map-tag-equiv-is-an-equivalence (and (booleanp (g-map-tag-equiv x y)) (g-map-tag-equiv x x) (implies (g-map-tag-equiv x y) (g-map-tag-equiv y x)) (implies (and (g-map-tag-equiv x y) (g-map-tag-equiv y z)) (g-map-tag-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm g-map-tag-equiv-implies-equal-g-map-tag-fix-1 (implies (g-map-tag-equiv x x-equiv) (equal (g-map-tag-fix x) (g-map-tag-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm g-map-tag-fix-under-g-map-tag-equiv (g-map-tag-equiv (g-map-tag-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-g-map-tag-fix-1-forward-to-g-map-tag-equiv (implies (equal (g-map-tag-fix x) y) (g-map-tag-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-g-map-tag-fix-2-forward-to-g-map-tag-equiv (implies (equal x (g-map-tag-fix y)) (g-map-tag-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm g-map-tag-equiv-of-g-map-tag-fix-1-forward (implies (g-map-tag-equiv (g-map-tag-fix x) y) (g-map-tag-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm g-map-tag-equiv-of-g-map-tag-fix-2-forward (implies (g-map-tag-equiv x (g-map-tag-fix y)) (g-map-tag-equiv x y)) :rule-classes :forward-chaining)