• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
      • Pretty-printing
      • Printtree
      • Base64
      • Charset-p
      • Strtok!
      • Cases
      • Concatenation
      • Html-encoding
      • Character-kinds
      • Substrings
      • Strtok
      • Equivalences
      • Url-encoding
      • Lines
      • Explode-implode-equalities
      • Ordering
      • Numbers
        • Decimal
          • Parse-nat-from-string
          • Parse-nat-from-charlist
          • Nat-to-dec-chars
          • Dec-digit-chars-value
          • Dec-digit-char-p
          • Dec-digit-char-listp
          • Take-leading-dec-digit-chars
          • Dec-digit-char-value
          • Dec-digit-char-list*p
          • Nat-to-dec-string-width
          • Nat-to-dec-string
          • Dec-digit-string-p
          • Strval
          • Skip-leading-digits
          • Nat-to-dec-string-size
          • Int-to-dec-string-width
          • Int-to-dec-string
          • Nonzero-dec-digit-char-p
          • Nat-to-dec-string-list
          • Int-to-dec-string-list
          • Revappend-nat-to-dec-chars
        • Hex
        • Octal
        • Binary
      • Pad-trim
      • Coercion
      • Std/strings/digit-to-char
      • Substitution
      • Symbols
    • Std/io
    • Std/osets
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Decimal

Skip-leading-digits

Skip over any leading digits at the start of a character list.

Signature

(skip-leading-digits x) → tail

Returns

tail — Type (character-listp tail), given (character-listp x).

Definitions and Theorems

Function: skip-leading-digits

(defun skip-leading-digits (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'skip-leading-digits))
    (declare (ignorable acl2::__function__))
    (cond ((atom x) nil)
          ((dec-digit-char-p (car x))
           (skip-leading-digits (cdr x)))
          (t x))))

Theorem: character-listp-of-skip-leading-digits

(defthm character-listp-of-skip-leading-digits
  (implies (character-listp x)
           (b* ((tail (skip-leading-digits x)))
             (character-listp tail)))
  :rule-classes :rewrite)

Theorem: charlisteqv-implies-charlisteqv-skip-leading-digits-1

(defthm charlisteqv-implies-charlisteqv-skip-leading-digits-1
  (implies (charlisteqv x x-equiv)
           (charlisteqv (skip-leading-digits x)
                        (skip-leading-digits x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-skip-leading-digits-1

(defthm icharlisteqv-implies-icharlisteqv-skip-leading-digits-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (skip-leading-digits x)
                         (skip-leading-digits x-equiv)))
  :rule-classes (:congruence))

Theorem: len-of-skip-leading-digits

(defthm len-of-skip-leading-digits
  (equal (< (len (skip-leading-digits x))
            (len x))
         (dec-digit-char-p (car x)))
  :rule-classes
  ((:rewrite)
   (:linear :corollary (implies (dec-digit-char-p (car x))
                                (< (len (skip-leading-digits x))
                                   (len x))))))