theorem equilibrium_output_decreasing_sigma {sigma1 sigma2 phi_val : ℝ}
(hphi : 0 < phi_val) (hs1 : 0 < sigma1) (_hs2 : 0 < sigma2)
(h12 : sigma1 < sigma2) :
phi_val / sigma2 < phi_val / sigma1 :=
div_lt_div_of_pos_left hphi hs1 h12Proposition 6, Theorem 9, Corollaries 1-2 and 4: