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Input-item

Input-item-fix

Fixing function for input-item structures.

Signature
(input-item-fix x) → new-x
Arguments: x — Guard (input-itemp x).
Returns: new-x — Type (input-itemp new-x).

Definitions and Theorems

Function: input-item-fix$inline

(defun input-item-fix$inline (x)
 (declare (xargs :guard (input-itemp x)))
 (let ((__function__ 'input-item-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((name (identifier-fix (cdr (std::da-nth 0 (cdr x)))))
       (type (input-type-fix (cdr (std::da-nth 1 (cdr x)))))
       (value (input-expression-fix (cdr (std::da-nth 2 (cdr x))))))
      (cons :input-item (list (cons 'name name)
                              (cons 'type type)
                              (cons 'value value))))
    :exec x)))

Theorem: input-itemp-of-input-item-fix

(defthm input-itemp-of-input-item-fix
  (b* ((new-x (input-item-fix$inline x)))
    (input-itemp new-x))
  :rule-classes :rewrite)

Theorem: input-item-fix-when-input-itemp

(defthm input-item-fix-when-input-itemp
  (implies (input-itemp x)
           (equal (input-item-fix x) x)))

Function: input-item-equiv$inline

(defun input-item-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (input-itemp acl2::x)
                              (input-itemp acl2::y))))
  (equal (input-item-fix acl2::x)
         (input-item-fix acl2::y)))

Theorem: input-item-equiv-is-an-equivalence

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

Theorem: input-item-equiv-implies-equal-input-item-fix-1

(defthm input-item-equiv-implies-equal-input-item-fix-1
  (implies (input-item-equiv acl2::x x-equiv)
           (equal (input-item-fix acl2::x)
                  (input-item-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: input-item-fix-under-input-item-equiv

(defthm input-item-fix-under-input-item-equiv
  (input-item-equiv (input-item-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-input-item-fix-1-forward-to-input-item-equiv

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

Theorem: equal-of-input-item-fix-2-forward-to-input-item-equiv

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

Theorem: input-item-equiv-of-input-item-fix-1-forward

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

Theorem: input-item-equiv-of-input-item-fix-2-forward

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