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Npn4

!npn4->negate

Update the |TRUTH|::|NEGATE| field of a npn4 bit structure.

Signature
(!npn4->negate negate x) → new-x
Arguments: negate — Guard (bitp negate).; x — Guard (npn4-p x).
Returns: new-x — Type (npn4-p new-x).

Definitions and Theorems

Function: !npn4->negate

(defun !npn4->negate (negate x)
 (declare (xargs :guard (and (bitp negate) (npn4-p x))))
 (mbe
     :logic
     (b* ((negate (mbe :logic (bfix negate) :exec negate))
          (x (npn4-fix x)))
       (part-install negate x
                     :width 1
                     :low 16))
     :exec (the (unsigned-byte 27)
                (logior (the (unsigned-byte 27)
                             (logand (the (unsigned-byte 27) x)
                                     (the (signed-byte 18) -65537)))
                        (the (unsigned-byte 17)
                             (ash (the (unsigned-byte 1) negate)
                                  16))))))

Theorem: npn4-p-of-!npn4->negate

(defthm npn4-p-of-!npn4->negate
  (b* ((new-x (!npn4->negate negate x)))
    (npn4-p new-x))
  :rule-classes :rewrite)

Theorem: !npn4->negate-of-bfix-negate

(defthm !npn4->negate-of-bfix-negate
  (equal (!npn4->negate (bfix negate) x)
         (!npn4->negate negate x)))

Theorem: !npn4->negate-bit-equiv-congruence-on-negate

(defthm !npn4->negate-bit-equiv-congruence-on-negate
  (implies (bit-equiv negate negate-equiv)
           (equal (!npn4->negate negate x)
                  (!npn4->negate negate-equiv x)))
  :rule-classes :congruence)

Theorem: !npn4->negate-of-npn4-fix-x

(defthm !npn4->negate-of-npn4-fix-x
  (equal (!npn4->negate negate (npn4-fix x))
         (!npn4->negate negate x)))

Theorem: !npn4->negate-npn4-equiv-congruence-on-x

(defthm !npn4->negate-npn4-equiv-congruence-on-x
  (implies (npn4-equiv x x-equiv)
           (equal (!npn4->negate negate x)
                  (!npn4->negate negate x-equiv)))
  :rule-classes :congruence)

Theorem: !npn4->negate-is-npn4

(defthm !npn4->negate-is-npn4
  (equal (!npn4->negate negate x)
         (change-npn4 x :negate negate)))

Theorem: npn4->negate-of-!npn4->negate

(defthm npn4->negate-of-!npn4->negate
  (b* ((?new-x (!npn4->negate negate x)))
    (equal (npn4->negate new-x)
           (bfix negate))))

Theorem: !npn4->negate-equiv-under-mask

(defthm !npn4->negate-equiv-under-mask
  (b* ((?new-x (!npn4->negate negate x)))
    (npn4-equiv-under-mask new-x x -65537)))