Run.lt_first: 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 47-48 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=47&end_line=48

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/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend as F

def lt_first(+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.mul(l, q), Nat.mul(p, q)) == True{} : Bool}:
  L.subst(Nat, z => {Nat.is_lt(z, Nat.mul(p, q)) == True{} : Bool}, Nat.add(Nat.mul(l, q), 0n), Nat.mul(l, q), N.add_zero(Nat.mul(l, q)), F.lt_mul_add(l, p, 0n, q, hl, N.lt_le_trans(0n, 2n, q, {==}, hq2)))

Uses (10):
  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/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le_trans