let V be CTLModel; :: thesis: for Kai being Function of atomic_WFF, the BasicAssign of V
for f being Function of CTL_WFF, the carrier of V st ( for n being Element of NAT holds f is-PreEvaluation-for n,Kai ) holds
f is-Evaluation-for Kai
let Kai be Function of atomic_WFF, the BasicAssign of V; :: thesis: for f being Function of CTL_WFF, the carrier of V st ( for n being Element of NAT holds f is-PreEvaluation-for n,Kai ) holds
f is-Evaluation-for Kai
let f be Function of CTL_WFF, the carrier of V; :: thesis: ( ( for n being Element of NAT holds f is-PreEvaluation-for n,Kai ) implies f is-Evaluation-for Kai )
assume A1: for n being Element of NAT holds f is-PreEvaluation-for n,Kai ; :: thesis: f is-Evaluation-for Kai
let H be CTL-formula; :: according to MODELC_1:def 26 :: thesis: ( ( H is atomic implies f . H = Kai . H ) & ( H is negative implies f . H = the Compl of V . (f . (the_argument_of H)) ) & ( H is conjunctive implies f . H = the L_meet of V . ((f . (the_left_argument_of H)),(f . (the_right_argument_of H))) ) & ( H is ExistNext implies f . H = the EneXt of V . (f . (the_argument_of H)) ) & ( H is ExistGlobal implies f . H = the EGlobal of V . (f . (the_argument_of H)) ) & ( H is ExistUntill implies f . H = the EUntill of V . ((f . (the_left_argument_of H)),(f . (the_right_argument_of H))) ) )
set n = len H;
f is-PreEvaluation-for len H,Kai by A1;
hence ( ( H is atomic implies f . H = Kai . H ) & ( H is negative implies f . H = the Compl of V . (f . (the_argument_of H)) ) & ( H is conjunctive implies f . H = the L_meet of V . ((f . (the_left_argument_of H)),(f . (the_right_argument_of H))) ) & ( H is ExistNext implies f . H = the EneXt of V . (f . (the_argument_of H)) ) & ( H is ExistGlobal implies f . H = the EGlobal of V . (f . (the_argument_of H)) ) & ( H is ExistUntill implies f . H = the EUntill of V . ((f . (the_left_argument_of H)),(f . (the_right_argument_of H))) ) ) ; :: thesis: verum