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• Design

Design-equiv

Basic equivalence relation for design structures.

Definitions and Theorems

Function: design-equiv$inline

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

Theorem: design-equiv-is-an-equivalence

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

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

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

Theorem: design-fix-under-design-equiv

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

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

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

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

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

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

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

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

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