Natlight.dmq: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/natlight.bend as Natlight
Lines 12-17 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/natlight.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/natlight.bend&start_line=12&end_line=17

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as NR

def dmq(+x: Nat, +D: Nat, +hD: {Nat.is_lt(0n, D) == True{} : Bool}) -> {Nat.add(Nat.mul(Nat.div(x, D), D), Nat.mod(x, D)) == x : Nat}:
  match D:
    case 0n:
      Empty.absurd({Nat.add(Nat.mul(Nat.div(x, 0n), 0n), Nat.mod(x, 0n)) == x : Nat}, N.lt_zero_absurd(0n, hD))
    case 1n+ +dp:
      Equal.sym(Nat, x, Nat.add(Nat.mul(Nat.div(x, 1n+dp), 1n+dp), Nat.mod(x, 1n+dp)), NR.dm_eq(dp, x))

Uses (11):
  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.div
  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=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=dm_eq