Uint64n.value_nz: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend as Uint64n
Lines 299-310 of bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&start_line=299&end_line=310

import Base
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
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/spec/math/random/source.bend as SRC
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as LE
import bend-collections-laws-math@1.0.0.0/spec/math/random.bend as SRM

def value_nz(~S: Data, ~next: S -> WU.U64 & S, +one: Nat, +h1: {one == 1n : Nat}, +s: S, +n: WU.U64, +m: Nat, +hv: {SW.value(n) == 1n+m : Nat}, +hz: {X.is_zero(n) == False{} : Bool}, +c: Bool, +hc: {Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) == c : Bool}) -> {SRM.val_pair(S, R.uint64n_pick(~S, ~next, s, n, c)) == SR.below(~S, ~next, 127n, 1n+m, s) : Nat & S}:
  match c:
    case True{}:
      +x = SW.value(SRC.fst64(S, next(s)))
      Equal.trans(Nat & S, SRM.val_pair(S, R.mask(S, n, next(s))), (SR.and_bits(64n, x, m), SRC.snd64(S, next(s))), SR.below(~S, ~next, 127n, 1n+m, s),
        mask_pair(S, n, m, next(s), hv),
        %Equal.sym(Maybe<&2, Nat>, SR.draw(64n, x, 1n+m), Some{SR.and_bits(64n, x, m)}, LE.draw_mask(64n, m, x, hc)) : {(SR.and_bits(64n, x, m), SRC.snd64(S, next(s))) == SR.below_go(~S, ~next, 127n, 1n+m, _, x, SRC.snd64(S, next(s))) : Nat & S}
        {==})
    case False{}:
      Equal.trans(Nat & S, SRM.val_pair(S, R.lemire_first(~S, ~next, n, R.draw(S, n, next(s)))), cont(~S, ~next, 127n, 1n+m, SW.value(SRC.fst64(S, next(s))), SRC.snd64(S, next(s))), SR.below(~S, ~next, 127n, 1n+m, s),
        top_first(~S, ~next, one, h1, n, m, next(s), hv, hz, hc),
        Equal.sym(Nat & S, SR.below(~S, ~next, 127n, 1n+m, s), cont(~S, ~next, 127n, 1n+m, SW.value(SRC.fst64(S, next(s))), SRC.snd64(S, next(s))), below_cont(~S, ~next, 127n, 1n+m, s)))

Uses (27):
  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=Equal.trans
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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/proofs/math/random/uint64n.bend&name=below_cont
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=cont
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=mask_pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=top_first
  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=below
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/rand.bend&name=below_go
  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/source.bend&name=fst64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random/source.bend&name=snd64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random.bend&name=val_pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=draw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=lemire_first
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=uint64n_pick
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=is_zero