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• Attributes

Attributes-equiv

Basic equivalence relation for attributes structures.

Definitions and Theorems

Function: attributes-equiv$inline

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

Theorem: attributes-equiv-is-an-equivalence

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

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

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

Theorem: attributes-fix-under-attributes-equiv

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

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

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

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

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

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

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

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

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