
theorem
  for G1, G2 being _Graph, G being GraphMeet of G1, G2
  st G1 tolerates G2 & the_Vertices_of G1 meets the_Vertices_of G2
  holds G is GraphMeet of G2, G1
proof
  let G1, G2 be _Graph, G be GraphMeet of G1, G2;
  assume A1: G1 tolerates G2 & the_Vertices_of G1 meets the_Vertices_of G2;
  then consider S being GraphMeetSet such that
    A2: S = {G1,G2} & G is GraphMeet of S by Def30;
  A3: G is Subgraph of G2 by A1, Th41;
  thus thesis by A1, A2, A3, Def30;
end;
