BinaryDivision.branch_total: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/binary_division.bend as BinaryDivision
Lines 81-89 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=81&end_line=89

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

def branch_total(+g: Bool,+q: Nat,+s: Nat,+b: Nat,guard: {Nat.is_ge(s,b) == g : Bool}) -> {total(branch(g,q,s,b),b) == Nat.add(Nat.mul(q,b),s) : Nat}:
  match g:
    case False{}:
      {==}
    case True{}:
      %Equal.sym(Nat,Nat.add(Nat.add(b,Nat.mul(q,b)),Nat.sub(s,b)),Nat.add(Nat.mul(q,b),Nat.add(Nat.sub(s,b),b)),rotate(b,Nat.mul(q,b),Nat.sub(s,
            b))) : {_ == Nat.add(Nat.mul(q,b),s) : Nat}
      %Subtraction.restore(s,b,Order.ge_true(s,b,guard)) : {Nat.add(Nat.mul(q,b),Nat.add(Nat.sub(s,b),b)) == Nat.add(Nat.mul(q,b),_) : Nat}
      {==}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  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.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  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=rotate
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&name=total
  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/word_subtraction.bend&name=restore