List.sc_nth_take: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend as List
Lines 299-308 of bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&start_line=299&end_line=308

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def sc_nth_take(-A: Data, +xs: List<&2, A>, +n: Nat, +i: Nat, +h: {Nat.is_lt(i, n) == True{} : Bool}) -> {SC.nth(A, SC.take(A, xs, n), i) == SC.nth(A, xs, i) : Maybe<&2, A>}:
  match xs n i:
    case Nil{} _ _:
      {==}
    case Con{a, t} 0n _:
      Empty.absurd({SC.nth(A, SC.take(A, Con{a, t}, 0n), i) == SC.nth(A, Con{a, t}, i) : Maybe<&2, A>}, N.lt_zero_absurd(i, h))
    case Con{a, t} 1n+m 0n:
      {==}
    case Con{a, t} 1n+m 1n+j:
      sc_nth_take(A, t, m, j, h)

Uses (9):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=take