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Simpcode

Simpcode->neg

Access the |AIGNET|::|NEG| field of a simpcode bit structure.

Signature
(simpcode->neg x) → neg
Arguments: x — Guard (simpcode-p x).
Returns: neg — Type (bitp neg).

Definitions and Theorems

Function: simpcode->neg

(defun simpcode->neg (x)
  (declare (xargs :guard (simpcode-p x)))
  (mbe :logic
       (let ((x (simpcode-fix x)))
         (part-select x :low 0 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 4) x)))))

Theorem: bitp-of-simpcode->neg

(defthm bitp-of-simpcode->neg
  (b* ((neg (simpcode->neg x)))
    (bitp neg))
  :rule-classes :rewrite)

Theorem: simpcode->neg-of-simpcode-fix-x

(defthm simpcode->neg-of-simpcode-fix-x
  (equal (simpcode->neg (simpcode-fix x))
         (simpcode->neg x)))

Theorem: simpcode->neg-simpcode-equiv-congruence-on-x

(defthm simpcode->neg-simpcode-equiv-congruence-on-x
  (implies (simpcode-equiv x x-equiv)
           (equal (simpcode->neg x)
                  (simpcode->neg x-equiv)))
  :rule-classes :congruence)

Theorem: simpcode->neg-of-simpcode

(defthm simpcode->neg-of-simpcode
  (equal (simpcode->neg (simpcode neg xor identity choice))
         (bfix neg)))

Theorem: simpcode->neg-of-write-with-mask

(defthm simpcode->neg-of-write-with-mask
 (implies
  (and
   (fty::bitstruct-read-over-write-hyps x simpcode-equiv-under-mask)
   (simpcode-equiv-under-mask x acl2::y fty::mask)
   (equal (logand (lognot fty::mask) 1) 0))
  (equal (simpcode->neg x)
         (simpcode->neg acl2::y))))