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Vl-shadowcheck-initial

Signature
(vl-shadowcheck-initial x st warnings) → (mv st warnings)
Arguments: x — Guard (vl-initial-p x).; st — Guard (vl-shadowcheck-state-p st).; warnings — Guard (vl-warninglist-p warnings).
Returns: st — Type (vl-shadowcheck-state-p st).; warnings — Type (vl-warninglist-p warnings).

Definitions and Theorems

Function: vl-shadowcheck-initial

(defun vl-shadowcheck-initial (x st warnings)
  (declare (xargs :guard (and (vl-initial-p x)
                              (vl-shadowcheck-state-p st)
                              (vl-warninglist-p warnings))))
  (let ((__function__ 'vl-shadowcheck-initial))
    (declare (ignorable __function__))
    (b* (((vl-initial x) (vl-initial-fix x))
         ((mv st warnings)
          (vl-shadowcheck-stmt x.stmt x st warnings)))
      (mv st warnings))))

Theorem: vl-shadowcheck-state-p-of-vl-shadowcheck-initial.st

(defthm vl-shadowcheck-state-p-of-vl-shadowcheck-initial.st
  (b* (((mv ?st ?warnings)
        (vl-shadowcheck-initial x st warnings)))
    (vl-shadowcheck-state-p st))
  :rule-classes :rewrite)

Theorem: vl-warninglist-p-of-vl-shadowcheck-initial.warnings

(defthm vl-warninglist-p-of-vl-shadowcheck-initial.warnings
  (b* (((mv ?st ?warnings)
        (vl-shadowcheck-initial x st warnings)))
    (vl-warninglist-p warnings))
  :rule-classes :rewrite)

Theorem: vl-shadowcheck-initial-of-vl-initial-fix-x

(defthm vl-shadowcheck-initial-of-vl-initial-fix-x
  (equal (vl-shadowcheck-initial (vl-initial-fix x)
                                 st warnings)
         (vl-shadowcheck-initial x st warnings)))

Theorem: vl-shadowcheck-initial-vl-initial-equiv-congruence-on-x

(defthm vl-shadowcheck-initial-vl-initial-equiv-congruence-on-x
  (implies (vl-initial-equiv x x-equiv)
           (equal (vl-shadowcheck-initial x st warnings)
                  (vl-shadowcheck-initial x-equiv st warnings)))
  :rule-classes :congruence)

Theorem: vl-shadowcheck-initial-of-vl-shadowcheck-state-fix-st

(defthm vl-shadowcheck-initial-of-vl-shadowcheck-state-fix-st
  (equal (vl-shadowcheck-initial x (vl-shadowcheck-state-fix st)
                                 warnings)
         (vl-shadowcheck-initial x st warnings)))

Theorem: vl-shadowcheck-initial-vl-shadowcheck-state-equiv-congruence-on-st

(defthm
 vl-shadowcheck-initial-vl-shadowcheck-state-equiv-congruence-on-st
 (implies (vl-shadowcheck-state-equiv st st-equiv)
          (equal (vl-shadowcheck-initial x st warnings)
                 (vl-shadowcheck-initial x st-equiv warnings)))
 :rule-classes :congruence)

Theorem: vl-shadowcheck-initial-of-vl-warninglist-fix-warnings

(defthm vl-shadowcheck-initial-of-vl-warninglist-fix-warnings
  (equal (vl-shadowcheck-initial x st (vl-warninglist-fix warnings))
         (vl-shadowcheck-initial x st warnings)))

Theorem: vl-shadowcheck-initial-vl-warninglist-equiv-congruence-on-warnings

(defthm
 vl-shadowcheck-initial-vl-warninglist-equiv-congruence-on-warnings
 (implies (vl-warninglist-equiv warnings warnings-equiv)
          (equal (vl-shadowcheck-initial x st warnings)
                 (vl-shadowcheck-initial x st warnings-equiv)))
 :rule-classes :congruence)