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• Decimal

Nonzero-dec-digit-char-p

Recognizer for non-zero numeric characters (1-9).

Signature

(nonzero-dec-digit-char-p x) → bool

Definitions and Theorems

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

(defun nonzero-dec-digit-char-p$inline (x)
 (declare (xargs :guard t))
 (let ((acl2::__function__ 'nonzero-dec-digit-char-p))
   (declare (ignorable acl2::__function__))
   (mbe :logic
        (let ((code (char-code (char-fix x))))
          (and (<= (char-code #\1) code)
               (<= code (char-code #\9))))
        :exec (and (characterp x)
                   (let ((code (the (unsigned-byte 8)
                                    (char-code (the character x)))))
                     (declare (type (unsigned-byte 8) code))
                     (and (<= (the (unsigned-byte 8) code)
                              (the (unsigned-byte 8) 57))
                          (<= (the (unsigned-byte 8) 49)
                              (the (unsigned-byte 8) code))))))))

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

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

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

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