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Store-funct

Store-funct-fix

Fixing function for store-funct structures.

Signature
(store-funct-fix x) → new-x
Arguments: x — Guard (store-funct-p x).
Returns: new-x — Type (store-funct-p new-x).

Definitions and Theorems

Function: store-funct-fix$inline

(defun store-funct-fix$inline (x)
  (declare (xargs :guard (store-funct-p x)))
  (let ((__function__ 'store-funct-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (store-funct-kind x)
           (:sb (cons :sb (list)))
           (:sh (cons :sh (list)))
           (:sw (cons :sw (list)))
           (:sd (cons :sd (list))))
         :exec x)))

Theorem: store-funct-p-of-store-funct-fix

(defthm store-funct-p-of-store-funct-fix
  (b* ((new-x (store-funct-fix$inline x)))
    (store-funct-p new-x))
  :rule-classes :rewrite)

Theorem: store-funct-fix-when-store-funct-p

(defthm store-funct-fix-when-store-funct-p
  (implies (store-funct-p x)
           (equal (store-funct-fix x) x)))

Function: store-funct-equiv$inline

(defun store-funct-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (store-funct-p acl2::x)
                              (store-funct-p acl2::y))))
  (equal (store-funct-fix acl2::x)
         (store-funct-fix acl2::y)))

Theorem: store-funct-equiv-is-an-equivalence

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

Theorem: store-funct-equiv-implies-equal-store-funct-fix-1

(defthm store-funct-equiv-implies-equal-store-funct-fix-1
  (implies (store-funct-equiv acl2::x x-equiv)
           (equal (store-funct-fix acl2::x)
                  (store-funct-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: store-funct-fix-under-store-funct-equiv

(defthm store-funct-fix-under-store-funct-equiv
  (store-funct-equiv (store-funct-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-store-funct-fix-1-forward-to-store-funct-equiv

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

Theorem: equal-of-store-funct-fix-2-forward-to-store-funct-equiv

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

Theorem: store-funct-equiv-of-store-funct-fix-1-forward

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

Theorem: store-funct-equiv-of-store-funct-fix-2-forward

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

Theorem: store-funct-kind$inline-of-store-funct-fix-x

(defthm store-funct-kind$inline-of-store-funct-fix-x
  (equal (store-funct-kind$inline (store-funct-fix x))
         (store-funct-kind$inline x)))

Theorem: store-funct-kind$inline-store-funct-equiv-congruence-on-x

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

Theorem: consp-of-store-funct-fix

(defthm consp-of-store-funct-fix
  (consp (store-funct-fix x))
  :rule-classes :type-prescription)