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Binary-info

Binary-info-fix

Fixing function for binary-info structures.

Signature
(binary-info-fix x) → new-x
Arguments: x — Guard (binary-infop x).
Returns: new-x — Type (binary-infop new-x).

Definitions and Theorems

Function: binary-info-fix$inline

(defun binary-info-fix$inline (x)
  (declare (xargs :guard (binary-infop x)))
  (let ((__function__ 'binary-info-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((type (type-fix (cdr (std::da-nth 0 x))))
              (table (valid-table-fix (cdr (std::da-nth 1 x)))
))
           (list (cons 'type type)
                 (cons 'table table)))
         :exec x)))

Theorem: binary-infop-of-binary-info-fix

(defthm binary-infop-of-binary-info-fix
  (b* ((new-x (binary-info-fix$inline x)))
    (binary-infop new-x))
  :rule-classes :rewrite)

Theorem: binary-info-fix-when-binary-infop

(defthm binary-info-fix-when-binary-infop
  (implies (binary-infop x)
           (equal (binary-info-fix x) x)))

Function: binary-info-equiv$inline

(defun binary-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (binary-infop acl2::x)
                              (binary-infop acl2::y))))
  (equal (binary-info-fix acl2::x)
         (binary-info-fix acl2::y)))

Theorem: binary-info-equiv-is-an-equivalence

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

Theorem: binary-info-equiv-implies-equal-binary-info-fix-1

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

Theorem: binary-info-fix-under-binary-info-equiv

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

Theorem: equal-of-binary-info-fix-1-forward-to-binary-info-equiv

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

Theorem: equal-of-binary-info-fix-2-forward-to-binary-info-equiv

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

Theorem: binary-info-equiv-of-binary-info-fix-1-forward

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

Theorem: binary-info-equiv-of-binary-info-fix-2-forward

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