Lemire.unbiased_c: 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 589-596 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=589&end_line=596

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

def unbiased_c(+w: Nat, +m: Nat, +k: Nat, +hw: {C.fits(w, 1n+m) == True{} : Bool}, +hk: {Nat.is_lt(k, 1n+m) == True{} : Bool}, +c: Bool, +hc: {Nat.is_eq(SR.and_bits(w, 1n+m, m), 0n) == c : Bool}) -> {SR.count(w, 1n+m, k, C.shift(w, 1n)) == Nat.div(C.shift(w, 1n), 1n+m) : Nat}:
  match c:
    case False{}:
      lemire_count(w, m, k, hc, hw, hk)
    case True{}:
      Equal.trans(Nat, SR.count(w, 1n+m, k, C.shift(w, 1n)), cm(w, m, k, C.shift(w, 1n)), Nat.div(C.shift(w, 1n), 1n+m),
        count_mask(w, m, k, C.shift(w, 1n), hc),
        mask(w, m, k, C.bit(m), C.half(m), {==}, {==}, N.eq_from_is_eq(SR.and_bits(w, 1n+m, m), 0n, hc), hw, hk))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=eq_from_is_eq
  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=count_mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=lemire_count
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=bit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=half
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift
  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