Lemire.count_mask: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 580-587 of bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&start_line=580&end_line=587

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend as SR

def count_mask(+w: Nat, +m: Nat, +k: Nat, +N: Nat, +hp: {Nat.is_eq(SR.and_bits(w, 1n+m, m), 0n) == True{} : Bool}) -> {SR.count(w, 1n+m, k, N) == cm(w, m, k, N) : Nat}:
  match N:
    case 0n:
      {==}
    case 1n+ +x:
      %Equal.sym(Nat, SR.count(w, 1n+m, k, x), cm(w, m, k, x), count_mask(w, m, k, x, hp)) : {Nat.add(_, SR.hit(SR.draw(w, x, 1n+m), k)) == Nat.add(cm(w, m, k, x), b2n(Nat.is_eq(SR.and_bits(w, x, m), k))) : Nat}
      %Equal.sym(Maybe<&2, Nat>, SR.draw(w, x, 1n+m), Some{SR.and_bits(w, x, m)}, draw_mask(w, m, x, hp)) : {Nat.add(cm(w, m, k, x), SR.hit(_, k)) == Nat.add(cm(w, m, k, x), b2n(Nat.is_eq(SR.and_bits(w, x, m), k))) : Nat}
      {==}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=b2n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=cm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=draw_mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=and_bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=count
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=draw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=hit