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• Vl-defaultskew-item-list

Vl-defaultskew-item-list-equiv

Basic equivalence relation for vl-defaultskew-item-list structures.

Definitions and Theorems

Function: vl-defaultskew-item-list-equiv$inline

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

Theorem: vl-defaultskew-item-list-equiv-is-an-equivalence

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

Theorem: vl-defaultskew-item-list-equiv-implies-equal-vl-defaultskew-item-list-fix-1

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

Theorem: vl-defaultskew-item-list-fix-under-vl-defaultskew-item-list-equiv

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

Theorem: equal-of-vl-defaultskew-item-list-fix-1-forward-to-vl-defaultskew-item-list-equiv

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

Theorem: equal-of-vl-defaultskew-item-list-fix-2-forward-to-vl-defaultskew-item-list-equiv

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

Theorem: vl-defaultskew-item-list-equiv-of-vl-defaultskew-item-list-fix-1-forward

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

Theorem: vl-defaultskew-item-list-equiv-of-vl-defaultskew-item-list-fix-2-forward

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