for T being _Tree
for P1, P2, P3, P4 being Path of T
for a, b, c being Vertex of T st P1 = T .pathBetween (a,b) & P2 = T .pathBetween (a,c) & P3 = T .pathBetween (b,a) & P4 = T .pathBetween (b,c) & not b in P2 .vertices() & not c in P1 .vertices() & not a in P4 .vertices() holds
P1 . (len (maxPrefix (P1,P2))) = P3 . (len (maxPrefix (P3,P4)))