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Vl-design-wildelim

Vl-initial-wildelim

Eliminate ==? and !=? operators throughout a vl-initial-p

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

Definitions and Theorems

Function: vl-initial-wildelim

(defun vl-initial-wildelim (x warnings)
  (declare (xargs :guard (and (vl-initial-p x)
                              (vl-warninglist-p warnings))))
  (let ((__function__ 'vl-initial-wildelim))
    (declare (ignorable __function__))
    (b* ((x (vl-initial-fix x))
         (warnings (vl-warninglist-fix warnings)))
      (b* (((vl-initial x) x)
           (ctx x)
           ((mv warnings stmt-prime)
            (vl-stmt-wildelim x.stmt ctx warnings))
           (x-prime (change-vl-initial x :stmt stmt-prime)))
        (mv warnings x-prime)))))

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

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

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

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

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

(defthm vl-initial-wildelim-of-vl-initial-fix-x
  (equal (vl-initial-wildelim (vl-initial-fix x)
                              warnings)
         (vl-initial-wildelim x warnings)))

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

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

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

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

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

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