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Output-section

Output-section-fix

Fixing function for output-section structures.

Signature
(output-section-fix x) → new-x
Arguments: x — Guard (output-sectionp x).
Returns: new-x — Type (output-sectionp new-x).

Definitions and Theorems

Function: output-section-fix$inline

(defun output-section-fix$inline (x)
 (declare (xargs :guard (output-sectionp x)))
 (let ((__function__ 'output-section-fix))
   (declare (ignorable __function__))
   (mbe :logic
        (b* ((item (output-item-fix (cdr (std::da-nth 0 (cdr x))))))
          (cons :output-section (list (cons 'item item))))
        :exec x)))

Theorem: output-sectionp-of-output-section-fix

(defthm output-sectionp-of-output-section-fix
  (b* ((new-x (output-section-fix$inline x)))
    (output-sectionp new-x))
  :rule-classes :rewrite)

Theorem: output-section-fix-when-output-sectionp

(defthm output-section-fix-when-output-sectionp
  (implies (output-sectionp x)
           (equal (output-section-fix x) x)))

Function: output-section-equiv$inline

(defun output-section-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (output-sectionp acl2::x)
                              (output-sectionp acl2::y))))
  (equal (output-section-fix acl2::x)
         (output-section-fix acl2::y)))

Theorem: output-section-equiv-is-an-equivalence

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

Theorem: output-section-equiv-implies-equal-output-section-fix-1

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

Theorem: output-section-fix-under-output-section-equiv

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

Theorem: equal-of-output-section-fix-1-forward-to-output-section-equiv

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

Theorem: equal-of-output-section-fix-2-forward-to-output-section-equiv

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

Theorem: output-section-equiv-of-output-section-fix-1-forward

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

Theorem: output-section-equiv-of-output-section-fix-2-forward

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