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• Junop

Junop-equiv

Basic equivalence relation for junop structures.

Definitions and Theorems

Function: junop-equiv$inline

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

Theorem: junop-equiv-is-an-equivalence

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

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

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

Theorem: junop-fix-under-junop-equiv

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

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

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

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

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

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

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

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

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