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Screen-message

Screen-message-fix

Fixing function for screen-message structures.

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

Definitions and Theorems

Function: screen-message-fix$inline

(defun screen-message-fix$inline (x)
 (declare (xargs :guard (screen-messagep x)))
 (let ((__function__ 'screen-message-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (screen-message-kind x)
     (:error (b* ((string (char-list-fix (std::da-nth 0 (cdr x))))
                  (values (value-list-fix (std::da-nth 1 (cdr x)))))
               (cons :error (list string values))))
     (:log (b* ((string (char-list-fix (std::da-nth 0 (cdr x))))
                (values (value-list-fix (std::da-nth 1 (cdr x)))))
             (cons :log (list string values)))))
   :exec x)))

Theorem: screen-messagep-of-screen-message-fix

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

Theorem: screen-message-fix-when-screen-messagep

(defthm screen-message-fix-when-screen-messagep
  (implies (screen-messagep x)
           (equal (screen-message-fix x) x)))

Function: screen-message-equiv$inline

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

Theorem: screen-message-equiv-is-an-equivalence

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

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

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

Theorem: screen-message-fix-under-screen-message-equiv

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

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

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

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

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

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

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

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

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

Theorem: screen-message-kind$inline-of-screen-message-fix-x

(defthm screen-message-kind$inline-of-screen-message-fix-x
  (equal (screen-message-kind$inline (screen-message-fix x))
         (screen-message-kind$inline x)))

Theorem: screen-message-kind$inline-screen-message-equiv-congruence-on-x

(defthm
    screen-message-kind$inline-screen-message-equiv-congruence-on-x
  (implies (screen-message-equiv x x-equiv)
           (equal (screen-message-kind$inline x)
                  (screen-message-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-screen-message-fix

(defthm consp-of-screen-message-fix
  (consp (screen-message-fix x))
  :rule-classes :type-prescription)