reserve k,n for Element of NAT,
  a,Y for set,
  D,D1,D2 for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for CTL-formula;
reserve sq,sq9 for FinSequence;
reserve V for CTLModel;
reserve Kai for Function of atomic_WFF,the BasicAssign of V;
reserve f,f1,f2 for Function of CTL_WFF,the carrier of V;
reserve S for non empty set;
reserve R for total Relation of S,S;
reserve s,s0,s1 for Element of S;
reserve BASSIGN for non empty Subset of ModelSP(S);
reserve kai for Function of atomic_WFF,the BasicAssign of BASSModel(R,BASSIGN);

theorem Th34:
  for G1,G2 being Subset of S holds G1 c= G2 implies for s being
  Element of S holds s|= Tau(G1,R,BASSIGN) implies s|= Tau(G2,R,BASSIGN)
proof
  let G1,G2 be Subset of S;
  set Tau1 = Tau(G1,R,BASSIGN);
  set Tau2 = Tau(G2,R,BASSIGN);
  assume
A1: G1 c= G2;
  let s be Element of S;
  assume s|= Tau1;
  then (Fid(Tau1,S)).s = TRUE;
  then chi(G1,S).s =1 by Def64;
  then s in G1 by FUNCT_3:def 3;
  then chi(G2,S).s =1 by A1,FUNCT_3:def 3;
  then (Fid(Tau2,S)).s = TRUE by Def64;
  hence thesis;
end;
