include('Axioms/HL4001^2.ax').
thf(tp_ty_2Enum_2Enum,type,( ty_2Enum_2Enum:del )).
thf(stp_ty_2Enum_2Enum,type,(tp__ty_2Enum_2Enum : $tType)).
thf(stp_inj_ty_2Enum_2Enum,type,(inj__ty_2Enum_2Enum : (tp__ty_2Enum_2Enum > $i))).
thf(stp_surj_ty_2Enum_2Enum,type,(surj__ty_2Enum_2Enum : ($i > tp__ty_2Enum_2Enum))).
thf(stp_inj_surj_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (mem @ (inj__ty_2Enum_2Enum @ X) @ ty_2Enum_2Enum))).
thf(stp_iso_mem_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Ebit_2ELOG2,type,(c_2Ebit_2ELOG2:$i)).
thf(mem_c_2Ebit_2ELOG2,axiom,(mem@c_2Ebit_2ELOG2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Ebit_2ELOG2,type,(fo__c_2Ebit_2ELOG2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Ebit_2ELOG2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Ebit_2ELOG2 @ X0)) = (ap @ c_2Ebit_2ELOG2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Emin_2E_40,type,(c_2Emin_2E_40:(del>$i))).
thf(mem_c_2Emin_2E_40,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_40@A_27a)@(arr@(arr@A_27a@bool)@A_27a)))).
thf(tp_c_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:(del>$i))).
thf(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2ECOND@A_27a)@(arr@bool@(arr@A_27a@(arr@A_27a@A_27a)))))).
thf(tp_c_2Ecombin_2ES,type,(c_2Ecombin_2ES:(del>(del>(del>$i))))).
thf(mem_c_2Ecombin_2ES,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Ecombin_2ES@A_27a@A_27b@A_27c)@(arr@(arr@A_27a@(arr@A_27b@A_27c))@(arr@(arr@A_27a@A_27b)@(arr@A_27a@A_27c)))))))).
thf(tp_c_2Ecombin_2EC,type,(c_2Ecombin_2EC:(del>(del>(del>$i))))).
thf(mem_c_2Ecombin_2EC,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Ecombin_2EC@A_27a@A_27b@A_27c)@(arr@(arr@A_27a@(arr@A_27b@A_27c))@(arr@A_27b@(arr@A_27a@A_27c)))))))).
thf(tp_c_2Ecombin_2EK,type,(c_2Ecombin_2EK:(del>(del>$i)))).
thf(mem_c_2Ecombin_2EK,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ecombin_2EK@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@A_27a)))))).
thf(tp_c_2Ecombin_2EI,type,(c_2Ecombin_2EI:(del>$i))).
thf(mem_c_2Ecombin_2EI,axiom,( ! [A_27a:del] : (mem@(c_2Ecombin_2EI@A_27a)@(arr@A_27a@A_27a)))).
thf(tp_ty_2Elist_2Elist,type,( ty_2Elist_2Elist: del >del )).
thf(tp_c_2Elist_2EFOLDL,type,(c_2Elist_2EFOLDL:(del>(del>$i)))).
thf(mem_c_2Elist_2EFOLDL,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Elist_2EFOLDL@A_27a@A_27b)@(arr@(arr@A_27b@(arr@A_27a@A_27b))@(arr@A_27b@(arr@(ty_2Elist_2Elist@A_27a)@A_27b))))))).
thf(tp_c_2Elogroot_2ELOG,type,(c_2Elogroot_2ELOG:$i)).
thf(mem_c_2Elogroot_2ELOG,axiom,(mem@c_2Elogroot_2ELOG@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Elogroot_2ELOG,type,(fo__c_2Elogroot_2ELOG:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Elogroot_2ELOG,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Elogroot_2ELOG @ X0) @ X1)) = (ap @ (ap @ c_2Elogroot_2ELOG @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Emarker_2EAbbrev,type,(c_2Emarker_2EAbbrev:$i)).
thf(mem_c_2Emarker_2EAbbrev,axiom,(mem@c_2Emarker_2EAbbrev@(arr@bool@bool))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
thf(mem_c_2Earithmetic_2EEVEN,axiom,(mem@c_2Earithmetic_2EEVEN@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2EODD,type,(c_2Earithmetic_2EODD:$i)).
thf(mem_c_2Earithmetic_2EODD,axiom,(mem@c_2Earithmetic_2EODD@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
thf(mem_c_2Earithmetic_2E_3E_3D,axiom,(mem@c_2Earithmetic_2E_3E_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$i)).
thf(mem_c_2Earithmetic_2E_3E,axiom,(mem@c_2Earithmetic_2E_3E@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EEXP @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EEXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2A @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2EiiSUC,type,(c_2Enumeral_2EiiSUC:$i)).
thf(mem_c_2Enumeral_2EiiSUC,axiom,(mem@c_2Enumeral_2EiiSUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiiSUC,type,(fo__c_2Enumeral_2EiiSUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiiSUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiiSUC @ X0)) = (ap @ c_2Enumeral_2EiiSUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
thf(mem_c_2Enumeral_2EiZ,axiom,(mem@c_2Enumeral_2EiZ@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiZ @ X0)) = (ap @ c_2Enumeral_2EiZ @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Elist_2EMAP,type,(c_2Elist_2EMAP:(del>(del>$i)))).
thf(mem_c_2Elist_2EMAP,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Elist_2EMAP@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27b))))))).
thf(tp_c_2Elist_2ECONS,type,(c_2Elist_2ECONS:(del>$i))).
thf(mem_c_2Elist_2ECONS,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ECONS@A_27a)@(arr@A_27a@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27a)))))).
thf(tp_c_2Elist_2ELIST__TO__SET,type,(c_2Elist_2ELIST__TO__SET:(del>$i))).
thf(mem_c_2Elist_2ELIST__TO__SET,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ELIST__TO__SET@A_27a)@(arr@(ty_2Elist_2Elist@A_27a)@(arr@A_27a@bool))))).
thf(tp_c_2Ebool_2EIN,type,(c_2Ebool_2EIN:(del>$i))).
thf(mem_c_2Ebool_2EIN,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2EIN@A_27a)@(arr@A_27a@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Elist_2ESNOC,type,(c_2Elist_2ESNOC:(del>$i))).
thf(mem_c_2Elist_2ESNOC,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ESNOC@A_27a)@(arr@A_27a@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27a)))))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X0)) = (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Elist_2ENIL,type,(c_2Elist_2ENIL:(del>$i))).
thf(mem_c_2Elist_2ENIL,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ENIL@A_27a)@(ty_2Elist_2Elist@A_27a)))).
thf(stp_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,(tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum : $tType)).
thf(stp_inj_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,(inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum : (tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > $i))).
thf(stp_surj_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,(surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum : ($i > tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum))).
thf(stp_inj_surj_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ((surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : (mem @ (inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X) @ (ty_2Elist_2Elist@ty_2Enum_2Enum)))).
thf(stp_iso_mem_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Elist_2Elist@ty_2Enum_2Enum)) => (X = (inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Erich__list_2ECOUNT__LIST,type,(c_2Erich__list_2ECOUNT__LIST:$i)).
thf(mem_c_2Erich__list_2ECOUNT__LIST,axiom,(mem@c_2Erich__list_2ECOUNT__LIST@(arr@ty_2Enum_2Enum@(ty_2Elist_2Elist@ty_2Enum_2Enum)))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
thf(mem_c_2Ebool_2EF,axiom,(mem@c_2Ebool_2EF@bool)).
thf(ax_false_p,axiom,(~ (p@c_2Ebool_2EF))).
thf(tp_c_2Ebool_2E_5C_2F,type,(c_2Ebool_2E_5C_2F:$i)).
thf(mem_c_2Ebool_2E_5C_2F,axiom,(mem@c_2Ebool_2E_5C_2F@(arr@bool@(arr@bool@bool)))).
thf(ax_or_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_5C_2F@Q)@R)) <=> ((p@Q) | (p@R)))))))).
thf(tp_c_2Ecombin_2Eo,type,(c_2Ecombin_2Eo:(del>(del>(del>$i))))).
thf(mem_c_2Ecombin_2Eo,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Ecombin_2Eo@A_27a@A_27b@A_27c)@(arr@(arr@A_27c@A_27b)@(arr@(arr@A_27a@A_27c)@(arr@A_27a@A_27b)))))))).
thf(tp_ty_2Efcp_2Ecart,type,( ty_2Efcp_2Ecart: del > del >del )).
thf(tp_c_2Efcp_2EFCP,type,(c_2Efcp_2EFCP:(del>(del>$i)))).
thf(mem_c_2Efcp_2EFCP,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Efcp_2EFCP@A_27a@A_27b)@(arr@(arr@ty_2Enum_2Enum@A_27a)@(ty_2Efcp_2Ecart@A_27a@A_27b)))))).
thf(tp_c_2Ewords_2Eword__lsl__bv,type,(c_2Ewords_2Eword__lsl__bv:(del>$i))).
thf(mem_c_2Ewords_2Eword__lsl__bv,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__lsl__bv@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Ewords_2Ew2n,type,(c_2Ewords_2Ew2n:(del>$i))).
thf(mem_c_2Ewords_2Ew2n,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Ew2n@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EMOD,type,(c_2Earithmetic_2EMOD:$i)).
thf(mem_c_2Earithmetic_2EMOD,axiom,(mem@c_2Earithmetic_2EMOD@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EMOD,type,(fo__c_2Earithmetic_2EMOD:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EMOD,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EMOD @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EMOD @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_ty_2Ebool_2Eitself,type,( ty_2Ebool_2Eitself: del >del )).
thf(tp_c_2Ewords_2Edimword,type,(c_2Ewords_2Edimword:(del>$i))).
thf(mem_c_2Ewords_2Edimword,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Edimword@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Ebool_2E_3F,type,(c_2Ebool_2E_3F:(del>$i))).
thf(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_3F@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_ex_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_3F@A)@Q)) <=> (? [X:$i] : ((mem@X@A) & (p@(ap@Q@X))))))))).
thf(tp_c_2Efcp_2Efcp__index,type,(c_2Efcp_2Efcp__index:(del>(del>$i)))).
thf(mem_c_2Efcp_2Efcp__index,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Efcp_2Efcp__index@A_27a@A_27b)@(arr@(ty_2Efcp_2Ecart@A_27a@A_27b)@(arr@ty_2Enum_2Enum@A_27a)))))).
thf(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
thf(mem_c_2Ebool_2E_7E,axiom,(mem@c_2Ebool_2E_7E@(arr@bool@bool))).
thf(ax_neg_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ((p@(ap@c_2Ebool_2E_7E@Q)) <=> (~ (p@Q)))))).
thf(tp_c_2Ebit_2EBITS,type,(c_2Ebit_2EBITS:$i)).
thf(mem_c_2Ebit_2EBITS,axiom,(mem@c_2Ebit_2EBITS@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(stp_fo_c_2Ebit_2EBITS,type,(fo__c_2Ebit_2EBITS:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))))).
thf(stp_eq_fo_c_2Ebit_2EBITS,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ( ! [X2:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (((fo__c_2Ebit_2EBITS @ X0) @ X1) @ X2)) = (ap @ (ap @ (ap @ c_2Ebit_2EBITS @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)) @ (inj__ty_2Enum_2Enum @ X2))))))).
thf(tp_c_2Ewords_2Ew2w,type,(c_2Ewords_2Ew2w:(del>(del>$i)))).
thf(mem_c_2Ewords_2Ew2w,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ewords_2Ew2w@A_27a@A_27b)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27b)))))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$i)).
thf(mem_c_2Eprim__rec_2E_3C,axiom,(mem@c_2Eprim__rec_2E_3C@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Ewords_2Eword__bits,type,(c_2Ewords_2Eword__bits:(del>$i))).
thf(mem_c_2Ewords_2Eword__bits,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__bits@A_27a)@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a))))))).
thf(tp_c_2Ebool_2Ethe__value,type,(c_2Ebool_2Ethe__value:(del>$i))).
thf(mem_c_2Ebool_2Ethe__value,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2Ethe__value@A_27a)@(ty_2Ebool_2Eitself@A_27a)))).
thf(tp_c_2Efcp_2Edimindex,type,(c_2Efcp_2Edimindex:(del>$i))).
thf(mem_c_2Efcp_2Edimindex,axiom,( ! [A_27a:del] : (mem@(c_2Efcp_2Edimindex@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EMIN,type,(c_2Earithmetic_2EMIN:$i)).
thf(mem_c_2Earithmetic_2EMIN,axiom,(mem@c_2Earithmetic_2EMIN@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EMIN,type,(fo__c_2Earithmetic_2EMIN:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EMIN,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EMIN @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EMIN @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ewords_2Eword__extract,type,(c_2Ewords_2Eword__extract:(del>(del>$i)))).
thf(mem_c_2Ewords_2Eword__extract,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27b)))))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
thf(mem_c_2Earithmetic_2E_2D,axiom,(mem@c_2Earithmetic_2E_2D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2D @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
thf(mem_c_2Earithmetic_2EBIT1,axiom,(mem@c_2Earithmetic_2EBIT1@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X0)) = (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X0)) = (ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2B @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$i)).
thf(mem_c_2Emin_2E_3D_3D_3E,axiom,(mem@c_2Emin_2E_3D_3D_3E@(arr@bool@(arr@bool@bool)))).
thf(ax_imp_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_c_2Ewords_2Eword__add,type,(c_2Ewords_2Eword__add:(del>$i))).
thf(mem_c_2Ewords_2Eword__add,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__add@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Ewords_2Eword__ror,type,(c_2Ewords_2Eword__ror:(del>$i))).
thf(mem_c_2Ewords_2Eword__ror,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__ror@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Ewords_2Eword__rol,type,(c_2Ewords_2Eword__rol:(del>$i))).
thf(mem_c_2Ewords_2Eword__rol,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__rol@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Ewords_2Eword__lsr,type,(c_2Ewords_2Eword__lsr:(del>$i))).
thf(mem_c_2Ewords_2Eword__lsr,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__lsr@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Ewords_2Eword__asr,type,(c_2Ewords_2Eword__asr:(del>$i))).
thf(mem_c_2Ewords_2Eword__asr,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__asr@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Ewords_2En2w,type,(c_2Ewords_2En2w:(del>$i))).
thf(mem_c_2Ewords_2En2w,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2En2w@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a))))).
thf(tp_c_2Ewords_2Eword__lsl,type,(c_2Ewords_2Eword__lsl:(del>$i))).
thf(mem_c_2Ewords_2Eword__lsl,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2Eword__lsl@A_27a)@(arr@(ty_2Efcp_2Ecart@bool@A_27a)@(arr@ty_2Enum_2Enum@(ty_2Efcp_2Ecart@bool@A_27a)))))).
thf(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:(del>$i))).
thf(mem_c_2Emin_2E_3D,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_3D@A_27a)@(arr@A_27a@(arr@A_27a@bool))))).
thf(ax_eq_p,axiom,( ! [A:del] : ( ! [X:$i] : ((mem@X@A) => ( ! [Y:$i] : ((mem@Y@A) => ((p@(ap@(ap@(c_2Emin_2E_3D@A)@X)@Y)) <=> (X = Y)))))))).
thf(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:(del>$i))).
thf(mem_c_2Ebool_2E_21,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_21@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_all_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_21@A)@Q)) <=> ( ! [X:$i] : ((mem@X@A) => (p@(ap@Q@X))))))))).
thf(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$i)).
thf(mem_c_2Ebool_2E_2F_5C,axiom,(mem@c_2Ebool_2E_2F_5C@(arr@bool@(arr@bool@bool)))).
thf(ax_and_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_2F_5C@Q)@R)) <=> ((p@Q) & (p@R)))))))).
thf(conj_thm_2Earithmetic_2EADD__0,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0m))).
thf(conj_thm_2Earithmetic_2EADD__CLAUSES,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0m))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))))))).
thf(conj_thm_2Earithmetic_2EADD__SYM,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2EADD__COMM,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2EADD__ASSOC,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Earithmetic_2EZERO__LESS__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))))).
thf(conj_thm_2Earithmetic_2ENOT__LESS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (V0n = fo__c_2Enum_2E0)))).
thf(conj_thm_2Earithmetic_2ESUB__0,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0m))) = fo__c_2Enum_2E0) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0m)))).
thf(conj_thm_2Earithmetic_2EADD1,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Earithmetic_2EMULT__CLAUSES,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0m))) = fo__c_2Enum_2E0) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0m))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0m) & (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V1n)))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))))))))).
thf(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) <=> (V0m = V1n)))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) => (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ__LESS__TRANS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) => (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ__REFL,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V0m))))).
thf(conj_thm_2Earithmetic_2ESUB__EQUAL__0,lemma,( ! [V0c:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0c))@(inj__ty_2Enum_2Enum @ V0c))) = fo__c_2Enum_2E0))).
thf(conj_thm_2Earithmetic_2EEQ__LESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((V0m = V1n) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m)))))))).
thf(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))))))).
thf(conj_thm_2Earithmetic_2ENOT__LEQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~ (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2ENOT__NUM__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((~ (V0m = V1n)) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))) | (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V0m)))))))).
thf(conj_thm_2Earithmetic_2ESUC__ONE__ADD,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))@(inj__ty_2Enum_2Enum @ V1n))) | (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V2p))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p))))))))).
thf(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V2p)))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V2p))) <=> ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2p)))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V2p))))))))).
thf(conj_thm_2Earithmetic_2ELESS__MOD,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1k:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1k))@(inj__ty_2Enum_2Enum @ V0n))) => ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V1k))@(inj__ty_2Enum_2Enum @ V0n))) = V1k))))).
thf(conj_thm_2Earithmetic_2EMOD__LESS,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n))) => (p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Earithmetic_2EX__MOD__Y__EQ__X,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1y:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1y))) => (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0x))@(inj__ty_2Enum_2Enum @ V1y))) = V0x) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0x))@(inj__ty_2Enum_2Enum @ V1y)))))))).
thf(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@A_27a))) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Enum_2Enum@A_27a)) => (( ! [V2n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n))) = (ap@(ap@V0f@(inj__ty_2Enum_2Enum @ V2n))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n))))) <=> (( ! [V3n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n)))) = (ap@(ap@V0f@(ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n)))))) & ( ! [V4n:tp__ty_2Enum_2Enum] : ((ap@V1g@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V4n)))) = (ap@(ap@V0f@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V4n))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V4n)))))))))))))).
thf(conj_thm_2Earithmetic_2ESUB__ELIM__THM,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Enum_2Enum@bool)) => ( ! [V1a:tp__ty_2Enum_2Enum] : ( ! [V2b:tp__ty_2Enum_2Enum] : ((p@(ap@V0P@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1a))@(inj__ty_2Enum_2Enum @ V2b)))) <=> ( ! [V3d:tp__ty_2Enum_2Enum] : (((V2b = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1a))@(inj__ty_2Enum_2Enum @ V3d)))) => (p@(ap@V0P@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & ((V1a = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2b))@(inj__ty_2Enum_2Enum @ V3d)))) => (p@(ap@V0P@(inj__ty_2Enum_2Enum @ V3d)))))))))))).
thf(conj_thm_2Earithmetic_2EMIN__LE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2p:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ V2p))) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V2p))) | (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V2p))))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2p))@(ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))) <=> ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2p))@(inj__ty_2Enum_2Enum @ V1m))) & (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2p))@(inj__ty_2Enum_2Enum @ V0n)))))))))).
thf(conj_thm_2Earithmetic_2EMIN__IDEM,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V0n))) = V0n))).
thf(ax_thm_2Ebit_2ELOG2__def,axiom,(c_2Ebit_2ELOG2 = (ap@c_2Elogroot_2ELOG@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))).
thf(conj_thm_2Ebit_2EBITS__LT__LOW,lemma,( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V2n))@(ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1l)))) => ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Ebit_2EBITS@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))@(inj__ty_2Enum_2Enum @ V2n))) = fo__c_2Enum_2E0)))))).
thf(ax_thm_2Ebool_2EEXISTS__DEF,axiom,( ! [A_27a:del]: ((c_2Ebool_2E_3F@A_27a) = (lam@(arr@A_27a@bool)@(^ [V0P:$i] : (ap@V0P@(ap@(c_2Emin_2E_40@A_27a)@V0P))))))).
thf(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom,( ! [V0t:$i] : ((mem@V0t@bool) => (((p@V0t) <=> $true) | ((p@V0t) <=> $false))))).
thf(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0t:$i] : ((mem@V0t@(arr@A_27a@A_27b)) => ((lam@A_27a@(^ [V1x:$i] : (ap@V0t@V1x))) = V0t)))))).
thf(ax_thm_2Ebool_2ESELECT__AX,axiom,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ((p@(ap@V0P@V1x)) => (p@(ap@V0P@(ap@(c_2Emin_2E_40@A_27a)@V0P)))))))))).
thf(conj_thm_2Ebool_2ETRUTH,lemma,$true).
thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => (((p@V0t1) => (p@V1t2)) => (((p@V1t2) => (p@V0t1)) => ((p@V0t1) <=> (p@V1t2))))))))).
thf(conj_thm_2Ebool_2EFALSITY,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ($false => (p@V0t))))).
thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((p@V0t) | (~ (p@V0t)))))).
thf(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a:del]: ( ! [V0t:$i] : ((mem@V0t@bool) => (( ! [V1x:$i] : ((mem@V1x@A_27a) => (p@V0t))) <=> (p@V0t)))))).
thf(conj_thm_2Ebool_2ECONJ__ASSOC,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => ( ! [V2t3:$i] : ((mem@V2t3@bool) => (((p@V0t1) & ((p@V1t2) & (p@V2t3))) <=> (((p@V0t1) & (p@V1t2)) & (p@V2t3)))))))))).
thf(conj_thm_2Ebool_2EF__IMP,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (p@V0t)) => ((p@V0t) => $false))))).
thf(conj_thm_2Ebool_2EAND__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true & (p@V0t)) <=> (p@V0t)) & ((((p@V0t) & $true) <=> (p@V0t)) & ((($false & (p@V0t)) <=> $false) & ((((p@V0t) & $false) <=> $false) & (((p@V0t) & (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EOR__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true | (p@V0t)) <=> $true) & ((((p@V0t) | $true) <=> $true) & ((($false | (p@V0t)) <=> (p@V0t)) & ((((p@V0t) | $false) <=> (p@V0t)) & (((p@V0t) | (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true => (p@V0t)) <=> (p@V0t)) & ((((p@V0t) => $true) <=> $true) & ((($false => (p@V0t)) <=> $true) & ((((p@V0t) => (p@V0t)) <=> $true) & (((p@V0t) => $false) <=> (~ (p@V0t)))))))))).
thf(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t)))) & (((~ ($true)) <=> $false) & ((~ ($false)) <=> $true)))).
thf(conj_thm_2Ebool_2EEQ__REFL,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (V0x = V0x))))).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((V0x = V0x) <=> $true))))).
thf(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2Ebool_2EFUN__EQ__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1g:$i] : ((mem@V1g@(arr@A_27a@A_27b)) => ((V0f = V1g) <=> ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((ap@V0f@V2x) = (ap@V1g@V2x)))))))))))).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((($true <=> (p@V0t)) <=> (p@V0t)) & ((((p@V0t) <=> $true) <=> (p@V0t)) & ((($false <=> (p@V0t)) <=> (~ (p@V0t))) & (((p@V0t) <=> $false) <=> (~ (p@V0t))))))))).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a:del]: ( ! [V0t1:$i] : ((mem@V0t1@A_27a) => ( ! [V1t2:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2ENOT__FORALL__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ((~ ( ! [V1x:$i] : ((mem@V1x@A_27a) => (p@(ap@V0P@V1x))))) <=> (? [V2x:$i] : ((mem@V2x@A_27a) & (~ (p@(ap@V0P@V2x)))))))))).
thf(conj_thm_2Ebool_2ENOT__IMP,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ((~ ((p@V0A) => (p@V1B))) <=> ((p@V0A) & (~ (p@V1B))))))))).
thf(conj_thm_2Ebool_2EDISJ__ASSOC,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => (((p@V0A) | ((p@V1B) | (p@V2C))) <=> (((p@V0A) | (p@V1B)) | (p@V2C)))))))))).
thf(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) & (p@V1B))) <=> ((~ (p@V0A)) | (~ (p@V1B)))) & ((~ ((p@V0A) | (p@V1B))) <=> ((~ (p@V0A)) & (~ (p@V1B)))))))))).
thf(conj_thm_2Ebool_2ELEFT__OR__OVER__AND,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => (((p@V0A) | ((p@V1B) & (p@V2C))) <=> (((p@V0A) | (p@V1B)) & ((p@V0A) | (p@V2C))))))))))).
thf(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => ( ! [V2C:$i] : ((mem@V2C@bool) => ((((p@V1B) & (p@V2C)) | (p@V0A)) <=> (((p@V1B) | (p@V0A)) & ((p@V2C) | (p@V0A))))))))))).
thf(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((p@V0A) => (p@V1B)) <=> ((~ (p@V0A)) | (p@V1B)))))))).
thf(conj_thm_2Ebool_2EDISJ__IMP__THM,lemma,( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => ( ! [V2R:$i] : ((mem@V2R@bool) => ((((p@V0P) | (p@V1Q)) => (p@V2R)) <=> (((p@V0P) => (p@V2R)) & ((p@V1Q) => (p@V2R))))))))))).
thf(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => (((p@V0t) => $false) <=> ((p@V0t) <=> $false))))).
thf(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => ( ! [V2t3:$i] : ((mem@V2t3@bool) => (((p@V0t1) => ((p@V1t2) => (p@V2t3))) <=> (((p@V0t1) & (p@V1t2)) => (p@V2t3)))))))))).
thf(conj_thm_2Ebool_2EIMP__CONG,lemma,( ! [V0x:$i] : ((mem@V0x@bool) => ( ! [V1x_27:$i] : ((mem@V1x_27@bool) => ( ! [V2y:$i] : ((mem@V2y@bool) => ( ! [V3y_27:$i] : ((mem@V3y_27@bool) => ((((p@V0x) <=> (p@V1x_27)) & ((p@V1x_27) => ((p@V2y) <=> (p@V3y_27)))) => (((p@V0x) => (p@V2y)) <=> ((p@V1x_27) => (p@V3y_27))))))))))))).
thf(conj_thm_2Ebool_2EUNWIND__FORALL__THM2,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@bool)) => ( ! [V1v:$i] : ((mem@V1v@A_27a) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((V2x = V1v) => (p@(ap@V0f@V2x))))) <=> (p@(ap@V0f@V1v))))))))).
thf(ax_thm_2Ecombin_2ES__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ((c_2Ecombin_2ES@A_27a@A_27b@A_27c) = (lam@(arr@A_27a@(arr@A_27b@A_27c))@(^ [V0f:$i] : (lam@(arr@A_27a@A_27b)@(^ [V1g:$i] : (lam@A_27a@(^ [V2x:$i] : (ap@(ap@V0f@V2x)@(ap@V1g@V2x))))))))))))).
thf(ax_thm_2Ecombin_2EC__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ((c_2Ecombin_2EC@A_27a@A_27b@A_27c) = (lam@(arr@A_27a@(arr@A_27b@A_27c))@(^ [V0f:$i] : (lam@A_27b@(^ [V1x:$i] : (lam@A_27a@(^ [V2y:$i] : (ap@(ap@V0f@V2y)@V1x)))))))))))).
thf(ax_thm_2Ecombin_2Eo__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27c@A_27b)) => ( ! [V1g:$i] : ((mem@V1g@(arr@A_27a@A_27c)) => ((ap@(ap@(c_2Ecombin_2Eo@A_27a@A_27b@A_27c)@V0f)@V1g) = (lam@A_27a@(^ [V2x:$i] : (ap@V0f@(ap@V1g@V2x))))))))))))).
thf(conj_thm_2Ecombin_2Eo__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1g:$i] : ((mem@V1g@(arr@A_27c@A_27a)) => ( ! [V2x:$i] : ((mem@V2x@A_27c) => ((ap@(ap@(ap@(c_2Ecombin_2Eo@A_27c@A_27b@A_27a)@V0f)@V1g)@V2x) = (ap@V0f@(ap@V1g@V2x))))))))))))).
thf(conj_thm_2Ecombin_2EK__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27b) => ((ap@(ap@(c_2Ecombin_2EK@A_27a@A_27b)@V0x)@V1y) = V0x)))))))).
thf(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((ap@(c_2Ecombin_2EI@A_27a)@V0x) = V0x))))).
thf(conj_thm_2Ecombin_2EI__o__ID,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => (((ap@(ap@(c_2Ecombin_2Eo@A_27a@A_27b@A_27b)@(c_2Ecombin_2EI@A_27b))@V0f) = V0f) & ((ap@(ap@(c_2Ecombin_2Eo@A_27a@A_27b@A_27a)@V0f)@(c_2Ecombin_2EI@A_27a)) = V0f))))))).
thf(conj_thm_2Efcp_2ECART__EQ,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@A_27a@A_27b)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@A_27a@A_27b)) => ((V0x = V1y) <=> ( ! [V2i:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V2i))@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((ap@(ap@(c_2Efcp_2Efcp__index@A_27a@A_27b)@V0x)@(inj__ty_2Enum_2Enum @ V2i)) = (ap@(ap@(c_2Efcp_2Efcp__index@A_27a@A_27b)@V1y)@(inj__ty_2Enum_2Enum @ V2i))))))))))))).
thf(conj_thm_2Efcp_2EFCP__BETA,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0g:$i] : ((mem@V0g@(arr@ty_2Enum_2Enum@A_27a)) => ( ! [V1i:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1i))@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((ap@(ap@(c_2Efcp_2Efcp__index@A_27a@A_27b)@(ap@(c_2Efcp_2EFCP@A_27a@A_27b)@V0g))@(inj__ty_2Enum_2Enum @ V1i)) = (ap@V0g@(inj__ty_2Enum_2Enum @ V1i)))))))))).
thf(ax_thm_2Elist_2EMAP,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: (( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ((ap@(ap@(c_2Elist_2EMAP@A_27a@A_27b)@V0f)@(c_2Elist_2ENIL@A_27a)) = (c_2Elist_2ENIL@A_27b)))) & ( ! [V1f:$i] : ((mem@V1f@(arr@A_27a@A_27b)) => ( ! [V2h:$i] : ((mem@V2h@A_27a) => ( ! [V3t:$i] : ((mem@V3t@(ty_2Elist_2Elist@A_27a)) => ((ap@(ap@(c_2Elist_2EMAP@A_27a@A_27b)@V1f)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V2h)@V3t)) = (ap@(ap@(c_2Elist_2ECONS@A_27b)@(ap@V1f@V2h))@(ap@(ap@(c_2Elist_2EMAP@A_27a@A_27b)@V1f)@V3t))))))))))))).
thf(ax_thm_2Elist_2EFOLDL,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: (( ! [V0f:$i] : ((mem@V0f@(arr@A_27b@(arr@A_27a@A_27b))) => ( ! [V1e:$i] : ((mem@V1e@A_27b) => ((ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V0f)@V1e)@(c_2Elist_2ENIL@A_27a)) = V1e))))) & ( ! [V2f:$i] : ((mem@V2f@(arr@A_27b@(arr@A_27a@A_27b))) => ( ! [V3e:$i] : ((mem@V3e@A_27b) => ( ! [V4x:$i] : ((mem@V4x@A_27a) => ( ! [V5l:$i] : ((mem@V5l@(ty_2Elist_2Elist@A_27a)) => ((ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V2f)@V3e)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V4x)@V5l)) = (ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V2f)@(ap@(ap@V2f@V3e)@V4x))@V5l)))))))))))))).
thf(conj_thm_2Elist_2Elist__induction,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@(ty_2Elist_2Elist@A_27a)@bool)) => (((p@(ap@V0P@(c_2Elist_2ENIL@A_27a))) & ( ! [V1t:$i] : ((mem@V1t@(ty_2Elist_2Elist@A_27a)) => ((p@(ap@V0P@V1t)) => ( ! [V2h:$i] : ((mem@V2h@A_27a) => (p@(ap@V0P@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V2h)@V1t))))))))) => ( ! [V3l:$i] : ((mem@V3l@(ty_2Elist_2Elist@A_27a)) => (p@(ap@V0P@V3l))))))))).
thf(conj_thm_2Elist_2EFOLDL__CONG,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => ( ! [V1l_27:$i] : ((mem@V1l_27@(ty_2Elist_2Elist@A_27a)) => ( ! [V2b:$i] : ((mem@V2b@A_27b) => ( ! [V3b_27:$i] : ((mem@V3b_27@A_27b) => ( ! [V4f:$i] : ((mem@V4f@(arr@A_27b@(arr@A_27a@A_27b))) => ( ! [V5f_27:$i] : ((mem@V5f_27@(arr@A_27b@(arr@A_27a@A_27b))) => (((V0l = V1l_27) & ((V2b = V3b_27) & ( ! [V6x:$i] : ((mem@V6x@A_27a) => ( ! [V7a:$i] : ((mem@V7a@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V6x)@(ap@(c_2Elist_2ELIST__TO__SET@A_27a)@V1l_27))) => ((ap@(ap@V4f@V7a)@V6x) = (ap@(ap@V5f_27@V7a)@V6x))))))))) => ((ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V4f)@V2b)@V0l) = (ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V5f_27)@V3b_27)@V1l_27)))))))))))))))))).
thf(conj_thm_2Elist_2EFOLDL__SNOC,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27b@(arr@A_27a@A_27b))) => ( ! [V1e:$i] : ((mem@V1e@A_27b) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ( ! [V3l:$i] : ((mem@V3l@(ty_2Elist_2Elist@A_27a)) => ((ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V0f)@V1e)@(ap@(ap@(c_2Elist_2ESNOC@A_27a)@V2x)@V3l)) = (ap@(ap@V0f@(ap@(ap@(ap@(c_2Elist_2EFOLDL@A_27a@A_27b)@V0f)@V1e)@V3l))@V2x))))))))))))).
thf(ax_thm_2Elogroot_2ELOG,axiom,( ! [V0a:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0a))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V0a))@(ap@(ap@c_2Elogroot_2ELOG@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1n))))@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1n))@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V0a))@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Elogroot_2ELOG@(inj__ty_2Enum_2Enum @ V0a))@(inj__ty_2Enum_2Enum @ V1n))))))))))).
thf(ax_thm_2Emarker_2EAbbrev__def,axiom,( ! [V0x:$i] : ((mem@V0x@bool) => ((p@(ap@c_2Emarker_2EAbbrev@V0x)) <=> (p@V0x))))).
thf(conj_thm_2Enum_2EINDUCTION,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Enum_2Enum@bool)) => (((p@(ap@V0P@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@V0P@(inj__ty_2Enum_2Enum @ V1n))) => (p@(ap@V0P@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))) => ( ! [V2n:tp__ty_2Enum_2Enum] : (p@(ap@V0P@(inj__ty_2Enum_2Enum @ V2n)))))))).
thf(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) = V0n)) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V1n)) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))) & (( ! [V4n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V4n))) = fo__c_2Enum_2E0)) & (( ! [V5n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V6n:tp__ty_2Enum_2Enum] : ( ! [V7m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V6n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V7m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V6n))@(inj__ty_2Enum_2Enum @ V7m))))))) & (( ! [V8n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V8n))) = fo__c_2Enum_2E0)) & (( ! [V9n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V9n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V9n)) & (( ! [V10n:tp__ty_2Enum_2Enum] : ( ! [V11m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V10n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V11m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V10n))@(inj__ty_2Enum_2Enum @ V11m))))))) & (( ! [V12n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V12n))))) = fo__c_2Enum_2E0)) & (( ! [V13n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V13n))))) = fo__c_2Enum_2E0)) & (( ! [V14n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V14n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (( ! [V15n:tp__ty_2Enum_2Enum] : ( ! [V16m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V15n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V16m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V15n))@(inj__ty_2Enum_2Enum @ V16m))))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V17n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V17n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V17n)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (( ! [V18n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V18n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ V18n)))))) & (( ! [V19n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V19n))) = fo__c_2Enum_2E0) <=> (V19n = fo__c_2Earithmetic_2EZERO))) & (( ! [V20n:tp__ty_2Enum_2Enum] : ((fo__c_2Enum_2E0 = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V20n)))) <=> (V20n = fo__c_2Earithmetic_2EZERO))) & (( ! [V21n:tp__ty_2Enum_2Enum] : ( ! [V22m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V21n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V22m)))) <=> (V21n = V22m)))) & (( ! [V23n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V23n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $false)) & (( ! [V24n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V24n)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V24n))))) & (( ! [V25n:tp__ty_2Enum_2Enum] : ( ! [V26m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V25n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V26m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V25n))@(inj__ty_2Enum_2Enum @ V26m)))))) & (( ! [V27n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V27n))) <=> $false)) & (( ! [V28n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V28n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V28n))))) & (( ! [V29n:tp__ty_2Enum_2Enum] : ( ! [V30m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V29n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V30m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V30m))@(inj__ty_2Enum_2Enum @ V29n)))))) & (( ! [V31n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V31n))) <=> $true)) & (( ! [V32n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V32n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V32n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V33n:tp__ty_2Enum_2Enum] : ( ! [V34m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V33n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V34m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V33n))@(inj__ty_2Enum_2Enum @ V34m)))))) & (( ! [V35n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V35n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $true)) & (( ! [V36n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V36n))) <=> (V36n = fo__c_2Enum_2E0))) & (( ! [V37n:tp__ty_2Enum_2Enum] : ( ! [V38m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V37n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V38m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V38m))@(inj__ty_2Enum_2Enum @ V37n)))))) & (( ! [V39n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V39n)))) <=> (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ V39n))))) & (( ! [V40n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V40n)))) <=> (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V40n))))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))))))))))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__add,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = V0n) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = V0n) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(inj__ty_2Enum_2Enum @ V0n)))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enum_2ESUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))) & ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiiSUC@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))))))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__lt,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__lte,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0n))) <=> $true) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Eprim__rec_2ELESS__REFL,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Eprim__rec_2ENOT__LESS__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Eprim__rec_2ELESS__THM,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n)))) <=> ((V0m = V1n) | (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n)))))))).
thf(ax_thm_2Erich__list_2ECOUNT__LIST__def,axiom,(((surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@c_2Erich__list_2ECOUNT__LIST@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (c_2Elist_2ENIL@ty_2Enum_2Enum))) & ( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@c_2Erich__list_2ECOUNT__LIST@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@(ap@(c_2Elist_2ECONS@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(ap@(c_2Elist_2EMAP@ty_2Enum_2Enum@ty_2Enum_2Enum)@c_2Enum_2ESUC)@(ap@c_2Erich__list_2ECOUNT__LIST@(inj__ty_2Enum_2Enum @ V0n))))))))).
thf(conj_thm_2Erich__list_2EMEM__COUNT__LIST,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@(c_2Ebool_2EIN@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0m))@(ap@(c_2Elist_2ELIST__TO__SET@ty_2Enum_2Enum)@(ap@c_2Erich__list_2ECOUNT__LIST@(inj__ty_2Enum_2Enum @ V1n))))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__SNOC,lemma,(((surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@c_2Erich__list_2ECOUNT__LIST@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (c_2Elist_2ENIL@ty_2Enum_2Enum))) & ( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@c_2Erich__list_2ECOUNT__LIST@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ (ap@(ap@(c_2Elist_2ESNOC@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ V0n))@(ap@c_2Erich__list_2ECOUNT__LIST@(inj__ty_2Enum_2Enum @ V0n)))))))).
thf(conj_thm_2Esat_2ENOT__NOT,lemma,( ! [V0t:$i] : ((mem@V0t@bool) => ((~ (~ (p@V0t))) <=> (p@V0t))))).
thf(conj_thm_2Esat_2EAND__INV__IMP,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ((p@V0A) => ((~ (p@V0A)) => $false))))).
thf(conj_thm_2Esat_2EOR__DUAL2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((p@V0A) | (p@V1B))) => $false) <=> (((p@V0A) => $false) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EOR__DUAL3,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => ( ! [V1B:$i] : ((mem@V1B@bool) => (((~ ((~ (p@V0A)) | (p@V1B))) => $false) <=> ((p@V0A) => ((~ (p@V1B)) => $false)))))))).
thf(conj_thm_2Esat_2EAND__INV2,lemma,( ! [V0A:$i] : ((mem@V0A@bool) => (((~ (p@V0A)) => $false) => (((p@V0A) => $false) => $false))))).
thf(conj_thm_2Esat_2Edc__eq,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) <=> (p@V2r))) <=> (((p@V0p) | ((p@V1q) | (p@V2r))) & (((p@V0p) | ((~ (p@V2r)) | (~ (p@V1q)))) & (((p@V1q) | ((~ (p@V2r)) | (~ (p@V0p)))) & ((p@V2r) | ((~ (p@V1q)) | (~ (p@V0p))))))))))))))).
thf(conj_thm_2Esat_2Edc__conj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) & (p@V2r))) <=> (((p@V0p) | ((~ (p@V1q)) | (~ (p@V2r)))) & (((p@V1q) | (~ (p@V0p))) & ((p@V2r) | (~ (p@V0p))))))))))))).
thf(conj_thm_2Esat_2Edc__disj,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) | (p@V2r))) <=> (((p@V0p) | (~ (p@V1q))) & (((p@V0p) | (~ (p@V2r))) & ((p@V1q) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__imp,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => (((p@V0p) <=> ((p@V1q) => (p@V2r))) <=> (((p@V0p) | (p@V1q)) & (((p@V0p) | (~ (p@V2r))) & ((~ (p@V1q)) | ((p@V2r) | (~ (p@V0p)))))))))))))).
thf(conj_thm_2Esat_2Edc__neg,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (~ (p@V1q))) <=> (((p@V0p) | (p@V1q)) & ((~ (p@V1q)) | (~ (p@V0p)))))))))).
thf(conj_thm_2Esat_2Epth__ni1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (p@V0p))))))).
thf(conj_thm_2Esat_2Epth__ni2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) => (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__no1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V0p)))))))).
thf(conj_thm_2Esat_2Epth__no2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~ ((p@V0p) | (p@V1q))) => (~ (p@V1q)))))))).
thf(conj_thm_2Esat_2Epth__nn,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((~ (~ (p@V0p))) => (p@V0p))))).
thf(ax_thm_2Ewords_2Eword__bits__def,axiom,( ! [A_27a:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l)) = (lam@(ty_2Efcp_2Ecart@bool@A_27a)@(^ [V2w:$i] : (ap@(c_2Efcp_2EFCP@bool@A_27a)@(lam@ty_2Enum_2Enum@(^ [V3i:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@V3i)@(inj__ty_2Enum_2Enum @ V1l)))@(ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V0h))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V2w)@(ap@(ap@c_2Earithmetic_2E_2B@V3i)@(inj__ty_2Enum_2Enum @ V1l)))))))))))))).
thf(ax_thm_2Ewords_2Eword__extract__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l)) = (ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@A_27a)@(ty_2Efcp_2Ecart@bool@A_27b)@(ty_2Efcp_2Ecart@bool@A_27a))@(c_2Ewords_2Ew2w@A_27a@A_27b))@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))))))))).
thf(ax_thm_2Ewords_2Eword__lsl__def,axiom,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__lsl@A_27a)@V0w)@(inj__ty_2Enum_2Enum @ V1n)) = (ap@(c_2Efcp_2EFCP@bool@A_27a)@(lam@ty_2Enum_2Enum@(^ [V2i:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Eprim__rec_2E_3C@V2i)@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a))))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1n))@V2i))@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V0w)@(ap@(ap@c_2Earithmetic_2E_2D@V2i)@(inj__ty_2Enum_2Enum @ V1n)))))))))))))).
thf(ax_thm_2Ewords_2Eword__lsl__bv__def,axiom,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1n:$i] : ((mem@V1n@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__lsl__bv@A_27a)@V0w)@V1n) = (ap@(ap@(c_2Ewords_2Eword__lsl@A_27a)@V0w)@(ap@(c_2Ewords_2Ew2n@A_27a)@V1n))))))))).
thf(conj_thm_2Ewords_2EZERO__LT__dimword,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2Ewords_2EDIMINDEX__GT__0,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2Ewords_2Edimindex__lt__dimword,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2Ewords_2Ew2n__n2w,lemma,( ! [A_27a:del]: ( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Ew2n@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))).
thf(conj_thm_2Ewords_2En2w__11,lemma,( ! [A_27a:del]: ( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0m)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V1n))) <=> ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V0m))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EMOD@(inj__ty_2Enum_2Enum @ V1n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))))).
thf(conj_thm_2Ewords_2Eranged__word__nchotomy,lemma,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => (? [V1n:tp__ty_2Enum_2Enum] : ((V0w = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V1n))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1n))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))))))).
thf(conj_thm_2Ewords_2Eword__0,lemma,( ! [A_27a:del]: ( ! [V0i:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0i))@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))) => (~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V0i)))))))).
thf(conj_thm_2Ewords_2Ew2w__id,lemma,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(c_2Ewords_2Ew2w@A_27a@A_27a)@V0w) = V0w))))).
thf(conj_thm_2Ewords_2Eword__bits__n2w,lemma,( ! [A_27a:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ( ! [V2n:tp__ty_2Enum_2Enum] : ((ap@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V2n))) = (ap@(c_2Ewords_2En2w@A_27a)@(ap@(ap@(ap@c_2Ebit_2EBITS@(ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V0h))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Enum_2Enum @ V1l))@(inj__ty_2Enum_2Enum @ V2n))))))))).
thf(conj_thm_2Ewords_2EWORD__w2w__EXTRACT,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(c_2Ewords_2Ew2w@A_27a@A_27b)@V0w) = (ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@V0w))))))).
thf(conj_thm_2Ewords_2EWORD__BITS__EXTRACT,lemma,( ! [A_27a:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ( ! [V2w:$i] : ((mem@V2w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))@V2w) = (ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27a)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))@V2w)))))))).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1l:tp__ty_2Enum_2Enum] : ( ! [V2w:$i] : ((mem@V2w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))) => ((ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V1l))@V2w) = (ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2Ewords_2EWORD__ALL__BITS,lemma,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1h:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1h))) => ((ap@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(inj__ty_2Enum_2Enum @ V1h))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@V0w) = V0w))))))).
thf(conj_thm_2Ewords_2EEXTRACT__JOIN__ADD,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0h:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2m_27:tp__ty_2Enum_2Enum] : ( ! [V3l:tp__ty_2Enum_2Enum] : ( ! [V4s:tp__ty_2Enum_2Enum] : ( ! [V5w:$i] : ((mem@V5w@(ty_2Efcp_2Ecart@bool@A_27a)) => (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V3l))@(inj__ty_2Enum_2Enum @ V1m))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V2m_27))@(inj__ty_2Enum_2Enum @ V0h))) & ((V2m_27 = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1m))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (V4s = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V2m_27))@(inj__ty_2Enum_2Enum @ V3l))))))) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27b)@(ap@(ap@(c_2Ewords_2Eword__lsl@A_27b)@(ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(inj__ty_2Enum_2Enum @ V0h))@(inj__ty_2Enum_2Enum @ V2m_27))@V5w))@(inj__ty_2Enum_2Enum @ V4s)))@(ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V3l))@V5w)) = (ap@(ap@(ap@(c_2Ewords_2Eword__extract@A_27a@A_27b)@(ap@(ap@c_2Earithmetic_2EMIN@(inj__ty_2Enum_2Enum @ V0h))@(ap@(ap@c_2Earithmetic_2EMIN@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))@(inj__ty_2Enum_2Enum @ V3l)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Enum_2Enum @ V3l))@V5w))))))))))))).
thf(conj_thm_2Ewords_2EWORD__ADD__0,lemma,( ! [A_27a:del]: (( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V0w)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0w))) & ( ! [V1w:$i] : ((mem@V1w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1w) = V1w)))))).
thf(conj_thm_2Ewords_2EWORD__ADD__COMM,lemma,( ! [A_27a:del]: ( ! [V0v:$i] : ((mem@V0v@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1w:$i] : ((mem@V1w@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V0v)@V1w) = (ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V1w)@V0v)))))))).
thf(conj_thm_2Ewords_2EZERO__SHIFT,lemma,( ! [A_27a:del]: (( ! [V0n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__lsl@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V0n)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__asr@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V1n)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (( ! [V2n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__lsr@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V2n)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (( ! [V3n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__rol@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V3n)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & ( ! [V4n:tp__ty_2Enum_2Enum] : ((ap@(ap@(c_2Ewords_2Eword__ror@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Enum_2Enum @ V4n)) = (ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2Eblast_2Eword__lsl__bv__expand,conjecture,( ! [A_27a:del]: ( ! [V0w:$i] : ((mem@V0w@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1m:$i] : ((mem@V1m@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__lsl__bv@A_27a)@V0w)@V1m) = (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Efcp_2Ecart@bool@A_27a))@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Efcp_2EFCP@bool@A_27a)@(ap@(c_2Ecombin_2EK@bool@ty_2Enum_2Enum)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@c_2Ebool_2E_7E@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V1m)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V0w)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))@(ap@(c_2Efcp_2EFCP@bool@A_27a)@(lam@ty_2Enum_2Enum@(^ [V2k:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@(ap@(c_2Elist_2EFOLDL@ty_2Enum_2Enum@bool)@(lam@bool@(^ [V3a:$i] : (lam@ty_2Enum_2Enum@(^ [V4j:$i] : (ap@(ap@c_2Ebool_2E_5C_2F@V3a)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@A_27a))@(ap@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(ap@c_2Ebit_2ELOG2@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@V1m))@(ap@(c_2Ewords_2En2w@A_27a)@V4j)))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Earithmetic_2E_3C_3D@V4j)@V2k))@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V0w)@(ap@(ap@c_2Earithmetic_2E_2D@V2k)@V4j))))))))))@c_2Ebool_2EF)@(ap@c_2Erich__list_2ECOUNT__LIST@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))@(ap@(ap@(c_2Emin_2E_3D@(ty_2Efcp_2Ecart@bool@A_27a))@(ap@(ap@(ap@(c_2Ewords_2Eword__bits@A_27a)@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Ebit_2ELOG2@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Efcp_2Edimindex@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V1m))@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))))).
