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
  G is_subformula_of H & H is_subformula_of G implies G = H
proof
  assume that
A1: G is_subformula_of H and
A2: H is_subformula_of G;
  assume
A3: G <> H;
  then G is_proper_subformula_of H by A1;
  then
A4: len G < len H by Th32;
  H is_proper_subformula_of G by A2,A3;
  hence contradiction by A4,Th32;
end;
