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Boolean-not

Boolean-not-spec

Specification of the circuit.

Signature
(boolean-not-spec x y prime) → yes/no
Arguments: x — Guard (pfield::fep x prime).; y — Guard (pfield::fep y prime).; prime — Guard (primep prime).
Returns: yes/no — Type (booleanp yes/no).

We use an if. An alternative is to use logand.

Definitions and Theorems

Function: boolean-not-spec

(defun boolean-not-spec (x y prime)
  (declare (xargs :guard (and (primep prime)
                              (pfield::fep x prime)
                              (pfield::fep y prime))))
  (declare (ignore prime))
  (declare (xargs :guard (bitp x)))
  (let ((__function__ 'boolean-not-spec))
    (declare (ignorable __function__))
    (equal y (if (= x 0) 1 0))))

Theorem: booleanp-of-boolean-not-spec

(defthm booleanp-of-boolean-not-spec
  (b* ((yes/no (boolean-not-spec x y prime)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bitp-y-when-boolean-not-spec

(defthm bitp-y-when-boolean-not-spec
  (implies (and (boolean-not-spec x y prime)
                (bitp x))
           (bitp y)))