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Prof-entry

Prof-entry-fix

Fixing function for prof-entry structures.

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

Definitions and Theorems

Function: prof-entry-fix$inline

(defun prof-entry-fix$inline (x)
  (declare (xargs :guard (prof-entry-p x)))
  (let ((__function__ 'prof-entry-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (std::da-nth 0 x))
              (tries-succ (nfix (std::da-nth 1 x)))
              (tries-fail (nfix (std::da-nth 2 x)))
              (frames-succ (nfix (std::da-nth 3 x)))
              (frames-fail (nfix (std::da-nth 4 x))))
           (list name tries-succ
                 tries-fail frames-succ frames-fail))
         :exec x)))

Theorem: prof-entry-p-of-prof-entry-fix

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

Theorem: prof-entry-fix-when-prof-entry-p

(defthm prof-entry-fix-when-prof-entry-p
  (implies (prof-entry-p x)
           (equal (prof-entry-fix x) x)))

Function: prof-entry-equiv$inline

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

Theorem: prof-entry-equiv-is-an-equivalence

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

Theorem: prof-entry-equiv-implies-equal-prof-entry-fix-1

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

Theorem: prof-entry-fix-under-prof-entry-equiv

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

Theorem: equal-of-prof-entry-fix-1-forward-to-prof-entry-equiv

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

Theorem: equal-of-prof-entry-fix-2-forward-to-prof-entry-equiv

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

Theorem: prof-entry-equiv-of-prof-entry-fix-1-forward

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

Theorem: prof-entry-equiv-of-prof-entry-fix-2-forward

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