TransformPROOF.natural_decided_success: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 1861-1875 of bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&start_line=1861&end_line=1875

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/layout.bend as Layout
import bendtorch-core@0.1.0.0/src/tensor/transform_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/transforms.bend as Transforms
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/tensor/permutation_mapping.bend as Mapping

def natural_decided_success(+input: Shape.Shape, +axes: List<&2, U32>, +plan: Layout.Plan<input, axes>, +cursor: Nat, +index: U32,
  decision: Shape.BoolCase<Nat.is_eq(U32.to_nat(index), cursor)>, source: Core.Tensor<input>, target: Core.Tensor<Layout.output(input, axes, plan)>,
  -candidate: {index == U32.from_nat(cursor) : U32}, -word_exact: {U32.to_nat(index) == cursor : Nat},
  +inside: {True{} == U32.is_lt(index, Shape.count(Layout.output(input, axes, plan))) : Bool}) ->
  Totality.NaturalSuccess<input, axes, plan, cursor, Transforms.natural_decided(input, axes, plan, cursor, index, source, target, candidate, decision)>:
  match decision:
    case Shape.BFalse{equal}:
      Totality.NaturalSuccess{Empty.absurd({False{} == True{} : Bool},
        Arith.clash(Equal.trans(Bool, False{}, Nat.is_eq(U32.to_nat(index), cursor), True{}, equal, Mapping.natural_equal_true(U32.to_nat(index), cursor, word_exact))))}
    case Shape.BTrue{equal}:
      Totality.NaturalSuccess{
        {\{Totality.CopyStepSuccess: successful => successful} :
          Totality.CopyStepSuccess<input, axes, plan, source, target, index> ->
            {Totality.copy_succeeded(input, axes, plan, Transforms.copy_step(input, axes, plan, source, target, index)) == True{} : Bool}}(
              Laws.copy_step_valid_success(input, axes, plan, source, target, index, inside))}

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BoolCase
  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/shape/core.bend&name=count
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash
  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/layout.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=output
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permutation_mapping.bend&name=natural_equal_true
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_LAWS.bend&name=copy_step_valid_success
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend&name=CopyStepSuccess
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend&name=NaturalSuccess
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend&name=copy_succeeded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=copy_step
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_decided