ReductionPROOF.preserved_read: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend as ReductionPROOF
Lines 174-194 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=174&end_line=194

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

def preserved_read(+fuel: Nat, -shape: Shape.Shape, -original: Core.Tensor<shape>, +cursor: Nat, +accumulator: F32,
  tensor: Core.Tensor<shape>, result: Result<&2, &2, Core.Error, F32>,
  -rec: @tensor: Core.Tensor<shape> -> @+value: F32 -> Laws.Preserved<shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value)>,
  -kept: @+other: U32 -> {Core.checked_observe(shape, tensor, other) == Core.checked_observe(shape, original, other) : Maybe<&2, F32>}) ->
  Laws.Preserved<shape, original, Reduction.read_step(shape,
    tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, (tensor, result))>:
  match result:
    case Fail{error}:
      Laws.Preserved{other => {==}}
    case Done{+value}:
      Laws.Preserved{other =>
        claim : @certificate: Laws.Preserved<shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value))> ->
          {Laws.retained_observe(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other) ==
            Laws.successful_observe(shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other) : Maybe<&2, F32>} =
          \{Laws.Preserved: kept => kept(other)}
        Equal.trans(Maybe<&2, F32>,
          Laws.retained_observe(shape, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
          Laws.successful_observe(shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
          Laws.successful_observe(shape, original, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other),
          claim(rec(tensor, F32.add(accumulator, value))), success_keeps(shape, original, tensor,
            Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, F32.add(accumulator, value)), other, kept(other)))}

Uses (18):
  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=F32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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/tensor/core.bend&name=Error
  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/core.bend&name=checked_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=natural_sum_loop
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction.bend&name=read_step
  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_LAWS.bend&name=retained_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=successful_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend&name=success_keeps