Run.lt_second: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/run.bend as Run
Lines 50-51 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/run.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/run.bend&start_line=50&end_line=51

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend as F

def lt_second(+l: Nat, +p: Nat, +q: Nat, +hl: {Nat.is_lt(l, p) == True{} : Bool}, +hq2: {Nat.is_le(2n, q) == True{} : Bool}) -> {Nat.is_lt(Nat.add(Nat.mul(l, q), 1n), Nat.mul(p, q)) == True{} : Bool}:
  F.lt_mul_add(l, p, 1n, q, hl, N.lt_le_trans(1n, 2n, q, {==}, hq2))

Uses (8):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend&name=lt_mul_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans