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• Sv::maybe-4veclist

Sv::maybe-4veclist-equiv

Basic equivalence relation for maybe-4veclist structures.

Definitions and Theorems

Function: maybe-4veclist-equiv$inline

(defun sv::maybe-4veclist-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (sv::maybe-4veclist-p acl2::x)
                              (sv::maybe-4veclist-p acl2::y))))
  (equal (sv::maybe-4veclist-fix acl2::x)
         (sv::maybe-4veclist-fix acl2::y)))

Theorem: maybe-4veclist-equiv-is-an-equivalence

(defthm sv::maybe-4veclist-equiv-is-an-equivalence
  (and (booleanp (sv::maybe-4veclist-equiv acl2::x acl2::y))
       (sv::maybe-4veclist-equiv acl2::x acl2::x)
       (implies (sv::maybe-4veclist-equiv acl2::x acl2::y)
                (sv::maybe-4veclist-equiv acl2::y acl2::x))
       (implies (and (sv::maybe-4veclist-equiv acl2::x acl2::y)
                     (sv::maybe-4veclist-equiv acl2::y acl2::z))
                (sv::maybe-4veclist-equiv acl2::x acl2::z)))
  :rule-classes (:equivalence))

Theorem: maybe-4veclist-equiv-implies-equal-maybe-4veclist-fix-1

(defthm sv::maybe-4veclist-equiv-implies-equal-maybe-4veclist-fix-1
  (implies (sv::maybe-4veclist-equiv acl2::x sv::x-equiv)
           (equal (sv::maybe-4veclist-fix acl2::x)
                  (sv::maybe-4veclist-fix sv::x-equiv)))
  :rule-classes (:congruence))

Theorem: maybe-4veclist-fix-under-maybe-4veclist-equiv

(defthm sv::maybe-4veclist-fix-under-maybe-4veclist-equiv
  (sv::maybe-4veclist-equiv (sv::maybe-4veclist-fix acl2::x)
                            acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-maybe-4veclist-fix-1-forward-to-maybe-4veclist-equiv

(defthm
  sv::equal-of-maybe-4veclist-fix-1-forward-to-maybe-4veclist-equiv
  (implies (equal (sv::maybe-4veclist-fix acl2::x)
                  acl2::y)
           (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-maybe-4veclist-fix-2-forward-to-maybe-4veclist-equiv

(defthm
  sv::equal-of-maybe-4veclist-fix-2-forward-to-maybe-4veclist-equiv
  (implies (equal acl2::x
                  (sv::maybe-4veclist-fix acl2::y))
           (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: maybe-4veclist-equiv-of-maybe-4veclist-fix-1-forward

(defthm sv::maybe-4veclist-equiv-of-maybe-4veclist-fix-1-forward
 (implies (sv::maybe-4veclist-equiv (sv::maybe-4veclist-fix acl2::x)
                                    acl2::y)
          (sv::maybe-4veclist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: maybe-4veclist-equiv-of-maybe-4veclist-fix-2-forward

(defthm sv::maybe-4veclist-equiv-of-maybe-4veclist-fix-2-forward
  (implies
       (sv::maybe-4veclist-equiv acl2::x
                                 (sv::maybe-4veclist-fix acl2::y))
       (sv::maybe-4veclist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)