Roots.search_top: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/roots.bend as Roots
Lines 177-178 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/roots.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/roots.bend&start_line=177&end_line=178

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

def 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)):
  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)), {==}, {==})

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/roots.bend&name=root_ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/roots.bend&name=search_ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=mid
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=root_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=search