BinaryDivision.branch_bound: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/binary_division.bend as BinaryDivision
Lines 102-108 of stelliferous@0.0.2.0/proofs/binary_division.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&start_line=102&end_line=108

import Base
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order

def branch_bound(+g: Bool,+q: Nat,+s: Nat,+b: Nat,guard: {Nat.is_ge(s,b) == g : Bool},bound: {Nat.is_lt(s,
      Nat.double(b)) == True{} : Bool}) -> {Nat.is_lt(remainder(branch(g,q,s,b)),b) == True{} : Bool}:
  match g:
    case False{}:
      Order.ge_false(s,b,guard)
    case True{}:
      Order.sub_lt(s,b,b,Order.ge_true(s,b,guard),sum_bound(s,b,bound))

Uses (11):
  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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_ge
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&name=branch
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&name=remainder
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&name=sum_bound
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=ge_false
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=ge_true
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=sub_lt