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Finite Approximation Code Bounds

Abstract

The finite set of codes in the first N approximation stages. Its complement has stage at least N, uniformly in the represented finite quotient point. This is the finite-support estimate needed to prove that the actual free representative differences have diagonal infinity fibers. It includes empty and finite S. New proofs, Apache-2.0; Rodriguez Camargo, Notes on Solid Geometry, Lemma 3.3.2.

Theorem 1.1 (finite Approximation Stage Codes mem).

Lean statement: D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationStageCodes_mem

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationStageCodes_mem (✓ std3). ∎

Source. Repository-derived.

Commentary.

The exact declaration is supplied by the compiled Lean source. The finite set of codes in the first N approximation stages. Its complement has stage at least N, uniformly in the represented finite quotient point. This is the finite-support estimate needed to prove that the actual free representative differences have diagonal infinity fibers. It includes empty and finite S. New proofs, Apache-2.0; Rodriguez Camargo, Notes on Solid Geometry, Lemma 3.3.2.

Theorem 1.2 (finite Approximation Index stage eventually).

Lean statement: D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationIndex_stage_eventually

Proof. Machine-checked in Lean as D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationIndex_stage_eventually (✓ std3). ∎

Source. Repository-derived.

Commentary.

The exact declaration is supplied by the compiled Lean source. The finite set of codes in the first N approximation stages. Its complement has stage at least N, uniformly in the represented finite quotient point. This is the finite-support estimate needed to prove that the actual free representative differences have diagonal infinity fibers. It includes empty and finite S. New proofs, Apache-2.0; Rodriguez Camargo, Notes on Solid Geometry, Lemma 3.3.2.

References

  • Truth anchor: D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationIndex_stage_eventually
  • Truth anchor: D5/S3/HomologicalAlgebra/Solid/FiniteApproximationCodeBounds.finiteApproximationStageCodes_mem
  • Dependency: D5/S3/HomologicalAlgebra/Solid/FiniteApproximationIndex