		Search-engine friendly clone of the ACL2 documentation.

Atc-fn-info

Atc-fn-info-fix

Fixing function for atc-fn-info structures.

Signature
(atc-fn-info-fix x) → new-x
Arguments: x — Guard (atc-fn-infop x).
Returns: new-x — Type (atc-fn-infop new-x).

Definitions and Theorems

Function: atc-fn-info-fix$inline

(defun atc-fn-info-fix$inline (x)
  (declare (xargs :guard (atc-fn-infop x)))
  (let ((__function__ 'atc-fn-info-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((out-type (type-option-fix (cdr (std::da-nth 0 x))))
              (in-types (type-list-fix (cdr (std::da-nth 1 x))))
              (loop? (stmt-option-fix (cdr (std::da-nth 2 x))))
              (affect (symbol-list-fix (cdr (std::da-nth 3 x))))
              (extobjs (symbol-list-fix (cdr (std::da-nth 4 x))))
              (result-thm (symbol-fix (cdr (std::da-nth 5 x))))
              (correct-thm (symbol-fix (cdr (std::da-nth 6 x))))
              (correct-mod-thm (symbol-fix (cdr (std::da-nth 7 x))))
              (measure-nat-thm (symbol-fix (cdr (std::da-nth 8 x))))
              (fun-env-thm (symbol-fix (cdr (std::da-nth 9 x))))
              (limit (pseudo-term-fix (cdr (std::da-nth 10 x))))
              (guard (symbol-fix (cdr (std::da-nth 11 x)))))
           (list (cons 'out-type out-type)
                 (cons 'in-types in-types)
                 (cons 'loop? loop?)
                 (cons 'affect affect)
                 (cons 'extobjs extobjs)
                 (cons 'result-thm result-thm)
                 (cons 'correct-thm correct-thm)
                 (cons 'correct-mod-thm correct-mod-thm)
                 (cons 'measure-nat-thm measure-nat-thm)
                 (cons 'fun-env-thm fun-env-thm)
                 (cons 'limit limit)
                 (cons 'guard guard)))
         :exec x)))

Theorem: atc-fn-infop-of-atc-fn-info-fix

(defthm atc-fn-infop-of-atc-fn-info-fix
  (b* ((new-x (atc-fn-info-fix$inline x)))
    (atc-fn-infop new-x))
  :rule-classes :rewrite)

Theorem: atc-fn-info-fix-when-atc-fn-infop

(defthm atc-fn-info-fix-when-atc-fn-infop
  (implies (atc-fn-infop x)
           (equal (atc-fn-info-fix x) x)))

Function: atc-fn-info-equiv$inline

(defun atc-fn-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (atc-fn-infop acl2::x)
                              (atc-fn-infop acl2::y))))
  (equal (atc-fn-info-fix acl2::x)
         (atc-fn-info-fix acl2::y)))

Theorem: atc-fn-info-equiv-is-an-equivalence

(defthm atc-fn-info-equiv-is-an-equivalence
  (and (booleanp (atc-fn-info-equiv x y))
       (atc-fn-info-equiv x x)
       (implies (atc-fn-info-equiv x y)
                (atc-fn-info-equiv y x))
       (implies (and (atc-fn-info-equiv x y)
                     (atc-fn-info-equiv y z))
                (atc-fn-info-equiv x z)))
  :rule-classes (:equivalence))

Theorem: atc-fn-info-equiv-implies-equal-atc-fn-info-fix-1

(defthm atc-fn-info-equiv-implies-equal-atc-fn-info-fix-1
  (implies (atc-fn-info-equiv acl2::x x-equiv)
           (equal (atc-fn-info-fix acl2::x)
                  (atc-fn-info-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: atc-fn-info-fix-under-atc-fn-info-equiv

(defthm atc-fn-info-fix-under-atc-fn-info-equiv
  (atc-fn-info-equiv (atc-fn-info-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-atc-fn-info-fix-1-forward-to-atc-fn-info-equiv

(defthm equal-of-atc-fn-info-fix-1-forward-to-atc-fn-info-equiv
  (implies (equal (atc-fn-info-fix acl2::x)
                  acl2::y)
           (atc-fn-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-atc-fn-info-fix-2-forward-to-atc-fn-info-equiv

(defthm equal-of-atc-fn-info-fix-2-forward-to-atc-fn-info-equiv
  (implies (equal acl2::x (atc-fn-info-fix acl2::y))
           (atc-fn-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atc-fn-info-equiv-of-atc-fn-info-fix-1-forward

(defthm atc-fn-info-equiv-of-atc-fn-info-fix-1-forward
  (implies (atc-fn-info-equiv (atc-fn-info-fix acl2::x)
                              acl2::y)
           (atc-fn-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atc-fn-info-equiv-of-atc-fn-info-fix-2-forward

(defthm atc-fn-info-equiv-of-atc-fn-info-fix-2-forward
  (implies (atc-fn-info-equiv acl2::x (atc-fn-info-fix acl2::y))
           (atc-fn-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)