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Double-value

Double-value-fix

Fixing function for double-value structures.

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

Definitions and Theorems

Function: double-value-fix$inline

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

Theorem: double-valuep-of-double-value-fix

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

Theorem: double-value-fix-when-double-valuep

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

Function: double-value-equiv$inline

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

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

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

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

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

Theorem: double-value-fix-under-double-value-equiv

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

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

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

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

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

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

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

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

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