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• Version

Version-equiv

Basic equivalence relation for version structures.

Definitions and Theorems

Function: version-equiv$inline

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

Theorem: version-equiv-is-an-equivalence

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

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

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

Theorem: version-fix-under-version-equiv

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

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

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

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

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

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

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

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

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