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Atc-premise

Atc-premise-fix

Fixing function for atc-premise structures.

Signature
(atc-premise-fix x) → new-x
Arguments: x — Guard (atc-premisep x).
Returns: new-x — Type (atc-premisep new-x).

Definitions and Theorems

Function: atc-premise-fix$inline

(defun atc-premise-fix$inline (x)
 (declare (xargs :guard (atc-premisep x)))
 (let ((__function__ 'atc-premise-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (atc-premise-kind x)
     (:compustate (b* ((var (symbol-fix (std::da-nth 0 (cdr x))))
                       (term (identity (std::da-nth 1 (cdr x)))))
                    (cons :compustate (list var term))))
     (:cvalue (b* ((var (symbol-fix (std::da-nth 0 (cdr x))))
                   (term (identity (std::da-nth 1 (cdr x)))))
                (cons :cvalue (list var term))))
     (:cvalues (b* ((vars (symbol-list-fix (std::da-nth 0 (cdr x))))
                    (term (identity (std::da-nth 1 (cdr x)))))
                 (cons :cvalues (list vars term))))
     (:test (b* ((term (identity (std::da-nth 0 (cdr x)))))
              (cons :test (list term)))))
   :exec x)))

Theorem: atc-premisep-of-atc-premise-fix

(defthm atc-premisep-of-atc-premise-fix
  (b* ((new-x (atc-premise-fix$inline x)))
    (atc-premisep new-x))
  :rule-classes :rewrite)

Theorem: atc-premise-fix-when-atc-premisep

(defthm atc-premise-fix-when-atc-premisep
  (implies (atc-premisep x)
           (equal (atc-premise-fix x) x)))

Function: atc-premise-equiv$inline

(defun atc-premise-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (atc-premisep acl2::x)
                              (atc-premisep acl2::y))))
  (equal (atc-premise-fix acl2::x)
         (atc-premise-fix acl2::y)))

Theorem: atc-premise-equiv-is-an-equivalence

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

Theorem: atc-premise-equiv-implies-equal-atc-premise-fix-1

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

Theorem: atc-premise-fix-under-atc-premise-equiv

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

Theorem: equal-of-atc-premise-fix-1-forward-to-atc-premise-equiv

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

Theorem: equal-of-atc-premise-fix-2-forward-to-atc-premise-equiv

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

Theorem: atc-premise-equiv-of-atc-premise-fix-1-forward

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

Theorem: atc-premise-equiv-of-atc-premise-fix-2-forward

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

Theorem: atc-premise-kind$inline-of-atc-premise-fix-x

(defthm atc-premise-kind$inline-of-atc-premise-fix-x
  (equal (atc-premise-kind$inline (atc-premise-fix x))
         (atc-premise-kind$inline x)))

Theorem: atc-premise-kind$inline-atc-premise-equiv-congruence-on-x

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

Theorem: consp-of-atc-premise-fix

(defthm consp-of-atc-premise-fix
  (consp (atc-premise-fix x))
  :rule-classes :type-prescription)