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Vl-design-wildelim

Vl-namedparamvaluelist-wildelim

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

Signature
(vl-namedparamvaluelist-wildelim x ctx warnings) → (mv warnings new-x)
Arguments: x — Guard (vl-namedparamvaluelist-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-namedparamvaluelist-p new-x).

Definitions and Theorems

Function: vl-namedparamvaluelist-wildelim

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

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

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

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

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

Theorem: vl-namedparamvaluelist-wildelim-when-atom

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

Theorem: vl-namedparamvaluelist-wildelim-of-cons

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

Theorem: len-of-vl-namedparamvaluelist-wildelim

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

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

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

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

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

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

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

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

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

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

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

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

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