reserve A,B,p,q,r for Element of LTLB_WFF,
  M for LTLModel,
  j,k,n for Element of NAT,
  i for Nat,
  X for Subset of LTLB_WFF,
  F for finite Subset of LTLB_WFF,
  f for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN,
  x,y,z for set,
  P,Q,R for PNPair;
reserve T for pnptree of P,t for Node of T;

theorem Th26:
 for n being Nat st t^<*n*> in dom T
  holds T.(t^<*n*>) in compn (T.t)
  proof let n be Nat;
    set tn = t^<*n*>;
    assume
A1: t^<*n*> in dom T;
    dom (succ (T,t)) = dom (t succ) by TREES_9:38;then
A2: (succ (T,t)).(n+1) in rng succ (T,t) by TREES_9:39,A1,FUNCT_1:3;
A3: succ (T,t) = the Enumeration of compn (T.t) by Def11;
    T.tn = (succ (T,t)).(n+1) by A1,TREES_9:40;
    hence T.tn in compn (T.t) by A3,A2,RLAFFIN3:def 1;
  end;
