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Svtv-composedata

Svtv-composedata-fix

Fixing function for svtv-composedata structures.

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

Definitions and Theorems

Function: svtv-composedata-fix$inline

(defun svtv-composedata-fix$inline (x)
 (declare (xargs :guard (svtv-composedata-p x)))
 (let ((__function__ 'svtv-composedata-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((simp (svex-simpconfig-fix (std::prod-car x)))
       (nextstates
            (svex-alistlist-fix (std::prod-car (std::prod-cdr x))))
       (input-substs
            (svex-alistlist-fix (std::prod-cdr (std::prod-cdr x)))))
      (std::prod-cons simp
                      (std::prod-cons nextstates input-substs)))
    :exec x)))

Theorem: svtv-composedata-p-of-svtv-composedata-fix

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

Theorem: svtv-composedata-fix-when-svtv-composedata-p

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

Function: svtv-composedata-equiv$inline

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

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

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

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

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

Theorem: svtv-composedata-fix-under-svtv-composedata-equiv

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

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

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

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

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

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

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

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

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