equal
deleted
inserted
replaced
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)"); |