# proof that SimpLe is fully expresive

Refering to this paper "SimplE Embedding for Link Prediction in Knowledge Graphs" by Seyed Mehran Kazemi and David Poole in 2018 :

In page 4, about the proof of SimpLE being fully expressive,

I understand that $$h_{e_i} =1 \text{ if }(n \text{ mod }|\mathcal{E}|)=i \text{ and }0 \text{ otherwise }$$, $$v_{r_j}=1 \text{ if }(n \text{ div } |\mathcal{E}|)=j \text{ and }0 \text{ otherwise }.$$ and that the $$(j*|\mathcal{E}|+i$$)-th element of $$t_{e_k}$$ is $$1$$ if $$(e_i,r_j,e_k)$$ holds and $$-1$$ otherwise. From that we get $$\langle h_{e_i},v_r, t_{e_k}\rangle=1$$ But what about $$v_{r^{-1}}$$?