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• Funscope

Funscope-fix

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

Signature

(funscope-fix x) → *

Arguments

x — Guard (funscopep x).

Definitions and Theorems

Function: funscope-fix

(defun funscope-fix (x)
  (declare (xargs :guard (funscopep x)))
  (mbe :logic (if (funscopep x) x nil)
       :exec x))

Theorem: funscopep-of-funscope-fix

(defthm funscopep-of-funscope-fix
  (funscopep (funscope-fix x)))

Theorem: funscope-fix-when-funscopep

(defthm funscope-fix-when-funscopep
  (implies (funscopep x)
           (equal (funscope-fix x) x)))

Theorem: emptyp-funscope-fix

(defthm emptyp-funscope-fix
  (implies (or (omap::emptyp x)
               (not (funscopep x)))
           (omap::emptyp (funscope-fix x))))

Theorem: emptyp-of-funscope-fix-to-not-funscope-or-emptyp

(defthm emptyp-of-funscope-fix-to-not-funscope-or-emptyp
  (equal (omap::emptyp (funscope-fix x))
         (or (not (funscopep x))
             (omap::emptyp x))))

Function: funscope-equiv$inline

(defun funscope-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (funscopep acl2::x)
                              (funscopep acl2::y))))
  (equal (funscope-fix acl2::x)
         (funscope-fix acl2::y)))

Theorem: funscope-equiv-is-an-equivalence

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

Theorem: funscope-equiv-implies-equal-funscope-fix-1

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

Theorem: funscope-fix-under-funscope-equiv

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

Theorem: equal-of-funscope-fix-1-forward-to-funscope-equiv

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

Theorem: equal-of-funscope-fix-2-forward-to-funscope-equiv

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

Theorem: funscope-equiv-of-funscope-fix-1-forward

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

Theorem: funscope-equiv-of-funscope-fix-2-forward

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