Word.inc_zero: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as Word
Lines 224-232 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&start_line=224&end_line=232

import Base

# an increment is zero iff it wrapped from all ones
def inc_zero(+n: Nat, +x: Word(n)) -> {Cmp.is_eq(Word.cmp(n, Word.inc(n, x), Word.zero(n))) == ones(n, x) : Bool}:
  match n x:
    case 0n WNil{}:
      {==}
    case 1n+p WCon{False{}, t}:
      eq_fin_tf(Word.cmp(p, t, Word.zero(p)))
    case 1n+p WCon{True{}, t}:
      Equal.trans(Bool, Cmp.is_eq(Word.cmp.fin(False{}, False{}, Word.cmp(p, Word.inc(p, t), Word.zero(p)))), Cmp.is_eq(Word.cmp(p, Word.inc(p, t), Word.zero(p))), ones(p, t), eq_fin_ff(Word.cmp(p, Word.inc(p, t), Word.zero(p))), inc_zero(p, t))

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp.fin
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.inc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=eq_fin_ff
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=eq_fin_tf
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=ones