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 Th35:
  for f1,f2 being Assign of BASSModel(R,BASSIGN) holds (for s being
  Element of S holds s|= f1 implies s|= f2) implies SIGMA(f1) c= SIGMA(f2)
proof
  let f1,f2 be Assign of BASSModel(R,BASSIGN);
  assume
A1: for s being Element of S holds s|= f1 implies s|= f2;
  let x be object;
  assume x in SIGMA(f1);
  then consider s be Element of S such that
A2: x=s and
A3: s|= f1;
  s|= f2 by A1,A3;
  hence thesis by A2;
end;
