NatDivision.add_divisor: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_division.bend as NatDivision
Lines 85-93 of stelliferous@0.0.2.0/proofs/nat_division.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_division.bend&start_line=85&end_line=93

import Base
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def add_divisor(+a: Nat,+b: Nat,h: {Nat.is_lt(0n,b) == True{} : Bool}) -> {Nat.divmod(Nat.add(b,a),b) == bump(Nat.divmod(a,b)) : Nat & Nat}:
  match b:
    case 0n:
      Empty.absurd({Nat.divmod(a,0n) == bump(Nat.divmod(a,0n)) : Nat & Nat},WordEncoding.false_true(h))
    case 1n+ +p:
      %Equal.sym(Nat & Nat,Nat.divmod.go(Nat.add(1n+p,a),p,0n,0n),Nat.divmod.go(a,Nat.add(p,0n),1n,0n),cycle(p,a,0n,
          0n)) : {_ == bump(Nat.divmod.go(a,p,0n,0n)) : Nat & Nat}
      %Equal.sym(Nat,Nat.add(p,0n),p,Addition.zero_right(p)) : {Nat.divmod.go(a,_,1n,0n) == bump(Nat.divmod.go(a,p,0n,0n)) : Nat & Nat}
      bump_go(a,p,0n,0n)

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.divmod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.divmod.go
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_division.bend&name=bump
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_division.bend&name=bump_go
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_division.bend&name=cycle
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=zero_right
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true