CorePROOF.independent_pair_mapping: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend as CorePROOF
Lines 1076-1086 of bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&start_line=1076&end_line=1086

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/elementwise.bend as Elementwise
import bendtorch-core@0.1.0.0/src/tensor/core_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend as Projection

def independent_pair_mapping(+operation: Elementwise.Operation, +plan: Shape.BroadcastPlan, -left: Core.Dynamic, -right: Core.Dynamic,
  result: (Core.Dynamic & Core.Dynamic) & Result<&2, &1, Core.Error, Core.Dynamic>,
  -shared: Elementwise.SuccessfulMapping(operation, plan, left, right, result)) -> Laws.IndependentModel<operation, plan, left, right, result>:
  (inputs, outcome) = result
  match outcome:
    case Fail{error}:
      Laws.IndependentModel{Unit{}}
    case Done{output}:
      Laws.IndependentModel{index => inside => Equal.trans(Maybe<&2, F32>, Core.observe_dynamic(output, index), Elementwise.expected(operation, plan, left, right, index),
        Projection.specified_expected(operation, left, right, Projection.offset_spec(plan, U32.to_nat(index))), shared(index)(inside),
        Projection.expected_projection_refines(operation, plan, left, right, index))}

Uses (19):
  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=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.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  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/tensor/core.bend&name=Dynamic
  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=observe_dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_LAWS.bend&name=IndependentModel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=Operation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=SuccessfulMapping
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=expected
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=expected_projection_refines
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=offset_spec
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=specified_expected