Roth Lemma

Abstract

Degree ratios bound the polynomial index in Roth’s lemma.

Theorem 1.1 (Roth Lemma).

Lean statement: D5/S3/Arith/DiophantineApproximation/RothLemma.index_le_of_degree_ratio

Proof. Machine-checked in Lean as D5/S3/Arith/DiophantineApproximation/RothLemma.index_le_of_degree_ratio (✓ std3). ∎

Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.

Commentary.

Degree ratios bound the polynomial index in Roth’s lemma.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/RothLemma.index_le_of_degree_ratio
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma
• Dependency: D5/S3/Arith/DiophantineApproximation/DisjointVariables
• Dependency: D5/S3/Arith/DiophantineApproximation/IndexRename
• Dependency: D5/S3/Arith/DiophantineApproximation/MvHasseDeriv
• Dependency: D5/S3/Arith/DiophantineApproximation/PolynomialDeterminantHeight
• Dependency: D5/S3/Arith/DiophantineApproximation/RothBaseCase
• Dependency: D5/S3/Arith/DiophantineApproximation/RothDecomposition