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
  H is atomic implies (s,kai |= H iff kai.H in (Label_(BASSIGN)).s)
proof
  assume
A1: H is atomic;
  ex f be Function of CTL_WFF,the carrier of BASSModel(R, BASSIGN) st
  f is-Evaluation-for kai & Evaluate(H,kai) = f.H by Def34;
  then
A2: Evaluate(H,kai) = kai.H by A1;
  H in atomic_WFF by A1;
  then Evaluate(H,kai) in BASSIGN by A2,FUNCT_2:5;
  hence thesis by A2,Th11;
end;
