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Char-format

Char-format-fix

Fixing function for char-format structures.

Signature
(char-format-fix x) → new-x
Arguments: x — Guard (char-formatp x).
Returns: new-x — Type (char-formatp new-x).

Definitions and Theorems

Function: char-format-fix$inline

(defun char-format-fix$inline (x)
  (declare (xargs :guard (char-formatp x)))
  (let ((__function__ 'char-format-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((signedp (acl2::bool-fix (cdr (std::da-nth 0 x)))))
           (list (cons 'signedp signedp)))
         :exec x)))

Theorem: char-formatp-of-char-format-fix

(defthm char-formatp-of-char-format-fix
  (b* ((new-x (char-format-fix$inline x)))
    (char-formatp new-x))
  :rule-classes :rewrite)

Theorem: char-format-fix-when-char-formatp

(defthm char-format-fix-when-char-formatp
  (implies (char-formatp x)
           (equal (char-format-fix x) x)))

Function: char-format-equiv$inline

(defun char-format-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (char-formatp acl2::x)
                              (char-formatp acl2::y))))
  (equal (char-format-fix acl2::x)
         (char-format-fix acl2::y)))

Theorem: char-format-equiv-is-an-equivalence

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

Theorem: char-format-equiv-implies-equal-char-format-fix-1

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

Theorem: char-format-fix-under-char-format-equiv

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

Theorem: equal-of-char-format-fix-1-forward-to-char-format-equiv

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

Theorem: equal-of-char-format-fix-2-forward-to-char-format-equiv

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

Theorem: char-format-equiv-of-char-format-fix-1-forward

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

Theorem: char-format-equiv-of-char-format-fix-2-forward

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