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• Vcscope-dinfo-result

Vcscope-dinfo-result-fix

Fixing function for vcscope-dinfo-result structures.

Signature

(vcscope-dinfo-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (vcscope-dinfo-resultp acl2::x).

Returns

new-x — Type (vcscope-dinfo-resultp new-x).

Definitions and Theorems

Function: vcscope-dinfo-result-fix$inline

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

Theorem: vcscope-dinfo-resultp-of-vcscope-dinfo-result-fix

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

Theorem: vcscope-dinfo-result-fix-when-vcscope-dinfo-resultp

(defthm vcscope-dinfo-result-fix-when-vcscope-dinfo-resultp
  (implies (vcscope-dinfo-resultp acl2::x)
           (equal (vcscope-dinfo-result-fix acl2::x)
                  acl2::x)))

Function: vcscope-dinfo-result-equiv$inline

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

Theorem: vcscope-dinfo-result-equiv-is-an-equivalence

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

Theorem: vcscope-dinfo-result-equiv-implies-equal-vcscope-dinfo-result-fix-1

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

Theorem: vcscope-dinfo-result-fix-under-vcscope-dinfo-result-equiv

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

Theorem: equal-of-vcscope-dinfo-result-fix-1-forward-to-vcscope-dinfo-result-equiv

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

Theorem: equal-of-vcscope-dinfo-result-fix-2-forward-to-vcscope-dinfo-result-equiv

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

Theorem: vcscope-dinfo-result-equiv-of-vcscope-dinfo-result-fix-1-forward

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

Theorem: vcscope-dinfo-result-equiv-of-vcscope-dinfo-result-fix-2-forward

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

Theorem: vcscope-dinfo-result-kind$inline-of-vcscope-dinfo-result-fix-x

(defthm
     vcscope-dinfo-result-kind$inline-of-vcscope-dinfo-result-fix-x
  (equal (vcscope-dinfo-result-kind$inline
              (vcscope-dinfo-result-fix acl2::x))
         (vcscope-dinfo-result-kind$inline acl2::x)))

Theorem: vcscope-dinfo-result-kind$inline-vcscope-dinfo-result-equiv-congruence-on-x

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