OAI/Combinatorics/ProgressionColoring/OuterRowRealBound.lean
2 declarations, 0 contain sorry, 0 declared as axioms
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.
- theorem
OAI.QuantitativeVanDerWaerden.real_div_ten_sub_one_ltline 17Source 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 … - theorem
OAI.QuantitativeVanDerWaerden.real_div_ten_sub_one_leline 24Source 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) := …