 We conclude this section with two observations prompted by this result. The first concerns whether anything was gained by our earlier looking at the argument for the weaker result (understood in the light of the above conventions) to the effect that, f ≠ g implies ⊢f ≠ ⊢g. The answer to this question is that although the result is weaker, the proof yields something stronger: any difference in determinants yields a difference in unconditional determinant-induced conditions. Considered as sequents (with propositional variables replacing the schematic letters in the induced conditions) these have a very special form, and, transferring Dummett’s terminology (seen earlier in this section) for rules, across to sequents, we note that they are all included in the class of pure and simple sequents: sequents in which there is only one connective to occur and it occurs only once in the sequent. Suitably abstracting from our earlier worked example, we can see that any connectives satisfying the conditions induced by even one pair of opposite determinants (whether or not any remaining determinant-induced conditions are satisfied) are bound to differ on a pair of pure and simple sequents. But the analogue of Rautenberg’s result does not hold in this form: that the set of pure and simple sequents satisfied by the one and the set satisfied by the other are incomparable with respect to inclusion. For example, consider the case of the 1-ary truth-functions Boolean negation and the constant-false function. We can cite #p ⊢ q as an example of a pure and simple sequent which holds on every valuation on which 1-ary # is associated with the constant-false function but not on every valuation on which it is associated with the negation function. But an inspection of possible cases reveals that there is no pure and simple sequent valid for the negation interpretation of # which is not also valid for the constant-false interpretation. (Of course there are sequents doing this—e.g., p ≻ ## p but, though pure, they are not simple. And, yes, in Set-Set, we can always find pure and simple witnesses to the non-inclusion of the one logic in the other: the determinant-induced conditions on generalized consequence relations will serve in this capacity.)