let H be LTL-formula; :: thesis: ( H is next implies ( not H is atomic & not H is negative & not H is conjunctive & not H is disjunctive & not H is Until & not H is Release ) )
assume H is next ; :: thesis: ( not H is atomic & not H is negative & not H is conjunctive & not H is disjunctive & not H is Until & not H is Release )
then H . 1 = 3 by Lm6;
hence ( not H is atomic & not H is negative & not H is conjunctive & not H is disjunctive & not H is Until & not H is Release ) by Lm3, Lm4, Lm5, Lm7, Lm8, Lm9; :: thesis: verum