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Vcd-wire

Vcd-wire-fix

Fixing function for vcd-wire structures.

Signature
(vcd-wire-fix x) → new-x
Arguments: x — Guard (vcd-wire-p x).
Returns: new-x — Type (vcd-wire-p new-x).

Definitions and Theorems

Function: vcd-wire-fix$inline

(defun vcd-wire-fix$inline (x)
  (declare (xargs :guard (vcd-wire-p x)))
  (let ((__function__ 'vcd-wire-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (str-fix (cdr (std::da-nth 0 x))))
              (msb (ifix (cdr (std::da-nth 1 x))))
              (lsb (ifix (cdr (std::da-nth 2 x))))
              (code (str-fix (cdr (std::da-nth 3 x)))))
           (list (cons 'name name)
                 (cons 'msb msb)
                 (cons 'lsb lsb)
                 (cons 'code code)))
         :exec x)))

Theorem: vcd-wire-p-of-vcd-wire-fix

(defthm vcd-wire-p-of-vcd-wire-fix
  (b* ((new-x (vcd-wire-fix$inline x)))
    (vcd-wire-p new-x))
  :rule-classes :rewrite)

Theorem: vcd-wire-fix-when-vcd-wire-p

(defthm vcd-wire-fix-when-vcd-wire-p
  (implies (vcd-wire-p x)
           (equal (vcd-wire-fix x) x)))

Function: vcd-wire-equiv$inline

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

Theorem: vcd-wire-equiv-is-an-equivalence

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

Theorem: vcd-wire-equiv-implies-equal-vcd-wire-fix-1

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

Theorem: vcd-wire-fix-under-vcd-wire-equiv

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

Theorem: equal-of-vcd-wire-fix-1-forward-to-vcd-wire-equiv

(defthm equal-of-vcd-wire-fix-1-forward-to-vcd-wire-equiv
  (implies (equal (vcd-wire-fix x) y)
           (vcd-wire-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-vcd-wire-fix-2-forward-to-vcd-wire-equiv

(defthm equal-of-vcd-wire-fix-2-forward-to-vcd-wire-equiv
  (implies (equal x (vcd-wire-fix y))
           (vcd-wire-equiv x y))
  :rule-classes :forward-chaining)

Theorem: vcd-wire-equiv-of-vcd-wire-fix-1-forward

(defthm vcd-wire-equiv-of-vcd-wire-fix-1-forward
  (implies (vcd-wire-equiv (vcd-wire-fix x) y)
           (vcd-wire-equiv x y))
  :rule-classes :forward-chaining)

Theorem: vcd-wire-equiv-of-vcd-wire-fix-2-forward

(defthm vcd-wire-equiv-of-vcd-wire-fix-2-forward
  (implies (vcd-wire-equiv x (vcd-wire-fix y))
           (vcd-wire-equiv x y))
  :rule-classes :forward-chaining)