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Icharlisteqv

Case-insensitive character-list equivalence test.

Signature
(icharlisteqv x y) → bool
Arguments: x — Guard (character-listp x).; y — Guard (character-listp y).

(icharlisteqv x y) determines if x and y are case-insensitively equivalent character lists. That is, x and y must have the same length and their elements must be ichareqv to one another.

See also charlisteqv for a case-sensitive alternative.

Definitions and Theorems

Function: icharlisteqv

(defun icharlisteqv (x y)
  (declare (xargs :guard (and (character-listp x)
                              (character-listp y))))
  (let ((acl2::__function__ 'icharlisteqv))
    (declare (ignorable acl2::__function__))
    (if (consp x)
        (and (consp y)
             (ichareqv (car x) (car y))
             (icharlisteqv (cdr x) (cdr y)))
      (atom y))))

Theorem: icharlisteqv-is-an-equivalence

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

Theorem: charlisteqv-refines-icharlisteqv

(defthm charlisteqv-refines-icharlisteqv
  (implies (charlisteqv x y)
           (icharlisteqv x y))
  :rule-classes (:refinement))

Theorem: icharlisteqv-implies-ichareqv-car-1

(defthm icharlisteqv-implies-ichareqv-car-1
  (implies (icharlisteqv x x-equiv)
           (ichareqv (car x) (car x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-cdr-1

(defthm icharlisteqv-implies-icharlisteqv-cdr-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (cdr x) (cdr x-equiv)))
  :rule-classes (:congruence))

Theorem: ichareqv-implies-icharlisteqv-cons-1

(defthm ichareqv-implies-icharlisteqv-cons-1
  (implies (ichareqv a a-equiv)
           (icharlisteqv (cons a x)
                         (cons a-equiv x)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-cons-2

(defthm icharlisteqv-implies-icharlisteqv-cons-2
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (cons a x)
                         (cons a x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-equal-len-1

(defthm icharlisteqv-implies-equal-len-1
  (implies (icharlisteqv x x-equiv)
           (equal (len x) (len x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-list-fix-1

(defthm icharlisteqv-implies-icharlisteqv-list-fix-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (list-fix x)
                         (list-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-ichareqv-nth-2

(defthm icharlisteqv-implies-ichareqv-nth-2
  (implies (icharlisteqv x x-equiv)
           (ichareqv (nth n x) (nth n x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-nthcdr-2

(defthm icharlisteqv-implies-icharlisteqv-nthcdr-2
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (nthcdr n x)
                         (nthcdr n x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-take-2

(defthm icharlisteqv-implies-icharlisteqv-take-2
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (take n x)
                         (take n x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-append-1

(defthm icharlisteqv-implies-icharlisteqv-append-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (append x y)
                         (append x-equiv y)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-append-2

(defthm icharlisteqv-implies-icharlisteqv-append-2
  (implies (icharlisteqv y y-equiv)
           (icharlisteqv (append x y)
                         (append x y-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-rev-1

(defthm icharlisteqv-implies-icharlisteqv-rev-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (rev x) (rev x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-revappend-2

(defthm icharlisteqv-implies-icharlisteqv-revappend-2
  (implies (icharlisteqv y y-equiv)
           (icharlisteqv (revappend x y)
                         (revappend x y-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-revappend-1

(defthm icharlisteqv-implies-icharlisteqv-revappend-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (revappend x y)
                         (revappend x-equiv y)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-make-character-list-1

(defthm icharlisteqv-implies-icharlisteqv-make-character-list-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (make-character-list x)
                         (make-character-list x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-when-not-consp-left

(defthm icharlisteqv-when-not-consp-left
  (implies (not (consp x))
           (equal (icharlisteqv x y) (atom y))))

Theorem: icharlisteqv-when-not-consp-right

(defthm icharlisteqv-when-not-consp-right
  (implies (not (consp y))
           (equal (icharlisteqv x y) (atom x))))

Theorem: icharlisteqv-of-cons-right

(defthm icharlisteqv-of-cons-right
  (equal (icharlisteqv x (cons a y))
         (and (consp x)
              (ichareqv (car x) (double-rewrite a))
              (icharlisteqv (cdr x)
                            (double-rewrite y)))))

Theorem: icharlisteqv-of-cons-left

(defthm icharlisteqv-of-cons-left
  (equal (icharlisteqv (cons a x) y)
         (and (consp y)
              (ichareqv (double-rewrite a) (car y))
              (icharlisteqv (double-rewrite x)
                            (cdr y)))))

Theorem: icharlisteqv-when-not-same-lens

(defthm icharlisteqv-when-not-same-lens
  (implies (not (equal (len x) (len y)))
           (not (icharlisteqv x y))))