Lemire.cm2: 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 365-371 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=365&end_line=371

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

# the same count taken over the pairs 2y, 2y + 1 with y < N
def cm2(+w: Nat, +m: Nat, +k: Nat, N: Nat) -> Nat:
  match N:
    case 0n:
      0n
    case 1n+ +y:
      Nat.add(cm2(w, m, k, y), Nat.add(b2n(Nat.is_eq(SR.and_bits(w, Nat.double(y), m), k)), b2n(Nat.is_eq(SR.and_bits(w, 1n+Nat.double(y), m), k))))

Uses (6):
  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.double
  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/spec/math/random/rand.bend&name=and_bits