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 Th28:
  for f being Assign of BASSModel(R,BASSIGN) holds s |= EX(f) iff
  ex s1 being Element of S st [s,s1] in R & s1 |= f
proof
  let f be Assign of BASSModel(R,BASSIGN);
A1: s |= EX(f) implies ex s1 being Element of S st [s,s1] in R & s1 |= f
  proof
    assume s |= EX(f);
    then consider pai be inf_path of R such that
A2: pai.0 = s and
A3: (pai.1) |= f by Th14;
    [pai.0,pai.(0+1)] in R by Def39;
    hence thesis by A2,A3;
  end;
  (ex s1 being Element of S st [s,s1] in R & s1 |= f ) implies s |= EX(f)
  proof
    given s1 be Element of S such that
A4: [s,s1] in R and
A5: s1 |= f;
    ex pai be inf_path of R st pai.0 = s & pai.1 = s1 by A4,Th27;
    hence thesis by A5,Th14;
  end;
  hence thesis by A1;
end;
