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Vcscope-dinfo

Vcscope-dinfo-fix

(vcscope-dinfo-fix x) is a usual ACL2::fty omap fixing function.

Signature
(vcscope-dinfo-fix x) → *
Arguments: x — Guard (vcscope-dinfop x).

Definitions and Theorems

Function: vcscope-dinfo-fix

(defun vcscope-dinfo-fix (x)
  (declare (xargs :guard (vcscope-dinfop x)))
  (mbe :logic (if (vcscope-dinfop x) x nil)
       :exec x))

Theorem: vcscope-dinfop-of-vcscope-dinfo-fix

(defthm vcscope-dinfop-of-vcscope-dinfo-fix
  (vcscope-dinfop (vcscope-dinfo-fix x)))

Theorem: vcscope-dinfo-fix-when-vcscope-dinfop

(defthm vcscope-dinfo-fix-when-vcscope-dinfop
  (implies (vcscope-dinfop x)
           (equal (vcscope-dinfo-fix x) x)))

Theorem: emptyp-vcscope-dinfo-fix

(defthm emptyp-vcscope-dinfo-fix
  (implies (or (omap::emptyp x)
               (not (vcscope-dinfop x)))
           (omap::emptyp (vcscope-dinfo-fix x))))

Theorem: emptyp-of-vcscope-dinfo-fix-to-not-vcscope-dinfo-or-emptyp

(defthm emptyp-of-vcscope-dinfo-fix-to-not-vcscope-dinfo-or-emptyp
  (equal (omap::emptyp (vcscope-dinfo-fix x))
         (or (not (vcscope-dinfop x))
             (omap::emptyp x))))

Function: vcscope-dinfo-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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