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Undocumented

Truth3

An 8-bit unsigned bitstruct type.

This is a bitstruct type introduced by fty::defbitstruct, represented as a unsigned 8-bit integer.

This is an atomic/empty structure; it has no fields.

Definitions and Theorems

Function: truth3-p

(defun truth3-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'truth3-p))
    (declare (ignorable __function__))
    (mbe :logic (unsigned-byte-p 8 x)
         :exec (and (natp x) (< x 256)))))

Theorem: truth3-p-when-unsigned-byte-p

(defthm truth3-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 x)
           (truth3-p x)))

Theorem: unsigned-byte-p-when-truth3-p

(defthm unsigned-byte-p-when-truth3-p
  (implies (truth3-p x)
           (unsigned-byte-p 8 x)))

Theorem: truth3-p-compound-recognizer

(defthm truth3-p-compound-recognizer
  (implies (truth3-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: truth3-fix

(defun truth3-fix (x)
  (declare (xargs :guard (truth3-p x)))
  (let ((__function__ 'truth3-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 8 x) :exec x)))

Theorem: truth3-p-of-truth3-fix

(defthm truth3-p-of-truth3-fix
  (b* ((fty::fixed (truth3-fix x)))
    (truth3-p fty::fixed))
  :rule-classes :rewrite)

Theorem: truth3-fix-when-truth3-p

(defthm truth3-fix-when-truth3-p
  (implies (truth3-p x)
           (equal (truth3-fix x) x)))

Function: truth3-equiv$inline

(defun truth3-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (truth3-p acl2::x)
                              (truth3-p acl2::y))))
  (equal (truth3-fix acl2::x)
         (truth3-fix acl2::y)))

Theorem: truth3-equiv-is-an-equivalence

(defthm truth3-equiv-is-an-equivalence
  (and (booleanp (truth3-equiv x y))
       (truth3-equiv x x)
       (implies (truth3-equiv x y)
                (truth3-equiv y x))
       (implies (and (truth3-equiv x y)
                     (truth3-equiv y z))
                (truth3-equiv x z)))
  :rule-classes (:equivalence))

Theorem: truth3-equiv-implies-equal-truth3-fix-1

(defthm truth3-equiv-implies-equal-truth3-fix-1
  (implies (truth3-equiv acl2::x x-equiv)
           (equal (truth3-fix acl2::x)
                  (truth3-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: truth3-fix-under-truth3-equiv

(defthm truth3-fix-under-truth3-equiv
  (truth3-equiv (truth3-fix acl2::x)
                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: truth3-fix-of-truth3-fix-x

(defthm truth3-fix-of-truth3-fix-x
  (equal (truth3-fix (truth3-fix x))
         (truth3-fix x)))

Theorem: truth3-fix-truth3-equiv-congruence-on-x

(defthm truth3-fix-truth3-equiv-congruence-on-x
  (implies (truth3-equiv x x-equiv)
           (equal (truth3-fix x)
                  (truth3-fix x-equiv)))
  :rule-classes :congruence)

Subtopics

Truth3-fix: Fixing function for truth3 bit structures.
Truth3-p: Recognizer for truth3 bit structures.