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 Th58:
  N is non elementary implies chosen_formula(U,N) in the LTLnew of N
proof
  set x = the LTLnew of N;
  set X = BOOL Subformulae v;
  assume
A1: not N is elementary;
  then ( not {} in X)& x in X by Th56,ORDERS_1:1;
  then U.x in x by ORDERS_1:89;
  hence thesis by A1,Def34;
end;
