 Note that p, #(p, q, q) ⊮f q, since otherwise it would follow (by the ‘cut’ condition on generalized consequence relations) from the first inset ⊩-statement here that p ⊩f q, which is not the case. Thus in view of the second ⊩-statement, ⊩f and ⊩g differ on the sequent σ = p, #(p, q, q)≻ q, since σ ∈ ⊩g while σ ∉ ⊩f. But σ is a sequent of Set-Fmla, so the consequence relations, ⊢f and ⊢g, say, determined respectively by Vf and Vg also differ (namely, on σ). We have worked through a simple illustration of the general result claimed above, but this case is sufficiently representative for the general proof to be reconstructed.