(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/library_auto/nat/relevant_equations".
+set "baseuri" "cic:/matita/library_autobatch/nat/relevant_equations".
include "auto/nat/times.ma".
include "auto/nat/minus.ma".
intros.
apply (trans_eq ? ? (p*(n+m)))
[ apply sym_times
-| apply (trans_eq ? ? (p*n+p*m));auto
+| apply (trans_eq ? ? (p*n+p*m));autobatch
(*[ apply distr_times_plus
| apply eq_f2;
apply sym_times
intros.
apply (trans_eq ? ? (p*(n-m)))
[ apply sym_times
-| apply (trans_eq ? ? (p*n-p*m));auto
+| apply (trans_eq ? ? (p*n-p*m));autobatch
(*[ apply distr_times_minus
| apply eq_f2;
apply sym_times
theorem times_plus_plus: \forall n,m,p,q:nat. (n + m)*(p + q) =
n*p + n*q + m*p + m*q.
intros.
-auto.
+autobatch.
(*apply (trans_eq nat ? ((n*(p+q) + m*(p+q))))
[ apply times_plus_l
| rewrite > distr_times_plus.