		Search-engine friendly clone of the ACL2 documentation.

Words

Word

Fixtype of words.

Definitions and Theorems

Function: word-equiv$inline

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

Theorem: word-equiv-is-an-equivalence

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

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

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

Theorem: word-fix-under-word-equiv

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

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

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

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

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

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

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

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

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

Subtopics

Wordp: Recognizer for word.
Word-fix: Fixer for word.