
theorem Th48: :: PMV(a,a,b) = a;
  for T being _Tree for a, b being Vertex of T holds MiddleVertex( a,a,b) = a
proof
  let T be _Tree;
  let a,b be Vertex of T;
  T.pathBetween(a,b).first() = a by Th28;
  then
A1: a in T.pathBetween(a,b).vertices() by GLIB_001:88;
  MiddleVertex(a,a,b) = MiddleVertex(a,b,a) by Th41;
  hence thesis by A1,Th46;
end;
