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• Output-expression-result

Output-expression-result-fix

Fixing function for output-expression-result structures.

Signature

(output-expression-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (output-expression-resultp acl2::x).

Returns

new-x — Type (output-expression-resultp new-x).

Definitions and Theorems

Function: output-expression-result-fix$inline

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

Theorem: output-expression-resultp-of-output-expression-result-fix

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

Theorem: output-expression-result-fix-when-output-expression-resultp

(defthm output-expression-result-fix-when-output-expression-resultp
  (implies (output-expression-resultp acl2::x)
           (equal (output-expression-result-fix acl2::x)
                  acl2::x)))

Function: output-expression-result-equiv$inline

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

Theorem: output-expression-result-equiv-is-an-equivalence

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

Theorem: output-expression-result-equiv-implies-equal-output-expression-result-fix-1

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

Theorem: output-expression-result-fix-under-output-expression-result-equiv

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

Theorem: equal-of-output-expression-result-fix-1-forward-to-output-expression-result-equiv

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

Theorem: equal-of-output-expression-result-fix-2-forward-to-output-expression-result-equiv

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

Theorem: output-expression-result-equiv-of-output-expression-result-fix-1-forward

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

Theorem: output-expression-result-equiv-of-output-expression-result-fix-2-forward

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

Theorem: output-expression-result-kind$inline-of-output-expression-result-fix-x

(defthm
 output-expression-result-kind$inline-of-output-expression-result-fix-x
 (equal (output-expression-result-kind$inline
             (output-expression-result-fix acl2::x))
        (output-expression-result-kind$inline acl2::x)))

Theorem: output-expression-result-kind$inline-output-expression-result-equiv-congruence-on-x

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

Theorem: consp-of-output-expression-result-fix

(defthm consp-of-output-expression-result-fix
  (consp (output-expression-result-fix acl2::x))
  :rule-classes :type-prescription)