
theorem Th36:
  for P being _finite non _trivial Path-like _Graph
  ex v1, v2 being Vertex of P st v1 <> v2 & Endvertices P = {v1,v2}
proof
  let P be _finite non _trivial Path-like _Graph;
  consider P0 being vertex-distinct Path of P such that
     P0.vertices() = the_Vertices_of P & P0.edges() = the_Edges_of P and
    A1: Endvertices P = {P0.first(),P0.last()} iff P is non _trivial and
    (P0 is trivial iff P is _trivial) and
    A2: P0 is closed iff P is _trivial and
    P0 is minlength by Th31;
  take P0.first(),P0.last();
  thus thesis by A1, A2, GLIB_001:def 24;
end;
