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• Transform-argument-value

Transform-argument-value-fix

Fixing function for transform-argument-value structures.

Signature

(transform-argument-value-fix x) → new-x

Arguments

x — Guard (transform-argument-valuep x).

Returns

new-x — Type (transform-argument-valuep new-x).

Definitions and Theorems

Function: transform-argument-value-fix$inline

(defun transform-argument-value-fix$inline (x)
 (declare (xargs :guard (transform-argument-valuep x)))
 (let ((__function__ 'transform-argument-value-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (transform-argument-value-kind x)
    (:identifier
         (b* ((name (identifier-fix (std::da-nth 0 (cdr x)))))
           (cons :identifier (list name))))
    (:identifier-list
         (b* ((names (identifier-list-fix (std::da-nth 0 (cdr x)))))
           (cons :identifier-list (list names))))
    (:term (b* ((get (expression-fix (std::da-nth 0 (cdr x)))))
             (cons :term (list get))))
    (:bool (b* ((val (bool-fix (std::da-nth 0 (cdr x)))))
             (cons :bool (list val)))))
   :exec x)))

Theorem: transform-argument-valuep-of-transform-argument-value-fix

(defthm transform-argument-valuep-of-transform-argument-value-fix
  (b* ((new-x (transform-argument-value-fix$inline x)))
    (transform-argument-valuep new-x))
  :rule-classes :rewrite)

Theorem: transform-argument-value-fix-when-transform-argument-valuep

(defthm transform-argument-value-fix-when-transform-argument-valuep
  (implies (transform-argument-valuep x)
           (equal (transform-argument-value-fix x)
                  x)))

Function: transform-argument-value-equiv$inline

(defun transform-argument-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (transform-argument-valuep acl2::x)
                              (transform-argument-valuep acl2::y))))
  (equal (transform-argument-value-fix acl2::x)
         (transform-argument-value-fix acl2::y)))

Theorem: transform-argument-value-equiv-is-an-equivalence

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

Theorem: transform-argument-value-equiv-implies-equal-transform-argument-value-fix-1

(defthm
 transform-argument-value-equiv-implies-equal-transform-argument-value-fix-1
 (implies (transform-argument-value-equiv acl2::x x-equiv)
          (equal (transform-argument-value-fix acl2::x)
                 (transform-argument-value-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: transform-argument-value-fix-under-transform-argument-value-equiv

(defthm
  transform-argument-value-fix-under-transform-argument-value-equiv
  (transform-argument-value-equiv
       (transform-argument-value-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-transform-argument-value-fix-1-forward-to-transform-argument-value-equiv

(defthm
 equal-of-transform-argument-value-fix-1-forward-to-transform-argument-value-equiv
 (implies (equal (transform-argument-value-fix acl2::x)
                 acl2::y)
          (transform-argument-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-transform-argument-value-fix-2-forward-to-transform-argument-value-equiv

(defthm
 equal-of-transform-argument-value-fix-2-forward-to-transform-argument-value-equiv
 (implies (equal acl2::x
                 (transform-argument-value-fix acl2::y))
          (transform-argument-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: transform-argument-value-equiv-of-transform-argument-value-fix-1-forward

(defthm
 transform-argument-value-equiv-of-transform-argument-value-fix-1-forward
 (implies (transform-argument-value-equiv
               (transform-argument-value-fix acl2::x)
               acl2::y)
          (transform-argument-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: transform-argument-value-equiv-of-transform-argument-value-fix-2-forward

(defthm
 transform-argument-value-equiv-of-transform-argument-value-fix-2-forward
 (implies (transform-argument-value-equiv
               acl2::x
               (transform-argument-value-fix acl2::y))
          (transform-argument-value-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: transform-argument-value-kind$inline-of-transform-argument-value-fix-x

(defthm
 transform-argument-value-kind$inline-of-transform-argument-value-fix-x
 (equal (transform-argument-value-kind$inline
             (transform-argument-value-fix x))
        (transform-argument-value-kind$inline x)))

Theorem: transform-argument-value-kind$inline-transform-argument-value-equiv-congruence-on-x

(defthm
 transform-argument-value-kind$inline-transform-argument-value-equiv-congruence-on-x
 (implies (transform-argument-value-equiv x x-equiv)
          (equal (transform-argument-value-kind$inline x)
                 (transform-argument-value-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-transform-argument-value-fix

(defthm consp-of-transform-argument-value-fix
  (consp (transform-argument-value-fix x))
  :rule-classes :type-prescription)