		Search-engine friendly clone of the ACL2 documentation.

Rangemap

Rangemap-equiv

Basic equivalence relation for rangemap structures.

Definitions and Theorems

Function: rangemap-equiv$inline

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

Theorem: rangemap-equiv-is-an-equivalence

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

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

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

Theorem: rangemap-fix-under-rangemap-equiv

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

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

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

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

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

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

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

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

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