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Iconst-base

Iconst-base-fix

Fixing function for iconst-base structures.

Signature
(iconst-base-fix x) → new-x
Arguments: x — Guard (iconst-basep x).
Returns: new-x — Type (iconst-basep new-x).

Definitions and Theorems

Function: iconst-base-fix$inline

(defun iconst-base-fix$inline (x)
  (declare (xargs :guard (iconst-basep x)))
  (let ((__function__ 'iconst-base-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (iconst-base-kind x)
           (:dec (cons :dec (list)))
           (:oct (cons :oct (list)))
           (:hex (cons :hex (list))))
         :exec x)))

Theorem: iconst-basep-of-iconst-base-fix

(defthm iconst-basep-of-iconst-base-fix
  (b* ((new-x (iconst-base-fix$inline x)))
    (iconst-basep new-x))
  :rule-classes :rewrite)

Theorem: iconst-base-fix-when-iconst-basep

(defthm iconst-base-fix-when-iconst-basep
  (implies (iconst-basep x)
           (equal (iconst-base-fix x) x)))

Function: iconst-base-equiv$inline

(defun iconst-base-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (iconst-basep acl2::x)
                              (iconst-basep acl2::y))))
  (equal (iconst-base-fix acl2::x)
         (iconst-base-fix acl2::y)))

Theorem: iconst-base-equiv-is-an-equivalence

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

Theorem: iconst-base-equiv-implies-equal-iconst-base-fix-1

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

Theorem: iconst-base-fix-under-iconst-base-equiv

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

Theorem: equal-of-iconst-base-fix-1-forward-to-iconst-base-equiv

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

Theorem: equal-of-iconst-base-fix-2-forward-to-iconst-base-equiv

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

Theorem: iconst-base-equiv-of-iconst-base-fix-1-forward

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

Theorem: iconst-base-equiv-of-iconst-base-fix-2-forward

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

Theorem: iconst-base-kind$inline-of-iconst-base-fix-x

(defthm iconst-base-kind$inline-of-iconst-base-fix-x
  (equal (iconst-base-kind$inline (iconst-base-fix x))
         (iconst-base-kind$inline x)))

Theorem: iconst-base-kind$inline-iconst-base-equiv-congruence-on-x

(defthm iconst-base-kind$inline-iconst-base-equiv-congruence-on-x
  (implies (iconst-base-equiv x x-equiv)
           (equal (iconst-base-kind$inline x)
                  (iconst-base-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-iconst-base-fix

(defthm consp-of-iconst-base-fix
  (consp (iconst-base-fix x))
  :rule-classes :type-prescription)