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Bits-as-digits-in-base-2

Bebits=>nat

Convert a big-endian list of bits, seen as digits in base 2, to their value.

Signature
(bebits=>nat digits) → nat
Arguments: digits — Guard (bit-listp digits).
Returns: nat — Type (natp nat).

Definitions and Theorems

Function: bebits=>nat

(defun bebits=>nat (digits)
  (declare (xargs :guard (bit-listp digits)))
  (let ((__function__ 'bebits=>nat))
    (declare (ignorable __function__))
    (bendian=>nat 2 digits)))

Theorem: natp-of-bebits=>nat

(defthm natp-of-bebits=>nat
  (b* ((nat (bebits=>nat digits)))
    (natp nat))
  :rule-classes :rewrite)

Theorem: bebits=>nat-of-bit-list-fix-digits

(defthm bebits=>nat-of-bit-list-fix-digits
  (equal (bebits=>nat (bit-list-fix digits))
         (bebits=>nat digits)))

Theorem: bebits=>nat-bit-list-equiv-congruence-on-digits

(defthm bebits=>nat-bit-list-equiv-congruence-on-digits
  (implies (bit-list-equiv digits digits-equiv)
           (equal (bebits=>nat digits)
                  (bebits=>nat digits-equiv)))
  :rule-classes :congruence)

Subtopics

Bebits=>nat-injectivity+
Bebits=>nat-injectivity*
Bebits=>nat-injectivity
Nat=>bebits+-of-bebits=>nat
Nat=>bebits*-of-bebits=>nat
Nat=>bebits-of-bebits=>nat
Bebits=>nat-of-nat=>bebits+
Bebits=>nat-of-nat=>bebits*
Bebits=>nat-of-nat=>bebits