U32div.div_mod: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend as U32div
Lines 196-200 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&start_line=196&end_line=200

import Base

# THEOREM: div and mod are Euclidean division by any nonzero divisor.
def div_mod(+a: U32, +b: U32, +hb: {U32.is_zero(b) == False{} : Bool}) -> {Nat.add(Nat.mul(v(U32.div(a, b)), v(b)), v(U32.mod(a, b))) == v(a) : Nat} & {Nat.is_lt(v(U32.mod(a, b)), v(b)) == True{} : Bool}:
  match a b:
    case U32{+aw} U32{+bw}:
      dm_if(aw, U32{bw}, U32.is_zero(U32{bw}), hb, pos(U32{bw}, hb))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=dm_if
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=v