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Screen

Screen-fix

Fixing function for screen structures.

Signature
(screen-fix x) → new-x
Arguments: x — Guard (screenp x).
Returns: new-x — Type (screenp new-x).

Definitions and Theorems

Function: screen-fix$inline

(defun screen-fix$inline (x)
 (declare (xargs :guard (screenp x)))
 (let ((__function__ 'screen-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((messages
           (screen-message-list-fix (cdr (std::da-nth 0 (cdr x))))))
     (cons :screen (list (cons 'messages messages))))
    :exec x)))

Theorem: screenp-of-screen-fix

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

Theorem: screen-fix-when-screenp

(defthm screen-fix-when-screenp
  (implies (screenp x)
           (equal (screen-fix x) x)))

Function: screen-equiv$inline

(defun screen-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (screenp acl2::x)
                              (screenp acl2::y))))
  (equal (screen-fix acl2::x)
         (screen-fix acl2::y)))

Theorem: screen-equiv-is-an-equivalence

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

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

(defthm screen-equiv-implies-equal-screen-fix-1
  (implies (screen-equiv acl2::x x-equiv)
           (equal (screen-fix acl2::x)
                  (screen-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: screen-fix-under-screen-equiv

(defthm screen-fix-under-screen-equiv
  (screen-equiv (screen-fix acl2::x)
                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-screen-fix-1-forward-to-screen-equiv
  (implies (equal (screen-fix acl2::x) acl2::y)
           (screen-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-screen-fix-2-forward-to-screen-equiv
  (implies (equal acl2::x (screen-fix acl2::y))
           (screen-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm screen-equiv-of-screen-fix-1-forward
  (implies (screen-equiv (screen-fix acl2::x)
                         acl2::y)
           (screen-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm screen-equiv-of-screen-fix-2-forward
  (implies (screen-equiv acl2::x (screen-fix acl2::y))
           (screen-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)