src/HOL/IntDiv.thy
changeset 29404 ee15ccdeaa72
parent 29403 fe17df4e4ab3
child 29405 98ab21b14f09
     1.1 --- a/src/HOL/IntDiv.thy	Thu Jan 08 08:24:08 2009 -0800
     1.2 +++ b/src/HOL/IntDiv.thy	Thu Jan 08 08:36:16 2009 -0800
     1.3 @@ -938,18 +938,8 @@
     1.4  apply (auto simp add: mult_commute)
     1.5  done
     1.6  
     1.7 -lemma zmod_zmod_cancel:
     1.8 -assumes "n dvd m" shows "(k::int) mod m mod n = k mod n"
     1.9 -proof -
    1.10 -  from `n dvd m` obtain r where "m = n*r" by(auto simp:dvd_def)
    1.11 -  have "k mod n = (m * (k div m) + k mod m) mod n"
    1.12 -    using zmod_zdiv_equality[of k m] by simp
    1.13 -  also have "\<dots> = (m * (k div m) mod n + k mod m mod n) mod n"
    1.14 -    by(subst zmod_zadd1_eq, rule refl)
    1.15 -  also have "m * (k div m) mod n = 0" using `m = n*r`
    1.16 -    by(simp add:mult_ac)
    1.17 -  finally show ?thesis by simp
    1.18 -qed
    1.19 +lemma zmod_zmod_cancel: "n dvd m \<Longrightarrow> (k::int) mod m mod n = k mod n"
    1.20 +by (rule mod_mod_cancel)
    1.21  
    1.22  
    1.23  subsection {*Splitting Rules for div and mod*}