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Parametrize

Bits->bools

Signature
(bits->bools x) → bools
Arguments: x — Guard (bit-listp x).
Returns: bools — Type (boolean-listp bools).

Definitions and Theorems

Function: bits->bools

(defun bits->bools (x)
  (declare (xargs :guard (bit-listp x)))
  (let ((__function__ 'bits->bools))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (cons (bit->bool (car x))
            (bits->bools (cdr x))))))

Theorem: boolean-listp-of-bits->bools

(defthm boolean-listp-of-bits->bools
  (b* ((bools (bits->bools x)))
    (boolean-listp bools))
  :rule-classes :rewrite)

Theorem: bits->bools-of-bit-list-fix-x

(defthm bits->bools-of-bit-list-fix-x
  (equal (bits->bools (bit-list-fix x))
         (bits->bools x)))

Theorem: bits->bools-bit-list-equiv-congruence-on-x

(defthm bits->bools-bit-list-equiv-congruence-on-x
  (implies (bit-list-equiv x x-equiv)
           (equal (bits->bools x)
                  (bits->bools x-equiv)))
  :rule-classes :congruence)