PROOFDiv.ud.dm_round: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF_div.bend as PROOFDiv
Lines 131-138 of bend-osdev-u32@0.1.0.0/PROOF_div.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF_div.bend&start_line=131&end_line=138

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# finishing a round: m steps, then one more starts the next
def ud.dm_round(+m: Nat, +n: Nat, +d: Nat, +r: Nat) -> {Nat.divmod.go(Nat.add(m, 1n+n), m, d, r) == Nat.divmod.go(n, Nat.add(m, r), 1n+d, 0n) : Nat & Nat}:
  match m:
    case 0n:
      {==}
    case 1n+mp:
      %UL.nat_add_succ(mp, r) : {Nat.divmod.go(Nat.add(1n+mp, 1n+n), 1n+mp, d, r) == Nat.divmod.go(n, _, 1n+d, 0n) : Nat & Nat}
      ud.dm_round(mp, n, d, 1n+r)

Uses (5):
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ