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• Hex

Nonzero-hex-digit-char-p

Recognizer for non-zero hexadecimal digit characters: 1-9, A-F, a-f.

Signature

(nonzero-hex-digit-char-p x) → bool

Definitions and Theorems

Function: nonzero-hex-digit-char-p$inline

(defun nonzero-hex-digit-char-p$inline (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'nonzero-hex-digit-char-p))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (let ((code (char-code (char-fix x))))
           (or (and (<= (char-code #\1) code)
                    (<= code (char-code #\9)))
               (and (<= (char-code #\a) code)
                    (<= code (char-code #\f)))
               (and (<= (char-code #\A) code)
                    (<= code (char-code #\F)))))
         :exec (and (characterp x)
                    (b* (((the (unsigned-byte 8) code)
                          (char-code (the character x))))
                      (if (<= code 70)
                          (if (<= code 57)
                              (<= 49 code)
                            (<= 65 code))
                        (and (<= code 102) (<= 97 code))))))))

Theorem: ichareqv-implies-equal-nonzero-hex-digit-char-p-1

(defthm ichareqv-implies-equal-nonzero-hex-digit-char-p-1
  (implies (ichareqv x x-equiv)
           (equal (nonzero-hex-digit-char-p x)
                  (nonzero-hex-digit-char-p x-equiv)))
  :rule-classes (:congruence))

Theorem: hex-digit-char-p-when-nonzero-hex-digit-char-p

(defthm hex-digit-char-p-when-nonzero-hex-digit-char-p
  (implies (nonzero-hex-digit-char-p x)
           (hex-digit-char-p x)))