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 Th35:
  F is_subformula_of G & G is_subformula_of H implies F is_subformula_of H
proof
  assume that
A1: F is_subformula_of G and
A2: G is_subformula_of H;
  now
    assume F <> G;
    then
A3: F is_proper_subformula_of G by A1;
    now
      assume G <> H;
      then G is_proper_subformula_of H by A2;
      then F is_proper_subformula_of H by A3,Th34;
      hence thesis;
    end;
    hence thesis by A1;
  end;
  hence thesis by A2;
end;
