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 Th11:
  for a being Assign of BASSModel(R,BASSIGN) st a in BASSIGN holds
  s |= a iff a in (Label_(BASSIGN)).s
proof
  let a be Assign of BASSModel(R,BASSIGN) such that
A1: a in BASSIGN;
  thus s |= a implies a in (Label_(BASSIGN)).s
  proof
    set f = Fid(a,S);
    assume s |= a;
    then
A2: f.s=TRUE;
    a= f by Def41;
    then a in F_LABEL(s,BASSIGN) by A1,A2,Def55;
    hence thesis by Def56;
  end;
  assume a in (Label_(BASSIGN)).s;
  then a in F_LABEL(s,BASSIGN) by Def56;
  then consider f being Function of S,BOOLEAN such that
A3: f =a and
A4: f.s=TRUE by Def55;
  Fid(a,S)=f by A3,Def41;
  hence thesis by A4;
end;
