Fill.le_mul_left: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend as Fill
Lines 168-173 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/fill.bend&start_line=168&end_line=173

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

def le_mul_left(+p: Nat, +q: Nat, +hp: {Nat.is_le(1n, p) == True{} : Bool}) -> {Nat.is_le(q, Nat.mul(p, q)) == True{} : Bool}:
  match p:
    case 0n:
      Empty.absurd({Nat.is_le(q, 0n) == True{} : Bool}, L.false_true(hp))
    case 1n+k:
      N.le_add_right(q, Nat.mul(k, q))

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=Empty.absurd
  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_le
  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/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_add_right