  This extended abstract is about an effort to build a formal description of a
triangulation algorithm starting with a naive description of the algorithm
where triangles, edges, and triangulations are simply given as sets and the
most complex notions are those of boundary and separating edges. When
performing proofs about this algorithm, questions of symmetry appear and this
exposition attempts to give an account of how these symmetries can be handled.
All this work relies on formal developments made with Coq and the mathematical
components library.
