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• Maybe-indname-result

Maybe-indname-result-fix

Fixing function for maybe-indname-result structures.

Signature

(maybe-indname-result-fix x) → new-x

Arguments

x — Guard (maybe-indname-result-p x).

Returns

new-x — Type (maybe-indname-result-p new-x).

Definitions and Theorems

Function: maybe-indname-result-fix$inline

(defun
   maybe-indname-result-fix$inline (x)
   (declare (xargs :guard (maybe-indname-result-p x)))
   (let ((__function__ 'maybe-indname-result-fix))
        (declare (ignorable __function__))
        (mbe :logic (cond ((not x) nil)
                          (t (b* ((fty::val (indname-result-fix x)))
                                 fty::val)))
             :exec x)))

Theorem: maybe-indname-result-p-of-maybe-indname-result-fix

(defthm maybe-indname-result-p-of-maybe-indname-result-fix
        (b* ((new-x (maybe-indname-result-fix$inline x)))
            (maybe-indname-result-p new-x))
        :rule-classes :rewrite)

Theorem: maybe-indname-result-fix-when-maybe-indname-result-p

(defthm maybe-indname-result-fix-when-maybe-indname-result-p
        (implies (maybe-indname-result-p x)
                 (equal (maybe-indname-result-fix x) x)))

Function: maybe-indname-result-equiv$inline

(defun maybe-indname-result-equiv$inline (x y)
       (declare (xargs :guard (and (maybe-indname-result-p x)
                                   (maybe-indname-result-p y))))
       (equal (maybe-indname-result-fix x)
              (maybe-indname-result-fix y)))

Theorem: maybe-indname-result-equiv-is-an-equivalence

(defthm maybe-indname-result-equiv-is-an-equivalence
        (and (booleanp (maybe-indname-result-equiv x y))
             (maybe-indname-result-equiv x x)
             (implies (maybe-indname-result-equiv x y)
                      (maybe-indname-result-equiv y x))
             (implies (and (maybe-indname-result-equiv x y)
                           (maybe-indname-result-equiv y z))
                      (maybe-indname-result-equiv x z)))
        :rule-classes (:equivalence))

Theorem: maybe-indname-result-equiv-implies-equal-maybe-indname-result-fix-1

(defthm
 maybe-indname-result-equiv-implies-equal-maybe-indname-result-fix-1
 (implies (maybe-indname-result-equiv x x-equiv)
          (equal (maybe-indname-result-fix x)
                 (maybe-indname-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: maybe-indname-result-fix-under-maybe-indname-result-equiv

(defthm maybe-indname-result-fix-under-maybe-indname-result-equiv
        (maybe-indname-result-equiv (maybe-indname-result-fix x)
                                    x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-maybe-indname-result-fix-1-forward-to-maybe-indname-result-equiv

(defthm
 equal-of-maybe-indname-result-fix-1-forward-to-maybe-indname-result-equiv
 (implies (equal (maybe-indname-result-fix x) y)
          (maybe-indname-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-maybe-indname-result-fix-2-forward-to-maybe-indname-result-equiv

(defthm
 equal-of-maybe-indname-result-fix-2-forward-to-maybe-indname-result-equiv
 (implies (equal x (maybe-indname-result-fix y))
          (maybe-indname-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: maybe-indname-result-equiv-of-maybe-indname-result-fix-1-forward

(defthm
   maybe-indname-result-equiv-of-maybe-indname-result-fix-1-forward
   (implies (maybe-indname-result-equiv (maybe-indname-result-fix x)
                                        y)
            (maybe-indname-result-equiv x y))
   :rule-classes :forward-chaining)

Theorem: maybe-indname-result-equiv-of-maybe-indname-result-fix-2-forward

(defthm
    maybe-indname-result-equiv-of-maybe-indname-result-fix-2-forward
    (implies
         (maybe-indname-result-equiv x (maybe-indname-result-fix y))
         (maybe-indname-result-equiv x y))
    :rule-classes :forward-chaining)