src/HOL/NumberTheory/Gauss.thy
changeset 14353 79f9fbef9106
parent 14271 8ed6989228bb
child 14981 e73f8140af78
equal deleted inserted replaced
14352:a8b1a44d8264 14353:79f9fbef9106
   178   apply (frule_tac a = x and b = a in zcong_zprime_prod_zero_contra)
   178   apply (frule_tac a = x and b = a in zcong_zprime_prod_zero_contra)
   179 by (auto simp add: A_greater_zero)
   179 by (auto simp add: A_greater_zero)
   180 
   180 
   181 lemma (in GAUSS) B_greater_zero: "x \<in> B ==> 0 < x";
   181 lemma (in GAUSS) B_greater_zero: "x \<in> B ==> 0 < x";
   182   apply (insert a_nonzero)
   182   apply (insert a_nonzero)
   183 by (auto simp add: B_def zmult_pos A_greater_zero)
   183 by (auto simp add: B_def mult_pos A_greater_zero)
   184 
   184 
   185 lemma (in GAUSS) C_ncong_p: "x \<in> C ==>  ~[x = 0](mod p)";
   185 lemma (in GAUSS) C_ncong_p: "x \<in> C ==>  ~[x = 0](mod p)";
   186   apply (auto simp add: C_def)
   186   apply (auto simp add: C_def)
   187   apply (frule B_ncong_p)
   187   apply (frule B_ncong_p)
   188   apply (subgoal_tac "[x = StandardRes p x](mod p)");
   188   apply (subgoal_tac "[x = StandardRes p x](mod p)");