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Netassigns

Netassigns-equiv

Basic equivalence relation for netassigns structures.

Definitions and Theorems

Function: netassigns-equiv$inline

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

Theorem: netassigns-equiv-is-an-equivalence

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

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

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

Theorem: netassigns-fix-under-netassigns-equiv

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

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

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

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

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

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

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

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

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