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Fconst

Fconst-fix

Fixing function for fconst structures.

Signature
(fconst-fix x) → new-x
Arguments: x — Guard (fconstp x).
Returns: new-x — Type (fconstp new-x).

Definitions and Theorems

Function: fconst-fix$inline

(defun fconst-fix$inline (x)
 (declare (xargs :guard (fconstp x)))
 (let ((__function__ 'fconst-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (fconst-kind x)
    (:dec
        (b* ((core (dec-core-fconst-fix (std::da-nth 0 (cdr x))))
             (suffix? (fsuffix-option-fix (std::da-nth 1 (cdr x)))))
          (cons :dec (list core suffix?))))
    (:hex
        (b* ((prefix (hprefix-fix (std::da-nth 0 (cdr x))))
             (core (hex-core-fconst-fix (std::da-nth 1 (cdr x))))
             (suffix? (fsuffix-option-fix (std::da-nth 2 (cdr x)))))
          (cons :hex (list prefix core suffix?)))))
   :exec x)))

Theorem: fconstp-of-fconst-fix

(defthm fconstp-of-fconst-fix
  (b* ((new-x (fconst-fix$inline x)))
    (fconstp new-x))
  :rule-classes :rewrite)

Theorem: fconst-fix-when-fconstp

(defthm fconst-fix-when-fconstp
  (implies (fconstp x)
           (equal (fconst-fix x) x)))

Function: fconst-equiv$inline

(defun fconst-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (fconstp acl2::x)
                              (fconstp acl2::y))))
  (equal (fconst-fix acl2::x)
         (fconst-fix acl2::y)))

Theorem: fconst-equiv-is-an-equivalence

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

Theorem: fconst-equiv-implies-equal-fconst-fix-1

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

Theorem: fconst-fix-under-fconst-equiv

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

Theorem: equal-of-fconst-fix-1-forward-to-fconst-equiv

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

Theorem: equal-of-fconst-fix-2-forward-to-fconst-equiv

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

Theorem: fconst-equiv-of-fconst-fix-1-forward

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

Theorem: fconst-equiv-of-fconst-fix-2-forward

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

Theorem: fconst-kind$inline-of-fconst-fix-x

(defthm fconst-kind$inline-of-fconst-fix-x
  (equal (fconst-kind$inline (fconst-fix x))
         (fconst-kind$inline x)))

Theorem: fconst-kind$inline-fconst-equiv-congruence-on-x

(defthm fconst-kind$inline-fconst-equiv-congruence-on-x
  (implies (fconst-equiv x x-equiv)
           (equal (fconst-kind$inline x)
                  (fconst-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-fconst-fix

(defthm consp-of-fconst-fix
  (consp (fconst-fix x))
  :rule-classes :type-prescription)