0.00/0.08	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.08	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.07/0.27	% Computer   : n008.cluster.edu
0.07/0.27	% Model      : x86_64 x86_64
0.07/0.27	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.07/0.27	% Memory     : 8042.1875MB
0.07/0.27	% OS         : Linux 3.10.0-693.el7.x86_64
0.07/0.27	% CPULimit   : 960
0.07/0.27	% WCLimit    : 120
0.07/0.27	% DateTime   : Thu Jul  2 08:58:29 EDT 2020
0.07/0.28	% CPUTime    : 
29.14/4.08	% SZS status Theorem
29.14/4.08	
29.14/4.08	% SZS output start Proof
29.14/4.08	Take the following subset of the input axioms:
33.63/4.64	  fof('thm.combin.K_THM', axiom, ![V_27B_27, V_27A_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)))).
33.63/4.65	  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)))).
33.63/4.65	  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)))))))).
33.99/4.66	  fof('thm.infer.inf_decls_accfupds', axiom, ![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, 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)))))=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))) & (![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))), 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)))))=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))))) & (![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__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)))))=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))))) & (![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, 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__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))), 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__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, 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)))))=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))) & ![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))))))))))))).
33.99/4.66	  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)))))).
33.99/4.66	  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__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_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, 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))))) & (![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__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_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_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), 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)))))=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))))) & (![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__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_2enamespace_2eid_27__02(c_27type_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))))) & (![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__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))))) & (![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__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))))))))))))).
33.99/4.66	  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_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(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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_2enamespace_2eid_27__02(c_27type_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_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(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))))))))).
33.99/4.67	  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)))).
33.99/4.67	  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)))))).
33.99/4.67	
33.99/4.67	Now clausify the problem and encode Horn clauses using encoding 3 of
33.99/4.67	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
33.99/4.67	We repeatedly replace C & s=t => u=v by the two clauses:
33.99/4.67	  fresh(y, y, x1...xn) = u
33.99/4.67	  C => fresh(s, t, x1...xn) = v
33.99/4.67	where fresh is a fresh function symbol and x1..xn are the free
33.99/4.67	variables of u and v.
33.99/4.67	A predicate p(X) is encoded as p(X)=true (this is sound, because the
33.99/4.67	input problem has no model of domain size 1).
33.99/4.67	
33.99/4.67	The encoding turns the above axioms into the following unit equations and goals:
33.99/4.67	
33.99/4.67	Axiom 1 (thm.typeSystem.decls_literal_11): fresh3(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).
33.99/4.67	Axiom 2 (thm.typeSystem.decls_literal_11_1): fresh2(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), Y).
33.99/4.67	Axiom 3 (thm.typeSystem.decls_literal_11_2): fresh(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), Y).
33.99/4.67	Axiom 4 (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))))))).
33.99/4.67	Axiom 5 (thm.typeSystem.decls_literal_11_3): fresh11(X, X, Y, Z, W, V, U, T) = fresh12(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(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Y), Y, Z, W, V, U, T).
33.99/4.67	Axiom 6 (thm.typeSystem.decls_literal_11_3): fresh10(X, X, Y, Z, W, V, U, T) = fresh11(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(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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), Y, Z, W, V, U, T).
33.99/4.67	Axiom 7 (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))))))).
33.99/4.68	Axiom 8 (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))).
33.99/4.68	Axiom 9 (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))))).
33.99/4.68	Axiom 10 (thm.typeSystem.decls_accfupds_8): 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))))).
33.99/4.68	Axiom 11 (thm.typeSystem.decls_accfupds_7): 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__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))))).
33.99/4.68	Axiom 12 (thm.typeSystem.decls_accfupds_6): 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))))) = 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))))).
33.99/4.68	Axiom 13 (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), 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))))) = 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))))).
33.99/4.68	Axiom 14 (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__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))))).
33.99/4.68	Axiom 15 (thm.typeSystem.decls_accfupds_2): 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))))).
33.99/4.68	Axiom 16 (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))).
33.99/4.68	Axiom 17 (thm.typeSystem.decls_literal_11_3): fresh10(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), Z, W, Y, V, U, X) = 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), 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(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), W))), 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), Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))).
33.99/4.68	Axiom 18 (thm.typeSystem.decls_literal_11_2): fresh(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), U).
33.99/4.68	Axiom 19 (thm.infer.inf_decls_accfupds_8): 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))).
33.99/4.68	Axiom 20 (thm.infer.inf_decls_accfupds_7): 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, 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)))), Y), s__02(c_27type_2einfer_2einf__decls_27__00, X))))).
33.99/4.68	Axiom 21 (thm.infer.inf_decls_accfupds_6): 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))))).
33.99/4.68	Axiom 22 (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__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))))) = 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))))).
33.99/4.68	Axiom 23 (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, 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))), 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))))).
33.99/4.68	Axiom 24 (thm.infer.inf_decls_accfupds): 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))))).
33.99/4.71	Axiom 25 (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))).
33.99/4.71	
33.99/4.71	Lemma 26: 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, T, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = fresh12(?, ?, ?, ?, ?, V, U, T).
33.99/4.71	Proof:
33.99/4.71	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, T, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.71	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
33.99/4.71	  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(fresh(?, ?, 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(fresh(?, ?, T, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.71	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.71	  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(fresh(?, ?, T, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.71	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.71	  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)))))))
33.99/4.71	= { by axiom 4 (thm.typeSystem.decls_literal_11_3) }
33.99/4.71	  fresh12(?, ?, ?, ?, ?, V, U, T)
33.99/4.71	
33.99/4.71	Lemma 27: fresh(X, X, Y, Z) = fresh(?, ?, Y, ?).
33.99/4.71	Proof:
33.99/4.71	  fresh(X, X, Y, Z)
33.99/4.71	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.71	  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)
33.99/4.71	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh(?, ?, Y, ?)
33.99/4.72	
33.99/4.72	Lemma 28: fresh11(?, ?, V, W, Z, V, Y, X) = fresh12(?, ?, ?, ?, ?, V, Y, X).
33.99/4.72	Proof:
33.99/4.72	  fresh11(?, ?, V, W, Z, V, Y, X)
33.99/4.72	= { by axiom 5 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh12(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(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V), V, W, Z, V, Y, X)
33.99/4.72	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
33.99/4.72	  fresh12(fresh3(?, ?, V, ?), 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), V, W, Z, V, Y, X)
33.99/4.72	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
33.99/4.72	  fresh12(fresh3(?, ?, V, ?), fresh3(?, ?, V, ?), V, W, Z, V, Y, X)
33.99/4.72	= { by axiom 4 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  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), 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), X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.72	= { by axiom 4 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh12(?, ?, ?, ?, ?, V, Y, X)
33.99/4.72	
33.99/4.72	Lemma 29: fresh10(?, ?, V, W, Z, Y, W, X) = fresh11(?, ?, V, W, Z, Y, W, X).
33.99/4.72	Proof:
33.99/4.72	  fresh10(?, ?, V, W, Z, Y, W, X)
33.99/4.72	= { by axiom 6 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh11(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), W), 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), W), V, W, Z, Y, W, X)
33.99/4.72	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh11(fresh(?, ?, W, ?), 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), W), V, W, Z, Y, W, X)
33.99/4.72	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh11(fresh(?, ?, W, ?), fresh(?, ?, W, ?), V, W, Z, Y, W, X)
33.99/4.72	= { by axiom 5 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh12(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), 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), V, W, Z, Y, W, X)
33.99/4.72	= { by axiom 5 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh11(?, ?, V, W, Z, Y, W, X)
33.99/4.72	
33.99/4.72	Lemma 30: fresh10(X, X, Y, Z, W, V, U, T) = fresh10(?, ?, Y, Z, W, V, U, T).
33.99/4.72	Proof:
33.99/4.72	  fresh10(X, X, Y, Z, W, V, U, T)
33.99/4.72	= { by axiom 6 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh11(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(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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), Y, Z, W, V, U, T)
33.99/4.72	= { by axiom 6 (thm.typeSystem.decls_literal_11_3) }
33.99/4.72	  fresh10(?, ?, Y, Z, W, V, U, T)
33.99/4.72	
33.99/4.72	Lemma 31: fresh2(?, ?, X, ?) = fresh(?, ?, X, ?).
33.99/4.72	Proof:
33.99/4.72	  fresh2(?, ?, X, ?)
33.99/4.72	= { by axiom 2 (thm.typeSystem.decls_literal_11_1) }
33.99/4.72	  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)
33.99/4.72	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh(?, ?, X, ?)
33.99/4.72	
33.99/4.72	Lemma 32: fresh(?, ?, 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(fresh(?, ?, Y, ?))), fresh(?, ?, X, ?)), ?) = fresh(?, ?, Y, ?).
33.99/4.72	Proof:
33.99/4.72	  fresh(?, ?, 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(fresh(?, ?, Y, ?))), fresh(?, ?, X, ?)), ?)
33.99/4.72	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh(?, ?, 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), Y))), fresh(?, ?, X, ?)), ?)
33.99/4.72	= { by lemma 31 }
33.99/4.72	  fresh2(?, ?, 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), Y))), fresh(?, ?, X, ?)), ?)
33.99/4.72	= { by axiom 2 (thm.typeSystem.decls_literal_11_1) }
33.99/4.72	  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), Y))), fresh(?, ?, X, ?)))
33.99/4.72	= { by lemma 31 }
33.99/4.72	  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), Y))), fresh2(?, ?, X, ?)))
33.99/4.72	= { by axiom 2 (thm.typeSystem.decls_literal_11_1) }
33.99/4.72	  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), 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), X)))
33.99/4.72	= { by axiom 25 (thm.combin.K_THM) }
33.99/4.72	  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)
33.99/4.72	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.72	  fresh(?, ?, Y, ?)
33.99/4.72	
33.99/4.72	Lemma 33: fresh10(fresh(?, ?, X, ?), fresh(?, ?, Y, ?), Z, W, Y, V, U, X) = fresh12(?, ?, ?, ?, ?, Z, W, Y).
33.99/4.72	Proof:
33.99/4.72	  fresh10(fresh(?, ?, X, ?), fresh(?, ?, Y, ?), Z, W, Y, V, U, X)
33.99/4.73	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.73	  fresh10(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), fresh(?, ?, Y, ?), Z, W, Y, V, U, X)
33.99/4.73	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.73	  fresh10(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), Z, W, Y, V, U, X)
33.99/4.73	= { by axiom 17 (thm.typeSystem.decls_literal_11_3) }
33.99/4.73	  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), 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(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), W))), 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), Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.73	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
33.99/4.73	  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(fresh3(?, ?, 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(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), W))), 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), Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.73	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.73	  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(fresh3(?, ?, 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(fresh(?, ?, W, ?))), 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), Y))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.73	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.73	  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(fresh3(?, ?, 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(fresh(?, ?, W, ?))), 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(fresh(?, ?, Y, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
33.99/4.73	= { by lemma 26 }
33.99/4.74	  fresh12(?, ?, ?, ?, ?, Z, W, Y)
33.99/4.74	
33.99/4.74	Lemma 34: fresh12(?, ?, ?, ?, ?, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z))) = fresh12(?, ?, ?, ?, ?, V, W, Z).
33.99/4.74	Proof:
33.99/4.74	  fresh12(?, ?, ?, ?, ?, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by lemma 28 }
33.99/4.74	  fresh11(?, ?, V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by lemma 29 }
33.99/4.74	  fresh10(?, ?, V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by lemma 30 }
33.99/4.74	  fresh10(fresh(?, ?, Z, ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by lemma 32 }
33.99/4.74	  fresh10(fresh(?, ?, 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(fresh(?, ?, Z, ?))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)), ?)), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.74	  fresh10(fresh(?, ?, 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(fresh(?, ?, 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), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.74	  fresh10(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(fresh(?, ?, 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), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 12 (thm.typeSystem.decls_accfupds_6) }
33.99/4.74	  fresh10(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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 11 (thm.typeSystem.decls_accfupds_7) }
33.99/4.74	  fresh10(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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 10 (thm.typeSystem.decls_accfupds_8) }
33.99/4.74	  fresh10(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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
33.99/4.74	  fresh10(fresh(?, ?, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, Z)))
33.99/4.74	= { by lemma 26 }
34.72/4.74	  fresh10(fresh(?, ?, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
34.72/4.74	= { by lemma 33 }
34.72/4.75	  fresh12(?, ?, ?, ?, ?, V, W, Z)
34.72/4.75	
34.72/4.75	Lemma 35: fresh(fresh12(?, ?, ?, ?, ?, X, Y, Z), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U) = fresh(?, ?, U, ?).
34.72/4.75	Proof:
34.72/4.75	  fresh(fresh12(?, ?, ?, ?, ?, X, Y, Z), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U)
34.72/4.75	= { by lemma 26 }
34.72/4.75	  fresh(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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U)
34.72/4.75	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
34.72/4.75	  fresh(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(fresh(?, ?, 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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U)
34.72/4.76	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.76	  fresh(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(fresh(?, ?, Z, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U)
34.72/4.76	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.76	  fresh(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))))))), fresh12(?, ?, ?, ?, ?, W, V, U), Z, U)
34.72/4.76	= { by lemma 26 }
34.72/4.76	  fresh(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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, U, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), Z, U)
34.72/4.76	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
34.72/4.76	  fresh(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(fresh(?, ?, 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(fresh(?, ?, U, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), Z, U)
34.72/4.76	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.76	  fresh(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(fresh(?, ?, U, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), Z, U)
34.72/4.76	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.77	  fresh(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)
34.72/4.77	= { by axiom 18 (thm.typeSystem.decls_literal_11_2) }
34.72/4.77	  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)
34.72/4.77	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.77	  fresh(?, ?, U, ?)
34.72/4.77	
34.72/4.77	Lemma 36: fresh(fresh12(?, ?, ?, ?, ?, T, U, V), fresh12(?, ?, ?, ?, ?, W, Z, S), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, V)), S) = fresh(?, ?, S, ?).
34.72/4.77	Proof:
34.72/4.77	  fresh(fresh12(?, ?, ?, ?, ?, T, U, V), fresh12(?, ?, ?, ?, ?, W, Z, S), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, V)), S)
34.72/4.77	= { by lemma 34 }
34.72/4.77	  fresh(fresh12(?, ?, ?, ?, ?, T, U, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, V))), fresh12(?, ?, ?, ?, ?, W, Z, S), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, X, V)), S)
34.72/4.77	= { by lemma 35 }
34.72/4.77	  fresh(?, ?, S, ?)
34.72/4.77	
34.72/4.77	Lemma 37: fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, V)), ?) = fresh(?, ?, V, ?).
34.72/4.77	Proof:
34.72/4.77	  fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, V)), ?)
34.72/4.77	= { by lemma 27 }
34.72/4.77	  fresh(fresh12(?, ?, ?, ?, ?, ?, ?, V), fresh12(?, ?, ?, ?, ?, ?, ?, V), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, V)), V)
34.72/4.77	= { by lemma 36 }
34.72/4.77	  fresh(?, ?, V, ?)
34.72/4.77	
34.72/4.77	Lemma 38: fresh12(?, ?, ?, ?, ?, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y)), X) = fresh12(?, ?, ?, ?, ?, V, Y, X).
34.72/4.77	Proof:
34.72/4.77	  fresh12(?, ?, ?, ?, ?, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, Y)), X)
34.72/4.77	= { by lemma 26 }
34.72/4.77	  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(fresh3(?, ?, 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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, W, Z, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
34.72/4.77	= { by lemma 37 }
34.72/4.77	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
34.72/4.77	= { by lemma 26 }
34.72/4.77	  fresh12(?, ?, ?, ?, ?, V, Y, X)
34.72/4.77	
34.72/4.77	Lemma 39: fresh12(?, ?, ?, ?, ?, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X))) = fresh12(?, ?, ?, ?, ?, V, W, Z).
34.72/4.77	Proof:
34.72/4.77	  fresh12(?, ?, ?, ?, ?, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.77	= { by lemma 28 }
34.72/4.77	  fresh11(?, ?, V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.77	= { by lemma 29 }
34.72/4.77	  fresh10(?, ?, V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.77	= { by lemma 30 }
34.72/4.77	  fresh10(fresh(?, ?, Z, ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.77	= { by lemma 32 }
34.72/4.77	  fresh10(fresh(?, ?, 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(fresh(?, ?, Z, ?))), fresh(?, ?, 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))), ?)), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.77	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.78	  fresh10(fresh(?, ?, 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(fresh(?, ?, 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.78	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.78	  fresh10(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(fresh(?, ?, 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.78	= { by axiom 13 (thm.typeSystem.decls_accfupds_5) }
34.72/4.78	  fresh10(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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.78	= { by axiom 14 (thm.typeSystem.decls_accfupds_4) }
34.72/4.78	  fresh10(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)), c_27const_2ecombin_2eK_27__01(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.78	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
34.72/4.78	  fresh10(fresh(?, ?, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, Y, Z, X)))
34.72/4.78	= { by lemma 26 }
34.72/4.78	  fresh10(fresh(?, ?, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?), fresh(?, ?, Z, ?), V, W, Z, V, W, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
34.72/4.78	= { by lemma 33 }
35.07/4.79	  fresh12(?, ?, ?, ?, ?, V, W, Z)
35.07/4.79	
35.07/4.79	Lemma 40: fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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))).
35.07/4.79	Proof:
35.07/4.79	  fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.79	  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))), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.79	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.79	  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))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.79	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.79	  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))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.79	  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)))))
35.07/4.79	= { by lemma 26 }
35.07/4.79	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.07/4.79	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.79	  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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.79	  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(fresh(?, ?, 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)))))))
35.07/4.79	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.80	  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)))))))
35.07/4.80	= { by axiom 16 (thm.typeSystem.union_decls_def) }
35.07/4.80	  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)))
35.07/4.80	
35.07/4.80	Lemma 41: fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, Z, Y, X)), ?) = fresh3(?, ?, Z, ?).
35.07/4.80	Proof:
35.07/4.80	  fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, Z, Y, X)), ?)
35.07/4.80	= { by lemma 26 }
35.07/4.80	  fresh3(?, ?, 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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?)
35.07/4.80	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.80	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
35.07/4.80	= { by axiom 15 (thm.typeSystem.decls_accfupds_2) }
35.07/4.80	  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(fresh3(?, ?, 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
35.07/4.80	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.80	  fresh3(?, ?, 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(fresh3(?, ?, 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?)
35.07/4.80	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.81	  fresh3(?, ?, 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), 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))), ?)
35.07/4.81	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.81	  fresh3(?, ?, 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), Z))), fresh3(?, ?, 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))), ?)), ?)
35.07/4.81	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.81	  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), Z))), fresh3(?, ?, 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))), ?)))
35.07/4.81	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.81	  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), 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), 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)), c_27const_2ecombin_2eK_27__01(fresh(?, ?, 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(fresh(?, ?, X, ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
35.07/4.81	= { by axiom 25 (thm.combin.K_THM) }
35.07/4.81	  s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), Z)
35.07/4.81	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.82	  fresh3(?, ?, Z, ?)
35.07/4.82	
35.07/4.82	Lemma 42: 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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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))).
35.07/4.82	Proof:
35.07/4.82	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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)))))
35.07/4.82	= { by lemma 40 }
35.07/4.82	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))))
35.07/4.82	= { by lemma 34 }
35.07/4.82	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.82	= { by lemma 40 }
35.07/4.83	  fresh12(?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by lemma 26 }
35.07/4.83	  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(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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_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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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)))))))
35.07/4.83	= { by lemma 41 }
35.07/4.83	  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(fresh3(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, 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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, 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)))))))
35.07/4.83	= { by lemma 26 }
35.07/4.83	  fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.83	  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))), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.83	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.83	  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))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.83	  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(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.83	  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))), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?)))
35.07/4.83	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.83	  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)))))
35.07/4.83	= { by lemma 26 }
35.07/4.84	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.07/4.84	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.07/4.84	  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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.07/4.84	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.84	  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(fresh(?, ?, 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)))))))
35.07/4.84	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.07/4.84	  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)))))))
35.07/4.84	= { by axiom 16 (thm.typeSystem.union_decls_def) }
35.07/4.84	  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)))
35.07/4.84	
35.07/4.84	Lemma 43: fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, V, W, Z)), ?) = fresh(?, ?, W, ?).
35.07/4.84	Proof:
35.07/4.84	  fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, V, W, Z)), ?)
35.07/4.84	= { by lemma 37 }
35.07/4.84	  fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(?, ?, ?, ?, ?, V, W, Z)))), ?)
35.07/4.84	= { by lemma 39 }
35.07/4.84	  fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, W)), ?)
35.07/4.84	= { by lemma 37 }
35.50/4.84	  fresh(?, ?, W, ?)
35.50/4.84	
35.50/4.84	Lemma 44: 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))).
35.50/4.84	Proof:
35.50/4.84	  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)))))
35.50/4.84	= { by lemma 26 }
35.50/4.84	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.50/4.84	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
35.50/4.84	  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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.50/4.84	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.50/4.84	  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(fresh(?, ?, 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)))))))
35.50/4.84	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.50/4.85	  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)))))))
35.50/4.85	= { by axiom 8 (thm.envRel.convert_decls_def) }
35.50/4.85	  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)))
35.50/4.85	
35.50/4.85	Lemma 45: fresh3(?, ?, 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)))), ?) = fresh3(?, ?, 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)))), ?).
35.50/4.85	Proof:
35.50/4.85	  fresh3(?, ?, 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)))), ?)
35.50/4.85	= { by lemma 41 }
35.50/4.85	  fresh3(?, ?, 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)))))), ?)
35.50/4.85	= { by lemma 44 }
35.50/4.85	  fresh3(?, ?, 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)))), ?)
35.50/4.85	
35.50/4.85	Lemma 46: fresh12(?, ?, ?, ?, ?, Z, 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, X))))) = fresh12(?, ?, ?, ?, ?, Z, 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))))).
35.50/4.85	Proof:
35.50/4.85	  fresh12(?, ?, ?, ?, ?, Z, 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, X)))))
35.50/4.85	= { by lemma 34 }
35.50/4.85	  fresh12(?, ?, ?, ?, ?, Z, Y, 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)))))))
35.50/4.85	= { by lemma 44 }
35.50/4.85	  fresh12(?, ?, ?, ?, ?, Z, 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)))))
35.50/4.85	
35.50/4.85	Lemma 47: 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))).
35.50/4.85	Proof:
35.50/4.85	  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)))))
35.50/4.85	= { by lemma 26 }
35.50/4.85	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.50/4.85	= { by lemma 45 }
35.58/4.85	  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(fresh3(?, ?, 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(fresh(?, ?, 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(fresh(?, ?, 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)))))))
35.58/4.85	= { by lemma 26 }
35.58/4.85	  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)))))
35.58/4.85	= { by lemma 46 }
35.58/4.85	  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)))))
35.58/4.85	= { by lemma 44 }
35.58/4.85	  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)))
35.58/4.85	
35.58/4.85	Lemma 48: fresh(?, ?, 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)))), ?) = fresh(?, ?, 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)))), ?).
35.58/4.85	Proof:
35.58/4.85	  fresh(?, ?, 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)))), ?)
35.58/4.85	= { by lemma 43 }
35.58/4.85	  fresh(?, ?, 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)))))), ?)
35.58/4.85	= { by lemma 47 }
35.58/4.85	  fresh(?, ?, 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)))), ?)
35.58/4.85	
35.58/4.85	Lemma 49: 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_2enamespace_2eid_27__02(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)), ?), fresh(?, ?, 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)), ?)), ?) = fresh(?, ?, 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))), 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))), X)))), ?).
35.58/4.85	Proof:
35.58/4.85	  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_2enamespace_2eid_27__02(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)), ?), fresh(?, ?, 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)), ?)), ?)
35.58/4.85	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.58/4.85	  fresh(?, ?, 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))), Y))), fresh(?, ?, 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)), ?)), ?)
35.58/4.85	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.58/4.85	  fresh(?, ?, 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))), 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_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)))), ?)
35.58/4.85	= { by lemma 31 }
35.58/4.86	  fresh2(?, ?, 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))), 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_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)))), ?)
35.58/4.86	= { by axiom 2 (thm.typeSystem.decls_literal_11_1) }
35.58/4.86	  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))), 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_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)))))
35.58/4.86	= { by axiom 9 (thm.list.LIST_TO_SET_APPEND) }
35.58/4.86	  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))), 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))), X)))))
35.58/4.86	= { by axiom 3 (thm.typeSystem.decls_literal_11_2) }
35.58/4.86	  fresh(?, ?, 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))), 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))), X)))), ?)
35.58/4.86	
35.58/4.86	Lemma 50: 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, 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, 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, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, Y), s__02(c_27type_2einfer_2einf__decls_27__00, X))))).
35.58/4.86	Proof:
35.58/4.86	  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, 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, X)))))
35.58/4.86	= { by axiom 25 (thm.combin.K_THM) }
35.58/4.86	  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, 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, 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, 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, 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, X))))))), 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, 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, X))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
35.58/4.86	= { by axiom 24 (thm.infer.inf_decls_accfupds) }
35.58/4.86	  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, 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, X))))))), 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, 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, X))))))), 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, 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, X))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
35.58/4.86	= { by axiom 7 (thm.infer.append_decls_def) }
35.58/4.86	  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, Y), s__02(c_27type_2einfer_2einf__decls_27__00, X)))))
35.58/4.87	
35.58/4.87	Lemma 51: fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?)), ?) = fresh(?, ?, 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, Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X)))), ?).
35.58/4.87	Proof:
35.58/4.87	  fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?)), ?)
35.58/4.87	= { by lemma 37 }
35.58/4.87	  fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?), fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y)), ?), fresh(?, ?, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, X)), ?)))), ?)
35.58/4.87	= { by lemma 40 }
35.58/4.87	  fresh(?, ?, 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, Y), s__02(c_27type_2etypeSystem_2edecls_27__00, X)))), ?)
35.58/4.87	
35.58/4.87	Lemma 52: fresh(?, ?, 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)))), ?) = fresh(?, ?, 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)))), ?).
35.58/4.87	Proof:
35.58/4.87	  fresh(?, ?, 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)))), ?)
35.58/4.87	= { by lemma 27 }
35.58/4.87	  fresh(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))), 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)))), 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)))))
35.58/4.87	= { by lemma 44 }
35.58/4.87	  fresh(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))), 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)))), 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)))))
35.58/4.87	= { by lemma 47 }
35.58/4.87	  fresh(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))))), 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))))), 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)))), 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)))))
35.58/4.87	= { by lemma 35 }
35.58/4.87	  fresh(?, ?, 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)))), ?)
35.58/4.87	
35.58/4.87	Lemma 53: fresh(?, ?, 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)))), Y), s__02(c_27type_2einfer_2einf__decls_27__00, X)))))), ?) = fresh(?, ?, 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)))), ?).
35.58/4.87	Proof:
35.58/4.87	  fresh(?, ?, 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)))), Y), s__02(c_27type_2einfer_2einf__decls_27__00, X)))))), ?)
35.58/4.87	= { by lemma 52 }
35.58/4.87	  fresh(?, ?, 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)))), Y), s__02(c_27type_2einfer_2einf__decls_27__00, X)))))), ?)
35.58/4.87	= { by axiom 19 (thm.infer.inf_decls_accfupds_8) }
35.58/4.87	  fresh(?, ?, 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)))), ?)
35.58/4.87	= { by lemma 52 }
35.58/4.87	  fresh(?, ?, 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)))), ?)
35.58/4.87	
35.58/4.87	Lemma 54: fresh(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_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, W))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, 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, Z)))))), 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, W))))) = fresh(?, ?, 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, W)))), ?).
35.58/4.87	Proof:
35.58/4.87	  fresh(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_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, W))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, 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, Z)))))), 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, W)))))
35.58/4.87	= { by lemma 44 }
35.58/4.87	  fresh(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, Z)))), 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, Z)))), 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_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, W))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, 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, Z)))))), 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, W)))))
35.58/4.87	= { by lemma 47 }
35.58/4.87	  fresh(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, Z)))), 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, Z)))), 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(?, ?, ?, ?, ?, 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, 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__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, 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, W))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, 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, Z)))))), 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, W)))))
35.58/4.87	= { by lemma 46 }
35.58/4.87	  fresh(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, Z)))), 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, Z)))), 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(?, ?, ?, ?, ?, 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, 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__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, 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, W))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, Y, 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, Z)))))), 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, W)))))
35.58/4.87	= { by lemma 36 }
41.65/5.67	  fresh(?, ?, 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, W)))), ?)
41.65/5.67	
41.65/5.67	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, sK2_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, sK1_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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_conjecture_V_27decls2_27))))).
41.65/5.67	Proof:
41.65/5.67	  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, sK2_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, sK1_conjecture_V_27decls2_27)))))
41.65/5.67	= { by lemma 42 }
41.65/5.67	  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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))))
41.65/5.67	= { by lemma 38 }
41.65/5.67	  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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))))
41.65/5.67	= { by lemma 39 }
41.65/5.67	  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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(?, ?, ?, ?, ?, ?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))))
41.65/5.67	= { by lemma 38 }
41.65/5.67	  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, sK2_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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))))
41.65/5.67	= { by lemma 42 }
41.65/5.67	  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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_conjecture_V_27decls2_27)))))))
41.65/5.67	= { by lemma 26 }
41.65/5.67	  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(fresh3(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
41.65/5.67	= { by lemma 40 }
41.65/5.68	  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(fresh3(?, ?, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(?, ?, ?, ?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, 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_27decls1_27)))), ?), fresh3(?, ?, 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, sK1_conjecture_V_27decls2_27)))), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_conjecture_V_27decls2_27)))), ?)), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
41.65/5.68	= { by lemma 41 }
41.65/5.68	  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(fresh3(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh3(?, ?, 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_27decls1_27)))), ?), fresh3(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
41.65/5.68	= { by lemma 45 }
41.65/5.68	  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(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_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_27decls1_27)))), ?), fresh3(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
41.65/5.68	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
41.65/5.68	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27))))), fresh3(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
41.65/5.68	= { by lemma 45 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27))))), fresh3(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
42.15/5.69	  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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by axiom 9 (thm.list.LIST_TO_SET_APPEND) }
42.15/5.69	  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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by axiom 1 (thm.typeSystem.decls_literal_11) }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 50 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 45 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 42 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 43 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 48 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(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_2enamespace_2eid_27__02(c_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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 48 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(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_2enamespace_2eid_27__02(c_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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by lemma 49 }
42.15/5.69	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.69	= { by axiom 25 (thm.combin.K_THM) }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by axiom 23 (thm.infer.inf_decls_accfupds_3) }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by axiom 21 (thm.infer.inf_decls_accfupds_6) }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by lemma 50 }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by axiom 7 (thm.infer.append_decls_def) }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by lemma 51 }
42.15/5.70	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, c_27const_2epred__set_2eUNION_27__02(fresh(?, ?, 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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.70	= { by lemma 52 }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(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_2enamespace_2eid_27__02(c_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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_conjecture_V_27decls2_27)))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.71	= { by lemma 53 }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(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_2enamespace_2eid_27__02(c_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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_conjecture_V_27decls2_27)))))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.71	= { by lemma 52 }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(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_2enamespace_2eid_27__02(c_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_27decls1_27)))), ?), fresh(?, ?, 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, sK1_conjecture_V_27decls2_27)))))), ?)), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.71	= { by lemma 49 }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.71	= { by axiom 19 (thm.infer.inf_decls_accfupds_8) }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.71	= { by axiom 25 (thm.combin.K_THM) }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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)))))))
42.15/5.71	= { by axiom 22 (thm.infer.inf_decls_accfupds_4) }
42.15/5.71	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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)))))))
42.15/5.71	= { by axiom 20 (thm.infer.inf_decls_accfupds_7) }
42.15/5.72	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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)))))))
42.15/5.72	= { by lemma 52 }
42.15/5.72	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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)))))))
42.15/5.72	= { by lemma 53 }
42.15/5.72	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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)))))))
42.15/5.72	= { by lemma 54 }
42.15/5.73	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(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_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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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, ?)))))), 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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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)))))))
42.15/5.73	= { by axiom 7 (thm.infer.append_decls_def) }
42.15/5.73	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(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_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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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, ?)))))), 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, sK2_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, sK1_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, sK2_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, sK1_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, sK2_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, sK1_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)))))))
42.15/5.73	= { by axiom 7 (thm.infer.append_decls_def) }
42.15/5.73	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(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_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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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, ?)))))), 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_conjecture_V_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.73	= { by lemma 54 }
42.15/5.73	  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(fresh3(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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(fresh(?, ?, 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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_conjecture_V_27decls2_27)))))), ?))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
42.15/5.73	= { by lemma 26 }
42.15/5.73	  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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_conjecture_V_27decls2_27)))))))
42.15/5.73	= { by lemma 47 }
42.15/5.73	  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, sK2_conjecture_V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, sK1_conjecture_V_27decls2_27)))))
42.15/5.73	% SZS output end Proof
42.15/5.73	
42.15/5.73	RESULT: Theorem (the conjecture is true).
42.15/5.75	EOF