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Lean-Workbook Plus 19379: Trigonometric inequality

Proved
WorkbookRestored.plus_19379

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every x∈[0,π/2]x\in[0,\pi/2], 1≤2−sin⁡x+cos⁡x≤31\le2-\sin x+\cos x\le3.

Source: Lean-Workbook row lean_workbook_plus_19379 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_19379 (x: ℝ) (hx: 0 ≤ x ∧ x ≤ π/2) :
  1 ≤ 2 - Real.sin x + Real.cos x ∧ 2 - Real.sin x + Real.cos x ≤ 3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_19379; immutable original Prove2Me node 29cf79bc-c978-4461-b1df-79ba1b418e31

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