reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem Th22:
  for G being _trivial _Graph holds ex v being Vertex of G st
  the_Vertices_of G = {v}
proof
  let G be _trivial _Graph;
  card (the_Vertices_of G) = 1 by Def19;
  then consider v being object such that
A1: the_Vertices_of G = {v} by CARD_2:42;
  reconsider v as Vertex of G by A1,TARSKI:def 1;
  take v;
  thus thesis by A1;
end;
