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• Integer-values

Bit-size

Fixtype of sizes in bits of the integer values.

These are all the integer multiples of 8 from 8 to 256.

This is a type defined by fty::deffixtype.

Definitions and Theorems

Function: bit-size-p

(defun bit-size-p (x)
  (declare (xargs :guard t))
  (and (integerp x)
       (integerp (/ x 8))
       (<= 8 x)
       (<= x 256)))

Theorem: booleanp-of-bit-size-p

(defthm booleanp-of-bit-size-p
  (b* ((yes/no (bit-size-p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bit-size-p-alt-def

(defthm bit-size-p-alt-def
  (iff (bit-size-p x)
       (member x
               (list 8 16 24 32 40 48 56 64 72 80 88 96 104
                     112 120 128 136 144 152 160 168 176 184
                     192 200 208 216 224 232 240 248 256))))

Function: bit-size-fix

(defun bit-size-fix (x)
  (declare (xargs :guard (bit-size-p x)))
  (mbe :logic (if (bit-size-p x) x 256)
       :exec x))

Theorem: bit-size-p-of-bit-size-fix

(defthm bit-size-p-of-bit-size-fix
  (b* ((fixed-x (bit-size-fix x)))
    (bit-size-p fixed-x))
  :rule-classes :rewrite)

Theorem: bit-size-fix-when-bit-size-p

(defthm bit-size-fix-when-bit-size-p
  (implies (bit-size-p x)
           (equal (bit-size-fix x) x)))

Theorem: posp-of-bit-size-fix

(defthm posp-of-bit-size-fix
  (posp (bit-size-fix x))
  :rule-classes :type-prescription)

Function: bit-size-equiv$inline

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

Theorem: bit-size-equiv-is-an-equivalence

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

Theorem: bit-size-equiv-implies-equal-bit-size-fix-1

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

Theorem: bit-size-fix-under-bit-size-equiv

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

Theorem: equal-of-bit-size-fix-1-forward-to-bit-size-equiv

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

Theorem: equal-of-bit-size-fix-2-forward-to-bit-size-equiv

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

Theorem: bit-size-equiv-of-bit-size-fix-1-forward

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

Theorem: bit-size-equiv-of-bit-size-fix-2-forward

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

Subtopics

Bit-size-p

Recognizer for bit-size.

Bit-size-fix

Fixer for bit-size.