BackwardPROOF.nodes_length: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 374-381 of bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&start_line=374&end_line=381

import Base
import bendtorch-core@0.1.0.0/src/autograd/backward.bend as Backward

def nodes_length(+entries: List<&2, Backward.Entry>) ->
  {List.length(&2, Backward.Entry, entries) == List.length(&2, Backward.Node, Backward.nodes(entries)) : Nat}:
  match entries:
    case Nil{}:
      {==}
    case Con{Backward.Entry{node, value, slot}, rest}:
      Equal.cong(Nat, Nat, number => 1n+number, List.length(&2, Backward.Entry, rest),
        List.length(&2, Backward.Node, Backward.nodes(rest)), nodes_length(rest))

Uses (7):
  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=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=Entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=Node
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=nodes