GatherPROOF.count_length: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 18-23 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=18&end_line=23

import Base
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws

def count_length(entries: List<&2, U32>) -> {Gather.count(entries) == Laws.length(entries) : Nat}:
  match entries:
    case Nil{}:
      {==}
    case head <> rest:
      Equal.cong(Nat, Nat, x => 1n+x, Gather.count(rest), Laws.length(rest), count_length(rest))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=count
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=length