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• Binary

Nat-to-bin-string

Convert a natural number into a string with its bits.

Signature

(nat-to-bin-string n) → str

Arguments

n — Guard (natp n).

Returns

str — Type (stringp str).

For instance, (nat-to-bin-string 8) is "1000".

Definitions and Theorems

Function: nat-to-bin-string$inline

(defun nat-to-bin-string$inline (n)
  (declare (xargs :guard (natp n)))
  (let ((acl2::__function__ 'nat-to-bin-string))
    (declare (ignorable acl2::__function__))
    (implode (nat-to-bin-chars n))))

Theorem: stringp-of-nat-to-bin-string

(defthm stringp-of-nat-to-bin-string
  (b* ((str (nat-to-bin-string$inline n)))
    (stringp str))
  :rule-classes :type-prescription)

Theorem: bin-digit-char-list*p-of-nat-to-dec-string

(defthm bin-digit-char-list*p-of-nat-to-dec-string
  (bin-digit-char-list*p (explode (nat-to-bin-string n))))

Theorem: nat-to-bin-string-one-to-one

(defthm nat-to-bin-string-one-to-one
  (equal (equal (nat-to-bin-string n)
                (nat-to-bin-string m))
         (equal (nfix n) (nfix m))))

Theorem: bin-digit-chars-value-of-nat-to-dec-string

(defthm bin-digit-chars-value-of-nat-to-dec-string
  (equal (bin-digit-chars-value (explode (nat-to-bin-string n)))
         (nfix n)))

Theorem: nat-to-bin-string-nonempty

(defthm nat-to-bin-string-nonempty
  (not (equal (nat-to-bin-string n) "")))