let H be CTL-formula; :: thesis: for V being CTLModelStr
for Kai being Function of atomic_WFF ,the BasicAssign of V holds Evaluate (EG H),Kai = EG (Evaluate H,Kai)
let V be CTLModelStr ; :: thesis: for Kai being Function of atomic_WFF ,the BasicAssign of V holds Evaluate (EG H),Kai = EG (Evaluate H,Kai)
let Kai be Function of atomic_WFF ,the BasicAssign of V; :: thesis: Evaluate (EG H),Kai = EG (Evaluate H,Kai)
consider f1 being Function of CTL_WFF ,the Assignations of V such that
A1: f1 is-Evaluation-for Kai and
A2: Evaluate (EG H),Kai = f1 . (EG H) by Def32;
consider f2 being Function of CTL_WFF ,the Assignations of V such that
A3: f2 is-Evaluation-for Kai and
A4: Evaluate H,Kai = f2 . H by Def32;
A5: EG H is ExistGlobal by Def18;
then A6: ( not EG H is negative & not EG H is ExistNext ) by Lm18;
Evaluate (EG H),Kai = the EGlobal of V . (f1 . (the_argument_of (EG H))) by A1, A2, A5, Def26
.= the EGlobal of V . (f1 . H) by A5, A6, Def21
.= EG (Evaluate H,Kai) by A1, A3, A4, Th4 ;
hence Evaluate (EG H),Kai = EG (Evaluate H,Kai) ; :: thesis: verum