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 Th21:
  N2 is_succ_of N1 implies len(N2) <= len(N1) - 1
proof
  set r1 = len(the LTLnew of N1);
  set r2 = len(the LTLnew of N2);
  assume N2 is_succ_of N1;
  then N2 is_succ1_of N1 or N2 is_succ2_of N1;
  then r2 <= r1-1 by Th19,Th20;
  hence thesis by Lm5;
end;
