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• Wire

Wire-fix

Fixing function for wire structures.

Signature

(wire-fix x) → new-x

Arguments

x — Guard (wire-p x).

Returns

new-x — Type (wire-p new-x).

Definitions and Theorems

Function: wire-fix$inline

(defun wire-fix$inline (x)
 (declare (xargs :guard (wire-p x)))
 (let ((__function__ 'wire-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((name (name-fix (std::prod-car (std::prod-car x))))
     (width
        (pos-fix (std::prod-car (std::prod-cdr (std::prod-car x)))))
     (low-idx
          (ifix (std::prod-cdr (std::prod-cdr (std::prod-car x)))))
     (delay (acl2::maybe-posp-fix
                 (std::prod-car (std::prod-car (std::prod-cdr x)))))
     (revp (std::prod-cdr (std::prod-car (std::prod-cdr x))))
     (type (wiretype-fix
                (std::prod-car (std::prod-cdr (std::prod-cdr x)))))
     (atts (attributes-fix
                (std::prod-cdr (std::prod-cdr (std::prod-cdr x))))))
    (std::prod-cons
         (std::prod-cons name (std::prod-cons width low-idx))
         (std::prod-cons (std::prod-cons delay revp)
                         (std::prod-cons type atts))))
   :exec x)))

Theorem: wire-p-of-wire-fix

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

Theorem: wire-fix-when-wire-p

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

Function: wire-equiv$inline

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

Theorem: wire-equiv-is-an-equivalence

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

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

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

Theorem: wire-fix-under-wire-equiv

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

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

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

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

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

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

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

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

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