
theorem Th12:
  for G1, G2 being _Graph st the_Edges_of G1 misses the_Edges_of G2
  holds G1 tolerates G2
proof
  let G1, G2 be _Graph;
  assume A1: the_Edges_of G1 misses the_Edges_of G2;
  then dom the_Source_of G1 misses the_Edges_of G2 by FUNCT_2:def 1;
  then dom the_Source_of G1 misses dom the_Source_of G2 by FUNCT_2:def 1;
  hence the_Source_of G1 tolerates the_Source_of G2 by PARTFUN1:56;
  dom the_Target_of G1 misses the_Edges_of G2 by A1, FUNCT_2:def 1;
  then dom the_Target_of G1 misses dom the_Target_of G2 by FUNCT_2:def 1;
  hence the_Target_of G1 tolerates the_Target_of G2 by PARTFUN1:56;
end;
