PROOF.AP.take_app: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1379-1388 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=1379&end_line=1388

import Base

def AP.take_app(-T: Data, xs: List<&2, T>, ys: List<&2, T>) -> {List.take(&2, T, List.append(&2, T, xs, ys), List.length(&2, T, xs)) == xs : List<&2, T>}:
  match xs:
    case Nil{}:
      match ys:
        case Nil{}:
          {==}
        case Con{y, t}:
          {==}
    case Con{x, t}:
      AP.con_cong(T, x, List.take(&2, T, List.append(&2, T, t, ys), List.length(&2, T, t)), t, AP.take_app(T, t, ys))

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.con_cong