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 Th45:
  G in Subformulae H iff G is_subformula_of H
proof
  G in Subformulae H implies G is_subformula_of H
  proof
    assume G in Subformulae H;
    then ex F st F = G & F is_subformula_of H by Def24;
    hence thesis;
  end;
  hence thesis by Def24;
end;
