theorem discretionary_gain_zero {c phi_prev sigma_old sigma_new delta : ℝ}
(hs1 : sigma_old ≠ 0) (hs2 : sigma_new ≠ 0) :
discretionaryGain c phi_prev sigma_old sigma_new delta = 0 := by
simp only [discretionaryGain]
have h1 := welfare_independent_of_own_sigma (phi_prev := phi_prev) (c := c)
(delta := delta) hs2 hs1
linarithTime Inconsistency Resolution via Upstream Reform (Gap 11)