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Svjumpstate

Svjumpstate-equiv

Basic equivalence relation for svjumpstate structures.

Definitions and Theorems

Function: svjumpstate-equiv$inline

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

Theorem: svjumpstate-equiv-is-an-equivalence

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

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

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

Theorem: svjumpstate-fix-under-svjumpstate-equiv

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

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

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

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

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

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

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

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

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