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Svtv-fsm

Svtv-fsm-fix

Fixing function for svtv-fsm structures.

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

Definitions and Theorems

Function: svtv-fsm-fix$inline

(defun svtv-fsm-fix$inline (x)
 (declare (xargs :guard (svtv-fsm-p x)))
 (let ((__function__ 'svtv-fsm-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((fsm (fsm-fix (cdr (std::da-nth 0 x))))
          (namemap (svtv-name-lhs-map-fix (cdr (std::da-nth 1 x)))))
       (list (cons 'fsm fsm)
             (cons 'namemap namemap)))
     :exec x)))

Theorem: svtv-fsm-p-of-svtv-fsm-fix

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

Theorem: svtv-fsm-fix-when-svtv-fsm-p

(defthm svtv-fsm-fix-when-svtv-fsm-p
  (implies (svtv-fsm-p x)
           (equal (svtv-fsm-fix x) x)))

Function: svtv-fsm-equiv$inline

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

Theorem: svtv-fsm-equiv-is-an-equivalence

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

Theorem: svtv-fsm-equiv-implies-equal-svtv-fsm-fix-1

(defthm svtv-fsm-equiv-implies-equal-svtv-fsm-fix-1
  (implies (svtv-fsm-equiv x x-equiv)
           (equal (svtv-fsm-fix x)
                  (svtv-fsm-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svtv-fsm-fix-under-svtv-fsm-equiv

(defthm svtv-fsm-fix-under-svtv-fsm-equiv
  (svtv-fsm-equiv (svtv-fsm-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svtv-fsm-fix-1-forward-to-svtv-fsm-equiv

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

Theorem: equal-of-svtv-fsm-fix-2-forward-to-svtv-fsm-equiv

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

Theorem: svtv-fsm-equiv-of-svtv-fsm-fix-1-forward

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

Theorem: svtv-fsm-equiv-of-svtv-fsm-fix-2-forward

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