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 Th20:
  for G being non _trivial _Graph, v being Vertex of G holds
  (the_Vertices_of G) \ {v} is non empty
proof
  let G be non _trivial _Graph, v be Vertex of G;
  set VG = the_Vertices_of G;
  now
    assume VG \ {v} = {};
    then VG c= {v} by XBOOLE_1:37;
    then VG = {v} by ZFMISC_1:33;
    then card VG = 1 by CARD_1:30;
    hence contradiction by Def19;
  end;
  hence thesis;
end;
