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• Jvaluex

Jvaluex-equiv

Basic equivalence relation for jvaluex structures.

Definitions and Theorems

Function: jvaluex-equiv$inline

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

Theorem: jvaluex-equiv-is-an-equivalence

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

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

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

Theorem: jvaluex-fix-under-jvaluex-equiv

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

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

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

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

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

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

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

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

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