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• Vl-assertionlist

Vl-assertionlist-equiv

Basic equivalence relation for vl-assertionlist structures.

Definitions and Theorems

Function: vl-assertionlist-equiv$inline

(defun vl-assertionlist-equiv$inline
       (acl2::x acl2::y)
       (declare (xargs :guard (and (vl-assertionlist-p acl2::x)
                                   (vl-assertionlist-p acl2::y))))
       (equal (vl-assertionlist-fix acl2::x)
              (vl-assertionlist-fix acl2::y)))

Theorem: vl-assertionlist-equiv-is-an-equivalence

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

Theorem: vl-assertionlist-equiv-implies-equal-vl-assertionlist-fix-1

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

Theorem: vl-assertionlist-fix-under-vl-assertionlist-equiv

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

Theorem: equal-of-vl-assertionlist-fix-1-forward-to-vl-assertionlist-equiv

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

Theorem: equal-of-vl-assertionlist-fix-2-forward-to-vl-assertionlist-equiv

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

Theorem: vl-assertionlist-equiv-of-vl-assertionlist-fix-1-forward

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

Theorem: vl-assertionlist-equiv-of-vl-assertionlist-fix-2-forward

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