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• Svtv-condoverride

Svtv-condoverride-fix

Fixing function for svtv-condoverride structures.

Signature

(svtv-condoverride-fix x) → new-x

Arguments

x — Guard (svtv-condoverride-p x).

Returns

new-x — Type (svtv-condoverride-p new-x).

Definitions and Theorems

Function: svtv-condoverride-fix$inline

(defun svtv-condoverride-fix$inline (x)
  (declare (xargs :guard (svtv-condoverride-p x)))
  (let ((__function__ 'svtv-condoverride-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((value (svtv-baseentry-fix (std::da-nth 0 x)))
              (test (svtv-baseentry-fix (std::da-nth 1 x))))
           (list value test))
         :exec x)))

Theorem: svtv-condoverride-p-of-svtv-condoverride-fix

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

Theorem: svtv-condoverride-fix-when-svtv-condoverride-p

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

Function: svtv-condoverride-equiv$inline

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

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

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

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

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

Theorem: svtv-condoverride-fix-under-svtv-condoverride-equiv

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

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

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

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

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

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

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

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

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