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• Lhprobe/4vec-p

Lhprobe/4vec-fix

Fixing function for lhprobe/4vec type

Signature

(lhprobe/4vec-fix x) → new-x

Arguments

x — Guard (lhprobe/4vec-p x).

Returns

new-x — Type (lhprobe/4vec-p new-x).

Definitions and Theorems

Function: lhprobe/4vec-fix

(defun lhprobe/4vec-fix (x)
  (declare (xargs :guard (lhprobe/4vec-p x)))
  (let ((__function__ 'lhprobe/4vec-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (eq (lhprobe/4vec-kind x) :4vec)
             (4vec-fix x)
           (lhprobe-fix x))
         :exec x)))

Theorem: lhprobe/4vec-p-of-lhprobe/4vec-fix

(defthm lhprobe/4vec-p-of-lhprobe/4vec-fix
  (b* ((new-x (lhprobe/4vec-fix x)))
    (lhprobe/4vec-p new-x))
  :rule-classes :rewrite)

Theorem: lhprobe/4vec-fix-when-lhprobe/4vec-p

(defthm lhprobe/4vec-fix-when-lhprobe/4vec-p
  (implies (lhprobe/4vec-p x)
           (equal (lhprobe/4vec-fix x) x)))

Function: lhprobe/4vec-equiv$inline

(defun lhprobe/4vec-equiv$inline (x y)
  (declare (xargs :guard (and (lhprobe/4vec-p x)
                              (lhprobe/4vec-p y))))
  (equal (lhprobe/4vec-fix x)
         (lhprobe/4vec-fix y)))

Theorem: lhprobe/4vec-equiv-is-an-equivalence

(defthm lhprobe/4vec-equiv-is-an-equivalence
  (and (booleanp (lhprobe/4vec-equiv x y))
       (lhprobe/4vec-equiv x x)
       (implies (lhprobe/4vec-equiv x y)
                (lhprobe/4vec-equiv y x))
       (implies (and (lhprobe/4vec-equiv x y)
                     (lhprobe/4vec-equiv y z))
                (lhprobe/4vec-equiv x z)))
  :rule-classes (:equivalence))

Theorem: lhprobe/4vec-equiv-implies-equal-lhprobe/4vec-fix-1

(defthm lhprobe/4vec-equiv-implies-equal-lhprobe/4vec-fix-1
  (implies (lhprobe/4vec-equiv x x-equiv)
           (equal (lhprobe/4vec-fix x)
                  (lhprobe/4vec-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: lhprobe/4vec-fix-under-lhprobe/4vec-equiv

(defthm lhprobe/4vec-fix-under-lhprobe/4vec-equiv
  (lhprobe/4vec-equiv (lhprobe/4vec-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: lhprobe/4vec-fix-when-kind-is-4vec

(defthm lhprobe/4vec-fix-when-kind-is-4vec
  (implies (equal (lhprobe/4vec-kind x) :4vec)
           (equal (lhprobe/4vec-fix x)
                  (4vec-fix x))))

Theorem: lhprobe/4vec-fix-when-kind-is-lhprobe

(defthm lhprobe/4vec-fix-when-kind-is-lhprobe
  (implies (equal (lhprobe/4vec-kind x) :lhprobe)
           (equal (lhprobe/4vec-fix x)
                  (lhprobe-fix x))))

Theorem: lhprobe/4vec-kind-of-lhprobe/4vec-fix-x

(defthm lhprobe/4vec-kind-of-lhprobe/4vec-fix-x
  (equal (lhprobe/4vec-kind (lhprobe/4vec-fix x))
         (lhprobe/4vec-kind x)))

Theorem: lhprobe/4vec-kind-lhprobe/4vec-equiv-congruence-on-x

(defthm lhprobe/4vec-kind-lhprobe/4vec-equiv-congruence-on-x
  (implies (lhprobe/4vec-equiv x x-equiv)
           (equal (lhprobe/4vec-kind x)
                  (lhprobe/4vec-kind x-equiv)))
  :rule-classes :congruence)