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formal statement (Lean)
54theorem b1_pos_lowNf (N_f : ℕ) (hNf : N_f ≤ 8) : 0 < b1 N_f := by
proof body
Tactic-mode proof.
55 unfold b1
56 apply div_pos _ (by positivity : (0 : ℝ) < 8 * Real.pi ^ 2)
57 have hNf_real : (N_f : ℝ) ≤ 8 := by exact_mod_cast hNf
58 linarith
59
60/-- At N_f = 5 (canonical between bottom and top thresholds): b1 > 0. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
-
b1_at_Nf5_pos
in IndisputableMonolith.Physics.QCDRGE.TwoLoopAlphaS
decl_use
depends on (5)
Lean names referenced from this declaration's body.
-
canonical
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
-
canonical
in IndisputableMonolith.Gap45.Beat
decl_use
-
canonical
in IndisputableMonolith.NavierStokes.RM2U.NonParasitism
decl_use
-
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
-
b1
in IndisputableMonolith.Physics.QCDRGE.TwoLoopAlphaS
decl_use