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• Fun-env-result

Fun-env-result-fix

Fixing function for fun-env-result structures.

Signature

(fun-env-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (fun-env-resultp acl2::x).

Returns

new-x — Type (fun-env-resultp new-x).

Definitions and Theorems

Function: fun-env-result-fix$inline

(defun fun-env-result-fix$inline (acl2::x)
  (declare (xargs :guard (fun-env-resultp acl2::x)))
  (mbe :logic
       (case (fun-env-result-kind acl2::x)
         (:ok (b* ((get (fun-env-fix acl2::x))) get))
         (:err (b* ((get (fty::reserr-fix acl2::x)))
                 get)))
       :exec acl2::x))

Theorem: fun-env-resultp-of-fun-env-result-fix

(defthm fun-env-resultp-of-fun-env-result-fix
  (b* ((new-x (fun-env-result-fix$inline acl2::x)))
    (fun-env-resultp new-x))
  :rule-classes :rewrite)

Theorem: fun-env-result-fix-when-fun-env-resultp

(defthm fun-env-result-fix-when-fun-env-resultp
  (implies (fun-env-resultp acl2::x)
           (equal (fun-env-result-fix acl2::x)
                  acl2::x)))

Function: fun-env-result-equiv$inline

(defun fun-env-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (fun-env-resultp acl2::x)
                              (fun-env-resultp acl2::y))))
  (equal (fun-env-result-fix acl2::x)
         (fun-env-result-fix acl2::y)))

Theorem: fun-env-result-equiv-is-an-equivalence

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

Theorem: fun-env-result-equiv-implies-equal-fun-env-result-fix-1

(defthm fun-env-result-equiv-implies-equal-fun-env-result-fix-1
  (implies (fun-env-result-equiv acl2::x x-equiv)
           (equal (fun-env-result-fix acl2::x)
                  (fun-env-result-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: fun-env-result-fix-under-fun-env-result-equiv

(defthm fun-env-result-fix-under-fun-env-result-equiv
  (fun-env-result-equiv (fun-env-result-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-fun-env-result-fix-1-forward-to-fun-env-result-equiv

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

Theorem: equal-of-fun-env-result-fix-2-forward-to-fun-env-result-equiv

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

Theorem: fun-env-result-equiv-of-fun-env-result-fix-1-forward

(defthm fun-env-result-equiv-of-fun-env-result-fix-1-forward
  (implies (fun-env-result-equiv (fun-env-result-fix acl2::x)
                                 acl2::y)
           (fun-env-result-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: fun-env-result-equiv-of-fun-env-result-fix-2-forward

(defthm fun-env-result-equiv-of-fun-env-result-fix-2-forward
  (implies
       (fun-env-result-equiv acl2::x (fun-env-result-fix acl2::y))
       (fun-env-result-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: fun-env-result-kind$inline-of-fun-env-result-fix-x

(defthm fun-env-result-kind$inline-of-fun-env-result-fix-x
  (equal (fun-env-result-kind$inline (fun-env-result-fix acl2::x))
         (fun-env-result-kind$inline acl2::x)))

Theorem: fun-env-result-kind$inline-fun-env-result-equiv-congruence-on-x

(defthm
    fun-env-result-kind$inline-fun-env-result-equiv-congruence-on-x
  (implies (fun-env-result-equiv acl2::x x-equiv)
           (equal (fun-env-result-kind$inline acl2::x)
                  (fun-env-result-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: fun-env-result-fix$inline-of-fun-env-result-fix-x

(defthm fun-env-result-fix$inline-of-fun-env-result-fix-x
  (equal (fun-env-result-fix$inline (fun-env-result-fix acl2::x))
         (fun-env-result-fix$inline acl2::x)))

Theorem: fun-env-result-fix$inline-fun-env-result-equiv-congruence-on-x

(defthm
     fun-env-result-fix$inline-fun-env-result-equiv-congruence-on-x
  (implies (fun-env-result-equiv acl2::x x-equiv)
           (equal (fun-env-result-fix$inline acl2::x)
                  (fun-env-result-fix$inline x-equiv)))
  :rule-classes :congruence)