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;
reserve s,s0,s1,s2 for elementary strict LTLnode over v;
reserve q for sequence of LTLStates(v);
reserve U for Choice_Function of BOOL Subformulae v;

theorem
  w|=*N & N is non elementary implies the LTLold of N c= the LTLold of
chosen_succ(w,v,U,N) & the LTLnext of N c= the LTLnext of chosen_succ(w,v,U,N)
proof
  assume w|=*N & N is non elementary;
  then chosen_succ(w,v,U,N) is_succ_of N by Th59;
  hence thesis by Th25;
end;
