Isabelle2018: TakeGrant
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@ -274,10 +274,10 @@ lemma tgs_connected_comm_eq:
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by (metis tgs_connected_comm)
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lemmas tgs_connected_trans =
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rtrancl_trans [where r="directly_tgs_connected s", simplified tgs_connected_def[symmetric]]
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rtrancl_trans [where r="directly_tgs_connected s" for s, simplified tgs_connected_def[symmetric]]
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lemmas directly_tgs_connected_rtrancl_into_rtrancl =
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rtrancl_into_rtrancl [where r="directly_tgs_connected s", simplified tgs_connected_def[symmetric]]
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rtrancl_into_rtrancl [where r="directly_tgs_connected s" for s, simplified tgs_connected_def[symmetric]]
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lemma take_caps_directly_tgs_connected:
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"\<lbrakk>c \<in> caps_of s e; Take \<in> rights c\<rbrakk> \<Longrightarrow> s \<turnstile> e \<leftrightarrow> target c"
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@ -18,7 +18,7 @@ lemma direct_caps_of_update [simp]:
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by (rule ext, simp add: direct_caps_of_def split:option.splits)
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lemma direct_caps_of_empty [simp]:
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"direct_caps_of empty = ( \<lambda> x. {})"
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"direct_caps_of Map.empty = ( \<lambda> x. {})"
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by (simp add: direct_caps_of_def fun_eq_iff)
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definition "id\<^sub>0 \<equiv> 0"
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