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Transaction

Transaction-equiv

Basic equivalence relation for transaction structures.

Definitions and Theorems

Function: transaction-equiv$inline

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

Theorem: transaction-equiv-is-an-equivalence

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

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

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

Theorem: transaction-fix-under-transaction-equiv

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

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

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

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

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

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

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

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

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