Sort.internal_cons_ins_step: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/sort.bend as Sort
Lines 55-60 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=55&end_line=60

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_cons_ins_step(~A: Data, ~le: A -> A -> Bool, ~le_total: @x: A -> @y: A -> {le(x, y) == False{} : Bool} -> {le(y, x) == True{} : Bool}, b: Bool, +y: A, +x: A, +z: A, +u: List<&2, A>, e: {le(x, z) == b : Bool}, hyx: {le(y, x) == True{} : Bool}, +h: MList.sorted_by(~A, ~le, y <> z <> u), k: {le(z, x) == True{} : Bool} -> MList.sorted_by(~A, ~le, z <> MPerm.insert_by(~A, ~le, x, u))) -> MList.sorted_by(~A, ~le, y <> Bool.pick(List<&2, A>, b, x <> z <> u, z <> MPerm.insert_by(~A, ~le, x, u))):
  match b:
    case True{}:
      internal_sorted_cons_cons_intro(~A, ~le, y, x, z <> u, hyx, internal_sorted_cons_cons_intro(~A, ~le, x, z, u, e, internal_sorted_cons_cons_elim_tail(~A, ~le, y, z, u, h)))
    case False{}:
      internal_sorted_cons_cons_intro(~A, ~le, y, z, MPerm.insert_by(~A, ~le, x, u), internal_sorted_cons_cons_elim_le(~A, ~le, y, z, u, h), k(le_total(x, z, e)))

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=Bool.pick
  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_sorted_cons_cons_elim_le
  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