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• Minor-frame

Minor-frame-fix

Fixing function for minor-frame structures.

Signature

(minor-frame-fix x) → new-x

Arguments

x — Guard (minor-frame-p x).

Returns

new-x — Type (minor-frame-p new-x).

Definitions and Theorems

Function: minor-frame-fix$inline

(defun minor-frame-fix$inline (x)
 (declare (xargs :guard (minor-frame-p x)))
 (let ((__function__ 'minor-frame-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((bindings (fgl-object-bindings-fix (cdr (std::da-nth 0 x))))
        (scratch (scratchlist-fix (cdr (std::da-nth 1 x))))
        (term (pseudo-term-fix (cdr (std::da-nth 2 x))))
        (term-index (acl2::maybe-natp-fix (cdr (std::da-nth 3 x)))))
     (list (cons 'bindings bindings)
           (cons 'scratch scratch)
           (cons 'term term)
           (cons 'term-index term-index)))
   :exec x)))

Theorem: minor-frame-p-of-minor-frame-fix

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

Theorem: minor-frame-fix-when-minor-frame-p

(defthm minor-frame-fix-when-minor-frame-p
  (implies (minor-frame-p x)
           (equal (minor-frame-fix x) x)))

Function: minor-frame-equiv$inline

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

Theorem: minor-frame-equiv-is-an-equivalence

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

Theorem: minor-frame-equiv-implies-equal-minor-frame-fix-1

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

Theorem: minor-frame-fix-under-minor-frame-equiv

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

Theorem: equal-of-minor-frame-fix-1-forward-to-minor-frame-equiv

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

Theorem: equal-of-minor-frame-fix-2-forward-to-minor-frame-equiv

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

Theorem: minor-frame-equiv-of-minor-frame-fix-1-forward

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

Theorem: minor-frame-equiv-of-minor-frame-fix-2-forward

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