let H be LTL-formula; :: thesis: for V being LTLModel
for Kai being Function of atomic_LTL, the BasicAssign of V holds Evaluate (('X' H),Kai) = 'X' (Evaluate (H,Kai))
let V be LTLModel; :: thesis: for Kai being Function of atomic_LTL, the BasicAssign of V holds Evaluate (('X' H),Kai) = 'X' (Evaluate (H,Kai))
let Kai be Function of atomic_LTL, the BasicAssign of V; :: thesis: Evaluate (('X' H),Kai) = 'X' (Evaluate (H,Kai))
consider f1 being Function of LTL_WFF, the carrier of V such that
A1: f1 is-Evaluation-for Kai and
A2: Evaluate (('X' H),Kai) = f1 . ('X' H) by Def35;
A3: ex f2 being Function of LTL_WFF, the carrier of V st
( f2 is-Evaluation-for Kai & Evaluate (H,Kai) = f2 . H ) by Def35;
A4: 'X' H is next ;
then A5: not 'X' H is negative by Lm19;
Evaluate (('X' H),Kai) = the NEXT of V . (f1 . (the_argument_of ('X' H))) by A1, A2, A4
.= the NEXT of V . (f1 . H) by A4, A5, Def18
.= 'X' (Evaluate (H,Kai)) by A1, A3, Th49 ;
hence Evaluate (('X' H),Kai) = 'X' (Evaluate (H,Kai)) ; :: thesis: verum