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 Th36:
  for f,g1,g2 being Assign of BASSModel(R,BASSIGN) holds (for s
being Element of S holds s|= g1 implies s|= g2) implies for s being Element of
  S holds s|= Fax(f,g1) implies s|= Fax(f,g2)
proof
  let f,g1,g2 be Assign of BASSModel(R,BASSIGN);
  assume
A1: for s being Element of S holds s|= g1 implies s|= g2;
  let s be Element of S;
  assume
A2: s|= Fax(f,g1);
  then s|= EX(g1) by Th13;
  then consider pai be inf_path of R such that
A3: pai.0 = s and
A4: (pai.1) |= g1 by Th14;
  (pai.1) |= g2 by A1,A4;
  then
A5: s|= EX(g2) by A3,Th14;
  s|= f by A2,Th13;
  hence thesis by A5,Th13;
end;
