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Vl-design-wildelim

Vl-evatom-wildelim

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

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

Definitions and Theorems

Function: vl-evatom-wildelim

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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