src/HOL/Decision_Procs/MIR.thy
changeset 31730 d74830dc3e4a
parent 31706 1db0c8f235fb
child 31952 40501bb2d57c
equal deleted inserted replaced
31729:b9299916d618 31730:d74830dc3e4a
  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)"