Sort.merge_by_sorted: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/sort.bend as Sort
Lines 161-169 of bend-mathlib@0.8.1.0/sort.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/sort.bend&start_line=161&end_line=169

import Base
import bend-mathlib@0.8.1.0/list.bend as MList
import bend-mathlib@0.8.1.0/perm.bend as MPerm

# Merging two sorted lists is sorted (needs transitivity, and totality for the un-taken branch).
def merge_by_sorted(~A: Data, ~le: A -> A -> Bool, ~le_trans: @x: A -> @y: A -> @z: A -> {le(x, y) == True{} : Bool} -> {le(y, z) == True{} : Bool} -> {le(x, z) == True{} : Bool}, ~le_total: @x: A -> @y: A -> {le(x, y) == False{} : Bool} -> {le(y, x) == True{} : Bool}, +xs: List<&2, A>, +ys: List<&2, A>, +hx: MList.sorted_by(~A, ~le, xs), +hy: MList.sorted_by(~A, ~le, ys)) -> MList.sorted_by(~A, ~le, MPerm.merge_by(~A, ~le, xs, ys)):
  match xs ys:
    case Nil{} _:
      hy
    case +x <> +xt Nil{}:
      hx
    case +x <> +xt +y <> +yt:
      internal_merge_sorted_pick(~A, ~le, ~le_trans, ~le_total, le(x, y), x, xt, y, yt, {==}, hx, hy, merge_by_sorted(~A, ~le, ~le_trans, ~le_total, xt, y <> yt, internal_sorted_tail(~A, ~le, x, xt, hx), hy), merge_by_sorted(~A, ~le, ~le_trans, ~le_total, x <> xt, yt, hx, internal_sorted_tail(~A, ~le, y, yt, hy)))

Uses (6):
  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=bend-mathlib@0.8.1.0/list.bend&name=sorted_by
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=merge_by
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_merge_sorted_pick
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_sorted_tail