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• Vl-selstep

Vl-selstep-fix

Fixing function for vl-selstep structures.

Signature

(vl-selstep-fix x) → new-x

Arguments

x — Guard (vl-selstep-p x).

Returns

new-x — Type (vl-selstep-p new-x).

Definitions and Theorems

Function: vl-selstep-fix$inline

(defun vl-selstep-fix$inline (x)
 (declare (xargs :guard (vl-selstep-p x)))
 (let ((__function__ 'vl-selstep-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((select (vl-select-fix (std::prod-car x)))
          (type (vl-datatype-fix (std::prod-car (std::prod-cdr x))))
          (caveat (std::prod-cdr (std::prod-cdr x))))
       (std::prod-cons select (std::prod-cons type caveat)))
     :exec x)))

Theorem: vl-selstep-p-of-vl-selstep-fix

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

Theorem: vl-selstep-fix-when-vl-selstep-p

(defthm vl-selstep-fix-when-vl-selstep-p
  (implies (vl-selstep-p x)
           (equal (vl-selstep-fix x) x)))

Function: vl-selstep-equiv$inline

(defun vl-selstep-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vl-selstep-p acl2::x)
                              (vl-selstep-p acl2::y))))
  (equal (vl-selstep-fix acl2::x)
         (vl-selstep-fix acl2::y)))

Theorem: vl-selstep-equiv-is-an-equivalence

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

Theorem: vl-selstep-equiv-implies-equal-vl-selstep-fix-1

(defthm vl-selstep-equiv-implies-equal-vl-selstep-fix-1
  (implies (vl-selstep-equiv acl2::x x-equiv)
           (equal (vl-selstep-fix acl2::x)
                  (vl-selstep-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vl-selstep-fix-under-vl-selstep-equiv

(defthm vl-selstep-fix-under-vl-selstep-equiv
  (vl-selstep-equiv (vl-selstep-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-selstep-fix-1-forward-to-vl-selstep-equiv

(defthm equal-of-vl-selstep-fix-1-forward-to-vl-selstep-equiv
  (implies (equal (vl-selstep-fix acl2::x) acl2::y)
           (vl-selstep-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-vl-selstep-fix-2-forward-to-vl-selstep-equiv

(defthm equal-of-vl-selstep-fix-2-forward-to-vl-selstep-equiv
  (implies (equal acl2::x (vl-selstep-fix acl2::y))
           (vl-selstep-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-selstep-equiv-of-vl-selstep-fix-1-forward

(defthm vl-selstep-equiv-of-vl-selstep-fix-1-forward
  (implies (vl-selstep-equiv (vl-selstep-fix acl2::x)
                             acl2::y)
           (vl-selstep-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-selstep-equiv-of-vl-selstep-fix-2-forward

(defthm vl-selstep-equiv-of-vl-selstep-fix-2-forward
  (implies (vl-selstep-equiv acl2::x (vl-selstep-fix acl2::y))
           (vl-selstep-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)