List.internal_sorted_skip: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 945-952 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=945&end_line=952

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

def internal_sorted_skip(+x: Nat, +z: Nat, t: List<&2, Nat>, h: sorted_by(~Nat, ~Nat.is_le, x <> z <> t)) -> sorted_by(~Nat, ~Nat.is_le, x <> t):
  match t:
    case Nil{}:
      {==}
    case +w <> u:
      +u = u
      +h = h
      sorted_cons_cons_intro(x, w, u, MNat.le_trans(x, z, w, sorted_cons_cons_elim_le(x, z, w <> u, h), sorted_cons_cons_elim_le(z, w, u, sorted_cons_cons_elim_tail(x, z, w <> u, h))), sorted_cons_cons_elim_tail(z, w, u, sorted_cons_cons_elim_tail(x, z, w <> 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=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
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_trans