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Message

Message-equiv

Basic equivalence relation for message structures.

Definitions and Theorems

Function: message-equiv$inline

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

Theorem: message-equiv-is-an-equivalence

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

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

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

Theorem: message-fix-under-message-equiv

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

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

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

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

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

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

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

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

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