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Fileset

Fileset-equiv

Basic equivalence relation for fileset structures.

Definitions and Theorems

Function: fileset-equiv$inline

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

Theorem: fileset-equiv-is-an-equivalence

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

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

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

Theorem: fileset-fix-under-fileset-equiv

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

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

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

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

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

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

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

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

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