ReductionPROOF.tensor_preserved: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend as ReductionPROOF
Lines 469-478 of bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&start_line=469&end_line=478

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/reduction.bend as Reduction
import bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage

# The tensor the fold hands back holds every word it held.
def tensor_preserved(-shape: Shape.Shape, +fuel: Nat, tensor: Core.Tensor<shape>) ->
  Fact<Laws.Preserved<shape, tensor, Reduction.tensor_sum(shape, fuel, tensor)>>:
  Core.TTensor{storage, exact} = tensor
  match storage:
    case Storage.Empty{}:
      Fact{Laws.Preserved{other => {==}}}
    case Storage.Owned{+depth, +length, array, balanced, valid}:
      owned_preserved(shape, depth, length, array, balanced, valid, exact, Reduction.array_sum(fuel, 0n, 0.0, array),
        Reduction.array_sum_keeps(depth, array, balanced, fuel, 0n, 0.0, array, {==}))

Uses (10):
  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/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/main.bend&name=Storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=array_sum
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=array_sum_keeps
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=tensor_sum
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=Preserved
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=Fact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=owned_preserved