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Svtv-assigns-override-config

Svtv-assigns-override-config-fix

Fixing function for svtv-assigns-override-config structures.

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

Definitions and Theorems

Function: svtv-assigns-override-config-fix$inline

(defun svtv-assigns-override-config-fix$inline (x)
 (declare (xargs :guard (svtv-assigns-override-config-p x)))
 (let ((__function__ 'svtv-assigns-override-config-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (case (svtv-assigns-override-config-kind x)
       (:omit (b* ((vars (svarlist-fix (std::da-nth 0 (cdr x)))))
                (cons :omit (list vars))))
       (:include (b* ((vars (svarlist-fix (std::da-nth 0 (cdr x)))))
                   (cons :include (list vars)))))
     :exec x)))

Theorem: svtv-assigns-override-config-p-of-svtv-assigns-override-config-fix

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

Theorem: svtv-assigns-override-config-fix-when-svtv-assigns-override-config-p

(defthm
 svtv-assigns-override-config-fix-when-svtv-assigns-override-config-p
 (implies (svtv-assigns-override-config-p x)
          (equal (svtv-assigns-override-config-fix x)
                 x)))

Function: svtv-assigns-override-config-equiv$inline

(defun svtv-assigns-override-config-equiv$inline (x y)
  (declare (xargs :guard (and (svtv-assigns-override-config-p x)
                              (svtv-assigns-override-config-p y))))
  (equal (svtv-assigns-override-config-fix x)
         (svtv-assigns-override-config-fix y)))

Theorem: svtv-assigns-override-config-equiv-is-an-equivalence

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

Theorem: svtv-assigns-override-config-equiv-implies-equal-svtv-assigns-override-config-fix-1

(defthm
 svtv-assigns-override-config-equiv-implies-equal-svtv-assigns-override-config-fix-1
 (implies (svtv-assigns-override-config-equiv x x-equiv)
          (equal (svtv-assigns-override-config-fix x)
                 (svtv-assigns-override-config-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: svtv-assigns-override-config-fix-under-svtv-assigns-override-config-equiv

(defthm
 svtv-assigns-override-config-fix-under-svtv-assigns-override-config-equiv
 (svtv-assigns-override-config-equiv
      (svtv-assigns-override-config-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svtv-assigns-override-config-fix-1-forward-to-svtv-assigns-override-config-equiv

(defthm
 equal-of-svtv-assigns-override-config-fix-1-forward-to-svtv-assigns-override-config-equiv
 (implies (equal (svtv-assigns-override-config-fix x)
                 y)
          (svtv-assigns-override-config-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-svtv-assigns-override-config-fix-2-forward-to-svtv-assigns-override-config-equiv

(defthm
 equal-of-svtv-assigns-override-config-fix-2-forward-to-svtv-assigns-override-config-equiv
 (implies (equal x (svtv-assigns-override-config-fix y))
          (svtv-assigns-override-config-equiv x y))
 :rule-classes :forward-chaining)

Theorem: svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-1-forward

(defthm
 svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-1-forward
 (implies (svtv-assigns-override-config-equiv
               (svtv-assigns-override-config-fix x)
               y)
          (svtv-assigns-override-config-equiv x y))
 :rule-classes :forward-chaining)

Theorem: svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-2-forward

(defthm
 svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-2-forward
 (implies (svtv-assigns-override-config-equiv
               x (svtv-assigns-override-config-fix y))
          (svtv-assigns-override-config-equiv x y))
 :rule-classes :forward-chaining)

Theorem: svtv-assigns-override-config-kind$inline-of-svtv-assigns-override-config-fix-x

(defthm
 svtv-assigns-override-config-kind$inline-of-svtv-assigns-override-config-fix-x
 (equal (svtv-assigns-override-config-kind$inline
             (svtv-assigns-override-config-fix x))
        (svtv-assigns-override-config-kind$inline x)))

Theorem: svtv-assigns-override-config-kind$inline-svtv-assigns-override-config-equiv-congruence-on-x

(defthm
 svtv-assigns-override-config-kind$inline-svtv-assigns-override-config-equiv-congruence-on-x
 (implies
      (svtv-assigns-override-config-equiv x x-equiv)
      (equal (svtv-assigns-override-config-kind$inline x)
             (svtv-assigns-override-config-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-svtv-assigns-override-config-fix

(defthm consp-of-svtv-assigns-override-config-fix
  (consp (svtv-assigns-override-config-fix x))
  :rule-classes :type-prescription)