Lcm.dvd_lcm_right: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend as Lcm
Lines 160-167 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend&start_line=160&end_line=167

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend as M

def dvd_lcm_right(+a: Nat, +b: Nat) -> {M.lcm(a, b) == Nat.mul(lcm_wr(a, b), b) : Nat}:
  match a b:
    case 0n b0:
      Equal.sym(Nat, Nat.mul(0n, b0), 0n, {==})
    case 1n+ ap 0n:
      Equal.sym(Nat, Nat.mul(0n, 0n), 0n, {==})
    case 1n+ +ap 1n+ +bp:
      lcm_pos(ap, bp)

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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/math/natural/lcm.bend&name=lcm_pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend&name=lcm_wr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=lcm