OAI/Combinatorics/ProgressionColoring/OuterRowRealBound.lean

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A real lower bound for integer row sizes

The natural-number row bound m / 10 ≤ n implies a real lower bound with an absolute loss of one, suitable for the exponential incidence estimates.

  1. theorem OAI.QuantitativeVanDerWaerden.real_div_ten_sub_one_lt line 17

    Source documentation

    Losing one converts the floored row-size bound to a strict real bound.

    theorem real_div_ten_sub_one_lt {m n : ℕ} (h : m / 10 ≤ n) :
        (m : ℝ) / 10 - 1 < (n : ℝ) := by
    …
  2. theorem OAI.QuantitativeVanDerWaerden.real_div_ten_sub_one_le line 24

    Source documentation

    The real row-size lower bound used in weighted incidence sums.

    theorem real_div_ten_sub_one_le {m n : ℕ} (h : m / 10 ≤ n) :
        (m : ℝ) / 10 - 1 ≤ (n : ℝ) :=
    …