theorem gain_decreasing_in_friction {K_eff₁ K_eff₂ a_base F_prev β : ℝ}
(ha : 0 < a_base) (hF : 0 < F_prev) (_hβ : 0 < β)
(hK : K_eff₁ < K_eff₂) :
a_base * K_eff₁ * F_prev ^ β < a_base * K_eff₂ * F_prev ^ β := by
apply mul_lt_mul_of_pos_right _ (rpow_pos_of_pos hF β)
exact mul_lt_mul_of_pos_left hK haProposition: Endogenous Crossing