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• Jresult

Jresult-equiv

Basic equivalence relation for jresult structures.

Definitions and Theorems

Function: jresult-equiv$inline

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

Theorem: jresult-equiv-is-an-equivalence

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

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

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

Theorem: jresult-fix-under-jresult-equiv

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

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

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

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

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

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

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

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

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