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 Th11:
  (not F in W) & W1 = W \/ {F} implies len(W1) = len(W) + len F
proof
  assume
A1: ( not F in W)& W1 = W \/ {F};
  consider L such that
A2: rng L = Subformulae H & L is one-to-one by FINSEQ_4:58;
  len(W1) = len(L,W1) by A2,Def26
    .= len(L,W) + len F by A1,A2,Th7;
  hence thesis by A2,Def26;
end;
