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 Th5:
  not F in W implies len(L,W \ {F}) = len(L,W)
proof
  assume
A1: not F in W;
A2: for x being object holds x in W implies x in W \ {F}
  proof let x be object;
    assume
A3: x in W;
    then not x in {F} by A1,TARSKI:def 1;
    hence thesis by A3,XBOOLE_0:def 5;
  end;
  for x being object holds x in W \ {F} implies x in W by XBOOLE_0:def 5;
  hence thesis by A2,TARSKI:2;
end;
