X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Farithmetics%2Fcongruence.ma;h=d9792b5ebbe3fd079b48548325e7e1235d98d39f;hb=29c979302cf398410bf6f10c11b146ebe42bd54a;hp=d1afc19eec57ae6674c1d5e67e06e453ef88998d;hpb=7ad16d18416a08382d62747fce4a0ac18ee557e0;p=helm.git diff --git a/matita/matita/lib/arithmetics/congruence.ma b/matita/matita/lib/arithmetics/congruence.ma index d1afc19ee..d9792b5eb 100644 --- a/matita/matita/lib/arithmetics/congruence.ma +++ b/matita/matita/lib/arithmetics/congruence.ma @@ -37,7 +37,7 @@ theorem le_to_mod: ∀n,m:nat. n < m → n = n \mod m. qed. theorem mod_mod : ∀n,p:nat. O

(div_mod (n \mod p) p) in ⊢ (? ? % ?) +#n #p #posp >(div_mod (n \mod p) p) in ⊢ (? ? % ?); >(eq_div_O ? p) // @lt_mod_m_m // qed. @@ -79,8 +79,8 @@ qed. theorem congruent_to_divides: ∀n,m,p:nat.O < p → n ≅_{p} m → p ∣ (n - m). #n #m #p #posp #congnm @(quotient ? ? ((n / p)-(m / p))) ->commutative_times >(div_mod n p) in ⊢ (??%?) ->(div_mod m p) in ⊢ (??%?) <(commutative_plus (m \mod p)) +>commutative_times >(div_mod n p) in ⊢ (??%?); +>(div_mod m p) in ⊢ (??%?); <(commutative_plus (m \mod p))