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Svex-substconfig

Svex-substconfig-fix

Fixing function for svex-substconfig structures.

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

Definitions and Theorems

Function: svex-substconfig-fix$inline

(defun svex-substconfig-fix$inline (x)
  (declare (xargs :guard (svex-substconfig-p x)))
  (let ((__function__ 'svex-substconfig-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((alist (svex-alist-fix (std::prod-car x)))
              (simp (svex-simpconfig-fix (std::prod-cdr x))))
           (std::prod-cons alist simp))
         :exec x)))

Theorem: svex-substconfig-p-of-svex-substconfig-fix

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

Theorem: svex-substconfig-fix-when-svex-substconfig-p

(defthm svex-substconfig-fix-when-svex-substconfig-p
  (implies (svex-substconfig-p x)
           (equal (svex-substconfig-fix x) x)))

Function: svex-substconfig-equiv$inline

(defun svex-substconfig-equiv$inline (x y)
  (declare (xargs :guard (and (svex-substconfig-p x)
                              (svex-substconfig-p y))))
  (equal (svex-substconfig-fix x)
         (svex-substconfig-fix y)))

Theorem: svex-substconfig-equiv-is-an-equivalence

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

Theorem: svex-substconfig-equiv-implies-equal-svex-substconfig-fix-1

(defthm svex-substconfig-equiv-implies-equal-svex-substconfig-fix-1
  (implies (svex-substconfig-equiv x x-equiv)
           (equal (svex-substconfig-fix x)
                  (svex-substconfig-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svex-substconfig-fix-under-svex-substconfig-equiv

(defthm svex-substconfig-fix-under-svex-substconfig-equiv
  (svex-substconfig-equiv (svex-substconfig-fix x)
                          x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svex-substconfig-fix-1-forward-to-svex-substconfig-equiv

(defthm
  equal-of-svex-substconfig-fix-1-forward-to-svex-substconfig-equiv
  (implies (equal (svex-substconfig-fix x) y)
           (svex-substconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-svex-substconfig-fix-2-forward-to-svex-substconfig-equiv

(defthm
  equal-of-svex-substconfig-fix-2-forward-to-svex-substconfig-equiv
  (implies (equal x (svex-substconfig-fix y))
           (svex-substconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svex-substconfig-equiv-of-svex-substconfig-fix-1-forward

(defthm svex-substconfig-equiv-of-svex-substconfig-fix-1-forward
  (implies (svex-substconfig-equiv (svex-substconfig-fix x)
                                   y)
           (svex-substconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svex-substconfig-equiv-of-svex-substconfig-fix-2-forward

(defthm svex-substconfig-equiv-of-svex-substconfig-fix-2-forward
  (implies (svex-substconfig-equiv x (svex-substconfig-fix y))
           (svex-substconfig-equiv x y))
  :rule-classes :forward-chaining)