The proof uses the property that the vertices of a triangulated planar graph with v vertices can be four coloured if the triangles of it can be given a +1 or -1 orientation in such a way that the sum of the triangle orientations around each vertex is a multiple of 3 (or their sumMod3 is 0). The proof is by association of each of v-2 vertices with two triangles. Together they form trios in such a way that each triangle belongs to a trio and only to one. The trios are formed in such a way that the two remaining vertices are linked by an edge. From this association it follows that there is always a combination for the orientations of the triangles so that their sum around the v-2 vertices is a multiple of 3. In that case it is provable that the sum of the triangle orientations around the two remaining vertices must also be a multiple of 3.