Proof.u32_mod: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend as Proof
Lines 30-31 of bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/proof.bend&start_line=30&end_line=31

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD

def u32_mod(+a: U32, +b: U32, +hb: {U32.is_zero(b) == False{} : Bool}) -> {U32.to_nat(U32.mod(a, b)) == Nat.mod(U32.to_nat(a), U32.to_nat(b)) : Nat}:
  UD.mod_nat(a, b, hb)

Uses (8):
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend&name=mod_nat