reserve k,n,m for Nat,
  a,x,X,Y for set,
  D,D1,D2,S for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for LTL-formula;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;
reserve j for Nat;
reserve j1 for Element of NAT;

theorem
  a is Subset of Subformulae H implies a is Subset of LTL_WFF
proof
  assume
A1: a is Subset of Subformulae H;
  for x being object holds x in a implies x in LTL_WFF
  proof let x be object;
    assume x in a;
    then ex F st F = x & F is_subformula_of H by A1,Def24;
    hence thesis by Th1;
  end;
  hence thesis by TARSKI:def 3;
end;
