reserve k,n,n1,m,m1,m0,h,i,j for Nat,
  a,x,y,X,X1,X2,X3,X4,Y for set;
reserve L,L1,L2 for FinSequence;
reserve F,F1,G,G1,H for LTL-formula;
reserve W,W1,W2 for Subset of Subformulae H;
reserve v for LTL-formula;
reserve N,N1,N2,N10,N20,M for strict LTLnode over v;
reserve w for Element of Inf_seq(AtomicFamily);
reserve R1,R2 for Real_Sequence;

theorem Th16:
  len(W)<1 implies W = {}H
proof
  assume
A1: len(W)<1;
  now
    assume W <> {}H;
    then consider x being object such that
A2: x in W by XBOOLE_0:def 1;
    x in Subformulae H by A2;
    then reconsider x as LTL-formula by MODELC_2:1;
    set X = {x};
A3: X c= W by A2,ZFMISC_1:31;
    x is_subformula_of H by A2,MODELC_2:45;
    then reconsider X as Subset of Subformulae H by Lm9;
    len(X) = len x by Th14;
    then
A4: len(X) >=1 by MODELC_2:3;
    len(X) <= len(W) by A3,Th15;
    hence contradiction by A1,A4,XXREAL_0:2;
  end;
  hence thesis;
end;
