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;

theorem Th8:
  Evaluate(EG H,Kai) = EG Evaluate(H,Kai)
proof
  consider f1 be Function of CTL_WFF,the carrier of V such that
A1: f1 is-Evaluation-for Kai and
A2: Evaluate(EG H,Kai) = f1.(EG H) by Def34;
A3: ex f2 be Function of CTL_WFF,the carrier of V st f2
  is-Evaluation-for Kai & Evaluate(H,Kai) = f2.H by Def34;
A4: EG H is ExistGlobal;
  then
A5: not EG H is negative by Lm18;
A6: not EG H is ExistNext by A4,Lm18;
  Evaluate(EG H,Kai) = (the EGlobal of V).(f1.(the_argument_of(EG H)) ) by A1
,A2,A4
    .= (the EGlobal of V).(f1.H ) by A4,A5,A6,Def21
    .= EG Evaluate(H,Kai) by A1,A3,Th4;
  hence thesis;
end;
