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• Svex-select

Svex-select-fix

Fixing function for svex-select structures.

Signature

(svex-select-fix x) → new-x

Arguments

x — Guard (svex-select-p x).

Returns

new-x — Type (svex-select-p new-x).

Definitions and Theorems

Function: svex-select-fix$inline

(defun svex-select-fix$inline (x)
 (declare (xargs :guard (svex-select-p x)))
 (let ((__function__ 'svex-select-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (svex-select-kind x)
    (:var (b* ((name (svar-fix (std::prod-car (cdr x))))
               (width (nfix (std::prod-cdr (cdr x)))))
            (cons :var (std::prod-cons name width))))
    (:part
     (b*
      ((lsb (svex-fix (std::prod-car (cdr x))))
       (width (nfix (std::prod-car (std::prod-cdr (cdr x)))))
       (subexp
         (svex-select-fix (std::prod-cdr (std::prod-cdr (cdr x))))))
      (cons
        :part (std::prod-cons lsb (std::prod-cons width subexp))))))
   :exec x)))

Theorem: svex-select-p-of-svex-select-fix

(defthm svex-select-p-of-svex-select-fix
  (b* ((new-x (svex-select-fix$inline x)))
    (svex-select-p new-x))
  :rule-classes :rewrite)

Theorem: svex-select-fix-when-svex-select-p

(defthm svex-select-fix-when-svex-select-p
  (implies (svex-select-p x)
           (equal (svex-select-fix x) x)))

Function: svex-select-equiv$inline

(defun svex-select-equiv$inline (x y)
  (declare (xargs :guard (and (svex-select-p x)
                              (svex-select-p y))))
  (equal (svex-select-fix x)
         (svex-select-fix y)))

Theorem: svex-select-equiv-is-an-equivalence

(defthm svex-select-equiv-is-an-equivalence
  (and (booleanp (svex-select-equiv x y))
       (svex-select-equiv x x)
       (implies (svex-select-equiv x y)
                (svex-select-equiv y x))
       (implies (and (svex-select-equiv x y)
                     (svex-select-equiv y z))
                (svex-select-equiv x z)))
  :rule-classes (:equivalence))

Theorem: svex-select-equiv-implies-equal-svex-select-fix-1

(defthm svex-select-equiv-implies-equal-svex-select-fix-1
  (implies (svex-select-equiv x x-equiv)
           (equal (svex-select-fix x)
                  (svex-select-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svex-select-fix-under-svex-select-equiv

(defthm svex-select-fix-under-svex-select-equiv
  (svex-select-equiv (svex-select-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svex-select-fix-1-forward-to-svex-select-equiv

(defthm equal-of-svex-select-fix-1-forward-to-svex-select-equiv
  (implies (equal (svex-select-fix x) y)
           (svex-select-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-svex-select-fix-2-forward-to-svex-select-equiv

(defthm equal-of-svex-select-fix-2-forward-to-svex-select-equiv
  (implies (equal x (svex-select-fix y))
           (svex-select-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svex-select-equiv-of-svex-select-fix-1-forward

(defthm svex-select-equiv-of-svex-select-fix-1-forward
  (implies (svex-select-equiv (svex-select-fix x)
                              y)
           (svex-select-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svex-select-equiv-of-svex-select-fix-2-forward

(defthm svex-select-equiv-of-svex-select-fix-2-forward
  (implies (svex-select-equiv x (svex-select-fix y))
           (svex-select-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svex-select-kind$inline-of-svex-select-fix-x

(defthm svex-select-kind$inline-of-svex-select-fix-x
  (equal (svex-select-kind$inline (svex-select-fix x))
         (svex-select-kind$inline x)))

Theorem: svex-select-kind$inline-svex-select-equiv-congruence-on-x

(defthm svex-select-kind$inline-svex-select-equiv-congruence-on-x
  (implies (svex-select-equiv x x-equiv)
           (equal (svex-select-kind$inline x)
                  (svex-select-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-svex-select-fix

(defthm consp-of-svex-select-fix
  (consp (svex-select-fix x))
  :rule-classes :type-prescription)