U32div.mod_nat: 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 226-228 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=226&end_line=228

import Base

# THEOREM: mod is Nat remainder.
def mod_nat(+a: U32, +b: U32, +hb: {U32.is_zero(b) == False{} : Bool}) -> {v(U32.mod(a, b)) == Nat.mod(v(a), v(b)) : Nat}:
  mod_of(a, b, div_mod(a, b, hb))

Uses (9):
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=div_mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=mod_of
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend&name=v