NatDivision.go_small: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_division.bend as NatDivision
Lines 25-35 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=25&end_line=35

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 go_small(+n: Nat,+m: Nat,+d: Nat,+r: Nat,h: {Nat.is_le(n,m) == True{} : Bool}) -> {Nat.divmod.go(n,m,d,r) == (d,Nat.add(n,r)) : Nat & Nat}:
  match n:
    case 0n:
      {==}
    case 1n+ +p:
      match m:
        case 0n:
          Empty.absurd({Nat.divmod.go(1n+p,0n,d,r) == (d,Nat.add(1n+p,r)) : Nat & Nat},WordEncoding.false_true(h))
        case 1n+ +q:
          %Addition.successor_right(p,r) : {Nat.divmod.go(p,q,d,1n+r) == (d,_) : Nat & Nat}
          go_small(p,q,d,1n+r,h)

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=Empty.absurd
  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.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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/word_encoding.bend&name=false_true