l_get_dom_component_get_scdom_component_axioms_def: fixes get_owner_document :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) document_ptr) prog"   and heap_is_wellformed :: "(_) heap \<Rightarrow> bool"   and type_wf :: "(_) heap \<Rightarrow> bool"   and known_ptrs :: "(_) heap \<Rightarrow> bool"   and get_scdom_component :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr list) prog"   and get_dom_component :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr list) prog" shows "l_get_dom_component_get_scdom_component_axioms get_owner_document heap_is_wellformed type_wf known_ptrs get_scdom_component get_dom_component \<equiv> (((\<forall>h ptr sc c. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> h \<turnstile> get_dom_component ptr \<rightarrow>\<^sub>r c \<longrightarrow> set c \<subseteq> set sc) \<and> (\<forall>h ptr sc ptr'. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> ptr' \<in> set sc \<longrightarrow> h \<turnstile> get_scdom_component ptr' \<rightarrow>\<^sub>r sc)) \<and> (\<forall>h ptr sc ptr' owner_document. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> ptr' \<in> set sc \<longrightarrow> h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document \<longrightarrow> h \<turnstile> get_owner_document ptr' \<rightarrow>\<^sub>r owner_document) \<and> (\<forall>h ptr. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> ptr |\<in>| object_ptr_kinds h \<longrightarrow> h \<turnstile> ok get_scdom_component ptr)) \<and> ((\<forall>h ptr sc ptr'. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> ptr' \<in> set sc \<longrightarrow> ptr' |\<in>| object_ptr_kinds h) \<and> (\<forall>h ptr' sc thesis ptr. (\<forall>c. h \<turnstile> get_dom_component ptr' \<rightarrow>\<^sub>r c \<longrightarrow> set c \<subseteq> set sc \<longrightarrow> thesis) \<longrightarrow> heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> ptr' \<in> set sc \<longrightarrow> thesis)) \<and> (\<forall>h ptr' sc thesis ptr. (\<forall>owner_document. h \<turnstile> get_owner_document ptr' \<rightarrow>\<^sub>r owner_document \<longrightarrow> cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r owner_document \<in> set sc \<longrightarrow> thesis) \<longrightarrow> heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_scdom_component ptr \<rightarrow>\<^sub>r sc \<longrightarrow> ptr' \<in> set sc \<longrightarrow> thesis) \<and> (\<forall>h ptr owner_document ptr' owner_document'. heap_is_wellformed h \<longrightarrow> type_wf h \<longrightarrow> known_ptrs h \<longrightarrow> h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document \<longrightarrow> h \<turnstile> get_owner_document ptr' \<rightarrow>\<^sub>r owner_document' \<longrightarrow> owner_document \<noteq> owner_document' \<longrightarrow> set |h \<turnstile> get_scdom_component ptr|\<^sub>r \<inter> set |h \<turnstile> get_scdom_component ptr'|\<^sub>r = {})"