`x + Out(x) ≤ 1` on `[0,1/2]`
ProvedBlockCycleRotation.add_Outt_le_oneblock-cycle-rotationintegrationreal-analysis
x + Out(x) ≤ 1 on [0,1/2].
This is an auxiliary lemma of the formalization rather than a result stated in the paper. It is used in the proof of psiPartial_le_two.
Preamble
import Definitions.Def_BlockCycleRotation_Theorem10 import Mathlib open BlockCycleRotation open Finset Real Filter Topology MeasureTheory BoxIntegral open scoped ENNReal
Formal statement
theorem BlockCycleRotation.add_Outt_le_one {x : ℝ} (hx0 : 0 ≤ x) (hx : x ≤ 1 / 2) : x + Outt x ≤ 1 := by sorrySource
Valentin Blomer and Kai-Uwe Bux, "The cost of cyclic permutations and remainder sums in the Euclidean algorithm", AofA 2026, LIPIcs vol. 381, pp. 14:1-14:17, doi:10.4230/LIPIcs.AofA.2026.14. Numbering follows the full version, arXiv:2601.00979v1. Lean source: https://github.com/dbenbenn/block-cycle-rotation/blob/f69003fd8b00c9b5d6d1a4f6807b4943bce0a92c/BlockCycleRotation/Theorem10.lean#L482-L499