src/HOL/Presburger.thy

 
 theorem conj_le_cong: "(0 <= x \<Longrightarrow> P = P') \<Longrightarrow> (0 <= (x::int) \<and> P) = (0 <= x \<and> P')" 
   by (simp cong: conj_cong)
 lemma int_eq_number_of_eq:
   "(((number_of v)::int) = (number_of w)) = iszero ((number_of (v + (uminus w)))::int)"
-  by simp
+  by (rule eq_number_of_eq)
 
 lemma mod_eq0_dvd_iff[presburger]: "(m::nat) mod n = 0 \<longleftrightarrow> n dvd m"
 unfolding dvd_eq_mod_eq_0[symmetric] ..
 
 lemma zmod_eq0_zdvd_iff[presburger]: "(m::int) mod n = 0 \<longleftrightarrow> n dvd m"