def lt_first

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/argon2/run.bend:47

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

47def 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}:
48  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)))