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Bitops/extra-defs

Notbit

Set X[n] := ~X[n]

Signature
(notbit n x) → ans
Arguments: n — Bit position to negate.
Guard (natp n).; x — Starting value.
Guard (integerp x).
Returns: ans — Type (integerp ans).

Definitions and Theorems

Function: notbit

(defun notbit (n x)
  (declare (xargs :guard (and (natp n) (integerp x))))
  (let ((__function__ 'notbit))
    (declare (ignorable __function__))
    (if (logbitp n x)
        (clearbit n x)
      (setbit n x))))

Theorem: integerp-of-notbit

(defthm acl2::integerp-of-notbit
  (b* ((ans (notbit n x))) (integerp ans))
  :rule-classes :type-prescription)

Theorem: nat-equiv-implies-equal-notbit-1

(defthm nat-equiv-implies-equal-notbit-1
  (implies (nat-equiv n n-equiv)
           (equal (notbit n x) (notbit n-equiv x)))
  :rule-classes (:congruence))

Theorem: int-equiv-implies-equal-notbit-2

(defthm int-equiv-implies-equal-notbit-2
  (implies (int-equiv x x-equiv)
           (equal (notbit n x) (notbit n x-equiv)))
  :rule-classes (:congruence))