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Simpcode

Simpcode-fix

Fixing function for simpcode bit structures.

Signature
(simpcode-fix x) → fty::fixed
Arguments: x — Guard (simpcode-p x).
Returns: fty::fixed — Type (simpcode-p fty::fixed).

Definitions and Theorems

Function: simpcode-fix

(defun simpcode-fix (x)
  (declare (xargs :guard (simpcode-p x)))
  (let ((__function__ 'simpcode-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 4 x) :exec x)))

Theorem: simpcode-p-of-simpcode-fix

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

Theorem: simpcode-fix-when-simpcode-p

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

Function: simpcode-equiv$inline

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

Theorem: simpcode-equiv-is-an-equivalence

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

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

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

Theorem: simpcode-fix-under-simpcode-equiv

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

Theorem: simpcode-fix-of-simpcode-fix-x

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

Theorem: simpcode-fix-simpcode-equiv-congruence-on-x

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