reserve i,j for Nat;

theorem Th22:
 for C being initialized standardized ConstructorSignature
 for t being expression of C holds
   t is non compound quasi-term of C iff (t.{})`1 in Vars
  proof let C be initialized standardized ConstructorSignature;
   let t be expression of C;
   thus
    now assume t is non compound quasi-term of C; then
     consider x being Element of Vars such that
A1:   t = x-term C by Th3;
      t.{} = [x,a_Term] & x in Vars by A1,TREES_4:3;
     hence (t.{})`1 in Vars;
    end;
   assume (t.{})`1 in Vars; then
    ex x being Element of Vars st x = (t.{})`1 & t = x-term C by Th17;
   hence thesis;
  end;
