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              • Lebits=>nat-of-nat=>lebits
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  • Bits-as-digits-in-base-2

Lebits=>nat

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

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

Definitions and Theorems

Function: lebits=>nat

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

Theorem: natp-of-lebits=>nat

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

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

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

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

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

Subtopics

Lebits=>nat-injectivity+
Lebits=>nat-injectivity*
Lebits=>nat-injectivity
Nat=>lebits+-of-lebits=>nat
Nat=>lebits*-of-lebits=>nat
Nat=>lebits-of-lebits=>nat
Lebits=>nat-of-nat=>lebits+
Lebits=>nat-of-nat=>lebits*
Lebits=>nat-of-nat=>lebits