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• Eviscconfig

Eviscconfig-equiv

Basic equivalence relation for eviscconfig structures.

Definitions and Theorems

Function: eviscconfig-equiv$inline

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

Theorem: eviscconfig-equiv-is-an-equivalence

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

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

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

Theorem: eviscconfig-fix-under-eviscconfig-equiv

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

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

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

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

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

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

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

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

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