List.internal_sorted_take_cons: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 901-910 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=901&end_line=910

import Base

def internal_sorted_take_cons(t: List<&2, Nat>, n: Nat, +x: Nat, h: sorted_by(~Nat, ~Nat.is_le, x <> t)) -> sorted_by(~Nat, ~Nat.is_le, x <> List.take(&2, Nat, t, n)):
  match t n:
    case Nil{} _:
      {==}
    case y <> u 0n:
      {==}
    case +y <> u 1n+q:
      +u = u
      +h = h
      sorted_cons_cons_intro(x, y, List.take(&2, Nat, u, q), sorted_cons_cons_elim_le(x, y, u, h), internal_sorted_take_cons(u, q, y, sorted_cons_cons_elim_tail(x, y, u, h)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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-mathlib@0.8.1.0/list.bend&name=sorted_by
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=sorted_cons_cons_elim_le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=sorted_cons_cons_elim_tail
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=sorted_cons_cons_intro