MatmulPROOF.left_certificate: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 216-234 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=216&end_line=234

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 left_certificate(+fuel: Nat, +left: Shape.Shape, +right: Shape.Shape, -a: Core.Tensor<left>, -b: Core.Tensor<right>,
  +row: U32, +column: U32, +cursor: Nat, +accumulator: F32,
  -rec: @a: Core.Tensor<left> -> @b: Core.Tensor<right> -> @+value: F32 ->
    Laws.SourceDot<fuel, left, right, a, b, row, column, 1n+cursor, value, Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value)>,
  -exact_cursor: {U32.to_nat(U32.from_nat(cursor)) == cursor : Nat},
  certificate: CoordinateRead<left, a, [row, U32.from_nat(cursor)]>) ->
  Laws.SourceDot<1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.left_read(left, right,
    a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), b, [U32.from_nat(cursor), column], accumulator,
    Core.read_coordinate(left, a, [row, U32.from_nat(cursor)]))>:
  CoordinateRead{ra, +result, +exact, meaning, left_kept} = certificate
  Laws.SourceDot{unit =>
    claim : @certificate: Laws.SourceDot<1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.left_read(left, right,
      a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), b, [U32.from_nat(cursor), column], accumulator, (ra, result))> ->
      Laws.DotResultMeaning(1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.left_read(left, right,
        a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), b, [U32.from_nat(cursor), column], accumulator, (ra, result))) =
      \{Laws.SourceDot: proof => proof(Unit{})}
    %exact : Laws.DotResultMeaning(1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.left_read(left, right,
      a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), b, [U32.from_nat(cursor), column], accumulator, _))
    claim(left_pair(fuel, left, right, a, b, ra, result, row, column, cursor, accumulator, rec, exact_cursor, meaning, left_kept))}

Uses (17):
  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=Sigma
  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.to_nat
  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/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=read_coordinate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=left_read
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=natural_dot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=DotResultMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=SourceDot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=CoordinateRead
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=left_pair