0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 14:46:45 EDT 2019 0.13/0.34 % CPUTime : 2.66/2.82 % SZS status Theorem 2.66/2.82 2.66/2.82 % SZS output start Proof 2.66/2.82 Take the following subset of the input axioms: 2.85/3.06 fof('thm.combin.K_THM', axiom, ![V_27A_27, V_27B_27, V_27x_27, V_27y_27]: s__02(V_27A_27, V_27x_27)=s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27)))). 2.85/3.06 fof('thm.envRel.convert_decls_def', axiom, ![V_27idecls_27]: s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))=s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27)))). 2.85/3.06 fof('thm.infer.append_decls_def', axiom, ![V_27idecls1_27, V_27idecls2_27]: s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27)))=s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))). 2.85/3.06 fof('thm.infer.inf_decls_accfupds', axiom, ![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & (![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))=s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27, V_27f_27]: s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))=s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))))))))). 2.85/3.06 fof('thm.list.LIST_TO_SET_APPEND', axiom, ![V_27A_27, V_27l1_27, V_27l2_27]: s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))=s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))). 2.85/3.06 fof('thm.typeSystem.decls_accfupds', axiom, ![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))=s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))=s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & (![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27, V_27d_27]: s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))=s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))))))))). 2.85/3.06 fof('thm.typeSystem.decls_literal_11', axiom, ![V_27f11_27, V_27f01_27, V_27f1_27, V_27f12_27, V_27f02_27, V_27f2_27]: ((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f1_27)=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f2_27) & (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f01_27)=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f02_27) & s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f12_27)=s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f11_27))) <=> s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f11_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f01_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))=s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f12_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f02_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f2_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))). 2.85/3.07 fof('thm.typeSystem.union_decls_def', axiom, ![V_27d1_27, V_27d2_27]: s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))=s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27)))). 2.85/3.07 fof(conjecture, conjecture, ![V_27decls1_27, V_27decls2_27]: s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27)))))=s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27)))))). 2.85/3.07 2.85/3.07 Now clausify the problem and encode Horn clauses using encoding 3 of 2.85/3.07 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 2.85/3.07 We repeatedly replace C & s=t => u=v by the two clauses: 2.85/3.07 fresh(y, y, x1...xn) = u 2.85/3.07 C => fresh(s, t, x1...xn) = v 2.85/3.07 where fresh is a fresh function symbol and x1..xn are the free 2.85/3.07 variables of u and v. 2.85/3.07 A predicate p(X) is encoded as p(X)=true (this is sound, because the 2.85/3.07 input problem has no model of domain size 1). 2.85/3.07 2.85/3.07 The encoding turns the above axioms into the following unit equations and goals: 2.85/3.07 2.85/3.07 Axiom 1 (thm.typeSystem.decls_literal_11): fresh3(X, X, Y, Z) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Z). 2.85/3.07 Axiom 2 (thm.typeSystem.decls_literal_11_2): fresh(X, X, Y, Z) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Y). 2.85/3.07 Axiom 3 (thm.typeSystem.decls_literal_11_3): fresh12(X, X, Y, Z, W, V, U, T) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))). 2.85/3.07 Axiom 4 (thm.envRel.convert_decls_def): s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))). 2.85/3.07 Axiom 5 (thm.infer.append_decls_def): s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))). 2.85/3.07 Axiom 6 (thm.typeSystem.decls_literal_11_1): fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), Z, U) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Z). 2.85/3.07 Axiom 7 (thm.typeSystem.decls_accfupds_8): s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))). 2.85/3.07 Axiom 8 (thm.typeSystem.decls_accfupds_7): s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))). 2.85/3.07 Axiom 9 (thm.typeSystem.decls_accfupds_5): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))). 2.85/3.07 Axiom 10 (thm.typeSystem.decls_accfupds_4): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))). 2.85/3.07 Axiom 11 (thm.typeSystem.decls_accfupds_3): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))). 2.85/3.07 Axiom 12 (thm.typeSystem.decls_accfupds_1): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))). 2.85/3.07 Axiom 13 (thm.typeSystem.decls_accfupds): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))). 2.85/3.07 Axiom 14 (thm.typeSystem.union_decls_def): s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))). 2.85/3.07 Axiom 15 (thm.infer.inf_decls_accfupds_6): s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))). 2.85/3.07 Axiom 16 (thm.infer.inf_decls_accfupds_5): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))). 2.85/3.07 Axiom 17 (thm.infer.inf_decls_accfupds_4): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))). 2.85/3.07 Axiom 18 (thm.infer.inf_decls_accfupds_3): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), Y), s__02(c_27type_2einfer_2einf__decls_27__00, X))))). 2.85/3.07 Axiom 19 (thm.infer.inf_decls_accfupds_1): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))). 2.85/3.07 Axiom 20 (thm.infer.inf_decls_accfupds): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))). 2.85/3.07 Axiom 21 (thm.combin.K_THM): s__02(X, Y) = s__02(X, chapp__02(s__02(cfun__02(Z, X), c_27const_2ecombin_2eK_27__01(s__02(X, Y))), s__02(Z, W))). 2.85/3.08 Axiom 22 (thm.list.LIST_TO_SET_APPEND): s__02(cfun__02(X, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(X), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(X), Y), s__02(c_27type_2elist_2elist_27__01(X), Z))))) = s__02(cfun__02(X, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(X, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(X), Y))), s__02(cfun__02(X, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(X), Z))))). 2.85/3.08 2.85/3.08 Lemma 23: s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, V, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = fresh12(?, ?, ?, ?, ?, V, U, T). 2.85/3.08 Proof: 2.85/3.08 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, V, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.08 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.08 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), U))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.08 = { by axiom 3 (thm.typeSystem.decls_literal_11_3) } 2.85/3.08 fresh12(?, ?, ?, ?, ?, V, U, T) 2.85/3.08 2.85/3.08 Lemma 24: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))). 2.85/3.08 Proof: 2.85/3.08 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X))))) 2.85/3.08 = { by axiom 11 (thm.typeSystem.decls_accfupds_3) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))) 2.85/3.08 2.85/3.08 Lemma 25: fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), fresh3(?, ?, ?, Y))) = fresh3(?, ?, ?, X). 2.85/3.08 Proof: 2.85/3.08 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), fresh3(?, ?, ?, Y))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), fresh3(?, ?, ?, Y))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), fresh3(?, ?, ?, Y))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Y))) 2.85/3.08 = { by axiom 21 (thm.combin.K_THM) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 fresh3(?, ?, ?, X) 2.85/3.08 2.85/3.08 Lemma 26: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = fresh3(?, ?, ?, X). 2.85/3.08 Proof: 2.85/3.08 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.08 = { by axiom 13 (thm.typeSystem.decls_accfupds) } 2.85/3.08 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.08 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.09 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.09 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.09 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.09 = { by lemma 25 } 2.85/3.09 fresh3(?, ?, ?, X) 2.85/3.09 2.85/3.09 Lemma 27: fresh12(?, ?, ?, ?, ?, X, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, V, Y, Z)), W) = fresh12(?, ?, ?, ?, ?, X, Y, W). 2.85/3.09 Proof: 2.85/3.09 fresh12(?, ?, ?, ?, ?, X, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, V, Y, Z)), W) 2.85/3.09 = { by lemma 23 } 2.85/3.09 fresh12(?, ?, ?, ?, ?, X, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, V, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), W) 2.85/3.09 = { by lemma 23 } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, V, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by lemma 24 } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by lemma 26 } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by lemma 23 } 2.85/3.09 fresh12(?, ?, ?, ?, ?, X, Y, W) 2.85/3.09 2.85/3.09 Lemma 28: fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), Z, W) = fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), Z, W). 2.85/3.09 Proof: 2.85/3.09 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), Z, W) 2.85/3.09 = { by lemma 23 } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by axiom 8 (thm.typeSystem.decls_accfupds_7) } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, W))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.09 = { by lemma 23 } 2.85/3.09 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), Z, W) 2.85/3.09 2.85/3.09 Lemma 29: fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?) = fresh(?, ?, X, ?). 2.85/3.09 Proof: 2.85/3.09 fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.09 = { by axiom 7 (thm.typeSystem.decls_accfupds_8) } 2.85/3.09 s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 fresh(?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 fresh(?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 fresh(?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), ?) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?))) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.09 s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.09 = { by axiom 21 (thm.combin.K_THM) } 2.85/3.09 s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), X) 2.85/3.09 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.10 fresh(?, ?, X, ?) 2.85/3.10 2.85/3.10 Lemma 30: fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))). 2.85/3.10 Proof: 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by lemma 23 } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.10 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.10 = { by axiom 14 (thm.typeSystem.union_decls_def) } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))) 2.85/3.10 2.85/3.10 Lemma 31: s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(W, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(?, ?, ?, ?, ?, X, Y, Z))), s__02(W, V))) = fresh12(?, ?, ?, ?, ?, X, Y, Z). 2.85/3.10 Proof: 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(W, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(?, ?, ?, ?, ?, X, Y, Z))), s__02(W, V))) 2.85/3.10 = { by lemma 23 } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(W, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(W, V))) 2.85/3.10 = { by axiom 21 (thm.combin.K_THM) } 2.85/3.10 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.85/3.10 = { by lemma 23 } 2.85/3.10 fresh12(?, ?, ?, ?, ?, X, Y, Z) 2.85/3.10 2.85/3.10 Lemma 32: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))). 2.85/3.10 Proof: 2.85/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.85/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.85/3.10 = { by axiom 10 (thm.typeSystem.decls_accfupds_4) } 2.85/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))) 2.85/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))) 2.94/3.10 2.94/3.10 Lemma 33: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y))) = fresh3(?, ?, ?, Y). 2.94/3.10 Proof: 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y))) 2.94/3.10 = { by lemma 31 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(?, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y))), s__02(?, ?))))) 2.94/3.10 = { by lemma 32 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(?, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y))), s__02(?, ?))))))) 2.94/3.10 = { by lemma 31 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), fresh12(?, ?, ?, ?, ?, W, Z, Y))))) 2.94/3.10 = { by lemma 23 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, W, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))))) 2.94/3.10 = { by lemma 32 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, W, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) 2.94/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, W, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) 2.94/3.10 = { by axiom 9 (thm.typeSystem.decls_accfupds_5) } 2.94/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.10 = { by lemma 32 } 2.94/3.10 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) 2.94/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) 2.94/3.10 = { by axiom 12 (thm.typeSystem.decls_accfupds_1) } 2.94/3.10 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) 2.94/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) 2.94/3.10 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.10 fresh3(?, ?, ?, chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) 2.94/3.10 = { by lemma 25 } 2.94/3.10 fresh3(?, ?, ?, Y) 2.94/3.10 2.94/3.10 Lemma 34: fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, V))) = fresh12(?, ?, ?, ?, ?, X, Y, V). 2.94/3.10 Proof: 2.94/3.10 fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, V))) 2.94/3.10 = { by lemma 23 } 2.94/3.11 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, V))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.11 = { by lemma 33 } 2.94/3.11 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, V))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.11 = { by lemma 23 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, X, Y, V) 2.94/3.11 2.94/3.11 Lemma 35: fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))). 2.94/3.11 Proof: 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 28 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 30 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 23 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), ?), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 28 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 23 } 2.94/3.11 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.11 = { by lemma 29 } 2.94/3.11 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.11 = { by lemma 23 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 30 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))) 2.94/3.11 = { by lemma 34 } 2.94/3.11 fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.11 = { by lemma 30 } 2.94/3.11 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))) 2.94/3.11 2.94/3.11 Lemma 36: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Z, X, Y))) = fresh3(?, ?, ?, X). 2.94/3.11 Proof: 2.94/3.11 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Z, X, Y))) 2.94/3.11 = { by lemma 23 } 2.94/3.11 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) 2.94/3.11 = { by lemma 24 } 2.94/3.11 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.11 = { by lemma 26 } 2.94/3.11 fresh3(?, ?, ?, X) 2.94/3.11 2.94/3.11 Lemma 37: fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, X, Y, Z)), ?) = fresh(?, ?, X, ?). 2.94/3.11 Proof: 2.94/3.11 fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, X, Y, Z)), ?) 2.94/3.11 = { by lemma 23 } 2.94/3.11 fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?) 2.94/3.11 = { by lemma 29 } 2.94/3.11 fresh(?, ?, X, ?) 2.94/3.11 2.94/3.12 Lemma 38: fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))). 2.94/3.12 Proof: 2.94/3.12 fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 23 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by axiom 4 (thm.envRel.convert_decls_def) } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))) 2.94/3.12 2.94/3.12 Lemma 39: fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?) = fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?). 2.94/3.12 Proof: 2.94/3.12 fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?) 2.94/3.12 = { by lemma 37 } 2.94/3.12 fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))))), ?) 2.94/3.12 = { by lemma 38 } 2.94/3.12 fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?) 2.94/3.12 2.94/3.12 Lemma 40: fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))). 2.94/3.12 Proof: 2.94/3.12 fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 33 } 2.94/3.12 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))) 2.94/3.12 = { by lemma 38 } 2.94/3.12 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 2.94/3.12 Lemma 41: fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))) = fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))). 2.94/3.12 Proof: 2.94/3.12 fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))) 2.94/3.12 = { by lemma 23 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by lemma 40 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by lemma 23 } 2.94/3.12 fresh12(?, ?, ?, ?, ?, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))) 2.94/3.12 2.94/3.12 Lemma 42: fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))). 2.94/3.12 Proof: 2.94/3.12 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 23 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by lemma 39 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 2.94/3.12 = { by lemma 23 } 2.94/3.12 fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 41 } 2.94/3.12 fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 38 } 2.94/3.12 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))) 2.94/3.12 2.94/3.12 Lemma 43: fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))). 2.94/3.12 Proof: 2.94/3.12 fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 = { by lemma 36 } 2.94/3.12 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))) 2.94/3.12 = { by lemma 42 } 2.94/3.12 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.12 2.94/3.12 Lemma 44: fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X))), fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) = fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))). 2.94/3.12 Proof: 2.94/3.12 fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X))), fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X))), fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 = { by axiom 22 (thm.list.LIST_TO_SET_APPEND) } 2.94/3.12 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.12 fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), X), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), Y))))) 2.94/3.12 2.94/3.12 Lemma 45: s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))). 2.94/3.12 Proof: 2.94/3.12 s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) 2.94/3.12 = { by axiom 21 (thm.combin.K_THM) } 2.94/3.12 s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) 2.94/3.12 = { by axiom 15 (thm.infer.inf_decls_accfupds_6) } 2.94/3.12 s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) 2.94/3.12 = { by axiom 5 (thm.infer.append_decls_def) } 2.94/3.12 s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) 2.94/3.12 2.94/3.12 Lemma 46: fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))). 2.94/3.12 Proof: 2.94/3.12 fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.12 = { by lemma 33 } 2.94/3.13 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))))) 2.94/3.13 = { by lemma 30 } 2.94/3.13 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) 2.94/3.13 2.94/3.13 Lemma 47: fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))). 2.94/3.13 Proof: 2.94/3.13 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.13 = { by lemma 40 } 2.94/3.13 fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.13 = { by axiom 16 (thm.infer.inf_decls_accfupds_5) } 2.94/3.13 fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) 2.94/3.13 = { by lemma 40 } 2.94/3.14 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) 2.94/3.14 2.94/3.14 Lemma 48: fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) = fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))). 2.94/3.14 Proof: 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 42 } 2.94/3.14 fresh2(fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 23 } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 38 } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 34 } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh12(?, ?, ?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 23 } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by lemma 41 } 2.94/3.14 fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Z, W, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) 2.94/3.14 = { by axiom 6 (thm.typeSystem.decls_literal_11_1) } 2.94/3.14 s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 2.94/3.14 = { by axiom 1 (thm.typeSystem.decls_literal_11) } 3.25/3.49 fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))) 3.25/3.49 3.25/3.49 Goal 1 (conjecture): s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))). 3.25/3.49 Proof: 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))) 3.25/3.49 = { by lemma 35 } 3.25/3.49 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.25/3.49 = { by lemma 27 } 3.25/3.49 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.25/3.49 = { by lemma 35 } 3.25/3.49 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.25/3.49 = { by lemma 23 } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by lemma 30 } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27)))), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))), ?)), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by lemma 37 } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27)))), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by lemma 39 } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27)))), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by lemma 39 } 3.25/3.49 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.49 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 22 (thm.list.LIST_TO_SET_APPEND) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 2 (thm.typeSystem.decls_literal_11_2) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 45 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 39 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 35 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 36 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 43 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 43 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 44 } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 21 (thm.combin.K_THM) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 20 (thm.infer.inf_decls_accfupds) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by axiom 18 (thm.infer.inf_decls_accfupds_3) } 3.25/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.25/3.50 = { by lemma 45 } 3.34/3.50 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.50 = { by axiom 5 (thm.infer.append_decls_def) } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 43 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 46 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 40 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 47 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), ?), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 40 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))))), fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), ?), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 44 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), ?), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by axiom 16 (thm.infer.inf_decls_accfupds_5) } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by axiom 21 (thm.combin.K_THM) } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by axiom 19 (thm.infer.inf_decls_accfupds_1) } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by axiom 17 (thm.infer.inf_decls_accfupds_4) } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 40 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 47 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.51 = { by lemma 48 } 3.34/3.51 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.52 = { by axiom 5 (thm.infer.append_decls_def) } 3.34/3.52 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.52 = { by axiom 5 (thm.infer.append_decls_def) } 3.34/3.52 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh2(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, ?))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.52 = { by lemma 48 } 3.34/3.52 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) 3.34/3.52 = { by lemma 23 } 3.34/3.52 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.34/3.52 = { by lemma 42 } 3.34/3.52 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.34/3.52 = { by lemma 27 } 3.34/3.52 fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))))) 3.34/3.52 = { by lemma 42 } 3.34/3.52 s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, sK3_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK2_conjecture_V_27decls2_27))))) 3.34/3.52 % SZS output end Proof 3.34/3.52 3.34/3.52 RESULT: Theorem (the conjecture is true). 3.34/3.52 EOF