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• Jimport

Jimport-equiv

Basic equivalence relation for jimport structures.

Definitions and Theorems

Function: jimport-equiv$inline

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

Theorem: jimport-equiv-is-an-equivalence

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

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

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

Theorem: jimport-fix-under-jimport-equiv

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

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

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

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

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

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

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

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

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