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Location

Location-equiv

Basic equivalence relation for location structures.

Definitions and Theorems

Function: location-equiv$inline

(defun location-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (locationp acl2::x)
                              (locationp acl2::y))))
  (equal (location-fix acl2::x)
         (location-fix acl2::y)))

Theorem: location-equiv-is-an-equivalence

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

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

(defthm location-equiv-implies-equal-location-fix-1
  (implies (location-equiv acl2::x x-equiv)
           (equal (location-fix acl2::x)
                  (location-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: location-fix-under-location-equiv

(defthm location-fix-under-location-equiv
  (location-equiv (location-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm equal-of-location-fix-1-forward-to-location-equiv
  (implies (equal (location-fix acl2::x) acl2::y)
           (location-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm equal-of-location-fix-2-forward-to-location-equiv
  (implies (equal acl2::x (location-fix acl2::y))
           (location-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm location-equiv-of-location-fix-1-forward
  (implies (location-equiv (location-fix acl2::x)
                           acl2::y)
           (location-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm location-equiv-of-location-fix-2-forward
  (implies (location-equiv acl2::x (location-fix acl2::y))
           (location-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)