mulConst_le_inv_dens — Mathlib

English

If A is nonempty, then 1 ≤ δ_m[A] (self-divConst bound).

Русский

Если A непусто, то 1 ≤ δ_m[A] (самоделConst ограничение).

LaTeX

$$1 \leq \delta_m[A] \quad (A \text{ nonempty})$$

Lean4

/-- Dense sets have small doubling. -/
@[to_additive addConst_le_inv_dens /-- Dense sets have small doubling. -/
    ]
theorem mulConst_le_inv_dens : σₘ[A, B] ≤ A.dens⁻¹ := by rw [dens, inv_div, mulConst]; gcongr; exact card_le_univ _

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