U32.and_low: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U32
Lines 245-254 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&start_line=245&end_line=254

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def and_low(+n: Nat, +d: Nat, +x: Word(n), +y: Word(n), +hy: {S.unsigned(n, y) == Nat.sub(SC.pow2(d), 1n) : Nat}, +hx: {Nat.is_lt(S.unsigned(n, x), SC.pow2(d)) == True{} : Bool}) -> {Word.and(n, x, y) == x : Word(n)}:
  match n:
    case 0n:
      match x y:
        case WNil{} WNil{}:
          {==}
    case 1n+m:
      match x y:
        case WCon{+xb, +xt} WCon{+yb, +yt}:
          and_low_step(m, d, xb, xt, yb, yt, hy, hx, and_low(m, and_low_prev(d), xt, yt, and_low_hy(m, d, yb, yt, hy), and_low_hx(m, d, xb, xt, hx)))

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=Nat
  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.sub
  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.and
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=and_low_hx
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=and_low_hy
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=and_low_prev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&name=and_low_step
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=pow2