CorePROOF.loop_certificate: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend as CorePROOF
Lines 974-988 of bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&start_line=974&end_line=988

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/elementwise.bend as Elementwise

def loop_certificate(fuel: Nat, +operation: Elementwise.Operation, +plan: Shape.BroadcastPlan, +cursor: Nat,
  -original_left: Core.Dynamic, -original_right: Core.Dynamic, state: Elementwise.State<Shape.output_shape(plan)>,
  -invariant: Elementwise.StateInvariant(operation, plan, original_left, original_right, cursor, state)) ->
  Elementwise.LoopCertificate<fuel, operation, plan, cursor, original_left, original_right, state>:
  match fuel:
    case 0n:
      Elementwise.State{left, right, output} = state
      Elementwise.LoopCertificate{((left, right), Done{Core.Packed{Shape.output_shape(plan), output}}), {==},
        %Equal.sym(Nat, Nat.add(cursor, 0n), cursor, add_zero_right(cursor)) :
          Elementwise.PrefixInvariant(operation, plan, original_left, original_right, _, Core.Packed{Shape.output_shape(plan), output})
        invariant_prefix(operation, plan, original_left, original_right, cursor, left, right, output, invariant)}
    case 1n++remaining:
      loop_after_certificate(remaining, operation, plan, cursor, original_left, original_right, state, invariant,
        natural_certificate(operation, plan, cursor, state),
        state => invariant => loop_certificate(remaining, operation, plan, 1n+cursor, original_left, original_right, state, invariant))

Uses (17):
  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=Sigma
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=output_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/core_PROOF.bend&name=add_zero_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&name=invariant_prefix
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&name=loop_after_certificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&name=natural_certificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=LoopCertificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=Operation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=PrefixInvariant
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=State
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=StateInvariant