Below.draw_lt: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/below.bend as Below
Lines 105-111 of bend-collections-laws-crypto@1.0.0.0/proofs/math/random/below.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/below.bend&start_line=105&end_line=111

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/proofs/lib/logic.bend as L

# THEOREM: an accepted draw is below n
def draw_lt(+x: Nat, +n: Nat, +k: Nat, +hx: {C.fits(64n, x) == True{} : Bool}, +hn: {Nat.is_lt(0n, n) == True{} : Bool}, +e: {SR.draw(64n, x, n) == Some{k} : Maybe<&2, Nat>}) -> {Nat.is_lt(k, n) == True{} : Bool}:
  match n:
    case 0n:
      Empty.absurd({Nat.is_lt(k, 0n) == True{} : Bool}, L.false_true(hn))
    case 1n+m:
      draw_pos_lt(x, m, k, hx, Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n), e)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/below.bend&name=draw_pos_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=fits
  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=draw