theorem Th110:
  for x holds
  x is Element of VarPoset iff x is finite Subset of Vars & varcl x = x
proof
  let x;
  set V = the set of all varcl A where A is finite Subset of Vars;
  set A0 = the finite Subset of Vars;
  varcl A0 in V;
  then reconsider V as non empty set;
  the carrier of InclPoset V = V by YELLOW_1:1;
  then x is Element of VarPoset iff x in V;
  then x is Element of VarPoset iff
  ex A being finite Subset of Vars st x = varcl A;
  hence thesis by Th24;
end;
