Uint64n.top_first: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend as Uint64n
Lines 294-297 of bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&start_line=294&end_line=297

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

def top_first(~S: Data, ~next: S -> WU.U64 & S, +one: Nat, +h1: {one == 1n : Nat}, +n: WU.U64, +m: Nat, p: WU.U64 & S, +hv: {SW.value(n) == 1n+m : Nat}, +hz: {X.is_zero(n) == False{} : Bool}, +hp: {Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) == False{} : Bool}) -> {SRM.val_pair(S, R.lemire_first(~S, ~next, n, R.draw(S, n, p))) == cont(~S, ~next, 127n, 1n+m, SW.value(SRC.fst64(S, p)), SRC.snd64(S, p)) : Nat & S}:
  match p:
    case Tuple{+x, +s1}:
      first_case(~S, ~next, one, h1, n, m, x, s1, hv, hz, hp, pm_lt(m, one, h1), X.lt(X.pfst(X.mul128(x, n)), n), {==})

Uses (20):
  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_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-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=cont
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=first_case
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=pm_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend&name=and_bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend&name=fst64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random/source.bend&name=snd64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/random.bend&name=val_pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=draw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=lemire_first
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=is_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=mul128
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=pfst