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Block

Block-fix

Fixing function for block structures.

Signature
(block-fix x) → new-x
Arguments: x — Guard (blockp x).
Returns: new-x — Type (blockp new-x).

Definitions and Theorems

Function: block-fix$inline

(defun block-fix$inline (x)
 (declare (xargs :guard (blockp x)))
 (let ((__function__ 'block-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((transactions (transaction-list-fix (cdr (std::da-nth 0 x))))
       (round (pos-fix (cdr (std::da-nth 1 x)))))
      (let ((round (if (evenp round) round 2)))
        (list (cons 'transactions transactions)
              (cons 'round round))))
    :exec x)))

Theorem: blockp-of-block-fix

(defthm blockp-of-block-fix
  (b* ((new-x (block-fix$inline x)))
    (blockp new-x))
  :rule-classes :rewrite)

Theorem: block-fix-when-blockp

(defthm block-fix-when-blockp
  (implies (blockp x)
           (equal (block-fix x) x)))

Function: block-equiv$inline

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

Theorem: block-equiv-is-an-equivalence

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

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

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

Theorem: block-fix-under-block-equiv

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

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

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

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

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

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

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

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

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