BroadcastPointwisePROOF.cells_length: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_PROOF.bend as BroadcastPointwisePROOF
Lines 38-48 of bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_PROOF.bend&start_line=38&end_line=48

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend as PointwiseBroadcast
import bendtorch-core@0.1.0.0/src/autograd/reduce_fold_PROOF.bend as FoldProof
import bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend as Laws

def cells_length(+plan: Shape.BroadcastPlan, +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +count: Nat) ->
  {List.length(&2, F32, Laws.cells(plan, shape, fill, ops, count)) == count : Nat}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +before = Laws.cells(plan, shape, fill, ops, previous)
      +last = Replayed.value(shape, fill, ops, U32.from_nat(PointwiseBroadcast.left_map(plan, previous)))
      Equal.trans(Nat, List.length(&2, F32, List.append(&2, F32, before, [last])), 1n+List.length(&2, F32, before), 1n+previous,
        FoldProof.length_snoc(before, last),
        Equal.cong(Nat, Nat, n => 1n+n, List.length(&2, F32, before), previous, cells_length(plan, shape, fill, ops, previous)))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  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=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/broadcast_pointwise_LAWS.bend&name=cells
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold_PROOF.bend&name=length_snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend&name=left_map
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=value