Sort.internal_length_evens_le: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/sort.bend as Sort
Lines 194-203 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=194&end_line=203

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

def internal_length_evens_le(~A: Data, +xs: List<&2, A>) -> {Nat.is_le(List.length(&2, A, MPerm.evens(A, xs)), List.length(&2, A, xs)) == True{} : Bool}:
  match xs:
    case Nil{}:
      {==}
    case +x <> +r:
      match r:
        case Nil{}:
          {==}
        case +y <> +t:
          MNat.succ_le_succ(List.length(&2, A, MPerm.evens(A, t)), 1n+List.length(&2, A, t), MNat.le_trans(List.length(&2, A, MPerm.evens(A, t)), List.length(&2, A, t), 1n+List.length(&2, A, t), internal_length_evens_le(~A, t), MNat.le_succ(List.length(&2, A, t))))

Uses (9):
  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=Base/base.bend&name=List.length
  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/nat.bend&name=le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=succ_le_succ
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=evens