PROOFDiv.ud.div_mod: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF_div.bend as PROOFDiv
Lines 94-95 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=94&end_line=95

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

def ud.div_mod(+k: Nat, +bp: Nat) -> {Nat.add(Nat.mul(Nat.div(k, 1n+bp), 1n+bp), Nat.mod(k, 1n+bp)) == k : Nat}:
  Equal.trans(Nat, ud.dm_lhs(k, bp, 0n, 0n, bp), Nat.add(k, 0n), k, ud.dm_sum(k, bp, 0n, 0n, bp, UL.nat_add_zero(bp)), UL.nat_add_zero(k))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF_div.bend&name=ud.dm_lhs
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/PROOF_div.bend&name=ud.dm_sum