Lists.prod_ok: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend as Lists
Lines 37-38 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&start_line=37&end_line=38

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/lcm.bend as LC
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S

def prod_ok(+xs: List<&2, Nat>) -> {M.prod(xs) == S.lprod(xs) : Nat}:
  Equal.trans(Nat, M.prod(xs), Nat.mul(1n, S.lprod(xs)), S.lprod(xs), prod_go(xs, 1n), LC.one_mul(S.lprod(xs)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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-math@1.0.0.0/proofs/math/natural/lcm.bend&name=one_mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=prod_go
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=lprod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=prod