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Short-value

Short-value-fix

Fixing function for short-value structures.

Signature
(short-value-fix x) → new-x
Arguments: x — Guard (short-valuep x).
Returns: new-x — Type (short-valuep new-x).

Definitions and Theorems

Function: short-value-fix$inline

(defun short-value-fix$inline (x)
  (declare (xargs :guard (short-valuep x)))
  (let ((__function__ 'short-value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((int (acl2::sbyte16-fix (std::da-nth 0 (cdr x)))))
           (cons :short (list int)))
         :exec x)))

Theorem: short-valuep-of-short-value-fix

(defthm short-valuep-of-short-value-fix
  (b* ((new-x (short-value-fix$inline x)))
    (short-valuep new-x))
  :rule-classes :rewrite)

Theorem: short-value-fix-when-short-valuep

(defthm short-value-fix-when-short-valuep
  (implies (short-valuep x)
           (equal (short-value-fix x) x)))

Function: short-value-equiv$inline

(defun short-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (short-valuep acl2::x)
                              (short-valuep acl2::y))))
  (equal (short-value-fix acl2::x)
         (short-value-fix acl2::y)))

Theorem: short-value-equiv-is-an-equivalence

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

Theorem: short-value-equiv-implies-equal-short-value-fix-1

(defthm short-value-equiv-implies-equal-short-value-fix-1
  (implies (short-value-equiv acl2::x x-equiv)
           (equal (short-value-fix acl2::x)
                  (short-value-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: short-value-fix-under-short-value-equiv

(defthm short-value-fix-under-short-value-equiv
  (short-value-equiv (short-value-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-short-value-fix-1-forward-to-short-value-equiv

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

Theorem: equal-of-short-value-fix-2-forward-to-short-value-equiv

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

Theorem: short-value-equiv-of-short-value-fix-1-forward

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

Theorem: short-value-equiv-of-short-value-fix-2-forward

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