ReduceParallelProof.padding_left: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend as ReduceParallelProof
Lines 36-41 of bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_parallel_proof.bend&start_line=36&end_line=41

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend as Broadcast
import bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend as ShapeProjection

def padding_left(+left: List<&2, Nat>, +right: List<&2, Nat>, +output: List<&2, Nat>, +lp: Nat, +rp: Nat,
  +aligned: Shape.Aligned(Shape.pad(lp, left), Shape.pad(rp, right), output)) ->
  {lp == Nat.sub(List.length(&2, Nat, output), List.length(&2, Nat, left)) : Nat}:
  ShapeProjection.padding_of(List.length(&2, Nat, output), lp, List.length(&2, Nat, left),
    Equal.trans(Nat, Nat.add(lp, List.length(&2, Nat, left)), List.length(&2, Nat, Shape.pad(lp, left)), List.length(&2, Nat, output),
      Broadcast.pad_length(lp, left), Broadcast.aligned_length_left(Shape.pad(lp, left), Shape.pad(rp, right), output, aligned)))

Uses (11):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=aligned_length_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=pad_length
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Aligned
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=pad
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/projection_proofs.bend&name=padding_of