List.sorted_append: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 1061-1068 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=1061&end_line=1068

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

# Appending two Nat lists sorted by Nat.is_le, with every element of the first <= every element of the second, gives a sorted list.
law sorted_append:
  for xs: List<&2, Nat>
  for ys: List<&2, Nat>
  for bnd: @x: Nat -> @y: Nat -> mem(~Nat, ~Nat.is_eq, x, xs) -> mem(~Nat, ~Nat.is_eq, y, ys) -> MNat.le(x, y)
  for hx: sorted_by(~Nat, ~Nat.is_le, xs)
  for hy: sorted_by(~Nat, ~Nat.is_le, ys)
  sorted_by(~Nat, ~Nat.is_le, List.append(&2, Nat, xs, ys))

Uses (9):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  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=internal_sorted_append_cons
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=mem
  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/nat.bend&name=le