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Iprefixp

Case-insensitive character-list prefix test.

(iprefixp x y) determines whether one character list is a prefix of another, where each character is tested using ichareqv.

Definitions and Theorems

Function: iprefixp

(defun iprefixp (x y)
  (declare (xargs :guard (and (character-listp x)
                              (character-listp y))))
  (if (consp x)
      (and (consp y)
           (ichareqv (car x) (car y))
           (iprefixp (cdr x) (cdr y)))
    t))

Theorem: iprefixp-when-not-consp-left

(defthm iprefixp-when-not-consp-left
  (implies (not (consp x))
           (iprefixp x y)))

Theorem: iprefixp-of-cons-left

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

Theorem: iprefixp-when-not-consp-right

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

Theorem: iprefixp-of-cons-right

(defthm iprefixp-of-cons-right
  (equal (iprefixp x (cons a y))
         (if (consp x)
             (and (ichareqv (car x) a)
                  (iprefixp (cdr x) y))
           t)))

Theorem: iprefixp-of-list-fix-left

(defthm iprefixp-of-list-fix-left
  (equal (iprefixp (list-fix x) y)
         (iprefixp x y)))

Theorem: iprefixp-of-list-fix-right

(defthm iprefixp-of-list-fix-right
  (equal (iprefixp x (list-fix y))
         (iprefixp x y)))

Theorem: icharlisteqv-implies-equal-iprefixp-1

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

Theorem: icharlisteqv-implies-equal-iprefixp-2

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

Theorem: iprefixp-when-prefixp

(defthm iprefixp-when-prefixp
  (implies (prefixp x y) (iprefixp x y)))