U64div.is_zero_eq: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend as U64div
Lines 319-326 of bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend&start_line=319&end_line=326

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend as W
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def is_zero_eq(+n: Nat, +w: Word(n), +h: {W.is_zero(n, w) == True{} : Bool}) -> {w == Word.zero(n) : Word(n)}:
  match n w:
    case 0n WNil{}:
      {==}
    case 1n+p WCon{True{}, t}:
      Empty.absurd({WCon{True{}, t} == Word.zero(1n+p) : Word(1n+p)}, L.false_true(h))
    case 1n+p WCon{False{}, t}:
      Equal.cong(Word(p), Word(1n+p), z => WCon{False{}, z}, t, Word.zero(p), is_zero_eq(p, t, h))

Uses (10):
  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.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend&name=is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true