
theorem Th35:
  for P being non _trivial Path-like _Graph, v being Vertex of P
  st v is non endvertex holds v.degree() = 2
proof
  let P be non _trivial Path-like _Graph, v be Vertex of P;
  assume v is non endvertex;
  then A1: v.degree() <> 1 by GLIB_000:174;
  v.degree() <> 0 by GLIB_000:157;
  then not v.degree() in {0,1} by A1, TARSKI:def 2;
  then A2: 2 c= v.degree() by CARD_1:50, ORDINAL1:16;
  v.degree() c= 2 by Def1;
  hence thesis by A2, XBOOLE_0:def 10;
end;
