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92 |
92 |
93 |
93 |
94 subsection {* Properties of SetS *} |
94 subsection {* Properties of SetS *} |
95 |
95 |
96 lemma SetS_finite: "2 < p ==> finite (SetS a p)" |
96 lemma SetS_finite: "2 < p ==> finite (SetS a p)" |
97 by (auto simp add: SetS_def SRStar_finite [of p] finite_imageI) |
97 by (auto simp add: SetS_def SRStar_finite [of p]) |
98 |
98 |
99 lemma SetS_elems_finite: "\<forall>X \<in> SetS a p. finite X" |
99 lemma SetS_elems_finite: "\<forall>X \<in> SetS a p. finite X" |
100 by (auto simp add: SetS_def MultInvPair_def) |
100 by (auto simp add: SetS_def MultInvPair_def) |
101 |
101 |
102 lemma SetS_elems_card: "[| zprime p; 2 < p; ~([a = 0] (mod p)); |
102 lemma SetS_elems_card: "[| zprime p; 2 < p; ~([a = 0] (mod p)); |