		Search-engine friendly clone of the ACL2 documentation.

Dimb-scope

Dimb-scope-equiv

Basic equivalence relation for dimb-scope structures.

Definitions and Theorems

Function: dimb-scope-equiv$inline

(defun dimb-scope-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (dimb-scopep acl2::x)
                              (dimb-scopep acl2::y))))
  (equal (dimb-scope-fix acl2::x)
         (dimb-scope-fix acl2::y)))

Theorem: dimb-scope-equiv-is-an-equivalence

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

Theorem: dimb-scope-equiv-implies-equal-dimb-scope-fix-1

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

Theorem: dimb-scope-fix-under-dimb-scope-equiv

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

Theorem: equal-of-dimb-scope-fix-1-forward-to-dimb-scope-equiv

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

Theorem: equal-of-dimb-scope-fix-2-forward-to-dimb-scope-equiv

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

Theorem: dimb-scope-equiv-of-dimb-scope-fix-1-forward

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

Theorem: dimb-scope-equiv-of-dimb-scope-fix-2-forward

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