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 Th37:
  for f being Assign of BASSModel(R,BASSIGN), G1,G2 being Subset of
S holds G1 c= G2 implies SigFaxTau(f,G1,R,BASSIGN) c= SigFaxTau(f,G2,R,BASSIGN)
proof
  let f be Assign of BASSModel(R,BASSIGN);
  let G1,G2 be Subset of S;
  assume G1 c= G2;
  then
  for s being Element of S holds s|= Tau(G1,R,BASSIGN) implies s|= Tau(G2,
  R,BASSIGN) by Th34;
  then
  for s being Element of S holds s|= Fax(f,Tau(G1,R,BASSIGN)) implies s|=
  Fax(f,Tau(G2,R,BASSIGN)) by Th36;
  hence thesis by Th35;
end;
