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 Th34:
  L is_Finseq_for v & 1<= m & m<=len(L) & the LTLnew of CastNode(L
  .(len(L)),v) = {} v implies the LTLnew of CastNode(L.m,v) c= the LTLold of
  CastNode(L.(len(L)),v)
proof
  assume that
A1: L is_Finseq_for v & 1<= m & m<=len(L) and
A2: the LTLnew of CastNode(L.(len(L)),v) = {} v;
  ex L1,L2 st L2 is_Finseq_for v & L = L1^L2 & L2.1=L.m & 1<=len(L2) & len(
  L2) =len(L)-(m-1) & L2.(len(L2)) = L.(len(L)) by A1,Lm15;
  hence thesis by A2,Th33;
end;
