Confusion on the Definition of Isolated Chord

Question

An isolated chord diagram is usually defined to be a chord diagram with a chord that doesn't intersect any other chord. But in this notes, it is defined to be a diagram with a chord that relates two consecutive points, so he has different (weaker) definition of 1T relation. Let $\mathcal A_n$ be the space of linear span of $n$-chord diagrams $\mathcal D_n$ modulo the 1T and 4T relations. (Kontsevich proved that $\mathcal A_n^*$ is isomorphic to the space of quotients of Vassiliev invariants $I_n/I_{n-1}$). Why do these two definitions give rise to equivalent $\mathcal A_n$?

Answer 1

This follows from the fact that there is a well defined product on $\mathcal D_n/\langle 4T\rangle$.