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• Package-name

Package-name-fix

Fixing function for package-name structures.

Signature

(package-name-fix x) → new-x

Arguments

x — Guard (package-namep x).

Returns

new-x — Type (package-namep new-x).

Definitions and Theorems

Function: package-name-fix$inline

(defun package-name-fix$inline (x)
 (declare (xargs :guard (package-namep x)))
 (let ((__function__ 'package-name-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((identifiers (identifier-list-fix (std::da-nth 0 (cdr x)))))
     (cons :package-name (list identifiers)))
   :exec x)))

Theorem: package-namep-of-package-name-fix

(defthm package-namep-of-package-name-fix
  (b* ((new-x (package-name-fix$inline x)))
    (package-namep new-x))
  :rule-classes :rewrite)

Theorem: package-name-fix-when-package-namep

(defthm package-name-fix-when-package-namep
  (implies (package-namep x)
           (equal (package-name-fix x) x)))

Function: package-name-equiv$inline

(defun package-name-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (package-namep acl2::x)
                              (package-namep acl2::y))))
  (equal (package-name-fix acl2::x)
         (package-name-fix acl2::y)))

Theorem: package-name-equiv-is-an-equivalence

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

Theorem: package-name-equiv-implies-equal-package-name-fix-1

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

Theorem: package-name-fix-under-package-name-equiv

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

Theorem: equal-of-package-name-fix-1-forward-to-package-name-equiv

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

Theorem: equal-of-package-name-fix-2-forward-to-package-name-equiv

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

Theorem: package-name-equiv-of-package-name-fix-1-forward

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

Theorem: package-name-equiv-of-package-name-fix-2-forward

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