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Printconfig

Printconfig-fix

Fixing function for printconfig structures.

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

Definitions and Theorems

Function: printconfig-fix$inline

(defun printconfig-fix$inline (x)
 (declare (xargs :guard (printconfig-p x)))
 (let ((acl2::__function__ 'printconfig-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (b*
    ((flat-right-margin
          (acl2::pos-fix (std::prod-car (std::prod-car (cdr x)))))
     (hard-right-margin
      (acl2::pos-fix
           (std::prod-car (std::prod-cdr (std::prod-car (cdr x))))))
     (print-base
      (print-base-fix
           (std::prod-cdr (std::prod-cdr (std::prod-car (cdr x))))))
     (print-radix
          (acl2::bool-fix (std::prod-car (std::prod-cdr (cdr x)))))
     (home-package
      (acl2::symbol-fix
           (std::prod-car (std::prod-cdr (std::prod-cdr (cdr x))))))
     (print-lowercase
      (acl2::bool-fix
          (std::prod-cdr (std::prod-cdr (std::prod-cdr (cdr x)))))))
    (cons
     :printconfig
     (std::prod-cons
      (std::prod-cons flat-right-margin
                      (std::prod-cons hard-right-margin print-base))
      (std::prod-cons
           print-radix
           (std::prod-cons home-package print-lowercase)))))
   :exec x)))

Theorem: printconfig-p-of-printconfig-fix

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

Theorem: printconfig-fix-when-printconfig-p

(defthm printconfig-fix-when-printconfig-p
  (implies (printconfig-p x)
           (equal (printconfig-fix x) x)))

Function: printconfig-equiv$inline

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

Theorem: printconfig-equiv-is-an-equivalence

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

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

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

Theorem: printconfig-fix-under-printconfig-equiv

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

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

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

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

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

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

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

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

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