let H1, H2 be LTL-formula; :: thesis: for V being LTLModelStr
for Kai being Function of atomic_LTL ,the BasicAssign of V holds Evaluate (H1 'or' H2),Kai = (Evaluate H1,Kai) 'or' (Evaluate H2,Kai)
let V be LTLModelStr ; :: thesis: for Kai being Function of atomic_LTL ,the BasicAssign of V holds Evaluate (H1 'or' H2),Kai = (Evaluate H1,Kai) 'or' (Evaluate H2,Kai)
let Kai be Function of atomic_LTL ,the BasicAssign of V; :: thesis: Evaluate (H1 'or' H2),Kai = (Evaluate H1,Kai) 'or' (Evaluate H2,Kai)
consider f0 being Function of LTL_WFF ,the Assignations of V such that
A1: f0 is-Evaluation-for Kai and
A2: Evaluate (H1 'or' H2),Kai = f0 . (H1 'or' H2) by Def33;
consider f1 being Function of LTL_WFF ,the Assignations of V such that
A3: f1 is-Evaluation-for Kai and
A4: Evaluate H1,Kai = f1 . H1 by Def33;
consider f2 being Function of LTL_WFF ,the Assignations of V such that
A5: f2 is-Evaluation-for Kai and
A6: Evaluate H2,Kai = f2 . H2 by Def33;
A7: f0 = f2 by A1, A5, Th49;
A8: H1 'or' H2 is disjunctive by Def14;
then A9: ( the_left_argument_of (H1 'or' H2) = H1 & the_right_argument_of (H1 'or' H2) = H2 ) by Def19, Def20;
f0 = f1 by A1, A3, Th49;
hence Evaluate (H1 'or' H2),Kai = (Evaluate H1,Kai) 'or' (Evaluate H2,Kai) by A1, A2, A4, A6, A7, A8, A9, Def27; :: thesis: verum