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• Gatesimp

Gatesimp-fix

Fixing function for gatesimp bit structures.

Signature

(gatesimp-fix x) → fty::fixed

Arguments

x — Guard (gatesimp-p x).

Returns

fty::fixed — Type (gatesimp-p fty::fixed).

Definitions and Theorems

Function: gatesimp-fix

(defun gatesimp-fix (x)
 (declare (xargs :guard (gatesimp-p x)))
 (let ((__function__ 'gatesimp-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (loghead
    6
    (logapp
     1 (part-select x :width 1 :low 0)
     (logapp
          3
          (gatesimp-level-fix (part-select x :width 3 :low 1))
          (gatesimp-xor-mode-fix (part-select x :width 2 :low 4)))))
   :exec x)))

Theorem: gatesimp-p-of-gatesimp-fix

(defthm gatesimp-p-of-gatesimp-fix
  (b* ((fty::fixed (gatesimp-fix x)))
    (gatesimp-p fty::fixed))
  :rule-classes :rewrite)

Theorem: gatesimp-fix-when-gatesimp-p

(defthm gatesimp-fix-when-gatesimp-p
  (implies (gatesimp-p x)
           (equal (gatesimp-fix x) x)))

Function: gatesimp-equiv$inline

(defun gatesimp-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (gatesimp-p x)
                              (gatesimp-p acl2::y))))
  (equal (gatesimp-fix x)
         (gatesimp-fix acl2::y)))

Theorem: gatesimp-equiv-is-an-equivalence

(defthm gatesimp-equiv-is-an-equivalence
  (and (booleanp (gatesimp-equiv x y))
       (gatesimp-equiv x x)
       (implies (gatesimp-equiv x y)
                (gatesimp-equiv y x))
       (implies (and (gatesimp-equiv x y)
                     (gatesimp-equiv y z))
                (gatesimp-equiv x z)))
  :rule-classes (:equivalence))

Theorem: gatesimp-equiv-implies-equal-gatesimp-fix-1

(defthm gatesimp-equiv-implies-equal-gatesimp-fix-1
  (implies (gatesimp-equiv x x-equiv)
           (equal (gatesimp-fix x)
                  (gatesimp-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: gatesimp-fix-under-gatesimp-equiv

(defthm gatesimp-fix-under-gatesimp-equiv
  (gatesimp-equiv (gatesimp-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))