Vidar and Vali shall survive, for neither the sea nor the fire of Surt shall harm them. They shall dwell in Idavoll, where Asgard once stood.

– Gylfaginning, chapter 51

The Gylfaginning does say that Vidar and Vali will rule after Ragnarök – The Gylfaginning names Vidar before Vali 

That is, spirituality (Vidar) must be repaired first before Vali (the principle of revenge) can be applied.

« the sea » : materialism 

« the fire of Surt » : resentment