Uint64n.first_case: 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 239-245 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=239&end_line=245

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/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

# the first draw: accepted at once when lo >= n, else the loop
def first_case(~S: Data, ~next: S -> WU.U64 & S, +one: Nat, +h1: {one == 1n : Nat}, +n: WU.U64, +m: Nat, +x: WU.U64, +s1: 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}, +htn: {Nat.is_lt(SR.pow2mod(64n, 1n+m), 1n+m) == True{} : Bool}, +c: Bool, +hc: {X.lt(X.pfst(X.mul128(x, n)), n) == c : Bool}) -> {SRM.val_pair(S, R.lemire_small(~S, ~next, n, X.psnd(X.mul128(x, n)), X.pfst(X.mul128(x, n)), s1, c)) == cont(~S, ~next, 127n, 1n+m, SW.value(x), s1) : Nat & S}:
  match c:
    case True{}:
      loop(~S, ~next, 127n, n, m, R.thresh(n), (x, s1), hv, hp, htn, thresh_m(one, h1, n, m, hv, hz))
    case False{}:
      first_false(~S, ~next, n, m, x, s1, hv, hp, htn, hc)

Uses (22):
  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=Nat.is_lt
  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_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=loop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/uint64n.bend&name=thresh_m
  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/rand.bend&name=pow2mod
  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=lemire_small
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend&name=thresh
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend&name=psnd