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• Package

Package-equiv

Basic equivalence relation for package structures.

Definitions and Theorems

Function: package-equiv$inline

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

Theorem: package-equiv-is-an-equivalence

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

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

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

Theorem: package-fix-under-package-equiv

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

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

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

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

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

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

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

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

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