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• Repeat-range

Repeat-range-fix

Fixing function for repeat-range structures.

Signature

(repeat-range-fix x) → new-x

Arguments

x — Guard (repeat-rangep x).

Returns

new-x — Type (repeat-rangep new-x).

Definitions and Theorems

Function: repeat-range-fix$inline

(defun repeat-range-fix$inline (x)
  (declare (xargs :guard (repeat-rangep x)))
  (let ((__function__ 'repeat-range-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((min (nfix (std::da-nth 0 (cdr x))))
              (max (acl2::nati-fix (std::da-nth 1 (cdr x)))))
           (cons :repeat (list min max)))
         :exec x)))

Theorem: repeat-rangep-of-repeat-range-fix

(defthm repeat-rangep-of-repeat-range-fix
  (b* ((new-x (repeat-range-fix$inline x)))
    (repeat-rangep new-x))
  :rule-classes :rewrite)

Theorem: repeat-range-fix-when-repeat-rangep

(defthm repeat-range-fix-when-repeat-rangep
  (implies (repeat-rangep x)
           (equal (repeat-range-fix x) x)))

Function: repeat-range-equiv$inline

(defun repeat-range-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (repeat-rangep acl2::x)
                              (repeat-rangep acl2::y))))
  (equal (repeat-range-fix acl2::x)
         (repeat-range-fix acl2::y)))

Theorem: repeat-range-equiv-is-an-equivalence

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

Theorem: repeat-range-equiv-implies-equal-repeat-range-fix-1

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

Theorem: repeat-range-fix-under-repeat-range-equiv

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

Theorem: equal-of-repeat-range-fix-1-forward-to-repeat-range-equiv

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

Theorem: equal-of-repeat-range-fix-2-forward-to-repeat-range-equiv

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

Theorem: repeat-range-equiv-of-repeat-range-fix-1-forward

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

Theorem: repeat-range-equiv-of-repeat-range-fix-2-forward

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