let H be LTL-formula; :: thesis: for V being LTLModelStr
for Kai being Function of atomic_LTL ,the BasicAssign of V holds Evaluate ('not' H),Kai = 'not' (Evaluate H,Kai)
let V be LTLModelStr ; :: thesis: for Kai being Function of atomic_LTL ,the BasicAssign of V holds Evaluate ('not' H),Kai = 'not' (Evaluate H,Kai)
let Kai be Function of atomic_LTL ,the BasicAssign of V; :: thesis: Evaluate ('not' H),Kai = 'not' (Evaluate H,Kai)
consider f1 being Function of LTL_WFF ,the Assignations of V such that
A1: f1 is-Evaluation-for Kai and
A2: Evaluate ('not' H),Kai = f1 . ('not' H) by Def33;
A3: ex f2 being Function of LTL_WFF ,the Assignations of V st
( f2 is-Evaluation-for Kai & Evaluate H,Kai = f2 . H ) by Def33;
A4: 'not' H is negative by Def12;
then Evaluate ('not' H),Kai = the Not of V . (f1 . (the_argument_of ('not' H))) by A1, A2, Def27
.= the Not of V . (f1 . H) by A4, Def18
.= 'not' (Evaluate H,Kai) by A1, A3, Th49 ;
hence Evaluate ('not' H),Kai = 'not' (Evaluate H,Kai) ; :: thesis: verum