Lift fundef-to-fun-declon to lists.
(fundef-list-to-fun-declon-list x) → declons
This is an ordinary std::defprojection.
Function:
(defun fundef-list-to-fun-declon-list-exec (x acc) (declare (xargs :guard (fundef-listp x))) (let ((__function__ 'fundef-list-to-fun-declon-list-exec)) (declare (ignorable __function__)) (if (consp x) (fundef-list-to-fun-declon-list-exec (cdr x) (cons (fundef-to-fun-declon (car x)) acc)) acc)))
Function:
(defun fundef-list-to-fun-declon-list-nrev (x acl2::nrev) (declare (xargs :stobjs (acl2::nrev))) (declare (xargs :guard (fundef-listp x))) (let ((__function__ 'fundef-list-to-fun-declon-list-nrev)) (declare (ignorable __function__)) (if (atom x) (acl2::nrev-fix acl2::nrev) (let ((acl2::nrev (acl2::nrev-push (fundef-to-fun-declon (car x)) acl2::nrev))) (fundef-list-to-fun-declon-list-nrev (cdr x) acl2::nrev)))))
Function:
(defun fundef-list-to-fun-declon-list (x) (declare (xargs :guard (fundef-listp x))) (let ((__function__ 'fundef-list-to-fun-declon-list)) (declare (ignorable __function__)) (mbe :logic (if (consp x) (cons (fundef-to-fun-declon (car x)) (fundef-list-to-fun-declon-list (cdr x))) nil) :exec (if (atom x) nil (acl2::with-local-nrev (fundef-list-to-fun-declon-list-nrev x acl2::nrev))))))
Theorem:
(defthm fun-declon-listp-of-fundef-list-to-fun-declon-list (b* ((declons (fundef-list-to-fun-declon-list x))) (fun-declon-listp declons)) :rule-classes :rewrite)
Theorem:
(defthm fundef-list-to-fun-declon-list-nrev-removal (equal (fundef-list-to-fun-declon-list-nrev acl2::x acl2::nrev) (append acl2::nrev (fundef-list-to-fun-declon-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-exec-removal (equal (fundef-list-to-fun-declon-list-exec acl2::x acl2::acc) (revappend (fundef-list-to-fun-declon-list acl2::x) acl2::acc)) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-of-rev (equal (fundef-list-to-fun-declon-list (rev acl2::x)) (rev (fundef-list-to-fun-declon-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-of-list-fix (equal (fundef-list-to-fun-declon-list (list-fix acl2::x)) (fundef-list-to-fun-declon-list acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-of-append (equal (fundef-list-to-fun-declon-list (append acl2::a acl2::b)) (append (fundef-list-to-fun-declon-list acl2::a) (fundef-list-to-fun-declon-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm cdr-of-fundef-list-to-fun-declon-list (equal (cdr (fundef-list-to-fun-declon-list acl2::x)) (fundef-list-to-fun-declon-list (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm car-of-fundef-list-to-fun-declon-list (equal (car (fundef-list-to-fun-declon-list acl2::x)) (and (consp acl2::x) (fundef-to-fun-declon (car acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-under-iff (iff (fundef-list-to-fun-declon-list acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm consp-of-fundef-list-to-fun-declon-list (equal (consp (fundef-list-to-fun-declon-list acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm len-of-fundef-list-to-fun-declon-list (equal (len (fundef-list-to-fun-declon-list acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-of-fundef-list-to-fun-declon-list (true-listp (fundef-list-to-fun-declon-list acl2::x)) :rule-classes :type-prescription)
Theorem:
(defthm fundef-list-to-fun-declon-list-when-not-consp (implies (not (consp acl2::x)) (equal (fundef-list-to-fun-declon-list acl2::x) nil)) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-of-cons (equal (fundef-list-to-fun-declon-list (cons acl2::a acl2::b)) (cons (fundef-to-fun-declon acl2::a) (fundef-list-to-fun-declon-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-to-fun-declon-list-of-fundef-list-fix-x (equal (fundef-list-to-fun-declon-list (fundef-list-fix x)) (fundef-list-to-fun-declon-list x)))
Theorem:
(defthm fundef-list-to-fun-declon-list-fundef-list-equiv-congruence-on-x (implies (fundef-list-equiv x x-equiv) (equal (fundef-list-to-fun-declon-list x) (fundef-list-to-fun-declon-list x-equiv))) :rule-classes :congruence)