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• Jcunit

Jcunit-equiv

Basic equivalence relation for jcunit structures.

Definitions and Theorems

Function: jcunit-equiv$inline

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

Theorem: jcunit-equiv-is-an-equivalence

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

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

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

Theorem: jcunit-fix-under-jcunit-equiv

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

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

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

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

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

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

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

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

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