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• Jclass

Jclass-equiv

Basic equivalence relation for jclass structures.

Definitions and Theorems

Function: jclass-equiv$inline

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

Theorem: jclass-equiv-is-an-equivalence

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

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

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

Theorem: jclass-fix-under-jclass-equiv

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

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

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

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

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

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

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

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

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