Below.lt_plus: 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 46-48 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=46&end_line=48

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WI

# a < n + a for n > 0
def lt_plus(+a: Nat, +n: Nat, +hn: {Nat.is_lt(0n, n) == True{} : Bool}) -> {Nat.is_lt(a, Nat.add(n, a)) == True{} : Bool}:
  Equal.trans(Bool, Nat.is_lt(a, Nat.add(n, a)), Nat.is_lt(0n, n), True{}, WI.lt_cancel_r(0n, n, a), hn)

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  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/math/typed/width.bend&name=lt_cancel_r