def search_top

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/roots.bend:177

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend as M

177def search_top(+n: Nat, +k: Nat, +lo: Nat, +hi: Nat, +hlo: {M.root_le(n, k, lo) == True{} : Bool}, +hhi: {M.root_le(n, k, hi) == False{} : Bool}, +hlt: {Nat.is_lt(lo, hi) == True{} : Bool}) -> root_ok(n, k, M.search(n, k, lo, hi)):
178  search_ok(Nat.sub(hi, lo), n, k, lo, hi, Nat.is_lt(1n+lo, hi), M.root_le(n, k, M.mid(lo, hi)), hlo, hhi, hlt, N.le_refl(Nat.sub(hi, lo)), {==}, {==})