let H be CTL-formula; for V being CTLModel
for Kai being Function of atomic_WFF, the BasicAssign of V holds Evaluate (('not' H),Kai) = 'not' (Evaluate (H,Kai))
let V be CTLModel; for Kai being Function of atomic_WFF, the BasicAssign of V holds Evaluate (('not' H),Kai) = 'not' (Evaluate (H,Kai))
let Kai be Function of atomic_WFF, the BasicAssign of V; Evaluate (('not' H),Kai) = 'not' (Evaluate (H,Kai))
consider f1 being Function of CTL_WFF, the carrier of V such that
A1:
f1 is-Evaluation-for Kai
and
A2:
Evaluate (('not' H),Kai) = f1 . ('not' H)
by Def34;
A3:
ex f2 being Function of CTL_WFF, the carrier of V st
( f2 is-Evaluation-for Kai & Evaluate (H,Kai) = f2 . H )
by Def34;
A4:
'not' H is negative
;
then Evaluate (('not' H),Kai) =
the Compl of V . (f1 . (the_argument_of ('not' H)))
by A1, A2
.=
the Compl of V . (f1 . H)
by A4, Def21
.=
'not' (Evaluate (H,Kai))
by A1, A3, Th4
;
hence
Evaluate (('not' H),Kai) = 'not' (Evaluate (H,Kai))
; verum