(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/nat/congruence".
-
include "nat/relevant_equations.ma".
include "nat/primes.ma".
(*rewrite > (sym_times p (m/p)).*)
(*rewrite > sym_times.*)
rewrite > assoc_plus.
-auto paramodulation.
+autobatch paramodulation.
rewrite < div_mod.
assumption.
assumption.
theorem divides_to_congruent: \forall n,m,p:nat. O < p \to m \le n \to
divides p (n - m) \to congruent n m p.
intros.elim H2.
-apply (eq_times_plus_to_congruent n m p n2).
+apply (eq_times_plus_to_congruent n m p n1).
assumption.
rewrite < sym_plus.
apply minus_to_plus.assumption.