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• Svtv-line

Svtv-line-fix

Fixing function for svtv-line structures.

Signature

(svtv-line-fix x) → new-x

Arguments

x — Guard (svtv-line-p x).

Returns

new-x — Type (svtv-line-p new-x).

Definitions and Theorems

Function: svtv-line-fix$inline

(defun svtv-line-fix$inline (x)
  (declare (xargs :guard (svtv-line-p x)))
  (let ((__function__ 'svtv-line-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((lhs (lhs-fix (std::prod-car x)))
              (entries (svtv-entrylist-fix (std::prod-cdr x))))
           (std::prod-cons lhs entries))
         :exec x)))

Theorem: svtv-line-p-of-svtv-line-fix

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

Theorem: svtv-line-fix-when-svtv-line-p

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

Function: svtv-line-equiv$inline

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

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

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

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

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

Theorem: svtv-line-fix-under-svtv-line-equiv

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

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

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

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

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

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

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

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

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