reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;
reserve e for expression of C;
reserve a,a9 for expression of C, an_Adj C;
reserve q for pure expression of C, a_Type C,
  A for finite Subset of QuasiAdjs C;
reserve T for quasi-type of C;

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;
