
theorem
  for S1, S2 being non empty Graph-membered set st S1 \/ S2 is /\-tolerating
  holds S1 is /\-tolerating & S2 is /\-tolerating
proof
  let S1, S2 be non empty Graph-membered set;
  assume A1: S1 \/ S2 is /\-tolerating;
  meet the_Vertices_of(S1 \/ S2)
     = meet(the_Vertices_of S1 \/ the_Vertices_of S2) by Th8
    .= meet the_Vertices_of S1 /\ meet the_Vertices_of S2 by SETFAM_1:9;
  then A2: meet the_Vertices_of S1 <> {} & meet the_Vertices_of S2 <> {}
    by A1;
  S1 is \/-tolerating & S2 is \/-tolerating by A1, Th20;
  hence thesis by A2;
end;
