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 Th4:
  len(L,{}H) = 0
proof
  set s = Partial_seq(L,{}H);
A1: for n being Nat holds s.n = 0*n+0 by Def24;
  for n holds Partial_Sums(s).n = 0
  proof
    let n;
A2: s.0 = 0 by Def24;
    Partial_Sums(s).n = (n+1)*(s.0 + s.n)/2 by A1,SERIES_2:42
      .= (n+1)*(0+0)/2 by A2,Def24;
    hence thesis;
  end;
  hence thesis;
end;
