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Attrib-name

Attrib-name-fix

Fixing function for attrib-name structures.

Signature
(attrib-name-fix x) → new-x
Arguments: x — Guard (attrib-namep x).
Returns: new-x — Type (attrib-namep new-x).

Definitions and Theorems

Function: attrib-name-fix$inline

(defun attrib-name-fix$inline (x)
 (declare (xargs :guard (attrib-namep x)))
 (let ((__function__ 'attrib-name-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (attrib-name-kind x)
    (:ident (b* ((unwrap (ident-fix (std::da-nth 0 (cdr x)))))
              (cons :ident (list unwrap))))
    (:keyword (b* ((unwrap (acl2::str-fix (std::da-nth 0 (cdr x)))))
                (cons :keyword (list unwrap)))))
   :exec x)))

Theorem: attrib-namep-of-attrib-name-fix

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

Theorem: attrib-name-fix-when-attrib-namep

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

Function: attrib-name-equiv$inline

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

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

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

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

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

Theorem: attrib-name-fix-under-attrib-name-equiv

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

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

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

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

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

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

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

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

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

Theorem: attrib-name-kind$inline-of-attrib-name-fix-x

(defthm attrib-name-kind$inline-of-attrib-name-fix-x
  (equal (attrib-name-kind$inline (attrib-name-fix x))
         (attrib-name-kind$inline x)))

Theorem: attrib-name-kind$inline-attrib-name-equiv-congruence-on-x

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

Theorem: consp-of-attrib-name-fix

(defthm consp-of-attrib-name-fix
  (consp (attrib-name-fix x))
  :rule-classes :type-prescription)