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 Th62:
  choice_succ_func(w,v,U) is_succ_homomorphism v,w
proof
  set f = choice_succ_func(w,v,U);
  for x st x in LTLNodes(v) & CastNode(x,v) is non elementary & w |= *
CastNode(x,v) holds CastNode(f.x,v) is_succ_of CastNode(x,v) & w |= *CastNode(f
  .x,v)
  proof
    let x such that
A1: x in LTLNodes(v) and
A2: CastNode(x,v) is non elementary & w|=*CastNode(x,v);
    set N = CastNode(x,v);
    set SN = chosen_succ(w,v,U,N);
    CastNode(f.x,v) = CastNode(SN,v) by A1,Def36
      .= SN by Def16;
    hence thesis by A2,Th59;
  end;
  hence thesis;
end;
