ReductionPROOF.owned_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 391-405 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=391&end_line=405

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 owned_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, +values: List<&2, F32>,
  logical: Laws.LogicalValues(fuel, shape, Core.TTensor{Storage.Owned{depth, length, original, balanced, valid}, exact}, 0n, values),
  pair: F32 & Array<F32>, -kept: Reduction.Fact<{Pair.snd(F32, Array<F32>, pair) == original : Array<F32>}>,
  -folded: {pair == Reduction.array_sum(fuel, 0n, 0.0, original) : F32 & Array<F32>}) ->
  Fact<{Laws.loop_value(shape, Reduction.owned_sum(shape, depth, length, original, balanced, valid, exact, pair, kept)) ==
    Some{Reduction.sequential_sum(values, 0.0)} : Maybe<&2, F32>}>:
  (value, retained) = pair
  Fact{Equal.cong(F32, Maybe<&2, F32>, x => Some{x}, value, Reduction.sequential_sum(values, 0.0),
    Equal.trans(F32, value, Pair.fst(F32, Array<F32>, Reduction.array_sum(fuel, 0n, 0.0, original)), Reduction.sequential_sum(values, 0.0),
      Equal.cong(F32 & Array<F32>, F32, p => Pair.fst(F32, Array<F32>, p), (value, retained), Reduction.array_sum(fuel, 0n, 0.0, original), folded),
      {\{Fact: p => p} : Fact<({Pair.fst(F32, Array<F32>, Reduction.array_sum(fuel, 0n, 0.0, original)) == Reduction.sequential_sum(values, 0.0) : F32})> ->
        {Pair.fst(F32, Array<F32>, Reduction.array_sum(fuel, 0n, 0.0, original)) == Reduction.sequential_sum(values, 0.0) : F32}}(
        fold_value(shape, depth, length, original, balanced, valid, exact, fuel, 0.0, values, logical))))}

Uses (27):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=List
  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=Pair.fst
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  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=Fact
  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=owned_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_LAWS.bend&name=loop_value
  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=fold_value