 This suffers from the same defects in respect of the analogy with Knot, so, finally, let Tonk+ be governed by the rules for Tonk and also the rules for Tonk*. It is Tonk+ that has Knot as its mirror image, since just as we Knot has the full force of the (∧ Right) and (∨ Left) rules, Tonk+ enjoys the full force of the (∧ Left) and (∨ Right) rules. (So here we arrive at the reason that Knot was originally described as only roughly speaking a mirror image of Tonk.) And this time the rules are indeed Id-inductive without being Cut-inductive. Indeed, Id-inductivity is secured by two independent routes: by the interaction of the Tonk Left rule for Tonk+ with the Tonk* Right rule to Tonk+, and then again by the interaction of Tonk+‘s Tonk* Left rule with its Tonk Right rule. (To give the former in more detail, by way of example, the Tonk Left rule for Tonk+ gives φ Tonk+ ψ ≻ψ from (Id)-for-ψ, from which applying the Tonk* Right rule for Tonk+ we obtain φ Tonk+ ψ ≻ φ Tonk+ ψ.)