2127 case (1 p q) |
2127 case (1 p q) |
2128 let ?d = "\<delta> (And p q)" |
2128 let ?d = "\<delta> (And p q)" |
2129 from prems int_lcm_pos have dp: "?d >0" by simp |
2129 from prems int_lcm_pos have dp: "?d >0" by simp |
2130 have d1: "\<delta> p dvd \<delta> (And p q)" using prems by simp |
2130 have d1: "\<delta> p dvd \<delta> (And p q)" using prems by simp |
2131 hence th: "d\<delta> p ?d" |
2131 hence th: "d\<delta> p ?d" |
2132 using delta_mono prems by (auto simp del: int_lcm_dvd1) |
2132 using delta_mono prems by(simp only: iszlfm.simps) blast |
2133 have "\<delta> q dvd \<delta> (And p q)" using prems by simp |
2133 have "\<delta> q dvd \<delta> (And p q)" using prems by simp |
2134 hence th': "d\<delta> q ?d" using delta_mono prems by (auto simp del: int_lcm_dvd2) |
2134 hence th': "d\<delta> q ?d" using delta_mono prems by(simp only: iszlfm.simps) blast |
2135 from th th' dp show ?case by simp |
2135 from th th' dp show ?case by simp |
2136 next |
2136 next |
2137 case (2 p q) |
2137 case (2 p q) |
2138 let ?d = "\<delta> (And p q)" |
2138 let ?d = "\<delta> (And p q)" |
2139 from prems int_lcm_pos have dp: "?d >0" by simp |
2139 from prems int_lcm_pos have dp: "?d >0" by simp |
2140 have "\<delta> p dvd \<delta> (And p q)" using prems by simp hence th: "d\<delta> p ?d" using delta_mono prems |
2140 have "\<delta> p dvd \<delta> (And p q)" using prems by simp hence th: "d\<delta> p ?d" using delta_mono prems |
2141 by (auto simp del: int_lcm_dvd1) |
2141 by(simp only: iszlfm.simps) blast |
2142 have "\<delta> q dvd \<delta> (And p q)" using prems by simp hence th': "d\<delta> q ?d" using delta_mono prems by (auto simp del: int_lcm_dvd2) |
2142 have "\<delta> q dvd \<delta> (And p q)" using prems by simp hence th': "d\<delta> q ?d" using delta_mono prems by(simp only: iszlfm.simps) blast |
2143 from th th' dp show ?case by simp |
2143 from th th' dp show ?case by simp |
2144 qed simp_all |
2144 qed simp_all |
2145 |
2145 |
2146 |
2146 |
2147 lemma minusinf_inf: |
2147 lemma minusinf_inf: |
2148 assumes linp: "iszlfm p (a # bs)" |
2148 assumes linp: "iszlfm p (a # bs)" |