MatmulPROOF.created_product: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 569-589 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=569&end_line=589

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/tensor/matmul_LAWS.bend as Laws

def created_product(+left: Shape.Shape, +right: Shape.Shape, +output: Shape.Shape, +inner: U32, +columns: U32,
  a: Core.Tensor<left>, b: Core.Tensor<right>, result: Result<&2, &1, Core.Error, Core.Tensor<output>>) ->
  Laws.SourceProduct<inner, left, right, a, b, output, Shape.logical_numel(Shape.dimensions(output)), Matrix.created(left, right, output, inner, columns, a, b, result)>:
  match result:
    case Fail{error}:
      Laws.SourceProduct{unit => Unit{}}
    case Done{out}:
      Laws.SourceProduct{unit =>
        claim : @certificate: Laws.SourceProduct<inner, left, right, a, b, output,
          Nat.add(Shape.logical_numel(Shape.dimensions(output)), 0n),
          Matrix.natural_product_loop(Shape.logical_numel(Shape.dimensions(output)), left, right, output, inner, columns, a, b, out, 0n)> ->
          Laws.ProductMeaning(inner, left, right, a, b, output, Nat.add(Shape.logical_numel(Shape.dimensions(output)), 0n),
            Matrix.natural_product_loop(Shape.logical_numel(Shape.dimensions(output)), left, right, output, inner, columns, a, b, out, 0n)) =
          \{Laws.SourceProduct: meaning => meaning(Unit{})}
        %Equal.sym(Nat, Shape.elements(output), Shape.logical_numel(Shape.dimensions(output)), Shape.elements_exact(output)) :
          Laws.ProductMeaning(inner, left, right, a, b, output, Shape.logical_numel(Shape.dimensions(output)),
            Matrix.natural_product_loop(_, left, right, output, inner, columns, a, b, out, 0n))
        %add_zero(Shape.logical_numel(Shape.dimensions(output))) : Laws.ProductMeaning(inner, left, right, a, b, output, _,
          Matrix.natural_product_loop(Shape.logical_numel(Shape.dimensions(output)), left, right, output, inner, columns, a, b, out, 0n))
        claim(Laws.successful_product_interpretation(Shape.logical_numel(Shape.dimensions(output)), left, right, output, inner, columns, a, b,
          a, b, out, 0n, empty_prefix(inner, left, right, a, b, output, out)))}

Uses (20):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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=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=elements
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=elements_exact
  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/tensor/core.bend&name=Error
  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/matmul.bend&name=created
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=natural_product_loop
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=ProductMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=SourceProduct
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=successful_product_interpretation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=empty_prefix