Lists.dvd_lcm_all: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend as Lists
Lines 157-159 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&start_line=157&end_line=159

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

# every element divides lcm_all(xs) (1 past the end)   (Mathlib Finset.dvd_lcm)
def dvd_lcm_all(+xs: List<&2, Nat>, +i: Nat) -> {M.lcm_all(xs) == Nat.mul(lw_nth(xs, 1n, i), nth0(xs, i, 1n)) : Nat}:
  l_nth(xs, 1n, i)

Uses (7):
  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-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=l_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=lw_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lists.bend&name=nth0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/math/natural.bend&name=lcm_all