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Vl-design-wildelim

Vl-plainarglist-wildelim

Eliminate ==? and !=? operators throughout a vl-plainarglist-p.

Signature
(vl-plainarglist-wildelim x ctx warnings) → (mv warnings new-x)
Arguments: x — Guard (vl-plainarglist-p x).; ctx — Guard (vl-context-p ctx).; warnings — Guard (vl-warninglist-p warnings).
Returns: warnings — Type (vl-warninglist-p warnings).; new-x — Type (vl-plainarglist-p new-x).

Definitions and Theorems

Function: vl-plainarglist-wildelim

(defun vl-plainarglist-wildelim (x ctx warnings)
  (declare (xargs :guard (and (vl-plainarglist-p x)
                              (vl-context-p ctx)
                              (vl-warninglist-p warnings))))
  (let ((__function__ 'vl-plainarglist-wildelim))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (mv (ok) x))
         ((mv warnings car-prime)
          (vl-plainarg-wildelim (car x)
                                ctx warnings))
         ((mv warnings cdr-prime)
          (vl-plainarglist-wildelim (cdr x)
                                    ctx warnings)))
      (mv warnings (cons car-prime cdr-prime)))))

Theorem: vl-warninglist-p-of-vl-plainarglist-wildelim.warnings

(defthm vl-warninglist-p-of-vl-plainarglist-wildelim.warnings
  (b* (((mv ?warnings ?new-x)
        (vl-plainarglist-wildelim x ctx warnings)))
    (vl-warninglist-p warnings))
  :rule-classes :rewrite)

Theorem: vl-plainarglist-p-of-vl-plainarglist-wildelim.new-x

(defthm vl-plainarglist-p-of-vl-plainarglist-wildelim.new-x
  (b* (((mv ?warnings ?new-x)
        (vl-plainarglist-wildelim x ctx warnings)))
    (vl-plainarglist-p new-x))
  :rule-classes :rewrite)

Theorem: vl-plainarglist-wildelim-when-atom

(defthm vl-plainarglist-wildelim-when-atom
  (implies (atom x)
           (equal (vl-plainarglist-wildelim x ctx warnings)
                  (mv (ok) x))))

Theorem: vl-plainarglist-wildelim-of-cons

(defthm vl-plainarglist-wildelim-of-cons
  (equal (vl-plainarglist-wildelim (cons a x)
                                   ctx warnings)
         (b* (((mv warnings car-prime)
               (vl-plainarg-wildelim a ctx warnings))
              ((mv warnings cdr-prime)
               (vl-plainarglist-wildelim x ctx warnings)))
           (mv warnings (cons car-prime cdr-prime)))))

Theorem: len-of-vl-plainarglist-wildelim

(defthm len-of-vl-plainarglist-wildelim
  (equal (len (mv-nth 1
                      (vl-plainarglist-wildelim x ctx warnings)))
         (len x)))

Theorem: vl-plainarglist-wildelim-of-vl-plainarglist-fix-x

(defthm vl-plainarglist-wildelim-of-vl-plainarglist-fix-x
  (equal (vl-plainarglist-wildelim (vl-plainarglist-fix x)
                                   ctx warnings)
         (vl-plainarglist-wildelim x ctx warnings)))

Theorem: vl-plainarglist-wildelim-vl-plainarglist-equiv-congruence-on-x

(defthm
     vl-plainarglist-wildelim-vl-plainarglist-equiv-congruence-on-x
  (implies (vl-plainarglist-equiv x x-equiv)
           (equal (vl-plainarglist-wildelim x ctx warnings)
                  (vl-plainarglist-wildelim x-equiv ctx warnings)))
  :rule-classes :congruence)

Theorem: vl-plainarglist-wildelim-of-vl-context-fix-ctx

(defthm vl-plainarglist-wildelim-of-vl-context-fix-ctx
  (equal (vl-plainarglist-wildelim x (vl-context-fix ctx)
                                   warnings)
         (vl-plainarglist-wildelim x ctx warnings)))

Theorem: vl-plainarglist-wildelim-vl-context-equiv-congruence-on-ctx

(defthm vl-plainarglist-wildelim-vl-context-equiv-congruence-on-ctx
  (implies (vl-context-equiv ctx ctx-equiv)
           (equal (vl-plainarglist-wildelim x ctx warnings)
                  (vl-plainarglist-wildelim x ctx-equiv warnings)))
  :rule-classes :congruence)

Theorem: vl-plainarglist-wildelim-of-vl-warninglist-fix-warnings

(defthm vl-plainarglist-wildelim-of-vl-warninglist-fix-warnings
 (equal
      (vl-plainarglist-wildelim x ctx (vl-warninglist-fix warnings))
      (vl-plainarglist-wildelim x ctx warnings)))

Theorem: vl-plainarglist-wildelim-vl-warninglist-equiv-congruence-on-warnings

(defthm
 vl-plainarglist-wildelim-vl-warninglist-equiv-congruence-on-warnings
 (implies (vl-warninglist-equiv warnings warnings-equiv)
          (equal (vl-plainarglist-wildelim x ctx warnings)
                 (vl-plainarglist-wildelim x ctx warnings-equiv)))
 :rule-classes :congruence)