		Search-engine friendly clone of the ACL2 documentation.

Bitops/extra-defs

Setbit

Set X[n] := 1

Signature
(setbit n x) → ans
Arguments: n — Bit position to set to 1.
Guard (natp n).; x — Starting value.
Guard (integerp x).
Returns: ans — Type (integerp ans).

Definitions and Theorems

Function: setbit

(defun setbit (n x)
  (declare (xargs :guard (and (natp n) (integerp x))))
  (let ((__function__ 'setbit))
    (declare (ignorable __function__))
    (let ((n (lnfix n)) (x (lifix x)))
      (logior (ash 1 n) x))))

Theorem: integerp-of-setbit

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

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

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

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

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