(vl-alwayslist-caseelim x warnings ss) → (mv warnings new-x)
Function:
(defun vl-alwayslist-caseelim (x warnings ss) (declare (xargs :guard (and (vl-alwayslist-p x) (vl-warninglist-p warnings) (vl-scopestack-p ss)))) (let ((__function__ 'vl-alwayslist-caseelim)) (declare (ignorable __function__)) (b* (((when (atom x)) (mv (ok) nil)) ((mv warnings car) (vl-always-caseelim (car x) warnings ss)) ((mv warnings cdr) (vl-alwayslist-caseelim (cdr x) warnings ss))) (mv warnings (cons car cdr)))))
Theorem:
(defthm vl-warninglist-p-of-vl-alwayslist-caseelim.warnings (b* (((mv ?warnings ?new-x) (vl-alwayslist-caseelim x warnings ss))) (vl-warninglist-p warnings)) :rule-classes :rewrite)
Theorem:
(defthm vl-alwayslist-p-of-vl-alwayslist-caseelim.new-x (b* (((mv ?warnings ?new-x) (vl-alwayslist-caseelim x warnings ss))) (vl-alwayslist-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm vl-alwayslist-caseelim-of-vl-alwayslist-fix-x (equal (vl-alwayslist-caseelim (vl-alwayslist-fix x) warnings ss) (vl-alwayslist-caseelim x warnings ss)))
Theorem:
(defthm vl-alwayslist-caseelim-vl-alwayslist-equiv-congruence-on-x (implies (vl-alwayslist-equiv x x-equiv) (equal (vl-alwayslist-caseelim x warnings ss) (vl-alwayslist-caseelim x-equiv warnings ss))) :rule-classes :congruence)
Theorem:
(defthm vl-alwayslist-caseelim-of-vl-warninglist-fix-warnings (equal (vl-alwayslist-caseelim x (vl-warninglist-fix warnings) ss) (vl-alwayslist-caseelim x warnings ss)))
Theorem:
(defthm vl-alwayslist-caseelim-vl-warninglist-equiv-congruence-on-warnings (implies (vl-warninglist-equiv warnings warnings-equiv) (equal (vl-alwayslist-caseelim x warnings ss) (vl-alwayslist-caseelim x warnings-equiv ss))) :rule-classes :congruence)
Theorem:
(defthm vl-alwayslist-caseelim-of-vl-scopestack-fix-ss (equal (vl-alwayslist-caseelim x warnings (vl-scopestack-fix ss)) (vl-alwayslist-caseelim x warnings ss)))
Theorem:
(defthm vl-alwayslist-caseelim-vl-scopestack-equiv-congruence-on-ss (implies (vl-scopestack-equiv ss ss-equiv) (equal (vl-alwayslist-caseelim x warnings ss) (vl-alwayslist-caseelim x warnings ss-equiv))) :rule-classes :congruence)