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Fraig-config

Fraig-config-fix

Fixing function for fraig-config structures.

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

Definitions and Theorems

Function: fraig-config-fix$inline

(defun fraig-config-fix$inline (x)
 (declare (xargs :guard (fraig-config-p x)))
 (let ((__function__ 'fraig-config-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((initial-sim-words (pos-fix (cdr (std::da-nth 0 (cdr x)))))
     (initial-sim-rounds (pos-fix (cdr (std::da-nth 1 (cdr x)))))
     (sim-words (pos-fix (cdr (std::da-nth 2 (cdr x)))))
     (ipasir-limit
          (acl2::maybe-natp-fix (cdr (std::da-nth 3 (cdr x)))))
     (ipasir-recycle-count
          (acl2::maybe-natp-fix (cdr (std::da-nth 4 (cdr x)))))
     (ctrex-queue-limit
          (acl2::maybe-natp-fix (cdr (std::da-nth 5 (cdr x)))))
     (ctrex-force-resim
          (acl2::bool-fix (cdr (std::da-nth 6 (cdr x)))))
     (final-force-resim
          (acl2::bool-fix (cdr (std::da-nth 7 (cdr x)))))
     (random-seed-name
          (acl2::symbol-fix (cdr (std::da-nth 8 (cdr x)))))
     (outs-only (acl2::bool-fix (cdr (std::da-nth 9 (cdr x)))))
     (miters-only (acl2::bool-fix (cdr (std::da-nth 10 (cdr x)))))
     (delete-class-on-fail (nfix (cdr (std::da-nth 11 (cdr x)))))
     (gatesimp (gatesimp-fix (cdr (std::da-nth 12 (cdr x)))))
     (level-limit (nfix (cdr (std::da-nth 13 (cdr x)))))
     (output-types
         (fraig-output-type-map-fix (cdr (std::da-nth 14 (cdr x)))))
     (save-candidate-equivs-as
          (acl2::symbol-fix (cdr (std::da-nth 15 (cdr x)))))
     (remove-candidate-equivs
          (acl2::symbol-fix (cdr (std::da-nth 16 (cdr x))))))
    (cons :fraig-config (list (cons 'initial-sim-words
                                    initial-sim-words)
                              (cons 'initial-sim-rounds
                                    initial-sim-rounds)
                              (cons 'sim-words sim-words)
                              (cons 'ipasir-limit ipasir-limit)
                              (cons 'ipasir-recycle-count
                                    ipasir-recycle-count)
                              (cons 'ctrex-queue-limit
                                    ctrex-queue-limit)
                              (cons 'ctrex-force-resim
                                    ctrex-force-resim)
                              (cons 'final-force-resim
                                    final-force-resim)
                              (cons 'random-seed-name
                                    random-seed-name)
                              (cons 'outs-only outs-only)
                              (cons 'miters-only miters-only)
                              (cons 'delete-class-on-fail
                                    delete-class-on-fail)
                              (cons 'gatesimp gatesimp)
                              (cons 'level-limit level-limit)
                              (cons 'output-types output-types)
                              (cons 'save-candidate-equivs-as
                                    save-candidate-equivs-as)
                              (cons 'remove-candidate-equivs
                                    remove-candidate-equivs))))
   :exec x)))

Theorem: fraig-config-p-of-fraig-config-fix

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

Theorem: fraig-config-fix-when-fraig-config-p

(defthm fraig-config-fix-when-fraig-config-p
  (implies (fraig-config-p x)
           (equal (fraig-config-fix x) x)))

Function: fraig-config-equiv$inline

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

Theorem: fraig-config-equiv-is-an-equivalence

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

Theorem: fraig-config-equiv-implies-equal-fraig-config-fix-1

(defthm fraig-config-equiv-implies-equal-fraig-config-fix-1
  (implies (fraig-config-equiv x x-equiv)
           (equal (fraig-config-fix x)
                  (fraig-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fraig-config-fix-under-fraig-config-equiv

(defthm fraig-config-fix-under-fraig-config-equiv
  (fraig-config-equiv (fraig-config-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-fraig-config-fix-1-forward-to-fraig-config-equiv

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

Theorem: equal-of-fraig-config-fix-2-forward-to-fraig-config-equiv

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

Theorem: fraig-config-equiv-of-fraig-config-fix-1-forward

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

Theorem: fraig-config-equiv-of-fraig-config-fix-2-forward

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