
theorem Th46:
  for T being _Tree for a, b, c being Vertex of T st c in T
  .pathBetween(a,b).vertices() holds MiddleVertex(a,b,c) = c
proof
  let T be _Tree;
  let a, b, c be Vertex of T;
  assume c in T.pathBetween(a,b).vertices();
  then T.pathBetween(a,b).vertices() /\ T.pathBetween(b,c).vertices() /\ T
  .pathBetween(c,a).vertices() = {c} by Lm1;
  hence thesis by Def3;
end;
