List.sc_take_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 310-321 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=310&end_line=321

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

def sc_take_take(-A: Data, +xs: List<&2, A>, +n: Nat, +e: Nat, +h: {Nat.is_le(e, n) == True{} : Bool}) -> {SC.take(A, SC.take(A, xs, n), e) == SC.take(A, xs, e) : List<&2, A>}:
  match xs n e:
    case Nil{} _ _:
      {==}
    case Con{a, t} 0n 0n:
      {==}
    case Con{a, t} 1n+m 0n:
      {==}
    case Con{a, t} 0n 1n+f:
      Empty.absurd({SC.take(A, SC.take(A, Con{a, t}, 0n), 1n+f) == SC.take(A, Con{a, t}, 1n+f) : List<&2, A>}, L.false_true(h))
    case Con{a, t} 1n+m 1n+f:
      cons_cong(A, a, SC.take(A, SC.take(A, t, m), f), SC.take(A, t, f), sc_take_take(A, t, m, f, h))

Uses (8):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=take