Sort.internal_sorted_cons_ins: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/sort.bend as Sort
Lines 62-67 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=62&end_line=67

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

def internal_sorted_cons_ins(~A: Data, ~le: A -> A -> Bool, ~le_total: @x: A -> @y: A -> {le(x, y) == False{} : Bool} -> {le(y, x) == True{} : Bool}, +t: List<&2, A>, +y: A, +x: A, hyx: {le(y, x) == True{} : Bool}, +h: MList.sorted_by(~A, ~le, y <> t)) -> MList.sorted_by(~A, ~le, y <> MPerm.insert_by(~A, ~le, x, t)):
  match t:
    case Nil{}:
      internal_sorted_cons_cons_intro(~A, ~le, y, x, Nil{}, hyx, internal_sorted_single(~A, ~le, x))
    case +z <> +u:
      internal_cons_ins_step(~A, ~le, ~le_total, le(x, z), y, x, z, u, {==}, hyx, h, hzx => internal_sorted_cons_ins(~A, ~le, ~le_total, u, z, x, hzx, internal_sorted_cons_cons_elim_tail(~A, ~le, y, z, u, h)))

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=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=insert_by
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_cons_ins_step
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_sorted_cons_cons_elim_tail
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_sorted_cons_cons_intro
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/sort.bend&name=internal_sorted_single