On digital planes (set of integer points between two parallel Euclidean planes), plane-probing algorithms initiate with a triangle, update one vertex at a time and approximate the plane on the fly. The L-algorithm is a plane-probing algorithm variant which takes into account a large neighborhood of points for its update process. We recall the framework of plane-probing algorithms, especially for the L-algorithm. We introduce the Delaunay property and prove that it is theoretically held by the L-algorithm. Lastly, we name a few consequences of such property, namely the research of minimal bases and an estimation for the locality. This technical report is provided as supplementary material to the DGMM2022 paper [11].