BinaryDivision.digit_total: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/binary_division.bend as BinaryDivision
Lines 70-79 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=70&end_line=79

import Base
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition
import stelliferous@0.0.2.0/proofs/u32_comparison.bend as Comparison

def digit_total(+bit: Bool,+q: Nat,+r: Nat,+b: Nat) -> {Nat.add(Nat.mul(Nat.double(q),b),Comparison.digit(bit,r)) == Comparison.digit(bit,
    Nat.add(Nat.mul(q,b),r)) : Nat}:
  match bit:
    case False{}:
      even_total(q,r,b)
    case True{}:
      %Equal.sym(Nat,Nat.add(Nat.mul(Nat.double(q),b),1n+Nat.double(r)),1n+Nat.add(Nat.mul(Nat.double(q),b),Nat.double(r)),
        Addition.successor_right(Nat.mul(Nat.double(q),b),Nat.double(r))) : {_ == 1n+Nat.double(Nat.add(Nat.mul(q,b),r)) : Nat}
      %even_total(q,r,b) : {1n+Nat.add(Nat.mul(Nat.double(q),b),Nat.double(r)) == 1n+_ : Nat}
      {==}

Uses (9):
  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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/binary_division.bend&name=even_total
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=successor_right
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/u32_comparison.bend&name=digit