right. apply I|intros (a at).simplify. left. apply I]]
simplify.
left.
-autobatch new|intros 2 (c l).
+autobatch |intros 2 (c l).
intros 2 (Hy).
elim y 0[
intros 2 (H z).
elim x 0[
intro y.
elim y 0[
- split[simplify.intro.autobatch new|simplify.intros.exact H1]|
+ split[simplify.intro.autobatch|simplify.intros.exact H1]|
intros (a at).
simplify.
-split[intro.autobatch new|intros. exact H1]
+split[intro.autobatch|intros. exact H1]
]
|
intros (a at IHx).
elim y 0[simplify.
- split[intro.autobatch new|intros.exact H]
+ split[intro.autobatch|intros.exact H]
|
intros 2 (c l).
generalize in match (IHx l).
[ apply (trans_lt ? (S O));
[ unfold lt; apply le_n;
| apply lt_SO_smallest_factor; assumption; ]
- | letin x \def le.autobatch new.
+ | letin x \def le.autobatch.
(*
apply divides_smallest_factor_n;
apply (trans_lt ? (S O));
assumption.unfold Not.
intro.
cut (r \mod (nth_prime (max_prime_factor n)) \neq O);
- [unfold Not in Hcut1.autobatch new.
+ [unfold Not in Hcut1.autobatch.
(*
apply Hcut1.apply divides_to_mod_O;
[ apply lt_O_nth_prime_n.