TensorBackwardPROOF.alone_spared: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend as TensorBackwardPROOF
Lines 158-170 of bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_PROOF.bend&start_line=158&end_line=170

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/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend as Backward
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend as Laws

def alone_spared(+id: Nat, +b: Nat, +right: Shape.Shape, -x: Core.Dynamic, -y: Core.Dynamic, -g: Core.Dynamic,
  other: {Nat.is_eq(id, b) == False{} : Bool}, result: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic>) ->
  {Laws.sends_to(id, Backward.Pass{Backward.Operands{x, y}, g, Backward.alone(Backward.multiplied(b, right, result))}) == False{} : Bool}:
  match result:
    case Fail{error}:
      {==}
    case Done{triple}:
      match triple:
        case (kept_left, rest):
          match rest:
            case (kept_right, product):
              %Equal.sym(Bool, Nat.is_eq(id, b), False{}, other) : {Bool.or(_, False{}) == False{} : Bool}
              {==}

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=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=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Pass
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Saved
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=alone
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=multiplied
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward_LAWS.bend&name=sends_to
  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=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Error