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• Jfield

Jfield-equiv

Basic equivalence relation for jfield structures.

Definitions and Theorems

Function: jfield-equiv$inline

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

Theorem: jfield-equiv-is-an-equivalence

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

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

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

Theorem: jfield-fix-under-jfield-equiv

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

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

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

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

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

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

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

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

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