Eliminate
(vl-initiallist-wildelim x warnings) → (mv warnings new-x)
Function:
(defun vl-initiallist-wildelim (x warnings) (declare (xargs :guard (and (vl-initiallist-p x) (vl-warninglist-p warnings)))) (let ((__function__ 'vl-initiallist-wildelim)) (declare (ignorable __function__)) (b* (((when (atom x)) (mv (ok) x)) ((mv warnings car-prime) (vl-initial-wildelim (car x) warnings)) ((mv warnings cdr-prime) (vl-initiallist-wildelim (cdr x) warnings))) (mv warnings (cons car-prime cdr-prime)))))
Theorem:
(defthm vl-warninglist-p-of-vl-initiallist-wildelim.warnings (b* (((mv ?warnings ?new-x) (vl-initiallist-wildelim x warnings))) (vl-warninglist-p warnings)) :rule-classes :rewrite)
Theorem:
(defthm vl-initiallist-p-of-vl-initiallist-wildelim.new-x (b* (((mv ?warnings ?new-x) (vl-initiallist-wildelim x warnings))) (vl-initiallist-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm vl-initiallist-wildelim-when-atom (implies (atom x) (equal (vl-initiallist-wildelim x warnings) (mv (ok) x))))
Theorem:
(defthm vl-initiallist-wildelim-of-cons (equal (vl-initiallist-wildelim (cons a x) warnings) (b* (((mv warnings car-prime) (vl-initial-wildelim a warnings)) ((mv warnings cdr-prime) (vl-initiallist-wildelim x warnings))) (mv warnings (cons car-prime cdr-prime)))))
Theorem:
(defthm len-of-vl-initiallist-wildelim (equal (len (mv-nth 1 (vl-initiallist-wildelim x warnings))) (len x)))
Theorem:
(defthm vl-initiallist-wildelim-of-vl-initiallist-fix-x (equal (vl-initiallist-wildelim (vl-initiallist-fix x) warnings) (vl-initiallist-wildelim x warnings)))
Theorem:
(defthm vl-initiallist-wildelim-vl-initiallist-equiv-congruence-on-x (implies (vl-initiallist-equiv x x-equiv) (equal (vl-initiallist-wildelim x warnings) (vl-initiallist-wildelim x-equiv warnings))) :rule-classes :congruence)
Theorem:
(defthm vl-initiallist-wildelim-of-vl-warninglist-fix-warnings (equal (vl-initiallist-wildelim x (vl-warninglist-fix warnings)) (vl-initiallist-wildelim x warnings)))
Theorem:
(defthm vl-initiallist-wildelim-vl-warninglist-equiv-congruence-on-warnings (implies (vl-warninglist-equiv warnings warnings-equiv) (equal (vl-initiallist-wildelim x warnings) (vl-initiallist-wildelim x warnings-equiv))) :rule-classes :congruence)