%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWW874+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 00:56:11 EDT 2023

% Result   : Theorem 25.16s 3.59s
% Output   : Proof 29.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW874+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 21:45:01 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 25.16/3.59  Command-line arguments: --no-flatten-goal
% 25.16/3.59  
% 25.16/3.59  % SZS status Theorem
% 25.16/3.59  
% 26.80/3.89  % SZS output start Proof
% 26.80/3.89  Take the following subset of the input axioms:
% 27.53/3.98    fof('thm.combin.K_THM', axiom, ![V_27A_27, V_27x_27, V_27B_27, V_27y_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)))=s__02(V_27A_27, V_27x_27)).
% 27.53/3.98    fof('thm.envRel.convert_decls_def', axiom, ![V_27idecls_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_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)))))))).
% 27.53/3.98    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)))))))).
% 27.53/3.98    fof('thm.infer.inf_decls_accfupds', axiom, ![V_27f_27, 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)))))=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_27f_27_2, V_27i_27_2]: 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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=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_2))) & (![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))) & (![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))) & (![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))) & (![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))) & (![V_27f_27_2, V_27i_27_2]: 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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=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_2), 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_2))))) & (![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(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_2), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))))) & ![V_27f_27_2, V_27i_27_2]: s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27_2)))))=s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(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_2), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_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_2))))))))))))).
% 27.53/3.98    fof('thm.list.LIST_TO_SET_APPEND', axiom, ![V_27l1_27, V_27l2_27, V_27A_27_2]: s__02(cfun__02(V_27A_27_2, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27_2), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27_2), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27_2), V_27l2_27)))))=s__02(cfun__02(V_27A_27_2, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27_2, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27_2), V_27l1_27))), s__02(cfun__02(V_27A_27_2, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27_2), V_27l2_27)))))).
% 28.22/3.99    fof('thm.typeSystem.decls_accfupds', axiom, ![V_27d_27, V_27f_27_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__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_2), 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_2, V_27d_27_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__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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_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, V_27d_27_2))) & (![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))) & (![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))) & (![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))) & (![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))) & (![V_27f_27_2, V_27d_27_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)), V_27f_27_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_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), 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_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, V_27d_27_2))))) & (![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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_2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))))) & ![V_27f_27_2, V_27d_27_2]: s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27_2)))))=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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_2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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_2))))))))))))).
% 28.22/3.99    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(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))))))) <=> (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_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_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f01_27)=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f02_27) & s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f1_27)=s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V_27f2_27))))).
% 28.22/3.99    fof('thm.typeSystem.union_decls_def', axiom, ![V_27d1_27, V_27d2_27]: 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)))=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)))))))).
% 28.22/3.99    fof(conjecture, conjecture, ![V_27decls1_27, 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)))))=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)))))).
% 28.22/3.99  
% 28.22/3.99  Now clausify the problem and encode Horn clauses using encoding 3 of
% 28.22/3.99  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 28.22/3.99  We repeatedly replace C & s=t => u=v by the two clauses:
% 28.22/3.99    fresh(y, y, x1...xn) = u
% 28.22/3.99    C => fresh(s, t, x1...xn) = v
% 28.22/3.99  where fresh is a fresh function symbol and x1..xn are the free
% 28.22/3.99  variables of u and v.
% 28.22/3.99  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 28.22/3.99  input problem has no model of domain size 1).
% 28.22/3.99  
% 28.22/3.99  The encoding turns the above axioms into the following unit equations and goals:
% 28.22/3.99  
% 28.22/3.99  Axiom 1 (thm.typeSystem.decls_literal_11_1): 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), Z).
% 28.22/3.99  Axiom 2 (thm.typeSystem.decls_literal_11_3): 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), Z).
% 28.22/3.99  Axiom 3 (thm.combin.K_THM): s__02(X, chapp__02(s__02(cfun__02(Y, X), c_27const_2ecombin_2eK_27__01(s__02(X, Z))), s__02(Y, W))) = s__02(X, Z).
% 28.22/3.99  Axiom 4 (thm.typeSystem.decls_literal_11): 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), 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), Y, Z, W, V, U, T).
% 28.22/3.99  Axiom 5 (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))))).
% 28.22/3.99  Axiom 6 (thm.typeSystem.decls_literal_11): 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), 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), U), Y, Z, W, V, U, T).
% 28.22/3.99  Axiom 7 (thm.infer.inf_decls_accfupds_5): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__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)))), 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__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))).
% 28.22/3.99  Axiom 8 (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, 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))).
% 28.22/3.99  Axiom 9 (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))), 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))))) = 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))))).
% 28.22/3.99  Axiom 10 (thm.infer.inf_decls_accfupds_1): 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)))), X), 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, Y))).
% 28.22/3.99  Axiom 11 (thm.typeSystem.decls_accfupds_5): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__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)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))).
% 28.22/3.99  Axiom 12 (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, 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_2enamespace_2eid_27__02(c_27type_2elist_2elist_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))).
% 28.22/3.99  Axiom 13 (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__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))).
% 28.22/3.99  Axiom 14 (thm.typeSystem.decls_accfupds): 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))))).
% 28.22/3.99  Axiom 15 (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, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))).
% 28.22/3.99  Axiom 16 (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))))).
% 28.22/3.99  Axiom 17 (thm.infer.inf_decls_accfupds_4): s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__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))))).
% 28.22/3.99  Axiom 18 (thm.typeSystem.decls_accfupds_3): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), X), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y))))).
% 28.22/3.99  Axiom 19 (thm.typeSystem.decls_accfupds_4): s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__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))))).
% 28.22/3.99  Axiom 20 (thm.typeSystem.decls_literal_11): 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, X, V, U, Y) = 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), X))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))).
% 28.22/3.99  Axiom 21 (thm.typeSystem.decls_literal_11): 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))))))).
% 28.22/4.00  Axiom 22 (thm.envRel.convert_decls_def): 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__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))))))).
% 28.22/4.00  Axiom 23 (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))))))).
% 28.22/4.00  Axiom 24 (thm.typeSystem.union_decls_def): 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_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))))))).
% 28.22/4.00  Axiom 25 (thm.typeSystem.decls_literal_11_3): 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), Z).
% 28.22/4.00  
% 28.22/4.00  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(Z2, Z2, W2, T))), 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(V2, V2, U2, S))), 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(T2, T2, S2, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = fresh10(fresh(X, X, Y, Z), fresh(W, W, V, U), T, S, Z, X2, Y2, U).
% 28.22/4.00  Proof:
% 28.22/4.00    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(Z2, Z2, W2, T))), 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(V2, V2, U2, S))), 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(T2, T2, S2, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.00    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(Z2, Z2, W2, T))), 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(V2, V2, U2, S))), 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)))))))
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.00    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(Z2, Z2, W2, T))), 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), S))), 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)))))))
% 28.22/4.00  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.00    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), T))), 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), S))), 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)))))))
% 28.22/4.00  = { by axiom 20 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.00    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), 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), U), T, S, Z, X2, Y2, U)
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.00    fresh10(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), U), T, S, Z, X2, Y2, U)
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.00    fresh10(fresh(X, X, Y, Z), fresh(W, W, V, U), T, S, Z, X2, Y2, U)
% 28.22/4.00  
% 28.22/4.00  Lemma 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(fresh3(X, X, Y, 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, W, V, 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, T, S, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = fresh12(Y2, Y2, Z2, W2, V2, Z, U, X2).
% 28.22/4.00  Proof:
% 28.22/4.00    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(X, X, Y, 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, W, V, 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, T, S, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.00    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(X, X, Y, 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, W, V, 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), X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.00    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(X, X, Y, 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), 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), X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.00    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), 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), 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), X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by axiom 21 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.00    fresh12(Y2, Y2, Z2, W2, V2, Z, U, X2)
% 28.22/4.00  
% 28.22/4.00  Lemma 28: fresh10(fresh(X, X, Y, Z), fresh(W, W, V, U), T, S, Z, X2, Y2, U) = fresh12(Z2, Z2, W2, V2, U2, T, S, Z).
% 28.22/4.00  Proof:
% 28.22/4.00    fresh10(fresh(X, X, Y, Z), fresh(W, W, V, U), T, S, Z, X2, Y2, U)
% 28.22/4.00  = { by lemma 26 R->L }
% 28.22/4.00    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(T2, T2, S2, T))), 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(X3, X3, Y3, S))), 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(Z3, Z3, W3, Z))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.00  = { by lemma 27 }
% 28.22/4.00    fresh12(Z2, Z2, W2, V2, U2, T, S, Z)
% 28.22/4.00  
% 28.22/4.00  Lemma 29: fresh3(X, X, Y, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(Z, Z, W, V, U, T, S, X2))) = fresh3(Y2, Y2, Z2, T).
% 28.22/4.00  Proof:
% 28.22/4.00    fresh3(X, X, Y, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(Z, Z, W, V, U, T, S, X2)))
% 28.22/4.00  = { by lemma 28 R->L }
% 28.22/4.00    fresh3(X, X, Y, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh10(fresh(W2, W2, V2, X2), fresh(U2, U2, T2, S2), T, S, X2, X3, Y3, S2)))
% 28.22/4.00  = { by lemma 26 R->L }
% 28.22/4.00    fresh3(X, X, Y, 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(Z3, Z3, W3, T))), 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.00  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.01    s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__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(Z3, Z3, W3, T))), 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 14 (thm.typeSystem.decls_accfupds) }
% 28.22/4.01    s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), 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(Z3, Z3, W3, T))), 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 28.22/4.01    fresh3(X4, X4, Y4, 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(Z3, Z3, W3, T))), 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 28.22/4.01    fresh3(X4, X4, Y4, 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(Z3, Z3, W3, T))), fresh3(Z4, Z4, W4, 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.01    fresh3(X4, X4, Y4, 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), T))), fresh3(Z4, Z4, W4, 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.01    s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), 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), T))), fresh3(Z4, Z4, W4, 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.01    s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), 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), T))), 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(V3, V3, U3, S))), 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(T3, T3, S3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.01  = { by axiom 3 (thm.combin.K_THM) }
% 28.22/4.01    s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), T)
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 28.22/4.01    fresh3(Y2, Y2, Z2, T)
% 28.22/4.01  
% 28.22/4.01  Lemma 30: fresh12(X, X, Y, Z, W, 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)))), 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)))), 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))))) = 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))).
% 28.22/4.01  Proof:
% 28.22/4.01    fresh12(X, X, Y, Z, W, 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)))), 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)))), 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)))))
% 28.22/4.01  = { by lemma 27 R->L }
% 28.22/4.01    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(U, U, T, 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))))))), 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(S, S, X2, 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))))))), 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(Y2, Y2, Z2, 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))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.01    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(U, U, T, 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))))))), 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(S, S, X2, 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))))))), 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))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.01    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(U, U, T, 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))))))), 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))))))), 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))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.01  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.01    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(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))))))), 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))))))), 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))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.01  = { by axiom 22 (thm.envRel.convert_decls_def) R->L }
% 28.22/4.01    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)))
% 28.22/4.01  
% 28.22/4.01  Lemma 31: fresh3(X, X, Y, 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))))) = fresh3(W, W, V, 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, Z))))).
% 28.22/4.01  Proof:
% 28.22/4.01    fresh3(X, X, Y, 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)))))
% 28.22/4.01  = { by lemma 29 R->L }
% 28.22/4.01    fresh3(W, W, V, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(U, U, T, S, X2, 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)))))))
% 28.22/4.01  = { by lemma 30 }
% 28.22/4.01    fresh3(W, W, V, 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, Z)))))
% 28.22/4.01  
% 28.22/4.01  Lemma 32: fresh(X, X, Y, 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, Z, W, V))), fresh(U, U, T, S))) = fresh(X2, X2, Y2, V).
% 28.22/4.01  Proof:
% 28.22/4.01    fresh(X, X, Y, 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, Z, W, V))), fresh(U, U, T, S)))
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.01    fresh(X, X, Y, 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), V))), fresh(U, U, T, S)))
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.01    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), 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), V))), fresh(U, U, T, S)))
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.01    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), 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), V))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), S)))
% 28.22/4.01  = { by axiom 3 (thm.combin.K_THM) }
% 28.22/4.01    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)
% 28.22/4.01  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.01    fresh(X2, X2, Y2, V)
% 28.22/4.01  
% 28.22/4.01  Lemma 33: fresh(X, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, X2))) = fresh(Y2, Y2, Z2, X2).
% 28.22/4.01  Proof:
% 28.22/4.01    fresh(X, X, Y, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, X2)))
% 28.22/4.01  = { by lemma 27 R->L }
% 28.22/4.01    fresh(X, X, Y, 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(W2, W2, V2, T))), 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(U2, U2, T2, S))), 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(S2, S2, X3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    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, 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(W2, W2, V2, T))), 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(U2, U2, T2, S))), 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(S2, S2, X3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.02  = { by axiom 12 (thm.typeSystem.decls_accfupds_7) }
% 28.22/4.02    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, 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(U2, U2, T2, S))), 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(S2, S2, X3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.02  = { by axiom 15 (thm.typeSystem.decls_accfupds_8) }
% 28.22/4.02    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, 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(S2, S2, X3, X2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))
% 28.22/4.02  = { by axiom 19 (thm.typeSystem.decls_accfupds_4) }
% 28.22/4.02    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), 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(S2, S2, X3, X2))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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)))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.02    fresh(Y3, Y3, Z3, 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(S2, S2, X3, X2))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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)))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.02    fresh(Y3, Y3, Z3, 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(S2, S2, X3, X2))), fresh(W3, W3, V3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))
% 28.22/4.02  = { by lemma 32 }
% 28.22/4.02    fresh(Y2, Y2, Z2, X2)
% 28.22/4.02  
% 28.22/4.02  Lemma 34: fresh(X, X, Y, 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)), Z), s__02(c_27type_2etypeSystem_2edecls_27__00, W))))) = fresh(V, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, W))).
% 28.22/4.02  Proof:
% 28.22/4.02    fresh(X, X, Y, 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)), Z), s__02(c_27type_2etypeSystem_2edecls_27__00, W)))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    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, 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)), Z), s__02(c_27type_2etypeSystem_2edecls_27__00, W)))))
% 28.22/4.02  = { by axiom 11 (thm.typeSystem.decls_accfupds_5) }
% 28.22/4.02    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, W)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.02    fresh(V, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, W)))
% 28.22/4.02  
% 28.22/4.02  Lemma 35: fresh12(X, X, Y, Z, W, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2))) = fresh12(U2, U2, T2, S2, X3, V, U, W2).
% 28.22/4.02  Proof:
% 28.22/4.02    fresh12(X, X, Y, Z, W, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 21 (thm.typeSystem.decls_literal_11) }
% 28.22/4.02    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), c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.02  = { by axiom 21 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.02    fresh12(fresh3(Y3, Y3, Z3, V), fresh3(Y3, Y3, Z3, V), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.02    fresh12(fresh3(Y3, Y3, Z3, 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, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.02    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, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 4 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.02    fresh11(fresh(W3, W3, V3, U), fresh(W3, W3, V3, U), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    fresh11(fresh(W3, W3, V3, 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), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    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), U), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by axiom 6 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(U3, U3, T3, W2), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.02  = { by lemma 28 R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(U3, U3, T3, W2), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by lemma 32 R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(T4, T4, S4, 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(X5, X5, Y5, W2))), fresh(Z5, Z5, W5, 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(T4, T4, S4, 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(X5, X5, Y5, W2))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_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(X5, X5, Y5, W2))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by axiom 18 (thm.typeSystem.decls_accfupds_3) R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(T5, T5, S5, 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh10(fresh(S3, S3, X4, V2), fresh(Y4, Y4, Z4, W4), Z2, W2, V2, V4, U4, W4)))
% 28.22/4.02  = { by lemma 26 R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(T5, T5, S5, 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), V, U, W2, V, U, 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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.02  = { by lemma 34 R->L }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), fresh(Z6, Z6, W6, 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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), V, U, W2, V, U, 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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.02    fresh10(fresh(U3, U3, T3, W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), V, U, W2, V, U, 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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.02  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.03    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), W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), V, U, W2, V, U, 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(X6, X6, Y6, Z2))), 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(X5, X5, Y5, W2))), 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(V5, V5, U5, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.03  = { by axiom 20 (thm.typeSystem.decls_literal_11) }
% 28.22/4.03    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), W2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by axiom 20 (thm.typeSystem.decls_literal_11) R->L }
% 28.22/4.03    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), W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V6), V, U, W2, U6, T6, V6)
% 28.22/4.03  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.03    fresh10(fresh(S6, S6, X7, W2), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), V6), V, U, W2, U6, T6, V6)
% 28.22/4.03  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.03    fresh10(fresh(S6, S6, X7, W2), fresh(Y7, Y7, Z7, V6), V, U, W2, U6, T6, V6)
% 28.22/4.03  = { by lemma 28 }
% 28.22/4.03    fresh12(U2, U2, T2, S2, X3, V, U, W2)
% 28.22/4.03  
% 28.22/4.03  Lemma 36: fresh(X, X, Y, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(Z, Z, W, V, U, T, S, X2))) = fresh(Y2, Y2, Z2, S).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh(X, X, Y, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(Z, Z, W, V, U, T, S, X2)))
% 28.22/4.03  = { by lemma 33 R->L }
% 28.22/4.03    fresh(W2, W2, V2, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U2, U2, T2, S2, X3, Y3, Z3, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(Z, Z, W, V, U, T, S, X2)))))
% 28.22/4.03  = { by lemma 35 }
% 28.22/4.03    fresh(W2, W2, V2, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(W3, W3, V3, U3, T3, Y3, Z3, S)))
% 28.22/4.03  = { by lemma 33 }
% 28.22/4.03    fresh(Y2, Y2, Z2, S)
% 28.22/4.03  
% 28.22/4.03  Lemma 37: fresh(X, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))) = fresh(W, W, V, 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))))).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh(X, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z)))))
% 28.22/4.03  = { by lemma 33 R->L }
% 28.22/4.03    fresh(W, W, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U, U, T, S, X2, 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)))))))
% 28.22/4.03  = { by lemma 30 }
% 28.22/4.03    fresh(W, W, V, 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)))))
% 28.22/4.03  
% 28.22/4.03  Lemma 38: fresh(X, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z))))) = fresh(W, W, V, 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, Z))))).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh(X, X, Y, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z)))))
% 28.22/4.03  = { by lemma 36 R->L }
% 28.22/4.03    fresh(W, W, V, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(U, U, T, S, X2, 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)))))))
% 28.22/4.03  = { by lemma 30 }
% 28.22/4.03    fresh(W, W, V, 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, Z)))))
% 28.22/4.03  
% 28.22/4.03  Lemma 39: fresh12(X, X, Y, Z, W, V, U, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2))) = fresh12(U2, U2, T2, S2, X3, V, U, V2).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh12(X, X, Y, Z, W, V, U, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)))
% 28.22/4.03  = { by lemma 28 R->L }
% 28.22/4.03    fresh10(fresh(Y3, Y3, Z3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2))), fresh(W3, W3, V3, U3), V, U, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2)), T3, S3, U3)
% 28.22/4.03  = { by lemma 26 R->L }
% 28.22/4.03    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(X4, X4, Y4, 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(Z4, Z4, W4, 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(V4, V4, U4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T, T, S, X2, Y2, Z2, W2, V2))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 33 }
% 28.22/4.03    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(X4, X4, Y4, 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(Z4, Z4, W4, 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(T4, T4, S4, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 27 }
% 28.22/4.03    fresh12(U2, U2, T2, S2, X3, V, U, V2)
% 28.22/4.03  
% 28.22/4.03  Lemma 40: fresh12(X, X, Y, Z, W, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)), V2) = fresh12(U2, U2, T2, S2, X3, V, W2, V2).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh12(X, X, Y, Z, W, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)), V2)
% 28.22/4.03  = { by lemma 28 R->L }
% 28.22/4.03    fresh10(fresh(Y3, Y3, Z3, V2), fresh(W3, W3, V3, U3), V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)), V2, T3, S3, U3)
% 28.22/4.03  = { by lemma 26 R->L }
% 28.22/4.03    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(X4, X4, Y4, 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(Z4, Z4, W4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2))))), 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(V4, V4, U4, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 33 }
% 28.22/4.03    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(X4, X4, Y4, 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(T4, T4, S4, W2))), 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(V4, V4, U4, V2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 27 }
% 28.22/4.03    fresh12(U2, U2, T2, S2, X3, V, W2, V2)
% 28.22/4.03  
% 28.22/4.03  Lemma 41: fresh12(X, X, Y, Z, W, V, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)), V2) = fresh12(U2, U2, T2, S2, X3, V, Z2, V2).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh12(X, X, Y, Z, W, V, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)), V2)
% 28.22/4.03  = { by lemma 40 R->L }
% 28.22/4.03    fresh12(Y3, Y3, Z3, W3, V3, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(U3, U3, T3, S3, X4, Y4, Z4, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(U, U, T, S, X2, Y2, Z2, W2)))), V2)
% 28.22/4.03  = { by lemma 35 }
% 28.22/4.03    fresh12(Y3, Y3, Z3, W3, V3, V, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(W4, W4, V4, U4, T4, Y4, Z4, Z2)), V2)
% 28.22/4.03  = { by lemma 40 }
% 28.22/4.03    fresh12(U2, U2, T2, S2, X3, V, Z2, V2)
% 28.22/4.03  
% 28.22/4.03  Lemma 42: fresh12(X, X, Y, Z, W, 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)))), U, T) = fresh12(S, S, X2, Y2, Z2, 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, V)))), U, T).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh12(X, X, Y, Z, W, 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)))), U, T)
% 28.22/4.03  = { by lemma 28 R->L }
% 28.22/4.03    fresh10(fresh(W2, W2, V2, T), fresh(U2, U2, T2, S2), 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)))), U, T, X3, Y3, S2)
% 28.22/4.03  = { by lemma 26 R->L }
% 28.22/4.03    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(Z3, Z3, W3, 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))))))), 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(V3, V3, U3, 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(T3, T3, S3, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 31 }
% 28.22/4.03    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(X4, X4, Y4, 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, 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(V3, V3, U3, 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(T3, T3, S3, T))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 27 }
% 28.22/4.03    fresh12(S, S, X2, Y2, Z2, 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, V)))), U, T)
% 28.22/4.03  
% 28.22/4.03  Lemma 43: s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(X, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(Y, Y, Z, W, V, U, T, S))), s__02(X, X2))) = fresh12(Y2, Y2, Z2, W2, V2, U, T, S).
% 28.22/4.03  Proof:
% 28.22/4.03    s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(X, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(Y, Y, Z, W, V, U, T, S))), s__02(X, X2)))
% 28.22/4.03  = { by lemma 27 R->L }
% 28.22/4.03    s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(X, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(U2, U2, T2, U))), 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(S2, S2, X3, T))), 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(Y3, Y3, Z3, S))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(X, X2)))
% 28.22/4.03  = { by axiom 3 (thm.combin.K_THM) }
% 28.22/4.03    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(U2, U2, T2, U))), 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(S2, S2, X3, T))), 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(Y3, Y3, Z3, S))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 27 }
% 28.22/4.03    fresh12(Y2, Y2, Z2, W2, V2, U, T, S)
% 28.22/4.03  
% 28.22/4.03  Lemma 44: fresh12(X, X, Y, Z, W, V, U, 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, T))))) = fresh12(S, S, X2, Y2, Z2, V, U, 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, T))))).
% 28.22/4.03  Proof:
% 28.22/4.03    fresh12(X, X, Y, Z, W, V, U, 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, T)))))
% 28.22/4.03  = { by lemma 28 R->L }
% 28.22/4.03    fresh10(fresh(W2, W2, V2, 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, T))))), fresh(U2, U2, T2, S2), V, U, 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, T)))), X3, Y3, S2)
% 28.22/4.03  = { by lemma 26 R->L }
% 28.22/4.03    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(Z3, Z3, W3, 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(V3, V3, U3, 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(T3, T3, S3, 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, T))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 37 }
% 28.22/4.03    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(Z3, Z3, W3, 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(V3, V3, U3, 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(X4, X4, Y4, 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, T))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.03  = { by lemma 27 }
% 28.22/4.04    fresh12(S, S, X2, Y2, Z2, V, U, 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, T)))))
% 28.22/4.04  
% 28.22/4.04  Lemma 45: s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, X), s__02(c_27type_2einfer_2einf__decls_27__00, Y))))).
% 28.22/4.04  Proof:
% 28.22/4.04    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)))))
% 28.22/4.04  = { by axiom 3 (thm.combin.K_THM) R->L }
% 28.22/4.04    s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.04  = { by axiom 9 (thm.infer.inf_decls_accfupds) R->L }
% 28.22/4.04    s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))
% 28.22/4.04  = { by axiom 23 (thm.infer.append_decls_def) R->L }
% 28.22/4.04    s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, X), s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))
% 28.22/4.04  
% 28.22/4.04  Lemma 46: fresh12(X, X, Y, Z, W, V, 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)), U), s__02(c_27type_2etypeSystem_2edecls_27__00, T)))), S) = fresh12(X2, X2, Y2, Z2, W2, V, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T)), S).
% 28.22/4.04  Proof:
% 28.22/4.04    fresh12(X, X, Y, Z, W, V, 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)), U), s__02(c_27type_2etypeSystem_2edecls_27__00, T)))), S)
% 28.22/4.04  = { by lemma 27 R->L }
% 28.22/4.04    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(V2, V2, U2, 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(T2, T2, S2, 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)), U), s__02(c_27type_2etypeSystem_2edecls_27__00, T))))))), 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(X3, X3, Y3, S))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.04  = { by lemma 34 }
% 28.22/4.04    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(V2, V2, U2, 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(Z3, Z3, W3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))))), 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(X3, X3, Y3, S))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.04  = { by lemma 27 }
% 28.22/4.04    fresh12(X2, X2, Y2, Z2, W2, V, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T)), S)
% 28.22/4.04  
% 28.22/4.04  Lemma 47: 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, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))) = fresh(X2, X2, Y2, 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))))).
% 28.22/4.04  Proof:
% 28.22/4.04    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, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 30 R->L }
% 28.22/4.04    fresh(fresh12(Z2, Z2, W2, V2, U2, 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, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 44 }
% 28.22/4.04    fresh(fresh12(T2, T2, S2, X3, Y3, 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))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 42 }
% 28.22/4.04    fresh(fresh12(Z3, Z3, W3, V3, U3, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z, Z, W, V, U, T, S, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 44 R->L }
% 28.22/4.04    fresh(fresh12(Z3, Z3, W3, V3, U3, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 30 R->L }
% 28.22/4.04    fresh(fresh12(Z3, Z3, W3, V3, U3, 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))))), fresh12(Z4, Z4, W4, V4, U4, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 39 R->L }
% 28.22/4.04    fresh(fresh12(Z3, Z3, W3, V3, U3, 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))))), fresh12(T4, T4, S4, X5, Y5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.04  = { by lemma 27 R->L }
% 28.22/4.04    fresh(fresh12(Z3, Z3, W3, V3, U3, 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_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(Z5, Z5, W5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(V5, V5, U5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(T5, T5, S5, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.05    fresh(fresh12(Z3, Z3, W3, V3, U3, 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_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(Z5, Z5, W5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh(V5, V5, U5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.05    fresh(fresh12(Z3, Z3, W3, V3, U3, 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_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(Z5, Z5, W5, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.05    fresh(fresh12(Z3, Z3, W3, V3, U3, 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_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by lemma 27 R->L }
% 28.22/4.05    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(X6, X6, Y6, 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(Z6, Z6, W6, 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(V6, V6, U6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.05    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(X6, X6, Y6, 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(Z6, Z6, W6, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.05    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(X6, X6, Y6, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.05  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.06    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), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(T3, T3, S3, X4, Y4, T, S, c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Y)))))))
% 28.22/4.06  = { by axiom 25 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.06    s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, X)))))
% 28.22/4.06  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 28.22/4.06    fresh(X2, X2, Y2, 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)))))
% 28.22/4.06  
% 28.22/4.06  Lemma 48: fresh12(X, X, Y, Z, W, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(T2, T2, S2, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(X3, X3, Y3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, T), s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))).
% 28.22/4.06  Proof:
% 28.22/4.06    fresh12(X, X, Y, Z, W, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(T2, T2, S2, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(X3, X3, Y3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))))
% 28.22/4.06  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.06    fresh12(X, X, Y, Z, W, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(T2, T2, S2, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2)))))
% 28.22/4.06  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.06    fresh12(X, X, Y, Z, W, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2)))))
% 28.22/4.06  = { by lemma 27 R->L }
% 28.22/4.06    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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(V3, V3, U3, c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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(T3, T3, S3, 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.06  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.06    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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(V3, V3, U3, c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh(V2, V2, U2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.07    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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(V3, V3, U3, c_27const_2epred__set_2eUNION_27__02(fresh(Z2, Z2, W2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.07    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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(V3, V3, U3, 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.07    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), fresh3(S, S, X2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.07    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(Z3, Z3, W3, c_27const_2epred__set_2eUNION_27__02(fresh3(V, V, U, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, T))), 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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.07    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(Z3, Z3, W3, 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, T))), 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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.07    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, T))), 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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), 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, T))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, Y2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by axiom 24 (thm.typeSystem.union_decls_def) R->L }
% 28.22/4.07    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, T), s__02(c_27type_2etypeSystem_2edecls_27__00, Y2)))
% 28.22/4.07  
% 28.22/4.07  Lemma 49: fresh12(X, X, Y, Z, W, 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U))).
% 28.22/4.07  Proof:
% 28.22/4.07    fresh12(X, X, Y, Z, W, 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))
% 28.22/4.07  = { by lemma 48 R->L }
% 28.22/4.07    fresh12(X, X, Y, Z, W, 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z2, Z2, W2, V2, U2, c_27const_2epred__set_2eUNION_27__02(fresh3(T2, T2, S2, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(X3, X3, Y3, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z3, Z3, W3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(V3, V3, U3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))))
% 28.22/4.07  = { by lemma 39 }
% 28.22/4.07    fresh12(Z4, Z4, W4, V4, U4, 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, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))
% 28.22/4.07  = { by lemma 48 R->L }
% 28.22/4.07    fresh12(Z4, Z4, W4, V4, U4, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(T4, T4, S4, X5, Y5, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T5, T5, S5, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X6, X6, Y6, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(V6, V6, U6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))
% 28.22/4.07  = { by lemma 28 R->L }
% 28.22/4.07    fresh10(fresh(T6, T6, S6, c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))), fresh(X7, X7, Y7, Z7), c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(T4, T4, S4, X5, Y5, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T5, T5, S5, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X6, X6, Y6, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(V6, V6, U6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), W7, V7, Z7)
% 28.22/4.07  = { by lemma 26 R->L }
% 28.22/4.07    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(U7, U7, T7, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(T4, T4, S4, X5, Y5, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T5, T5, S5, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X6, X6, Y6, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(V6, V6, U6, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))))), 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(S7, S7, X8, c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__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(Y8, Y8, Z8, c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by lemma 29 }
% 28.22/4.07    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(W8, W8, V8, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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(S7, S7, X8, c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__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(Y8, Y8, Z8, c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.07  = { by lemma 27 }
% 28.22/4.07    fresh12(U8, U8, T8, S8, X9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X4, X4, Y4, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    fresh12(U8, U8, T8, S8, X9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U)))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    fresh12(U8, U8, T8, S8, X9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U)))), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U)))))
% 28.22/4.08  = { by lemma 27 R->L }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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(W9, W9, V9, c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__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(U9, U9, T9, 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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(W9, W9, V9, c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh(X2, X2, Y2, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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(W9, W9, V9, c_27const_2epred__set_2eUNION_27__02(fresh(T, T, S, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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(W9, W9, V9, 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V))), fresh3(V5, V5, U5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(Z5, Z5, W5, c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__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), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, U))))))), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.22/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(Y9, Y9, Z9, 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))), 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, U))))))), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.22/4.08  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 28.98/4.08    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), 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))), 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, U))))))), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, 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), 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))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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, U))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 28.98/4.08  = { by axiom 24 (thm.typeSystem.union_decls_def) R->L }
% 28.98/4.09    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V), s__02(c_27type_2etypeSystem_2edecls_27__00, U)))
% 28.98/4.09  
% 28.98/4.09  Goal 1 (conjecture): 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))))) = 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))))).
% 28.98/4.09  Proof:
% 28.98/4.09    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)))))
% 28.98/4.09  = { by lemma 30 R->L }
% 28.98/4.09    fresh12(X, X, Y, Z, W, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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__exns_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)))))))
% 28.98/4.09  = { by lemma 41 R->L }
% 28.98/4.09    fresh12(V, V, U, T, S, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(X2, X2, Y2, Z2, W2, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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__exns_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)))))))), 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_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)))))))
% 28.98/4.09  = { by lemma 30 }
% 28.98/4.09    fresh12(V, V, U, T, S, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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__exns_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)))))))
% 28.98/4.09  = { by lemma 42 }
% 28.98/4.09    fresh12(V2, V2, U2, T2, S2, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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__exns_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)))))))
% 28.98/4.09  = { by lemma 44 }
% 28.98/4.09    fresh12(X3, X3, Y3, Z3, W3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))))
% 28.98/4.09  = { by lemma 27 R->L }
% 28.98/4.09    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X4, X4, Y4, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.07/4.10  = { by lemma 47 R->L }
% 29.07/4.10    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z4))), 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls2_27)))))), c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(W4, W4, V4, U4, T4, S4, X5, 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, Z4))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.07/4.10  = { by axiom 23 (thm.infer.append_decls_def) }
% 29.07/4.10    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z4))), 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, 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, 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, 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, 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, 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, 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(W4, W4, V4, U4, T4, S4, X5, 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, Z4))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.07/4.10  = { by axiom 23 (thm.infer.append_decls_def) }
% 29.17/4.11    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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_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, 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, 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, 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, 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, v_27decls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, Z4))), 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, 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, 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, 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, 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, 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, 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(W4, W4, V4, U4, T4, S4, X5, 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, Z4))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.11  = { by lemma 47 }
% 29.19/4.11    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(Y5, Y5, Z5, 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, 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, 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, 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, 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, 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, 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)))))))
% 29.19/4.11  = { by lemma 37 R->L }
% 29.19/4.11    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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)))), 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_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, 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, 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, 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, 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, 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)))))))
% 29.19/4.11  = { by axiom 8 (thm.infer.inf_decls_accfupds_7) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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, 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, 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, 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, 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)))))))
% 29.19/4.12  = { by axiom 13 (thm.infer.inf_decls_accfupds_8) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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, 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, 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)))))))
% 29.19/4.12  = { by axiom 17 (thm.infer.inf_decls_accfupds_4) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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, 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, 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)))))))
% 29.19/4.12  = { by axiom 3 (thm.combin.K_THM) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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, 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, v_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.12  = { by axiom 8 (thm.infer.inf_decls_accfupds_7) R->L }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(W5, W5, V5, 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, 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)))), U5), s__02(c_27type_2einfer_2einf__decls_27__00, 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, v_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.12  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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))), 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)))), U5), s__02(c_27type_2einfer_2einf__decls_27__00, 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, v_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.12  = { by axiom 5 (thm.list.LIST_TO_SET_APPEND) }
% 29.19/4.12    s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(fresh3(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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))), 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)))), U5), s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_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_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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by axiom 8 (thm.infer.inf_decls_accfupds_7) }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_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))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_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_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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T5, T5, S5, 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))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_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_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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T5, T5, S5, c_27const_2epred__set_2eUNION_27__02(fresh(X6, X6, Y6, 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_27decls1_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_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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by lemma 37 }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T5, T5, S5, c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, 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, v_27decls1_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_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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T5, T5, S5, c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, 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, v_27decls1_27))))), fresh(V6, V6, U6, 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_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by lemma 37 }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T5, T5, S5, c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, 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, v_27decls1_27))))), fresh(T6, T6, S6, 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, v_27decls2_27))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by lemma 33 R->L }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, c_27const_2etypeSystem_2edecls__defined__exns_27__01(fresh12(Z7, Z7, W7, V7, U7, c_27const_2epred__set_2eUNION_27__02(fresh3(T7, T7, S7, 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, v_27decls1_27))))), fresh3(X8, X8, Y8, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(Z8, Z8, W8, 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, v_27decls1_27))))), fresh(V8, V8, U8, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(Z6, Z6, W6, 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, v_27decls1_27))))), fresh(T6, T6, S6, 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, v_27decls2_27))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))
% 29.19/4.13  = { by lemma 48 }
% 29.19/4.13    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(V3, V3, U3, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by lemma 31 R->L }
% 29.19/4.14    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(T8, T8, S8, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by lemma 45 R->L }
% 29.19/4.14    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(T8, T8, S8, 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, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 10 (thm.infer.inf_decls_accfupds_1) R->L }
% 29.19/4.14    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(T8, T8, S8, 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, 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)))), X9), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) }
% 29.19/4.14    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, 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)))), X9), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 5 (thm.list.LIST_TO_SET_APPEND) }
% 29.19/4.14    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, 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)))), X9), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 10 (thm.infer.inf_decls_accfupds_1) }
% 29.19/4.14    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, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 29.19/4.14    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(Y9, Y9, Z9, 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, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 29.19/4.14    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(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(W9, W9, V9, 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_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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by lemma 31 }
% 29.19/4.14    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(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(U9, U9, T9, 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, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.14  = { by axiom 1 (thm.typeSystem.decls_literal_11_1) R->L }
% 29.19/4.14    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(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(U9, U9, T9, 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, v_27decls1_27))))), fresh3(S9, S9, X10, 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_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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.15  = { by lemma 31 }
% 29.19/4.15    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(Y9, Y9, Z9, c_27const_2epred__set_2eUNION_27__02(fresh3(U9, U9, T9, 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, v_27decls1_27))))), fresh3(Y10, Y10, Z10, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.15  = { by lemma 29 R->L }
% 29.19/4.15    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(W10, W10, V10, c_27const_2etypeSystem_2edecls__defined__mods_27__01(fresh12(U10, U10, T10, S10, X11, c_27const_2epred__set_2eUNION_27__02(fresh3(U9, U9, T9, 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, v_27decls1_27))))), fresh3(Y10, Y10, Z10, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(Y11, Y11, Z11, 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, v_27decls1_27))))), fresh(W11, W11, V11, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(U11, U11, T11, 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, v_27decls1_27))))), fresh(S11, S11, X12, 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, 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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.15  = { by lemma 48 }
% 29.19/4.15    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(W10, W10, V10, 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, 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_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(T3, T3, S3, c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.15  = { by lemma 38 R->L }
% 29.19/4.15    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.15  = { by axiom 23 (thm.infer.append_decls_def) }
% 29.19/4.16    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, 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, 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, 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, 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, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.16  = { by lemma 45 }
% 29.19/4.16    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, v_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, 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, 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, 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, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.16  = { by axiom 7 (thm.infer.inf_decls_accfupds_5) }
% 29.19/4.16    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, 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, 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, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.16  = { by axiom 16 (thm.infer.inf_decls_accfupds_3) }
% 29.19/4.16    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, 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, 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, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 3 (thm.combin.K_THM) }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(Y12, Y12, Z12, 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, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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_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_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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 5 (thm.list.LIST_TO_SET_APPEND) }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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_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_27decls1_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_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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(W12, W12, V12, 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))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, v_27decls1_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_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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(W12, W12, V12, c_27const_2epred__set_2eUNION_27__02(fresh(U12, U12, T12, 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_27decls1_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_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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by axiom 2 (thm.typeSystem.decls_literal_11_3) R->L }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(W12, W12, V12, c_27const_2epred__set_2eUNION_27__02(fresh(U12, U12, T12, 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_27decls1_27))))), fresh(S12, S12, X13, 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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by lemma 38 }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(W12, W12, V12, c_27const_2epred__set_2eUNION_27__02(fresh(Y13, Y13, Z13, 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, v_27decls1_27))))), fresh(S12, S12, X13, 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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by lemma 38 }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(W12, W12, V12, c_27const_2epred__set_2eUNION_27__02(fresh(Y13, Y13, Z13, 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, v_27decls1_27))))), fresh(W13, W13, V13, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by lemma 36 R->L }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(U13, U13, T13, c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(S13, S13, X14, Y14, Z14, c_27const_2epred__set_2eUNION_27__02(fresh3(W14, W14, V14, 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, v_27decls1_27))))), fresh3(U14, U14, T14, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(Y13, Y13, Z13, 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, v_27decls1_27))))), fresh(W13, W13, V13, 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, v_27decls2_27)))))), c_27const_2epred__set_2eUNION_27__02(fresh(S14, S14, X15, 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, v_27decls1_27))))), fresh(Y15, Y15, Z15, 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, 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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by lemma 48 }
% 29.19/4.17    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(W10, W10, V10, 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, 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_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(U13, U13, T13, 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, 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_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(X7, X7, Y7, 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, 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_2ebool_2eARB_27__00)))))))
% 29.19/4.17  = { by lemma 27 }
% 29.19/4.18    fresh12(W15, W15, V15, U15, T15, 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, 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)))))), 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, 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)))))), 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, 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)))))))
% 29.19/4.18  = { by lemma 46 R->L }
% 29.19/4.18    fresh12(S15, S15, X16, Y16, Z16, 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, 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)))))), 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)), W16), 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)))))))), 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, 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)))))))
% 29.19/4.18  = { by lemma 49 R->L }
% 29.19/4.18    fresh12(S15, S15, X16, Y16, Z16, 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, 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)))))), 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)), W16), fresh12(V16, V16, U16, T16, S16, 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, 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)))))), c_27const_2epred__set_2eUNION_27__02(fresh(X17, X17, Y17, 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, v_27decls1_27))))), fresh(Z17, Z17, W17, 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, 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, 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)))))))))), 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, 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)))))))
% 29.19/4.18  = { by lemma 43 R->L }
% 29.19/4.18    fresh12(S15, S15, X16, Y16, Z16, 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, 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)))))), 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)), W16), s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(V17, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(U17, U17, T17, S17, X18, 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, 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)))))), c_27const_2epred__set_2eUNION_27__02(fresh(X17, X17, Y17, 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, v_27decls1_27))))), fresh(Z17, Z17, W17, 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, 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, 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(V17, Y18)))))), 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, 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)))))))
% 29.19/4.18  = { by lemma 46 }
% 29.19/4.18    fresh12(Z18, Z18, W18, V18, U18, 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, 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)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, chapp__02(s__02(cfun__02(V17, c_27type_2etypeSystem_2edecls_27__00), c_27const_2ecombin_2eK_27__01(fresh12(U17, U17, T17, S17, X18, 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, 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)))))), c_27const_2epred__set_2eUNION_27__02(fresh(X17, X17, Y17, 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, v_27decls1_27))))), fresh(Z17, Z17, W17, 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, 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, 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(V17, Y18)))), 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, 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)))))))
% 29.19/4.18  = { by lemma 43 }
% 29.19/4.18    fresh12(Z18, Z18, W18, V18, U18, 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, 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)))))), c_27const_2etypeSystem_2edecls__defined__types_27__01(fresh12(T18, T18, S18, X19, Y19, 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, 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)))))), c_27const_2epred__set_2eUNION_27__02(fresh(X17, X17, Y17, 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, v_27decls1_27))))), fresh(Z17, Z17, W17, 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, 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, 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)))))))), 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, 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)))))))
% 29.19/4.18  = { by lemma 41 }
% 29.19/4.18    fresh12(Z19, Z19, W19, V19, U19, 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, 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)))))), c_27const_2epred__set_2eUNION_27__02(fresh(X17, X17, Y17, 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, v_27decls1_27))))), fresh(Z17, Z17, W17, 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, 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, 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)))))))
% 29.19/4.18  = { by lemma 49 }
% 29.19/4.18    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)))))
% 29.19/4.18  % SZS output end Proof
% 29.19/4.18  
% 29.19/4.18  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------