Convert a natural number to its non-empty minimum-length big-endian list of bits, seen as sigits in base 2.
Function:
(defun nat=>bebits+ (nat) (declare (xargs :guard (natp nat))) (let ((__function__ 'nat=>bebits+)) (declare (ignorable __function__)) (nat=>bendian+ 2 nat)))
Theorem:
(defthm bit-listp-of-nat=>bebits+ (b* ((digits (nat=>bebits+ nat))) (bit-listp digits)) :rule-classes :rewrite)
Theorem:
(defthm nat=>bebits+-of-nfix-nat (equal (nat=>bebits+ (nfix nat)) (nat=>bebits+ nat)))
Theorem:
(defthm nat=>bebits+-nat-equiv-congruence-on-nat (implies (nat-equiv nat nat-equiv) (equal (nat=>bebits+ nat) (nat=>bebits+ nat-equiv))) :rule-classes :congruence)