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Svexlist

Svexlist-equiv

Basic equivalence relation for svexlist structures.

Definitions and Theorems

Function: svexlist-equiv$inline

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

Theorem: svexlist-equiv-is-an-equivalence

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

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

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

Theorem: svexlist-fix-under-svexlist-equiv

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

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

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

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

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

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

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

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

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