include('Axioms/HL4001^2.ax').
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_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:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$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:$i)).
thf(mem_c_2Earithmetic_2E_3E,axiom,(mem@c_2Earithmetic_2E_3E@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$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_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$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_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EEXP @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EEXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$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_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2A @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$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_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X0)) = (ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$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_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$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_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: del > del >del )).
thf(tp_c_2Epair_2EUNCURRY,type,(c_2Epair_2EUNCURRY:(del>(del>(del>$i))))).
thf(mem_c_2Epair_2EUNCURRY,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : ( ! [A_27c:del] : (mem@(c_2Epair_2EUNCURRY@A_27a@A_27b@A_27c)@(arr@(arr@A_27a@(arr@A_27b@A_27c))@(arr@(ty_2Epair_2Eprod@A_27a@A_27b)@A_27c))))))).
thf(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del>(del>$i)))).
thf(mem_c_2Epair_2E_2C,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epair_2E_2C@A_27a@A_27b)@(arr@A_27a@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@A_27b))))))).
thf(tp_c_2Epred__set_2EGSPEC,type,(c_2Epred__set_2EGSPEC:(del>(del>$i)))).
thf(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epred__set_2EGSPEC@A_27a@A_27b)@(arr@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@bool))@(arr@A_27a@bool)))))).
thf(tp_ty_2Erealax_2Ereal,type,( ty_2Erealax_2Ereal:del )).
thf(stp_ty_2Erealax_2Ereal,type,(tp__ty_2Erealax_2Ereal : $tType)).
thf(stp_inj_ty_2Erealax_2Ereal,type,(inj__ty_2Erealax_2Ereal : (tp__ty_2Erealax_2Ereal > $i))).
thf(stp_surj_ty_2Erealax_2Ereal,type,(surj__ty_2Erealax_2Ereal : ($i > tp__ty_2Erealax_2Ereal))).
thf(stp_inj_surj_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (inj__ty_2Erealax_2Ereal @ X)) = X))).
thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,( ! [X:tp__ty_2Erealax_2Ereal] : (mem @ (inj__ty_2Erealax_2Ereal @ X) @ ty_2Erealax_2Ereal))).
thf(stp_iso_mem_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : ((mem @ X @ ty_2Erealax_2Ereal) => (X = (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X)))))).
thf(tp_ty_2Etopology_2Etopology,type,( ty_2Etopology_2Etopology: del >del )).
thf(stp_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,type,(tp__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal : $tType)).
thf(stp_inj_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,type,(inj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal : (tp__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal > $i))).
thf(stp_surj_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,type,(surj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal : ($i > tp__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal))).
thf(stp_inj_surj_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,axiom,( ! [X:tp__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal] : ((surj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal @ (inj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal @ X)) = X))).
thf(stp_inj_mem_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,axiom,( ! [X:tp__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal] : (mem @ (inj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal @ X) @ (ty_2Etopology_2Etopology@ty_2Erealax_2Ereal)))).
thf(stp_iso_mem_c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Etopology_2Etopology@ty_2Erealax_2Ereal)) => (X = (inj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal @ (surj__c_ty_2Etopology_2Etopology_ty_2Erealax_2Ereal @ X)))))).
thf(tp_c_2Ereal__topology_2Eeuclidean,type,(c_2Ereal__topology_2Eeuclidean:$i)).
thf(mem_c_2Ereal__topology_2Eeuclidean,axiom,(mem@c_2Ereal__topology_2Eeuclidean@(ty_2Etopology_2Etopology@ty_2Erealax_2Ereal))).
thf(tp_c_2Ereal__topology_2Esubtopology,type,(c_2Ereal__topology_2Esubtopology:(del>$i))).
thf(mem_c_2Ereal__topology_2Esubtopology,axiom,( ! [A_27a:del] : (mem@(c_2Ereal__topology_2Esubtopology@A_27a)@(arr@(ty_2Etopology_2Etopology@A_27a)@(arr@(arr@A_27a@bool)@(ty_2Etopology_2Etopology@A_27a)))))).
thf(tp_c_2Epred__set_2EDELETE,type,(c_2Epred__set_2EDELETE:(del>$i))).
thf(mem_c_2Epred__set_2EDELETE,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EDELETE@A_27a)@(arr@(arr@A_27a@bool)@(arr@A_27a@(arr@A_27a@bool)))))).
thf(tp_c_2Ereal__topology_2Elimit__point__of,type,(c_2Ereal__topology_2Elimit__point__of:$i)).
thf(mem_c_2Ereal__topology_2Elimit__point__of,axiom,(mem@c_2Ereal__topology_2Elimit__point__of@(arr@ty_2Erealax_2Ereal@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)))).
thf(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$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_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:$i] : ((mem@X@A) & (p@(ap@Q@X))))))))).
thf(tp_c_2Epred__set_2EBIGUNION,type,(c_2Epred__set_2EBIGUNION:(del>$i))).
thf(mem_c_2Epred__set_2EBIGUNION,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EBIGUNION@A_27a)@(arr@(arr@(arr@A_27a@bool)@bool)@(arr@A_27a@bool))))).
thf(tp_c_2Ereal__topology_2EOpen,type,(c_2Ereal__topology_2EOpen:$i)).
thf(mem_c_2Ereal__topology_2EOpen,axiom,(mem@c_2Ereal__topology_2EOpen@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool))).
thf(tp_c_2Epred__set_2EUNIV,type,(c_2Epred__set_2EUNIV:(del>$i))).
thf(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EUNIV@A_27a)@(arr@A_27a@bool)))).
thf(tp_c_2Epred__set_2EIMAGE,type,(c_2Epred__set_2EIMAGE:(del>(del>$i)))).
thf(mem_c_2Epred__set_2EIMAGE,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epred__set_2EIMAGE@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@(arr@A_27a@bool)@(arr@A_27b@bool))))))).
thf(tp_ty_2Ereal__topology_2Enet,type,( ty_2Ereal__topology_2Enet: del >del )).
thf(stp_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,type,(tp__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum : $tType)).
thf(stp_inj_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,type,(inj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum : (tp__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum > $i))).
thf(stp_surj_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,type,(surj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum : ($i > tp__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum))).
thf(stp_inj_surj_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum] : ((surj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum @ (inj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,axiom,( ! [X:tp__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum] : (mem @ (inj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum @ X) @ (ty_2Ereal__topology_2Enet@ty_2Enum_2Enum)))).
thf(stp_iso_mem_c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Ereal__topology_2Enet@ty_2Enum_2Enum)) => (X = (inj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum @ (surj__c_ty_2Ereal__topology_2Enet_ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Ereal__topology_2Esequentially,type,(c_2Ereal__topology_2Esequentially:$i)).
thf(mem_c_2Ereal__topology_2Esequentially,axiom,(mem@c_2Ereal__topology_2Esequentially@(ty_2Ereal__topology_2Enet@ty_2Enum_2Enum))).
thf(tp_c_2Ereal__topology_2E_2D_2D_3E,type,(c_2Ereal__topology_2E_2D_2D_3E:(del>$i))).
thf(mem_c_2Ereal__topology_2E_2D_2D_3E,axiom,( ! [A_27a:del] : (mem@(c_2Ereal__topology_2E_2D_2D_3E@A_27a)@(arr@(arr@A_27a@ty_2Erealax_2Ereal)@(arr@ty_2Erealax_2Ereal@(arr@(ty_2Ereal__topology_2Enet@A_27a)@bool)))))).
thf(tp_c_2Epred__set_2EINTER,type,(c_2Epred__set_2EINTER:(del>$i))).
thf(mem_c_2Epred__set_2EINTER,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EINTER@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@(arr@A_27a@bool)))))).
thf(tp_c_2Ereal__topology_2EClosed,type,(c_2Ereal__topology_2EClosed:$i)).
thf(mem_c_2Ereal__topology_2EClosed,axiom,(mem@c_2Ereal__topology_2EClosed@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool))).
thf(tp_c_2Epred__set_2EINSERT,type,(c_2Epred__set_2EINSERT:(del>$i))).
thf(mem_c_2Epred__set_2EINSERT,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EINSERT@A_27a)@(arr@A_27a@(arr@(arr@A_27a@bool)@(arr@A_27a@bool)))))).
thf(tp_c_2Epred__set_2EEMPTY,type,(c_2Epred__set_2EEMPTY:(del>$i))).
thf(mem_c_2Epred__set_2EEMPTY,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EEMPTY@A_27a)@(arr@A_27a@bool)))).
thf(tp_c_2Epred__set_2EBIGINTER,type,(c_2Epred__set_2EBIGINTER:(del>$i))).
thf(mem_c_2Epred__set_2EBIGINTER,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EBIGINTER@A_27a)@(arr@(arr@(arr@A_27a@bool)@bool)@(arr@A_27a@bool))))).
thf(tp_c_2Epred__set_2EFINITE,type,(c_2Epred__set_2EFINITE:(del>$i))).
thf(mem_c_2Epred__set_2EFINITE,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EFINITE@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(tp_c_2Ereal__topology_2Ecompact,type,(c_2Ereal__topology_2Ecompact:$i)).
thf(mem_c_2Ereal__topology_2Ecompact,axiom,(mem@c_2Ereal__topology_2Ecompact@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool))).
thf(tp_c_2Ebool_2EIN,type,(c_2Ebool_2EIN:(del>$i))).
thf(mem_c_2Ebool_2EIN,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2EIN@A_27a)@(arr@A_27a@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$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:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_5C_2F@Q)@R)) <=> ((p@Q) | (p@R)))))))).
thf(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
thf(mem_c_2Ebool_2E_7E,axiom,(mem@c_2Ebool_2E_7E@(arr@bool@bool))).
thf(ax_neg_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ((p@(ap@c_2Ebool_2E_7E@Q)) <=> (~ (p@Q)))))).
thf(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$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_2Epred__set_2EDIFF,type,(c_2Epred__set_2EDIFF:(del>$i))).
thf(mem_c_2Epred__set_2EDIFF,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EDIFF@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@(arr@A_27a@bool)))))).
thf(tp_c_2Etopology_2Eopen__in,type,(c_2Etopology_2Eopen__in:(del>$i))).
thf(mem_c_2Etopology_2Eopen__in,axiom,( ! [A_27a:del] : (mem@(c_2Etopology_2Eopen__in@A_27a)@(arr@(ty_2Etopology_2Etopology@A_27a)@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Etopology_2Etopspace,type,(c_2Etopology_2Etopspace:(del>$i))).
thf(mem_c_2Etopology_2Etopspace,axiom,( ! [A_27a:del] : (mem@(c_2Etopology_2Etopspace@A_27a)@(arr@(ty_2Etopology_2Etopology@A_27a)@(arr@A_27a@bool))))).
thf(tp_c_2Epred__set_2ESUBSET,type,(c_2Epred__set_2ESUBSET:(del>$i))).
thf(mem_c_2Epred__set_2ESUBSET,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2ESUBSET@A_27a)@(arr@(arr@A_27a@bool)@(arr@(arr@A_27a@bool)@bool))))).
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:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_2F_5C@Q)@R)) <=> ((p@Q) & (p@R)))))))).
thf(tp_c_2Etopology_2Eclosed__in,type,(c_2Etopology_2Eclosed__in:(del>$i))).
thf(mem_c_2Etopology_2Eclosed__in,axiom,( ! [A_27a:del] : (mem@(c_2Etopology_2Eclosed__in@A_27a)@(arr@(ty_2Etopology_2Etopology@A_27a)@(arr@(arr@A_27a@bool)@bool))))).
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(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_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_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_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_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__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__ELIM__THM,lemma,( ! [V0P:$i] : ((mem@V0P@(arr@ty_2Enum_2Enum@bool)) => ( ! [V1a:tp__ty_2Enum_2Enum] : ( ! [V2b:tp__ty_2Enum_2Enum] : ((p@(ap@V0P@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V1a))@(inj__ty_2Enum_2Enum @ V2b)))) <=> ( ! [V3d:tp__ty_2Enum_2Enum] : (((V2b = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1a))@(inj__ty_2Enum_2Enum @ V3d)))) => (p@(ap@V0P@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & ((V1a = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2b))@(inj__ty_2Enum_2Enum @ V3d)))) => (p@(ap@V0P@(inj__ty_2Enum_2Enum @ V3d)))))))))))).
thf(ax_thm_2Ebool_2EEXISTS__DEF,axiom,( ! [A_27a:del]: ((c_2Ebool_2E_3F@A_27a) = (lam@(arr@A_27a@bool)@(^ [V0P:$i] : (ap@V0P@(ap@(c_2Emin_2E_40@A_27a)@V0P))))))).
thf(ax_thm_2Ebool_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(ax_thm_2Ebool_2EIN__DEF,axiom,( ! [A_27a:del]: ((c_2Ebool_2EIN@A_27a) = (lam@A_27a@(^ [V0x:$i] : (lam@(arr@A_27a@bool)@(^ [V1f:$i] : (ap@V1f@V0x)))))))).
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) <=> $false) <=> (~ (p@V0t))))))))).
thf(conj_thm_2Ebool_2ENOT__FORALL__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$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__EXISTS__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ((~ (? [V1x:$i] : ((mem@V1x@A_27a) & (p@(ap@V0P@V1x))))) <=> ( ! [V2x:$i] : ((mem@V2x@A_27a) => (~ (p@(ap@V0P@V2x)))))))))).
thf(conj_thm_2Ebool_2EFORALL__AND__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@V0P@V2x)) & (p@(ap@V1Q@V2x))))) <=> (( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V0P@V3x)))) & ( ! [V4x:$i] : ((mem@V4x@A_27a) => (p@(ap@V1Q@V4x)))))))))))).
thf(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => ((( ! [V2x:$i] : ((mem@V2x@A_27a) => (p@(ap@V0P@V2x)))) & (p@V1Q)) <=> ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@(ap@V0P@V3x)) & (p@V1Q))))))))))).
thf(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (((p@V0P) & ( ! [V2x:$i] : ((mem@V2x@A_27a) => (p@(ap@V1Q@V2x))))) <=> ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@V0P) & (p@(ap@V1Q@V3x)))))))))))).
thf(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => ((? [V2x:$i] : ((mem@V2x@A_27a) & ((p@(ap@V0P@V2x)) & (p@V1Q)))) <=> ((? [V3x:$i] : ((mem@V3x@A_27a) & (p@(ap@V0P@V3x)))) & (p@V1Q))))))))).
thf(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,lemma,( ! [A_27a:del]: ( ! [V0Q:$i] : ((mem@V0Q@bool) => ( ! [V1P:$i] : ((mem@V1P@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@V1P@V2x)) | (p@V0Q)))) <=> (( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V1P@V3x)))) | (p@V0Q))))))))).
thf(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@V0P) | (p@(ap@V1Q@V2x))))) <=> ((p@V0P) | ( ! [V3x:$i] : ((mem@V3x@A_27a) => (p@(ap@V1Q@V3x)))))))))))).
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:$i] : ((mem@V1B@bool) => (((p@V0A) => (p@V1B)) <=> ((~ (p@V0A)) | (p@V1B)))))))).
thf(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,( ! [V0t:$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_2EMONO__NOT__EQ,lemma,( ! [V0y:$i] : ((mem@V0y@bool) => ( ! [V1x:$i] : ((mem@V1x@bool) => (((p@V0y) => (p@V1x)) <=> ((~ (p@V1x)) => (~ (p@V0y))))))))).
thf(conj_thm_2Ebool_2EUNWIND__THM2,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1a:$i] : ((mem@V1a@A_27a) => ((? [V2x:$i] : ((mem@V2x@A_27a) & ((V2x = V1a) & (p@(ap@V0P@V2x))))) <=> (p@(ap@V0P@V1a))))))))).
thf(conj_thm_2Ebool_2ESKOLEM__THM,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@(arr@A_27b@bool))) => (( ! [V1x:$i] : ((mem@V1x@A_27a) => (? [V2y:$i] : ((mem@V2y@A_27b) & (p@(ap@(ap@V0P@V1x)@V2y)))))) <=> (? [V3f:$i] : ((mem@V3f@(arr@A_27a@A_27b)) & ( ! [V4x:$i] : ((mem@V4x@A_27a) => (p@(ap@(ap@V0P@V4x)@(ap@V3f@V4x))))))))))))).
thf(conj_thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => (((? [V2x:$i] : ((mem@V2x@A_27a) & (p@(ap@V0P@V2x)))) => (p@V1Q)) <=> ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@(ap@V0P@V3x)) => (p@V1Q))))))))))).
thf(conj_thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@bool) => ( ! [V1Q:$i] : ((mem@V1Q@(arr@A_27a@bool)) => (((p@V0P) => (? [V2x:$i] : ((mem@V2x@A_27a) & (p@(ap@V1Q@V2x))))) <=> (? [V3x:$i] : ((mem@V3x@A_27a) & ((p@V0P) => (p@(ap@V1Q@V3x)))))))))))).
thf(conj_thm_2Ecardinal_2ESING__SUBSET,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27a)@(ap@(ap@(c_2Epred__set_2EINSERT@A_27a)@V1x)@(c_2Epred__set_2EEMPTY@A_27a)))@V0s)) <=> (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V1x)@V0s))))))))).
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__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))) <=> $false) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Epair_2ECLOSED__PAIR__EQ,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27b) => ( ! [V2a:$i] : ((mem@V2a@A_27a) => ( ! [V3b:$i] : ((mem@V3b@A_27b) => (((ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V0x)@V1y) = (ap@(ap@(c_2Epair_2E_2C@A_27a@A_27b)@V2a)@V3b)) <=> ((V0x = V2a) & (V1y = V3b)))))))))))))).
thf(conj_thm_2Epred__set_2EEXTENSION,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@A_27a@bool)) => ((V0s = V1t) <=> ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) <=> (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t)))))))))))).
thf(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27b@(ty_2Epair_2Eprod@A_27a@bool))) => ( ! [V1v:$i] : ((mem@V1v@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V1v)@(ap@(c_2Epred__set_2EGSPEC@A_27a@A_27b)@V0f))) <=> (? [V2x:$i] : ((mem@V2x@A_27b) & ((ap@(ap@(c_2Epair_2E_2C@A_27a@bool)@V1v)@c_2Ebool_2ET) = (ap@V0f@V2x)))))))))))).
thf(conj_thm_2Epred__set_2ENOT__IN__EMPTY,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(c_2Epred__set_2EEMPTY@A_27a)))))))).
thf(conj_thm_2Epred__set_2EMEMBER__NOT__EMPTY,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ((? [V1x:$i] : ((mem@V1x@A_27a) & (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V1x)@V0s)))) <=> (~ (V0s = (c_2Epred__set_2EEMPTY@A_27a)))))))).
thf(conj_thm_2Epred__set_2EIN__UNIV,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(c_2Epred__set_2EUNIV@A_27a))))))).
thf(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27a)@V0s)@V1t)) <=> ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) => (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t)))))))))))).
thf(conj_thm_2Epred__set_2EIN__INTER,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@A_27a@bool)) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@(ap@(ap@(c_2Epred__set_2EINTER@A_27a)@V0s)@V1t))) <=> ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) & (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t)))))))))))).
thf(conj_thm_2Epred__set_2EIN__DIFF,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@A_27a@bool)) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@(ap@(ap@(c_2Epred__set_2EDIFF@A_27a)@V0s)@V1t))) <=> ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V0s)) & (~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1t))))))))))))).
thf(conj_thm_2Epred__set_2EIN__INSERT,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2s:$i] : ((mem@V2s@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(ap@(c_2Epred__set_2EINSERT@A_27a)@V1y)@V2s))) <=> ((V0x = V1y) | (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@V2s)))))))))))).
thf(conj_thm_2Epred__set_2EIN__DELETE,lemma,( ! [A_27a:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V1x)@(ap@(ap@(c_2Epred__set_2EDELETE@A_27a)@V0s)@V2y))) <=> ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V1x)@V0s)) & (~ (V1x = V2y)))))))))))).
thf(ax_thm_2Epred__set_2EIMAGE__DEF,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((ap@(ap@(c_2Epred__set_2EIMAGE@A_27a@A_27b)@V0f)@V1s) = (ap@(c_2Epred__set_2EGSPEC@A_27b@A_27a)@(lam@A_27a@(^ [V2x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@(ap@V0f@V2x))@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V2x)@V1s))))))))))))).
thf(conj_thm_2Epred__set_2EIN__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0y:$i] : ((mem@V0y@A_27b) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ( ! [V2f:$i] : ((mem@V2f@(arr@A_27a@A_27b)) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V0y)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27a@A_27b)@V2f)@V1s))) <=> (? [V3x:$i] : ((mem@V3x@A_27a) & ((V0y = (ap@V2f@V3x)) & (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3x)@V1s))))))))))))))).
thf(conj_thm_2Epred__set_2EFORALL__IN__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27b@A_27a)) => ( ! [V2s:$i] : ((mem@V2s@(arr@A_27b@bool)) => (( ! [V3y:$i] : ((mem@V3y@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3y)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27b@A_27a)@V1f)@V2s))) => (p@(ap@V0P@V3y))))) <=> ( ! [V4x:$i] : ((mem@V4x@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V4x)@V2s)) => (p@(ap@V0P@(ap@V1f@V4x)))))))))))))))).
thf(conj_thm_2Epred__set_2EIMAGE__FINITE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0s:$i] : ((mem@V0s@(arr@A_27a@bool)) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@V0s)) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27a@A_27b)) => (p@(ap@(c_2Epred__set_2EFINITE@A_27b)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27a@A_27b)@V1f)@V0s))))))))))).
thf(conj_thm_2Epred__set_2EIN__BIGUNION,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1sos:$i] : ((mem@V1sos@(arr@(arr@A_27a@bool)@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(c_2Epred__set_2EBIGUNION@A_27a)@V1sos))) <=> (? [V2s:$i] : ((mem@V2s@(arr@A_27a@bool)) & ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@V2s)) & (p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V2s)@V1sos)))))))))))).
thf(conj_thm_2Epred__set_2EFINITE__BIGUNION__EQ,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@(arr@A_27a@bool)@bool)) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(ap@(c_2Epred__set_2EBIGUNION@A_27a)@V0P))) <=> ((p@(ap@(c_2Epred__set_2EFINITE@(arr@A_27a@bool))@V0P)) & ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@A_27a@bool))@V1s)@V0P)) => (p@(ap@(c_2Epred__set_2EFINITE@A_27a)@V1s))))))))))).
thf(conj_thm_2Ereal__topology_2EFORALL__FINITE__SUBSET__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@(arr@A_27a@bool)@bool)) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27b@A_27a)) => ( ! [V2s:$i] : ((mem@V2s@(arr@A_27b@bool)) => (( ! [V3t:$i] : ((mem@V3t@(arr@A_27a@bool)) => (((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@V3t)) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27a)@V3t)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27b@A_27a)@V1f)@V2s)))) => (p@(ap@V0P@V3t))))) <=> ( ! [V4t:$i] : ((mem@V4t@(arr@A_27b@bool)) => (((p@(ap@(c_2Epred__set_2EFINITE@A_27b)@V4t)) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27b)@V4t)@V2s))) => (p@(ap@V0P@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27b@A_27a)@V1f)@V4t)))))))))))))))).
thf(conj_thm_2Ereal__topology_2EFORALL__IN__GSPEC,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [A_27e:del]: ( ! [A_27f:del]: ( ! [A_27g:del]: ( ! [V0Q:$i] : ((mem@V0Q@(arr@A_27b@bool)) => (( ! [V1P:$i] : ((mem@V1P@(arr@A_27a@bool)) => ( ! [V2f:$i] : ((mem@V2f@(arr@A_27a@A_27b)) => (( ! [V3z:$i] : ((mem@V3z@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V3z)@(ap@(c_2Epred__set_2EGSPEC@A_27b@A_27a)@(lam@A_27a@(^ [V4x:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@(ap@V2f@V4x))@(ap@V1P@V4x))))))) => (p@(ap@V0Q@V3z))))) <=> ( ! [V5x:$i] : ((mem@V5x@A_27a) => ((p@(ap@V1P@V5x)) => (p@(ap@V0Q@(ap@V2f@V5x))))))))))) & (( ! [V6P:$i] : ((mem@V6P@(arr@A_27c@(arr@A_27d@bool))) => ( ! [V7f:$i] : ((mem@V7f@(arr@A_27c@(arr@A_27d@A_27b))) => (( ! [V8z:$i] : ((mem@V8z@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V8z)@(ap@(c_2Epred__set_2EGSPEC@A_27b@(ty_2Epair_2Eprod@A_27c@A_27d))@(ap@(c_2Epair_2EUNCURRY@A_27c@A_27d@(ty_2Epair_2Eprod@A_27b@bool))@(lam@A_27c@(^ [V9x:$i] : (lam@A_27d@(^ [V10y:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@(ap@(ap@V7f@V9x)@V10y))@(ap@(ap@V6P@V9x)@V10y)))))))))) => (p@(ap@V0Q@V8z))))) <=> ( ! [V11x:$i] : ((mem@V11x@A_27c) => ( ! [V12y:$i] : ((mem@V12y@A_27d) => ((p@(ap@(ap@V6P@V11x)@V12y)) => (p@(ap@V0Q@(ap@(ap@V7f@V11x)@V12y))))))))))))) & ( ! [V13P:$i] : ((mem@V13P@(arr@A_27e@(arr@A_27f@(arr@A_27g@bool)))) => ( ! [V14f:$i] : ((mem@V14f@(arr@A_27e@(arr@A_27f@(arr@A_27g@A_27b)))) => (( ! [V15z:$i] : ((mem@V15z@A_27b) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V15z)@(ap@(c_2Epred__set_2EGSPEC@A_27b@(ty_2Epair_2Eprod@A_27e@(ty_2Epair_2Eprod@A_27f@A_27g)))@(ap@(c_2Epair_2EUNCURRY@A_27e@(ty_2Epair_2Eprod@A_27f@A_27g)@(ty_2Epair_2Eprod@A_27b@bool))@(lam@A_27e@(^ [V16w:$i] : (ap@(c_2Epair_2EUNCURRY@A_27f@A_27g@(ty_2Epair_2Eprod@A_27b@bool))@(lam@A_27f@(^ [V17x:$i] : (lam@A_27g@(^ [V18y:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@(ap@(ap@(ap@V14f@V16w)@V17x)@V18y))@(ap@(ap@(ap@V13P@V16w)@V17x)@V18y))))))))))))) => (p@(ap@V0Q@V15z))))) <=> ( ! [V19w:$i] : ((mem@V19w@A_27e) => ( ! [V20x:$i] : ((mem@V20x@A_27f) => ( ! [V21y:$i] : ((mem@V21y@A_27g) => ((p@(ap@(ap@(ap@V13P@V19w)@V20x)@V21y)) => (p@(ap@V0Q@(ap@(ap@(ap@V14f@V19w)@V20x)@V21y))))))))))))))))))))))))))).
thf(conj_thm_2Ereal__topology_2EUPPER__BOUND__FINITE__SET,lemma,( ! [A_27a:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@ty_2Enum_2Enum)) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@V1s)) => (? [V2a:tp__ty_2Enum_2Enum] : ( ! [V3x:$i] : ((mem@V3x@A_27a) => ((p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3x)@V1s)) => (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@V0f@V3x))@(inj__ty_2Enum_2Enum @ V2a)))))))))))))).
thf(conj_thm_2Ereal__topology_2EBIGINTER__IMAGE,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@(arr@A_27b@bool))) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((ap@(c_2Epred__set_2EBIGINTER@A_27b)@(ap@(ap@(c_2Epred__set_2EIMAGE@A_27a@(arr@A_27b@bool))@V0f)@V1s)) = (ap@(c_2Epred__set_2EGSPEC@A_27b@A_27b)@(lam@A_27b@(^ [V2y:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@V2y)@(ap@(c_2Ebool_2E_21@A_27a)@(lam@A_27a@(^ [V3x:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V3x)@V1s))@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V2y)@(ap@V0f@V3x)))))))))))))))))).
thf(conj_thm_2Ereal__topology_2ECLOSED__IN__IMP__SUBSET,lemma,( ! [A_27a:del]: ( ! [V0top:$i] : ((mem@V0top@(ty_2Etopology_2Etopology@A_27a)) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ( ! [V2t:$i] : ((mem@V2t@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eclosed__in@A_27a)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@A_27a)@V0top)@V1s))@V2t)) => (p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27a)@V2t)@V1s))))))))))).
thf(conj_thm_2Ereal__topology_2EOPEN__BIGUNION,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)) => (( ! [V1s:$i] : ((mem@V1s@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@ty_2Erealax_2Ereal@bool))@V1s)@V0f)) => (p@(ap@c_2Ereal__topology_2EOpen@V1s))))) => (p@(ap@c_2Ereal__topology_2EOpen@(ap@(c_2Epred__set_2EBIGUNION@ty_2Erealax_2Ereal)@V0f))))))).
thf(conj_thm_2Ereal__topology_2ETOPSPACE__EUCLIDEAN__SUBTOPOLOGY,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ((ap@(c_2Etopology_2Etopspace@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V0s)) = V0s)))).
thf(conj_thm_2Ereal__topology_2EBIGINTER__GSPEC,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [A_27d:del]: ( ! [A_27e:del]: ( ! [A_27f:del]: ( ! [A_27g:del]: ( ! [A_27h:del]: ( ! [A_27i:del]: (( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27a@(arr@A_27b@bool))) => ((ap@(c_2Epred__set_2EBIGINTER@A_27b)@(ap@(c_2Epred__set_2EGSPEC@(arr@A_27b@bool)@A_27a)@(lam@A_27a@(^ [V2x:$i] : (ap@(ap@(c_2Epair_2E_2C@(arr@A_27b@bool)@bool)@(ap@V1f@V2x))@(ap@V0P@V2x)))))) = (ap@(c_2Epred__set_2EGSPEC@A_27b@A_27b)@(lam@A_27b@(^ [V3a:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27b@bool)@V3a)@(ap@(c_2Ebool_2E_21@A_27a)@(lam@A_27a@(^ [V4x:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@V0P@V4x))@(ap@(ap@(c_2Ebool_2EIN@A_27b)@V3a)@(ap@V1f@V4x))))))))))))))) & (( ! [V5P:$i] : ((mem@V5P@(arr@A_27c@(arr@A_27d@bool))) => ( ! [V6f:$i] : ((mem@V6f@(arr@A_27c@(arr@A_27d@(arr@A_27e@bool)))) => ((ap@(c_2Epred__set_2EBIGINTER@A_27e)@(ap@(c_2Epred__set_2EGSPEC@(arr@A_27e@bool)@(ty_2Epair_2Eprod@A_27c@A_27d))@(ap@(c_2Epair_2EUNCURRY@A_27c@A_27d@(ty_2Epair_2Eprod@(arr@A_27e@bool)@bool))@(lam@A_27c@(^ [V7x:$i] : (lam@A_27d@(^ [V8y:$i] : (ap@(ap@(c_2Epair_2E_2C@(arr@A_27e@bool)@bool)@(ap@(ap@V6f@V7x)@V8y))@(ap@(ap@V5P@V7x)@V8y))))))))) = (ap@(c_2Epred__set_2EGSPEC@A_27e@A_27e)@(lam@A_27e@(^ [V9a:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27e@bool)@V9a)@(ap@(c_2Ebool_2E_21@A_27c)@(lam@A_27c@(^ [V10x:$i] : (ap@(c_2Ebool_2E_21@A_27d)@(lam@A_27d@(^ [V11y:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@V5P@V10x)@V11y))@(ap@(ap@(c_2Ebool_2EIN@A_27e)@V9a)@(ap@(ap@V6f@V10x)@V11y)))))))))))))))))) & ( ! [V12P:$i] : ((mem@V12P@(arr@A_27f@(arr@A_27g@(arr@A_27h@bool)))) => ( ! [V13f:$i] : ((mem@V13f@(arr@A_27f@(arr@A_27g@(arr@A_27h@(arr@A_27i@bool))))) => ((ap@(c_2Epred__set_2EBIGINTER@A_27i)@(ap@(c_2Epred__set_2EGSPEC@(arr@A_27i@bool)@(ty_2Epair_2Eprod@A_27f@(ty_2Epair_2Eprod@A_27g@A_27h)))@(ap@(c_2Epair_2EUNCURRY@A_27f@(ty_2Epair_2Eprod@A_27g@A_27h)@(ty_2Epair_2Eprod@(arr@A_27i@bool)@bool))@(lam@A_27f@(^ [V14x:$i] : (ap@(c_2Epair_2EUNCURRY@A_27g@A_27h@(ty_2Epair_2Eprod@(arr@A_27i@bool)@bool))@(lam@A_27g@(^ [V15y:$i] : (lam@A_27h@(^ [V16z:$i] : (ap@(ap@(c_2Epair_2E_2C@(arr@A_27i@bool)@bool)@(ap@(ap@(ap@V13f@V14x)@V15y)@V16z))@(ap@(ap@(ap@V12P@V14x)@V15y)@V16z)))))))))))) = (ap@(c_2Epred__set_2EGSPEC@A_27i@A_27i)@(lam@A_27i@(^ [V17a:$i] : (ap@(ap@(c_2Epair_2E_2C@A_27i@bool)@V17a)@(ap@(c_2Ebool_2E_21@A_27f)@(lam@A_27f@(^ [V18x:$i] : (ap@(c_2Ebool_2E_21@A_27g)@(lam@A_27g@(^ [V19y:$i] : (ap@(c_2Ebool_2E_21@A_27h)@(lam@A_27h@(^ [V20z:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@(ap@V12P@V18x)@V19y)@V20z))@(ap@(ap@(c_2Ebool_2EIN@A_27i)@V17a)@(ap@(ap@(ap@V13f@V18x)@V19y)@V20z))))))))))))))))))))))))))))))))).
thf(conj_thm_2Ereal__topology_2EOPEN__IN__OPEN,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1u:$i] : ((mem@V1u@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eopen__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V1u))@V0s)) <=> (? [V2t:$i] : ((mem@V2t@(arr@ty_2Erealax_2Ereal@bool)) & ((p@(ap@c_2Ereal__topology_2EOpen@V2t)) & (V0s = (ap@(ap@(c_2Epred__set_2EINTER@ty_2Erealax_2Ereal)@V1u)@V2t))))))))))).
thf(conj_thm_2Ereal__topology_2EOPEN__IN__OPEN__INTER,lemma,( ! [V0u:$i] : ((mem@V0u@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1s:$i] : ((mem@V1s@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@c_2Ereal__topology_2EOpen@V1s)) => (p@(ap@(ap@(c_2Etopology_2Eopen__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V0u))@(ap@(ap@(c_2Epred__set_2EINTER@ty_2Erealax_2Ereal)@V0u)@V1s))))))))).
thf(conj_thm_2Ereal__topology_2ECLOSED__IN__CLOSED,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1u:$i] : ((mem@V1u@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eclosed__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V1u))@V0s)) <=> (? [V2t:$i] : ((mem@V2t@(arr@ty_2Erealax_2Ereal@bool)) & ((p@(ap@c_2Ereal__topology_2EClosed@V2t)) & (V0s = (ap@(ap@(c_2Epred__set_2EINTER@ty_2Erealax_2Ereal)@V1u)@V2t))))))))))).
thf(conj_thm_2Ereal__topology_2ECLOSED__IN__LIMPT,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eclosed__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V1t))@V0s)) <=> ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@ty_2Erealax_2Ereal)@V0s)@V1t)) & ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal__topology_2Elimit__point__of@(inj__ty_2Erealax_2Ereal @ V2x))@V0s)) & (p@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2x))@V1t))) => (p@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2x))@V0s))))))))))).
thf(conj_thm_2Ereal__topology_2ELIMPT__SEQUENTIAL__INJ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1s:$i] : ((mem@V1s@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@c_2Ereal__topology_2Elimit__point__of@(inj__ty_2Erealax_2Ereal @ V0x))@V1s)) <=> (? [V2f:$i] : ((mem@V2f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & (( ! [V3n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(ap@V2f@(inj__ty_2Enum_2Enum @ V3n)))@(ap@(ap@(c_2Epred__set_2EDELETE@ty_2Erealax_2Ereal)@V1s)@(inj__ty_2Erealax_2Ereal @ V0x))))) & (( ! [V4m:tp__ty_2Enum_2Enum] : ( ! [V5n:tp__ty_2Enum_2Enum] : (((surj__ty_2Erealax_2Ereal @ (ap@V2f@(inj__ty_2Enum_2Enum @ V4m))) = (surj__ty_2Erealax_2Ereal @ (ap@V2f@(inj__ty_2Enum_2Enum @ V5n)))) <=> (V4m = V5n)))) & (p@(ap@(ap@(ap@(c_2Ereal__topology_2E_2D_2D_3E@ty_2Enum_2Enum)@V2f)@(inj__ty_2Erealax_2Ereal @ V0x))@c_2Ereal__topology_2Esequentially))))))))))).
thf(conj_thm_2Ereal__topology_2ESEQ__OFFSET,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2k:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@(ap@(c_2Ereal__topology_2E_2D_2D_3E@ty_2Enum_2Enum)@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@c_2Ereal__topology_2Esequentially)) => (p@(ap@(ap@(ap@(c_2Ereal__topology_2E_2D_2D_3E@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V3i:$i] : (ap@V0f@(ap@(ap@c_2Earithmetic_2E_2B@V3i)@(inj__ty_2Enum_2Enum @ V2k))))))@(inj__ty_2Erealax_2Ereal @ V1l))@c_2Ereal__topology_2Esequentially)))))))).
thf(conj_thm_2Ereal__topology_2ECOMPACT__EQ__HEINE__BOREL,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@c_2Ereal__topology_2Ecompact@V0s)) <=> ( ! [V1f:$i] : ((mem@V1f@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)) => ((( ! [V2t:$i] : ((mem@V2t@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@ty_2Erealax_2Ereal@bool))@V2t)@V1f)) => (p@(ap@c_2Ereal__topology_2EOpen@V2t))))) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@ty_2Erealax_2Ereal)@V0s)@(ap@(c_2Epred__set_2EBIGUNION@ty_2Erealax_2Ereal)@V1f)))) => (? [V3f_27:$i] : ((mem@V3f_27@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)) & ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@(arr@ty_2Erealax_2Ereal@bool))@V3f_27)@V1f)) & ((p@(ap@(c_2Epred__set_2EFINITE@(arr@ty_2Erealax_2Ereal@bool))@V3f_27)) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@ty_2Erealax_2Ereal)@V0s)@(ap@(c_2Epred__set_2EBIGUNION@ty_2Erealax_2Ereal)@V3f_27)))))))))))))).
thf(conj_thm_2Ereal__topology_2ECOMPACT__SEQUENCE__WITH__LIMIT,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1l:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@(ap@(c_2Ereal__topology_2E_2D_2D_3E@ty_2Enum_2Enum)@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@c_2Ereal__topology_2Esequentially)) => (p@(ap@c_2Ereal__topology_2Ecompact@(ap@(ap@(c_2Epred__set_2EINSERT@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1l))@(ap@(ap@(c_2Epred__set_2EIMAGE@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@V0f)@(c_2Epred__set_2EUNIV@ty_2Enum_2Enum)))))))))).
thf(conj_thm_2Ereal__topology_2ECLOSED__INTER__COMPACT,lemma,( ! [V0s:$i] : ((mem@V0s@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1t:$i] : ((mem@V1t@(arr@ty_2Erealax_2Ereal@bool)) => (((p@(ap@c_2Ereal__topology_2EClosed@V0s)) & (p@(ap@c_2Ereal__topology_2Ecompact@V1t))) => (p@(ap@c_2Ereal__topology_2Ecompact@(ap@(ap@(c_2Epred__set_2EINTER@ty_2Erealax_2Ereal)@V0s)@V1t))))))))).
thf(conj_thm_2Ereal__topology_2ECOMPACT__SING,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : (p@(ap@c_2Ereal__topology_2Ecompact@(ap@(ap@(c_2Epred__set_2EINSERT@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(c_2Epred__set_2EEMPTY@ty_2Erealax_2Ereal)))))).
thf(conj_thm_2Ereal__topology_2ECOMPACT__FIP,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)) => ((( ! [V1t:$i] : ((mem@V1t@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Ebool_2EIN@(arr@ty_2Erealax_2Ereal@bool))@V1t)@V0f)) => (p@(ap@c_2Ereal__topology_2Ecompact@V1t))))) & ( ! [V2f_27:$i] : ((mem@V2f_27@(arr@(arr@ty_2Erealax_2Ereal@bool)@bool)) => (((p@(ap@(c_2Epred__set_2EFINITE@(arr@ty_2Erealax_2Ereal@bool))@V2f_27)) & (p@(ap@(ap@(c_2Epred__set_2ESUBSET@(arr@ty_2Erealax_2Ereal@bool))@V2f_27)@V0f))) => (~ ((ap@(c_2Epred__set_2EBIGINTER@ty_2Erealax_2Ereal)@V2f_27) = (c_2Epred__set_2EEMPTY@ty_2Erealax_2Ereal))))))) => (~ ((ap@(c_2Epred__set_2EBIGINTER@ty_2Erealax_2Ereal)@V0f) = (c_2Epred__set_2EEMPTY@ty_2Erealax_2Ereal))))))).
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_2Etopology_2Eclosed__in,axiom,( ! [A_27a:del]: ( ! [V0top:$i] : ((mem@V0top@(ty_2Etopology_2Etopology@A_27a)) => ( ! [V1s:$i] : ((mem@V1s@(arr@A_27a@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eclosed__in@A_27a)@V0top)@V1s)) <=> ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@A_27a)@V1s)@(ap@(c_2Etopology_2Etopspace@A_27a)@V0top))) & (p@(ap@(ap@(c_2Etopology_2Eopen__in@A_27a)@V0top)@(ap@(ap@(c_2Epred__set_2EDIFF@A_27a)@(ap@(c_2Etopology_2Etopspace@A_27a)@V0top))@V1s))))))))))).
thf(conj_thm_2Ereal__topology_2EPROPER__MAP,conjecture,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1s:$i] : ((mem@V1s@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V2t:$i] : ((mem@V2t@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Epred__set_2ESUBSET@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Epred__set_2EIMAGE@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@V0f)@V1s))@V2t)) => (( ! [V3k:$i] : ((mem@V3k@(arr@ty_2Erealax_2Ereal@bool)) => (((p@(ap@(ap@(c_2Epred__set_2ESUBSET@ty_2Erealax_2Ereal)@V3k)@V2t)) & (p@(ap@c_2Ereal__topology_2Ecompact@V3k))) => (p@(ap@c_2Ereal__topology_2Ecompact@(ap@(c_2Epred__set_2EGSPEC@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V4x:$i] : (ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@bool)@V4x)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@V4x)@V1s))@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(ap@V0f@V4x))@V3k))))))))))) <=> (( ! [V5k:$i] : ((mem@V5k@(arr@ty_2Erealax_2Ereal@bool)) => ((p@(ap@(ap@(c_2Etopology_2Eclosed__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V1s))@V5k)) => (p@(ap@(ap@(c_2Etopology_2Eclosed__in@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Ereal__topology_2Esubtopology@ty_2Erealax_2Ereal)@c_2Ereal__topology_2Eeuclidean)@V2t))@(ap@(ap@(c_2Epred__set_2EIMAGE@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@V0f)@V5k)))))) & ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V6a))@V2t)) => (p@(ap@c_2Ereal__topology_2Ecompact@(ap@(c_2Epred__set_2EGSPEC@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V7x:$i] : (ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@bool)@V7x)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@V7x)@V1s))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@V0f@V7x))@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))))))))))).
