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e320e82 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | import OAI.Combinatorics.ExpectationThreshold.SelectorDefinitions
namespace OAI
/-! Elementary bounds on the literal truncation scales. -/
namespace TalagrandThreshold.Selector
theorem dscale_pos {s : ℕ} (i : Fin s) : 0 < dscale i := by
exact inv_pos.mpr (pow_pos (by norm_num : (0 : ℝ) < 2) _)
theorem dscale_nonneg {s : ℕ} (i : Fin s) : 0 ≤ dscale i :=
(dscale_pos i).le
theorem dscale_lt_one {s : ℕ} (i : Fin s) : dscale i < 1 := by
exact inv_lt_one_of_one_lt₀
(one_lt_pow₀ (by norm_num : (1 : ℝ) < 2) (Nat.succ_ne_zero i.val))
end TalagrandThreshold.Selector
end OAI
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