BackwardPROOF.somes_nones: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend as BackwardPROOF
Lines 225-230 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=225&end_line=230

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

def somes_nones(+count: Nat) -> {Laws.somes(Backward.nones(count)) == Laws.falses(count) : List<&2, Bool>}:
  match count:
    case 0n:
      {==}
    case 1n+rest:
      Equal.cong(List<&2, Bool>, List<&2, Bool>, xs => False{} <> xs, Laws.somes(Backward.nones(rest)), Laws.falses(rest), somes_nones(rest))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=nones
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=falses
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=somes