src/HOL/ex/CTL.thy
changeset 32960 69916a850301
parent 32587 caa5ada96a00
child 41460 ea56b98aee83
equal deleted inserted replaced
32959:23a8c5ac35f8 32960:69916a850301
   249     show "?lhs \<subseteq> p \<inter> \<AX> ?lhs"
   249     show "?lhs \<subseteq> p \<inter> \<AX> ?lhs"
   250     proof
   250     proof
   251       show "?lhs \<subseteq> p" ..
   251       show "?lhs \<subseteq> p" ..
   252       show "?lhs \<subseteq> \<AX> ?lhs"
   252       show "?lhs \<subseteq> \<AX> ?lhs"
   253       proof -
   253       proof -
   254 	{
   254         {
   255 	  have "\<AG> (p \<rightarrow> \<AX> p) \<subseteq> p \<rightarrow> \<AX> p" by (rule AG_fp_1)
   255           have "\<AG> (p \<rightarrow> \<AX> p) \<subseteq> p \<rightarrow> \<AX> p" by (rule AG_fp_1)
   256           moreover have "p \<inter> p \<rightarrow> \<AX> p \<subseteq> \<AX> p" ..
   256           moreover have "p \<inter> p \<rightarrow> \<AX> p \<subseteq> \<AX> p" ..
   257           ultimately have "?lhs \<subseteq> \<AX> p" by auto
   257           ultimately have "?lhs \<subseteq> \<AX> p" by auto
   258 	}  
   258         }  
   259 	moreover
   259         moreover
   260 	{
   260         {
   261 	  have "p \<inter> \<AG> (p \<rightarrow> \<AX> p) \<subseteq> \<AG> (p \<rightarrow> \<AX> p)" ..
   261           have "p \<inter> \<AG> (p \<rightarrow> \<AX> p) \<subseteq> \<AG> (p \<rightarrow> \<AX> p)" ..
   262           also have "\<dots> \<subseteq> \<AX> \<dots>" by (rule AG_fp_2)
   262           also have "\<dots> \<subseteq> \<AX> \<dots>" by (rule AG_fp_2)
   263           finally have "?lhs \<subseteq> \<AX> \<AG> (p \<rightarrow> \<AX> p)" .
   263           finally have "?lhs \<subseteq> \<AX> \<AG> (p \<rightarrow> \<AX> p)" .
   264 	}  
   264         }  
   265 	ultimately have "?lhs \<subseteq> \<AX> p \<inter> \<AX> \<AG> (p \<rightarrow> \<AX> p)"
   265         ultimately have "?lhs \<subseteq> \<AX> p \<inter> \<AX> \<AG> (p \<rightarrow> \<AX> p)"
   266 	  by (rule Int_greatest)
   266           by (rule Int_greatest)
   267 	also have "\<dots> = \<AX> ?lhs" by (simp only: AX_int)
   267         also have "\<dots> = \<AX> ?lhs" by (simp only: AX_int)
   268 	finally show ?thesis .
   268         finally show ?thesis .
   269       qed
   269       qed
   270     qed
   270     qed
   271   qed
   271   qed
   272 next
   272 next
   273   show "\<AG> p \<subseteq> p \<inter> \<AG> (p \<rightarrow> \<AX> p)"
   273   show "\<AG> p \<subseteq> p \<inter> \<AG> (p \<rightarrow> \<AX> p)"