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Vl-evatom

Vl-evatom-fix

Fixing function for vl-evatom structures.

Signature
(vl-evatom-fix x) → new-x
Arguments: x — Guard (vl-evatom-p x).
Returns: new-x — Type (vl-evatom-p new-x).

Definitions and Theorems

Function: vl-evatom-fix$inline

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

Theorem: vl-evatom-p-of-vl-evatom-fix

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

Theorem: vl-evatom-fix-when-vl-evatom-p

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

Function: vl-evatom-equiv$inline

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

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

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

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

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

Theorem: vl-evatom-fix-under-vl-evatom-equiv

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

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

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

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

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

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

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

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

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