def cap_inv
import bend-ml-tensor-array@0.1.19.0/main.bend as BendMlTensorArrayimport Base
711# the invariant of cap_pair: the second component is 2^(first) and is >= n
712def cap_inv(n: Nat) -> {snd_nat(cap_pair(n)) == pow2(fst_nat(cap_pair(n))) : Nat} & {True{} == leb(n, snd_nat(cap_pair(n))) : Bool}:
713 match n:
714 case 0n:
715 ({==}, {==})
716 case 1n++m:
717 cap_succ(m, cap_inv(m))