BackwardLAWS.backward_accepts_bound_operands: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend as BackwardLAWS
Lines 412-420 of bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&start_line=412&end_line=420

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

# A tape whose every operand is bound is accepted for every output it holds.
law backward_accepts_bound_operands:
  for +entries: List<&2, Backward.Entry>
  for +output: Nat
  for inside: {Nat.is_lt(output, List.length(&2, Backward.Entry, entries)) == True{} : Bool}
  for bound: {well_formed(Backward.nodes(entries)) == True{} : Bool}
  {Backward.backward(Backward.Tape{entries}, output) ==
    Done{Backward.Tape{Backward.merge(entries, Backward.pass(Backward.nodes(entries), List.length(&2, Backward.Entry, entries), output))}} :
    Result<&2, &2, Backward.Error, Backward.Tape>}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  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=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=Tape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=backward
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=merge
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=nodes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=pass
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=wired
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=backward_success
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&name=well_formed
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=wired_entries