Lemire.and_lt: 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 37-45 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=37&end_line=45

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

# lo < n and lo < t is lo < t, when t < n
def and_lt(+lo: Nat, +n: Nat, +t: Nat, +ht: {Nat.is_lt(t, n) == True{} : Bool}, +c: Bool, +hc: {Nat.is_lt(lo, t) == c : Bool}) -> {Bool.and(Nat.is_lt(lo, n), Nat.is_lt(lo, t)) == c : Bool}:
  match c:
    case True{}:
      %Equal.sym(Bool, Nat.is_lt(lo, n), True{}, N.lt_trans(lo, t, n, hc, ht)) : {Bool.and(_, Nat.is_lt(lo, t)) == True{} : Bool}
      hc
    case False{}:
      %Equal.sym(Bool, Nat.is_lt(lo, t), False{}, hc) : {Bool.and(Nat.is_lt(lo, n), _) == False{} : Bool}
      and_false(Nat.is_lt(lo, n))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=and_false