Lists.g_nth: 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 82-89 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=82&end_line=89

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/gcd.bend as G

def g_nth(+xs: List<&2, Nat>, +acc: Nat, +i: Nat) -> {nth0(xs, i, 0n) == Nat.mul(gw_nth(xs, acc, i), M.gcd_all_go(xs, acc)) : Nat}:
  match xs i:
    case Nil{} i0:
      {==}
    case Con{+x, +t} 0n:
      dvd_trans(x, M.gcd(acc, x), M.gcd_all_go(t, M.gcd(acc, x)), G.wr(G.ws(x, acc, x)), gw_acc(t, M.gcd(acc, x)), G.gcd_dvd_right(acc, x), g_acc(t, M.gcd(acc, x)))
    case Con{+x, +t} 1n+ +j:
      g_nth(t, M.gcd(acc, x), j)

Uses (13):
  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/gcd.bend&name=gcd_dvd_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&name=wr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/gcd.bend&name=ws
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=dvd_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=g_acc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=gw_acc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=gw_nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/lists.bend&name=nth0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=gcd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=gcd_all_go