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• Bfrstate

Bfrstate-fix

Fixing function for bfrstate objects.

Signature

(bfrstate-fix x) → new-x

Arguments

x — Guard (bfrstate-p x).

Returns

new-x — Type (bfrstate-p new-x).

Definitions and Theorems

Function: bfrstate-fix$inline

(defun bfrstate-fix$inline (x)
  (declare (xargs :guard (bfrstate-p x)))
  (let ((__function__ 'bfrstate-fix))
    (declare (ignorable __function__))
    (mbe :logic (logior (logand -4 (nfix x))
                        (bfr-mode-fix (logand 3 (nfix x))))
         :exec x)))

Theorem: bfrstate-p-of-bfrstate-fix

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

Theorem: bfrstate-fix-when-bfrstate-p

(defthm bfrstate-fix-when-bfrstate-p
  (implies (bfrstate-p x)
           (equal (bfrstate-fix x) x)))

Function: bfrstate-equiv$inline

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

Theorem: bfrstate-equiv-is-an-equivalence

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

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

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

Theorem: bfrstate-fix-under-bfrstate-equiv

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

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

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

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

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

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

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

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

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

Theorem: bfrstate-fix$inline-of-bfrstate-fix-x

(defthm bfrstate-fix$inline-of-bfrstate-fix-x
  (equal (bfrstate-fix$inline (bfrstate-fix x))
         (bfrstate-fix$inline x)))

Theorem: bfrstate-fix$inline-bfrstate-equiv-congruence-on-x

(defthm bfrstate-fix$inline-bfrstate-equiv-congruence-on-x
  (implies (bfrstate-equiv x x-equiv)
           (equal (bfrstate-fix$inline x)
                  (bfrstate-fix$inline x-equiv)))
  :rule-classes :congruence)