def bs.le_len
import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOFimport Base
import bend-osdev-algo@0.1.0.0/bsearch.bend as S
1090def bs.le_len(xs: List<&2, U32>, +key: U32) -> {Nat.is_le(S.bsearch.lower_bound(xs, key), List.length(&2, U32, xs)) == True{} : Bool}:
1091 match xs:
1092 case Nil{}:
1093 {==}
1094 case Con{x, +t}:
1095 bs.le_len.h(U32.is_lt(x, key), S.bsearch.lower_bound(t, key), List.length(&2, U32, t), bs.le_len(t, key))