DCEL operations on quad-edges, Twin, Next, and Prev
It looks like you took these diagrams from this CMU publication. This publication also refers to the C++ header cell/edge.hh, describing basic and derived operations on edges.

So, according to this header, operations Rot, InvRot, Sym and Onext are considered basic ones, and all the other operations - derived ones. The DCEL operations next and prev are equivalent to quad-edge operations Lnext and Lprev, which are defined in this header as inline functions (I'm dropping the C++ syntax and keeping the meaning):

e.Lnext = e.InvRot.Onext.Rot
e.Lprev = e.Onext.Sym


So, your formulas look correct, with slightly overused operation Rot.