ReductionPROOF.fold_value: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/reduction_PROOF.bend as ReductionPROOF
Lines 357-373 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=357&end_line=373

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
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model

def fold_value(-shape: Shape.Shape, +depth: Nat, +length: Nat, -original: Array<F32>, -balanced: Model.Balanced(F32, depth, original),
  -valid: {Storage.bounds(depth, length) == True{} : Bool},
  -exact: {length == Shape.logical_numel(Shape.dimensions(shape)) : Nat}, +fuel: Nat, +accumulator: F32,
  +values: List<&2, F32>,
  logical: Laws.LogicalValues(fuel, shape, Core.TTensor{Storage.Owned{depth, length, original, balanced, valid}, exact}, 0n, values)) ->
  Fact<{Pair.fst(F32, Array<F32>, Reduction.array_sum(fuel, 0n, accumulator, original)) == Reduction.sequential_sum(values, accumulator) : F32}>:
  match fuel values:
    case 0n Nil{}:
      Fact{{==}}
    case 1n+rest values:
      Fact{{\{Fact: p => p} : Fact<({Pair.fst(F32, Array<F32>, Reduction.array_sum(1n+rest, 0n, accumulator, original)) == Reduction.sequential_sum(values, accumulator) : F32})> ->
        {Pair.fst(F32, Array<F32>, Reduction.array_sum(1n+rest, 0n, accumulator, original)) == Reduction.sequential_sum(values, accumulator) : F32}}(
        run_value(shape, depth, length, original, balanced, valid, exact, rest, 0n, accumulator, original,
          Array.get(F32, original, U32.from_nat(0n)), {==}, {==}, values, logical))}
    case 0n value <> others:
      Empty.absurd(Fact<{Pair.fst(F32, Array<F32>, Reduction.array_sum(0n, 0n, accumulator, original)) ==
        Reduction.sequential_sum(value <> others, accumulator) : F32}>, logical)

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  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=F32
  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=Pair.fst
  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/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=logical_numel
  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/storage/main.bend&name=bounds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Balanced
  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=sequential_sum
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/reduction_LAWS.bend&name=LogicalValues
  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=run_value