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• Vcscope-dinfo-option

Vcscope-dinfo-option-fix

Fixing function for vcscope-dinfo-option structures.

Signature

(vcscope-dinfo-option-fix x) → new-x

Arguments

x — Guard (vcscope-dinfo-optionp x).

Returns

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

Definitions and Theorems

Function: vcscope-dinfo-option-fix$inline

(defun vcscope-dinfo-option-fix$inline (x)
 (declare (xargs :guard (vcscope-dinfo-optionp x)))
 (let ((__function__ 'vcscope-dinfo-option-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (vcscope-dinfo-option-kind x)
      (:some (b* ((get (vcscope-dinfo-fix (std::da-nth 0 (cdr x)))))
               (cons :some (list get))))
      (:none (cons :none (list))))
    :exec x)))

Theorem: vcscope-dinfo-optionp-of-vcscope-dinfo-option-fix

(defthm vcscope-dinfo-optionp-of-vcscope-dinfo-option-fix
  (b* ((new-x (vcscope-dinfo-option-fix$inline x)))
    (vcscope-dinfo-optionp new-x))
  :rule-classes :rewrite)

Theorem: vcscope-dinfo-option-fix-when-vcscope-dinfo-optionp

(defthm vcscope-dinfo-option-fix-when-vcscope-dinfo-optionp
  (implies (vcscope-dinfo-optionp x)
           (equal (vcscope-dinfo-option-fix x) x)))

Function: vcscope-dinfo-option-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm
     vcscope-dinfo-option-kind$inline-of-vcscope-dinfo-option-fix-x
 (equal
     (vcscope-dinfo-option-kind$inline (vcscope-dinfo-option-fix x))
     (vcscope-dinfo-option-kind$inline x)))

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

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

Theorem: consp-of-vcscope-dinfo-option-fix

(defthm consp-of-vcscope-dinfo-option-fix
  (consp (vcscope-dinfo-option-fix x))
  :rule-classes :type-prescription)