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Feat-bits

Feat-bits-fix

Fixing function for feat-bits structures.

Signature
(feat-bits-fix x) → new-x
Arguments: x — Guard (feat-bitsp x).
Returns: new-x — Type (feat-bitsp new-x).

Definitions and Theorems

Function: feat-bits-fix$inline

(defun feat-bits-fix$inline (x)
  (declare (xargs :guard (feat-bitsp x)))
  (let ((__function__ 'feat-bits-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (feat-bits-kind x)
           (:|32| (cons :|32| (list)))
           (:|64| (cons :|64| (list))))
         :exec x)))

Theorem: feat-bitsp-of-feat-bits-fix

(defthm feat-bitsp-of-feat-bits-fix
  (b* ((new-x (feat-bits-fix$inline x)))
    (feat-bitsp new-x))
  :rule-classes :rewrite)

Theorem: feat-bits-fix-when-feat-bitsp

(defthm feat-bits-fix-when-feat-bitsp
  (implies (feat-bitsp x)
           (equal (feat-bits-fix x) x)))

Function: feat-bits-equiv$inline

(defun feat-bits-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (feat-bitsp acl2::x)
                              (feat-bitsp acl2::y))))
  (equal (feat-bits-fix acl2::x)
         (feat-bits-fix acl2::y)))

Theorem: feat-bits-equiv-is-an-equivalence

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

Theorem: feat-bits-equiv-implies-equal-feat-bits-fix-1

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

Theorem: feat-bits-fix-under-feat-bits-equiv

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

Theorem: equal-of-feat-bits-fix-1-forward-to-feat-bits-equiv

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

Theorem: equal-of-feat-bits-fix-2-forward-to-feat-bits-equiv

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

Theorem: feat-bits-equiv-of-feat-bits-fix-1-forward

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

Theorem: feat-bits-equiv-of-feat-bits-fix-2-forward

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

Theorem: feat-bits-kind$inline-of-feat-bits-fix-x

(defthm feat-bits-kind$inline-of-feat-bits-fix-x
  (equal (feat-bits-kind$inline (feat-bits-fix x))
         (feat-bits-kind$inline x)))

Theorem: feat-bits-kind$inline-feat-bits-equiv-congruence-on-x

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

Theorem: consp-of-feat-bits-fix

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