theorem pareto_ranking_strengthened {J_high J_low ρ c : ℝ}
(hJl : 1 < J_low) (hJh : J_low < J_high)
(hρ0 : 0 < ρ) (hρ1 : ρ < 1) (hc : 0 < c) :
valueFunction J_low ρ c < valueFunction J_high ρ c :=
valueFunction_increasing hJl hJh hρ0 hρ1 hcPaper 1c: Formal Calculus on K(J) and V(J)