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• Valuemap+denv-result

Valuemap+denv-result-fix

Fixing function for valuemap+denv-result structures.

Signature

(valuemap+denv-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (valuemap+denv-resultp acl2::x).

Returns

new-x — Type (valuemap+denv-resultp new-x).

Definitions and Theorems

Function: valuemap+denv-result-fix$inline

(defun valuemap+denv-result-fix$inline (acl2::x)
  (declare (xargs :guard (valuemap+denv-resultp acl2::x)))
  (let ((__function__ 'valuemap+denv-result-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (valuemap+denv-result-kind acl2::x)
           (:ok (b* ((get (valuemap+denv-fix acl2::x)))
                  get))
           (:err (b* ((get (fty::reserr-fix acl2::x)))
                   get)))
         :exec acl2::x)))

Theorem: valuemap+denv-resultp-of-valuemap+denv-result-fix

(defthm valuemap+denv-resultp-of-valuemap+denv-result-fix
  (b* ((new-x (valuemap+denv-result-fix$inline acl2::x)))
    (valuemap+denv-resultp new-x))
  :rule-classes :rewrite)

Theorem: valuemap+denv-result-fix-when-valuemap+denv-resultp

(defthm valuemap+denv-result-fix-when-valuemap+denv-resultp
  (implies (valuemap+denv-resultp acl2::x)
           (equal (valuemap+denv-result-fix acl2::x)
                  acl2::x)))

Function: valuemap+denv-result-equiv$inline

(defun valuemap+denv-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (valuemap+denv-resultp acl2::x)
                              (valuemap+denv-resultp acl2::y))))
  (equal (valuemap+denv-result-fix acl2::x)
         (valuemap+denv-result-fix acl2::y)))

Theorem: valuemap+denv-result-equiv-is-an-equivalence

(defthm valuemap+denv-result-equiv-is-an-equivalence
  (and (booleanp (valuemap+denv-result-equiv x y))
       (valuemap+denv-result-equiv x x)
       (implies (valuemap+denv-result-equiv x y)
                (valuemap+denv-result-equiv y x))
       (implies (and (valuemap+denv-result-equiv x y)
                     (valuemap+denv-result-equiv y z))
                (valuemap+denv-result-equiv x z)))
  :rule-classes (:equivalence))

Theorem: valuemap+denv-result-equiv-implies-equal-valuemap+denv-result-fix-1

(defthm
 valuemap+denv-result-equiv-implies-equal-valuemap+denv-result-fix-1
 (implies (valuemap+denv-result-equiv acl2::x x-equiv)
          (equal (valuemap+denv-result-fix acl2::x)
                 (valuemap+denv-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: valuemap+denv-result-fix-under-valuemap+denv-result-equiv

(defthm valuemap+denv-result-fix-under-valuemap+denv-result-equiv
  (valuemap+denv-result-equiv (valuemap+denv-result-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-valuemap+denv-result-fix-1-forward-to-valuemap+denv-result-equiv

(defthm
 equal-of-valuemap+denv-result-fix-1-forward-to-valuemap+denv-result-equiv
 (implies (equal (valuemap+denv-result-fix acl2::x)
                 acl2::y)
          (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-valuemap+denv-result-fix-2-forward-to-valuemap+denv-result-equiv

(defthm
 equal-of-valuemap+denv-result-fix-2-forward-to-valuemap+denv-result-equiv
 (implies (equal acl2::x
                 (valuemap+denv-result-fix acl2::y))
          (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: valuemap+denv-result-equiv-of-valuemap+denv-result-fix-1-forward

(defthm
   valuemap+denv-result-equiv-of-valuemap+denv-result-fix-1-forward
 (implies
      (valuemap+denv-result-equiv (valuemap+denv-result-fix acl2::x)
                                  acl2::y)
      (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: valuemap+denv-result-equiv-of-valuemap+denv-result-fix-2-forward

(defthm
   valuemap+denv-result-equiv-of-valuemap+denv-result-fix-2-forward
 (implies
     (valuemap+denv-result-equiv acl2::x
                                 (valuemap+denv-result-fix acl2::y))
     (valuemap+denv-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: valuemap+denv-result-kind$inline-of-valuemap+denv-result-fix-x

(defthm
     valuemap+denv-result-kind$inline-of-valuemap+denv-result-fix-x
  (equal (valuemap+denv-result-kind$inline
              (valuemap+denv-result-fix acl2::x))
         (valuemap+denv-result-kind$inline acl2::x)))

Theorem: valuemap+denv-result-kind$inline-valuemap+denv-result-equiv-congruence-on-x

(defthm
 valuemap+denv-result-kind$inline-valuemap+denv-result-equiv-congruence-on-x
 (implies (valuemap+denv-result-equiv acl2::x x-equiv)
          (equal (valuemap+denv-result-kind$inline acl2::x)
                 (valuemap+denv-result-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-valuemap+denv-result-fix

(defthm consp-of-valuemap+denv-result-fix
  (consp (valuemap+denv-result-fix acl2::x))
  :rule-classes :type-prescription)