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;
