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Filedata

Filedata-equiv

Basic equivalence relation for filedata structures.

Definitions and Theorems

Function: filedata-equiv$inline

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

Theorem: filedata-equiv-is-an-equivalence

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

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

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

Theorem: filedata-fix-under-filedata-equiv

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

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

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

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

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

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

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

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

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