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3col4vecline

3col4vecline-fix

Fixing function for 3col4vecline structures.

Signature
(3col4vecline-fix x) → new-x
Arguments: x — Guard (3col4vecline-p x).
Returns: new-x — Type (3col4vecline-p new-x).

Definitions and Theorems

Function: 3col4vecline-fix$inline

(defun 3col4vecline-fix$inline (x)
 (declare (xargs :guard (3col4vecline-p x)))
 (let ((__function__ '3col4vecline-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((label (msg-fix (std::prod-car x)))
          (val (maybe-4vec-fix (std::prod-car (std::prod-cdr x))))
          (val2 (maybe-4vec-fix (std::prod-cdr (std::prod-cdr x)))))
       (std::prod-cons label (std::prod-cons val val2)))
     :exec x)))

Theorem: 3col4vecline-p-of-3col4vecline-fix

(defthm 3col4vecline-p-of-3col4vecline-fix
  (b* ((new-x (3col4vecline-fix$inline x)))
    (3col4vecline-p new-x))
  :rule-classes :rewrite)

Theorem: 3col4vecline-fix-when-3col4vecline-p

(defthm 3col4vecline-fix-when-3col4vecline-p
  (implies (3col4vecline-p x)
           (equal (3col4vecline-fix x) x)))

Function: 3col4vecline-equiv$inline

(defun 3col4vecline-equiv$inline (x y)
  (declare (xargs :guard (and (3col4vecline-p x)
                              (3col4vecline-p y))))
  (equal (3col4vecline-fix x)
         (3col4vecline-fix y)))

Theorem: 3col4vecline-equiv-is-an-equivalence

(defthm 3col4vecline-equiv-is-an-equivalence
  (and (booleanp (3col4vecline-equiv x y))
       (3col4vecline-equiv x x)
       (implies (3col4vecline-equiv x y)
                (3col4vecline-equiv y x))
       (implies (and (3col4vecline-equiv x y)
                     (3col4vecline-equiv y z))
                (3col4vecline-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 3col4vecline-equiv-implies-equal-3col4vecline-fix-1

(defthm 3col4vecline-equiv-implies-equal-3col4vecline-fix-1
  (implies (3col4vecline-equiv x x-equiv)
           (equal (3col4vecline-fix x)
                  (3col4vecline-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 3col4vecline-fix-under-3col4vecline-equiv

(defthm 3col4vecline-fix-under-3col4vecline-equiv
  (3col4vecline-equiv (3col4vecline-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-3col4vecline-fix-1-forward-to-3col4vecline-equiv

(defthm equal-of-3col4vecline-fix-1-forward-to-3col4vecline-equiv
  (implies (equal (3col4vecline-fix x) y)
           (3col4vecline-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-3col4vecline-fix-2-forward-to-3col4vecline-equiv

(defthm equal-of-3col4vecline-fix-2-forward-to-3col4vecline-equiv
  (implies (equal x (3col4vecline-fix y))
           (3col4vecline-equiv x y))
  :rule-classes :forward-chaining)

Theorem: 3col4vecline-equiv-of-3col4vecline-fix-1-forward

(defthm 3col4vecline-equiv-of-3col4vecline-fix-1-forward
  (implies (3col4vecline-equiv (3col4vecline-fix x)
                               y)
           (3col4vecline-equiv x y))
  :rule-classes :forward-chaining)

Theorem: 3col4vecline-equiv-of-3col4vecline-fix-2-forward

(defthm 3col4vecline-equiv-of-3col4vecline-fix-2-forward
  (implies (3col4vecline-equiv x (3col4vecline-fix y))
           (3col4vecline-equiv x y))
  :rule-classes :forward-chaining)