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Svtv-baseentry-fix

Signature

(svtv-baseentry-fix x) → xx

Arguments

x — Guard (svtv-baseentry-p x).

Returns

xx — Type (svtv-baseentry-p xx).

Definitions and Theorems

Function: svtv-baseentry-fix

(defun svtv-baseentry-fix (x)
  (declare (xargs :guard (svtv-baseentry-p x)))
  (let ((__function__ 'svtv-baseentry-fix))
    (declare (ignorable __function__))
    (mbe :logic (if (svtv-baseentry-p x) x (4vec-x))
         :exec x)))

Theorem: svtv-baseentry-p-of-svtv-baseentry-fix

(defthm svtv-baseentry-p-of-svtv-baseentry-fix
  (b* ((xx (svtv-baseentry-fix x)))
    (svtv-baseentry-p xx))
  :rule-classes :rewrite)

Theorem: svtv-baseentry-fix-of-svtv-baseentry-p

(defthm svtv-baseentry-fix-of-svtv-baseentry-p
  (implies (svtv-baseentry-p x)
           (equal (svtv-baseentry-fix x) x)))

Function: svtv-baseentry-equiv$inline

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

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

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

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

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

Theorem: svtv-baseentry-fix-under-svtv-baseentry-equiv

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

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

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

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

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

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

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

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

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