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• Jvalue

Jvalue-equiv

Basic equivalence relation for jvalue structures.

Definitions and Theorems

Function: jvalue-equiv$inline

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

Theorem: jvalue-equiv-is-an-equivalence

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

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

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

Theorem: jvalue-fix-under-jvalue-equiv

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

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

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

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

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

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

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

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

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