(cutinfolist-fix x) is a usual ACL2::fty list fixing function.
(cutinfolist-fix x) → fty::newx
In the logic, we apply cutinfo-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.
Function:
(defun cutinfolist-fix$inline (x) (declare (xargs :guard (cutinfolist-p x))) (let ((__function__ 'cutinfolist-fix)) (declare (ignorable __function__)) (mbe :logic (if (atom x) nil (cons (cutinfo-fix (car x)) (cutinfolist-fix (cdr x)))) :exec x)))
Theorem:
(defthm cutinfolist-p-of-cutinfolist-fix (b* ((fty::newx (cutinfolist-fix$inline x))) (cutinfolist-p fty::newx)) :rule-classes :rewrite)
Theorem:
(defthm cutinfolist-fix-when-cutinfolist-p (implies (cutinfolist-p x) (equal (cutinfolist-fix x) x)))
Function:
(defun cutinfolist-equiv$inline (x acl2::y) (declare (xargs :guard (and (cutinfolist-p x) (cutinfolist-p acl2::y)))) (equal (cutinfolist-fix x) (cutinfolist-fix acl2::y)))
Theorem:
(defthm cutinfolist-equiv-is-an-equivalence (and (booleanp (cutinfolist-equiv x y)) (cutinfolist-equiv x x) (implies (cutinfolist-equiv x y) (cutinfolist-equiv y x)) (implies (and (cutinfolist-equiv x y) (cutinfolist-equiv y z)) (cutinfolist-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm cutinfolist-equiv-implies-equal-cutinfolist-fix-1 (implies (cutinfolist-equiv x x-equiv) (equal (cutinfolist-fix x) (cutinfolist-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm cutinfolist-fix-under-cutinfolist-equiv (cutinfolist-equiv (cutinfolist-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-cutinfolist-fix-1-forward-to-cutinfolist-equiv (implies (equal (cutinfolist-fix x) acl2::y) (cutinfolist-equiv x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-cutinfolist-fix-2-forward-to-cutinfolist-equiv (implies (equal x (cutinfolist-fix acl2::y)) (cutinfolist-equiv x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm cutinfolist-equiv-of-cutinfolist-fix-1-forward (implies (cutinfolist-equiv (cutinfolist-fix x) acl2::y) (cutinfolist-equiv x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm cutinfolist-equiv-of-cutinfolist-fix-2-forward (implies (cutinfolist-equiv x (cutinfolist-fix acl2::y)) (cutinfolist-equiv x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm car-of-cutinfolist-fix-x-under-cutinfo-equiv (cutinfo-equiv (car (cutinfolist-fix x)) (car x)))
Theorem:
(defthm car-cutinfolist-equiv-congruence-on-x-under-cutinfo-equiv (implies (cutinfolist-equiv x x-equiv) (cutinfo-equiv (car x) (car x-equiv))) :rule-classes :congruence)
Theorem:
(defthm cdr-of-cutinfolist-fix-x-under-cutinfolist-equiv (cutinfolist-equiv (cdr (cutinfolist-fix x)) (cdr x)))
Theorem:
(defthm cdr-cutinfolist-equiv-congruence-on-x-under-cutinfolist-equiv (implies (cutinfolist-equiv x x-equiv) (cutinfolist-equiv (cdr x) (cdr x-equiv))) :rule-classes :congruence)
Theorem:
(defthm cons-of-cutinfo-fix-x-under-cutinfolist-equiv (cutinfolist-equiv (cons (cutinfo-fix x) acl2::y) (cons x acl2::y)))
Theorem:
(defthm cons-cutinfo-equiv-congruence-on-x-under-cutinfolist-equiv (implies (cutinfo-equiv x x-equiv) (cutinfolist-equiv (cons x acl2::y) (cons x-equiv acl2::y))) :rule-classes :congruence)
Theorem:
(defthm cons-of-cutinfolist-fix-y-under-cutinfolist-equiv (cutinfolist-equiv (cons x (cutinfolist-fix acl2::y)) (cons x acl2::y)))
Theorem:
(defthm cons-cutinfolist-equiv-congruence-on-y-under-cutinfolist-equiv (implies (cutinfolist-equiv acl2::y y-equiv) (cutinfolist-equiv (cons x acl2::y) (cons x y-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-cutinfolist-fix (equal (consp (cutinfolist-fix x)) (consp x)))
Theorem:
(defthm cutinfolist-fix-under-iff (iff (cutinfolist-fix x) (consp x)))
Theorem:
(defthm cutinfolist-fix-of-cons (equal (cutinfolist-fix (cons a x)) (cons (cutinfo-fix a) (cutinfolist-fix x))))
Theorem:
(defthm len-of-cutinfolist-fix (equal (len (cutinfolist-fix x)) (len x)))
Theorem:
(defthm cutinfolist-fix-of-append (equal (cutinfolist-fix (append std::a std::b)) (append (cutinfolist-fix std::a) (cutinfolist-fix std::b))))
Theorem:
(defthm cutinfolist-fix-of-repeat (equal (cutinfolist-fix (acl2::repeat acl2::n x)) (acl2::repeat acl2::n (cutinfo-fix x))))
Theorem:
(defthm list-equiv-refines-cutinfolist-equiv (implies (list-equiv x acl2::y) (cutinfolist-equiv x acl2::y)) :rule-classes :refinement)
Theorem:
(defthm nth-of-cutinfolist-fix (equal (nth acl2::n (cutinfolist-fix x)) (if (< (nfix acl2::n) (len x)) (cutinfo-fix (nth acl2::n x)) nil)))
Theorem:
(defthm cutinfolist-equiv-implies-cutinfolist-equiv-append-1 (implies (cutinfolist-equiv x fty::x-equiv) (cutinfolist-equiv (append x acl2::y) (append fty::x-equiv acl2::y))) :rule-classes (:congruence))
Theorem:
(defthm cutinfolist-equiv-implies-cutinfolist-equiv-append-2 (implies (cutinfolist-equiv acl2::y fty::y-equiv) (cutinfolist-equiv (append x acl2::y) (append x fty::y-equiv))) :rule-classes (:congruence))
Theorem:
(defthm cutinfolist-equiv-implies-cutinfolist-equiv-nthcdr-2 (implies (cutinfolist-equiv acl2::l l-equiv) (cutinfolist-equiv (nthcdr acl2::n acl2::l) (nthcdr acl2::n l-equiv))) :rule-classes (:congruence))
Theorem:
(defthm cutinfolist-equiv-implies-cutinfolist-equiv-take-2 (implies (cutinfolist-equiv acl2::l l-equiv) (cutinfolist-equiv (take acl2::n acl2::l) (take acl2::n l-equiv))) :rule-classes (:congruence))