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• Jstatem

Jstatem-equiv

Basic equivalence relation for jstatem structures.

Definitions and Theorems

Function: jstatem-equiv$inline

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

Theorem: jstatem-equiv-is-an-equivalence

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

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

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

Theorem: jstatem-fix-under-jstatem-equiv

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

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

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

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

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

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

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

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

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