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Character-list

Fixtype of lists of characters.

The recognizer is character-listp and the fixer is str::character-list-fix.

Definitions and Theorems

Function: character-list-equiv$inline

(defun character-list-equiv$inline (x y)
       (declare (xargs :guard (and (character-listp x)
                                   (character-listp y))))
       (equal (str::character-list-fix x)
              (str::character-list-fix y)))

Theorem: character-list-equiv-is-an-equivalence

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

Theorem: character-list-equiv-implies-equal-character-list-fix-1

(defthm character-list-equiv-implies-equal-character-list-fix-1
        (implies (character-list-equiv x x-equiv)
                 (equal (str::character-list-fix x)
                        (str::character-list-fix x-equiv)))
        :rule-classes (:congruence))

Theorem: character-list-fix-under-character-list-equiv

(defthm character-list-fix-under-character-list-equiv
        (character-list-equiv (str::character-list-fix x)
                              x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-character-list-fix-1-forward-to-character-list-equiv

(defthm
     equal-of-character-list-fix-1-forward-to-character-list-equiv
     (implies (equal (str::character-list-fix x) y)
              (character-list-equiv x y))
     :rule-classes :forward-chaining)

Theorem: equal-of-character-list-fix-2-forward-to-character-list-equiv

(defthm
     equal-of-character-list-fix-2-forward-to-character-list-equiv
     (implies (equal x (str::character-list-fix y))
              (character-list-equiv x y))
     :rule-classes :forward-chaining)

Theorem: character-list-equiv-of-character-list-fix-1-forward

(defthm character-list-equiv-of-character-list-fix-1-forward
        (implies (character-list-equiv (str::character-list-fix x)
                                       y)
                 (character-list-equiv x y))
        :rule-classes :forward-chaining)

Theorem: character-list-equiv-of-character-list-fix-2-forward

(defthm
     character-list-equiv-of-character-list-fix-2-forward
     (implies (character-list-equiv x (str::character-list-fix y))
              (character-list-equiv x y))
     :rule-classes :forward-chaining)