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• Statassert

Statassert-equiv

Basic equivalence relation for statassert structures.

Definitions and Theorems

Function: statassert-equiv$inline

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

Theorem: statassert-equiv-is-an-equivalence

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

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

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

Theorem: statassert-fix-under-statassert-equiv

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

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

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

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

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

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

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

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

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