
theorem Th41:
  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 Subgraph of G2
proof
  let G1, G2 be _Graph, G be GraphMeet of G1, G2;
  assume G1 tolerates G2 & the_Vertices_of G1 meets the_Vertices_of G2;
  then consider S being GraphMeetSet such that
    A1: S = {G1,G2} & G is GraphMeet of S by Def30;
  G2 is Element of S by A1, TARSKI:def 2;
  then G2 is Supergraph of G by A1, Th37;
  hence thesis by GLIB_006:57;
end;
