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Vl-oddinfo

Vl-oddinfo-fix

Fixing function for vl-oddinfo structures.

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

Definitions and Theorems

Function: vl-oddinfo-fix$inline

(defun vl-oddinfo-fix$inline (x)
  (declare (xargs :guard (vl-oddinfo-p x)))
  (let ((__function__ 'vl-oddinfo-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((type (acl2::symbol-fix (cdr (std::da-nth 0 x))))
              (subexpr (vl-expr-fix (cdr (std::da-nth 1 x))))
              (simple (vl-expr-fix (cdr (std::da-nth 2 x))))
              (complex (vl-expr-fix (cdr (std::da-nth 3 x))))
              (swidth (maybe-natp-fix (cdr (std::da-nth 4 x))))
              (cwidth (maybe-natp-fix (cdr (std::da-nth 5 x)))))
           (list (cons 'type type)
                 (cons 'subexpr subexpr)
                 (cons 'simple simple)
                 (cons 'complex complex)
                 (cons 'swidth swidth)
                 (cons 'cwidth cwidth)))
         :exec x)))

Theorem: vl-oddinfo-p-of-vl-oddinfo-fix

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

Theorem: vl-oddinfo-fix-when-vl-oddinfo-p

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

Function: vl-oddinfo-equiv$inline

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

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

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

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

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

Theorem: vl-oddinfo-fix-under-vl-oddinfo-equiv

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

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

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

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

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

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

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

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

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