PROOF.li.len_take: def of bend-osdev-mode-core@0.1.0.0
Import: import bend-osdev-mode-core@0.1.0.0/PROOF.bend as PROOF
Lines 165-175 of bend-osdev-mode-core@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-mode-core@0.1.0.0/PROOF.bend&start_line=165&end_line=175

import Base
import bend-osdev-bytes@0.1.1.0/bytes.bend as B

def li.len_take(+n: Nat, +xs: List<&2, U32>) -> {Nat.is_le(n, B.len(xs)) == True{} : Bool} -> {B.len(B.take(n, xs)) == n : Nat}:
  match n:
    case 0n:
      h => {==}
    case 1n+p:
      match xs:
        case Nil{}:
          h => bo.absurd({B.len(B.take(1n+p, Nil{})) == 1n+p : Nat}, h)
        case Con{+x, +t}:
          h => %li.len_take(p, t)(h) : {1n+B.len(B.take(p, t)) == 1n+_ : Nat}
            {==}

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=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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-mode-core@0.1.0.0/PROOF.bend&name=bo.absurd