theorem welfare_gap_proportional_to_K {J_high J_low ρ : ℝ}
(hJl : 1 < J_low) (hJh : J_low < J_high) (hρ : ρ < 1)
(benefit : ℝ) (hb : 0 < benefit) :
0 < coordinationGap J_high J_low ρ * benefit := by
exact mul_pos (coordinationGap_pos hJl hJh hρ) hbPaper 1c, Section 4: Welfare and Coordination Failure