ReductionPROOF.preserved_certificate: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend as ReductionPROOF
Lines 196-226 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=196&end_line=226

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_certificate(+fuel: Nat, -shape: Shape.Shape, -original: Core.Tensor<shape>, +cursor: Nat, +accumulator: F32,
  -rec: @tensor: Core.Tensor<shape> -> @+value: F32 -> Laws.Preserved<shape, tensor, Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value)>,
  certificate: Core.Read<shape, original, U32.from_nat(cursor)>, -retention: Core.SourceReadKeeps<shape, original, U32.from_nat(cursor)>) ->
  Laws.Preserved<shape, original, Reduction.read_step(shape,
    tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, Core.read_flat(shape, original, U32.from_nat(cursor)))>:
  Core.Read{tensor, +result, +exact} = certificate
  Laws.Preserved{other =>
    claim : @certificate: Laws.Preserved<shape, original, Reduction.read_step(shape,
      tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, (tensor, result))> ->
      {Laws.retained_observe(shape, Reduction.read_step(shape,
        tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, (tensor, result)), other) ==
        Laws.successful_observe(shape, original, Reduction.read_step(shape,
          tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, (tensor, result)), other) : Maybe<&2, F32>} =
      \{Laws.Preserved: kept => kept(other)}
    prove : @retention: Core.SourceReadKeeps<shape, original, U32.from_nat(cursor)> ->
      {Laws.retained_observe(shape, Reduction.read_step(shape,
        tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, Core.read_flat(shape, original, U32.from_nat(cursor))), other) ==
        Laws.successful_observe(shape, original, Reduction.read_step(shape,
          tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, Core.read_flat(shape, original, U32.from_nat(cursor))), other) : Maybe<&2, F32>} =
      \{Core.SourceReadKeeps: kept =>
      %exact :
        {Laws.retained_observe(shape, Reduction.read_step(shape,
          tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, _), other) ==
          Laws.successful_observe(shape, original, Reduction.read_step(shape,
            tensor => value => Reduction.natural_sum_loop(fuel, shape, tensor, 1n+cursor, value), accumulator, _), other) : Maybe<&2, F32>}
      claim(preserved_read(fuel, shape, original, cursor, accumulator, tensor, result, rec,
        other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(shape, tensor, other),
          Core.retained_read_observe(shape, Core.read_flat(shape, original, U32.from_nat(cursor)), other), Core.checked_observe(shape, original, other),
          Equal.cong(Core.Tensor<shape> & Result<&2, &2, Core.Error, F32>, Maybe<&2, F32>, pair => Core.retained_read_observe(shape, pair, other),
            (tensor, result), Core.read_flat(shape, original, U32.from_nat(cursor)), exact), kept(other))))}
    prove(retention)}

Uses (23):
  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=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  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.from_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/tensor/core.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Read
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=SourceReadKeeps
  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/core.bend&name=read_flat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=retained_read_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=preserved_read