theorem modeRate_pos {k : ℕ} (hk : 1 ≤ k) (m : ℕ) : 0 < modeRate k m := by simp only [modeRate] split · exact one_pos · exact rpow_pos_of_pos (Nat.cast_pos.mpr (by omega)) _
thesis/CESProofs/Foundations/Emergence.lean:145
Emergence results from Paper 1, Sections 3-5: