X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fcongruence.ma;h=4266d3f6ffb22412d869bd4a357237937e3dcc67;hb=5c10d402b5de7233bc83d7f685b274832e383212;hp=86f7b98143c0bbf0cbe10e75db88d14e8c33885e;hpb=c864b3853bbe90664e6ad3128038fc8fa4b5d641;p=helm.git diff --git a/helm/software/matita/library/nat/congruence.ma b/helm/software/matita/library/nat/congruence.ma index 86f7b9814..4266d3f6f 100644 --- a/helm/software/matita/library/nat/congruence.ma +++ b/helm/software/matita/library/nat/congruence.ma @@ -12,8 +12,6 @@ (* *) (**************************************************************************) -set "baseuri" "cic:/matita/nat/congruence". - include "nat/relevant_equations.ma". include "nat/primes.ma". @@ -23,8 +21,7 @@ definition S_mod: nat \to nat \to nat \def definition congruent: nat \to nat \to nat \to Prop \def \lambda n,m,p:nat. mod n p = mod m p. -interpretation "congruent" 'congruent n m p = - (cic:/matita/nat/congruence/congruent.con n m p). +interpretation "congruent" 'congruent n m p = (congruent n m p). notation < "hvbox(n break \cong\sub p m)" (*non associative*) with precedence 45 @@ -103,7 +100,7 @@ rewrite > distr_times_plus. (*rewrite > (sym_times p (m/p)).*) (*rewrite > sym_times.*) rewrite > assoc_plus. -auto paramodulation. +autobatch paramodulation. rewrite < div_mod. assumption. assumption. @@ -120,7 +117,7 @@ qed. 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.