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Bytes-as-digits-in-base-256

Nat=>bebytes

Convert a natural number to its big-endian list of bytes, seen as digits in base 256, of specified length.

Signature
(nat=>bebytes width nat) → digits
Arguments: width — Guard (natp width).; nat — Guard (natp nat).
Returns: digits — Type (byte-listp digits).

Definitions and Theorems

Function: nat=>bebytes

(defun nat=>bebytes (width nat)
  (declare (xargs :guard (and (natp width) (natp nat))))
  (declare (xargs :guard (< nat (expt 256 width))))
  (let ((__function__ 'nat=>bebytes))
    (declare (ignorable __function__))
    (nat=>bendian 256 width nat)))

Theorem: byte-listp-of-nat=>bebytes

(defthm byte-listp-of-nat=>bebytes
  (b* ((digits (nat=>bebytes width nat)))
    (byte-listp digits))
  :rule-classes :rewrite)

Theorem: nat=>bebytes-of-nfix-width

(defthm nat=>bebytes-of-nfix-width
  (equal (nat=>bebytes (nfix width) nat)
         (nat=>bebytes width nat)))

Theorem: nat=>bebytes-nat-equiv-congruence-on-width

(defthm nat=>bebytes-nat-equiv-congruence-on-width
  (implies (nat-equiv width width-equiv)
           (equal (nat=>bebytes width nat)
                  (nat=>bebytes width-equiv nat)))
  :rule-classes :congruence)

Theorem: nat=>bebytes-of-nfix-nat

(defthm nat=>bebytes-of-nfix-nat
  (equal (nat=>bebytes width (nfix nat))
         (nat=>bebytes width nat)))

Theorem: nat=>bebytes-nat-equiv-congruence-on-nat

(defthm nat=>bebytes-nat-equiv-congruence-on-nat
  (implies (nat-equiv nat nat-equiv)
           (equal (nat=>bebytes width nat)
                  (nat=>bebytes width nat-equiv)))
  :rule-classes :congruence)

Theorem: len-of-nat=>bebytes

(defthm len-of-nat=>bebytes
  (equal (len (nat=>bebytes width nat))
         (nfix width)))

Subtopics

Nat=>bebytes-injectivity
Nat=>bebytes-of-bebytes=>nat
Bebytes=>nat-of-nat=>bebytes