include('Axioms/HL4001^2.ax').
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:$i] : ((mem @ X @ ty_2Erealax_2Ereal) => (X = (inj__ty_2Erealax_2Ereal @ (surj__ty_2Erealax_2Ereal @ X)))))).
thf(tp_c_2Ereal_2Ereal__sub,type,(c_2Ereal_2Ereal__sub:$i)).
thf(mem_c_2Ereal_2Ereal__sub,axiom,(mem@c_2Ereal_2Ereal__sub@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Ereal__sub,type,(fo__c_2Ereal_2Ereal__sub:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Ereal__sub,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Ereal__sub @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Ereal__sub @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Epred__set_2EUNIV,type,(c_2Epred__set_2EUNIV:(del>$i))).
thf(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a:del] : (mem@(c_2Epred__set_2EUNIV@A_27a)@(arr@A_27a@bool)))).
thf(tp_c_2Epred__set_2EFINITE,type,(c_2Epred__set_2EFINITE:(del>$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_ty_2Epair_2Eprod,type,( ty_2Epair_2Eprod: del > del >del )).
thf(tp_ty_2Ebool_2Eitself,type,( ty_2Ebool_2Eitself: del >del )).
thf(tp_c_2Ebinary__ieee_2Ethreshold,type,(c_2Ebinary__ieee_2Ethreshold:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Ethreshold,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Ethreshold@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@ty_2Erealax_2Ereal))))).
thf(tp_c_2Erealax_2Ereal__add,type,(c_2Erealax_2Ereal__add:$i)).
thf(mem_c_2Erealax_2Ereal__add,axiom,(mem@c_2Erealax_2Ereal__add@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Erealax_2Ereal__add,type,(fo__c_2Erealax_2Ereal__add:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Erealax_2Ereal__add,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Erealax_2Ereal__add @ X0) @ X1)) = (ap @ (ap @ c_2Erealax_2Ereal__add @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
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:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Ereal_2Epow,type,(c_2Ereal_2Epow:$i)).
thf(mem_c_2Ereal_2Epow,axiom,(mem@c_2Ereal_2Epow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2Epow,type,(fo__c_2Ereal_2Epow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2Epow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2Epow @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2Epow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ereal_2Eabs,type,(c_2Ereal_2Eabs:$i)).
thf(mem_c_2Ereal_2Eabs,axiom,(mem@c_2Ereal_2Eabs@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Eabs,type,(fo__c_2Ereal_2Eabs:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Eabs,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Eabs @ X0)) = (ap @ c_2Ereal_2Eabs @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_ty_2Ebinary__ieee_2Erounding,type,( ty_2Ebinary__ieee_2Erounding:del )).
thf(stp_ty_2Ebinary__ieee_2Erounding,type,(tp__ty_2Ebinary__ieee_2Erounding : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Erounding,type,(inj__ty_2Ebinary__ieee_2Erounding : (tp__ty_2Ebinary__ieee_2Erounding > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Erounding,type,(surj__ty_2Ebinary__ieee_2Erounding : ($i > tp__ty_2Ebinary__ieee_2Erounding))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : ((surj__ty_2Ebinary__ieee_2Erounding @ (inj__ty_2Ebinary__ieee_2Erounding @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Erounding] : (mem @ (inj__ty_2Ebinary__ieee_2Erounding @ X) @ ty_2Ebinary__ieee_2Erounding))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Erounding,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Erounding) => (X = (inj__ty_2Ebinary__ieee_2Erounding @ (surj__ty_2Ebinary__ieee_2Erounding @ X)))))).
thf(tp_c_2Ebinary__ieee_2EroundTiesToEven,type,(c_2Ebinary__ieee_2EroundTiesToEven:$i)).
thf(mem_c_2Ebinary__ieee_2EroundTiesToEven,axiom,(mem@c_2Ebinary__ieee_2EroundTiesToEven@ty_2Ebinary__ieee_2Erounding)).
thf(stp_fo_c_2Ebinary__ieee_2EroundTiesToEven,type,(fo__c_2Ebinary__ieee_2EroundTiesToEven:tp__ty_2Ebinary__ieee_2Erounding)).
thf(stp_eq_fo_c_2Ebinary__ieee_2EroundTiesToEven,axiom,((inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven) = c_2Ebinary__ieee_2EroundTiesToEven)).
thf(tp_c_2Erealax_2Ereal__mul,type,(c_2Erealax_2Ereal__mul:$i)).
thf(mem_c_2Erealax_2Ereal__mul,axiom,(mem@c_2Erealax_2Ereal__mul@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Erealax_2Ereal__mul,type,(fo__c_2Erealax_2Ereal__mul:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Erealax_2Ereal__mul,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Erealax_2Ereal__mul @ X0) @ X1)) = (ap @ (ap @ c_2Erealax_2Ereal__mul @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Elift__ieee_2Enormalizes,type,(c_2Elift__ieee_2Enormalizes:(del>(del>$i)))).
thf(mem_c_2Elift__ieee_2Enormalizes,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Elift__ieee_2Enormalizes@A_27t@A_27w)@(arr@(ty_2Ebool_2Eitself@(ty_2Epair_2Eprod@A_27t@A_27w))@(arr@ty_2Erealax_2Ereal@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:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_c_2Erealax_2Ereal__lt,type,(c_2Erealax_2Ereal__lt:$i)).
thf(mem_c_2Erealax_2Ereal__lt,axiom,(mem@c_2Erealax_2Ereal__lt@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Ereal_2Ereal__lte,type,(c_2Ereal_2Ereal__lte:$i)).
thf(mem_c_2Ereal_2Ereal__lte,axiom,(mem@c_2Ereal_2Ereal__lte@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool)))).
thf(tp_c_2Elift__machine__ieee_2Einterval,type,(c_2Elift__machine__ieee_2Einterval:$i)).
thf(mem_c_2Elift__machine__ieee_2Einterval,axiom,(mem@c_2Elift__machine__ieee_2Einterval@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@bool))))).
thf(tp_ty_2Ebinary__ieee_2Efloat,type,( ty_2Ebinary__ieee_2Efloat: del > del >del )).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real,type,(c_2Ebinary__ieee_2Efloat__to__real:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@ty_2Erealax_2Ereal))))).
thf(tp_ty_2Eone_2Eone,type,( ty_2Eone_2Eone:del )).
thf(stp_ty_2Eone_2Eone,type,(tp__ty_2Eone_2Eone : $tType)).
thf(stp_inj_ty_2Eone_2Eone,type,(inj__ty_2Eone_2Eone : (tp__ty_2Eone_2Eone > $i))).
thf(stp_surj_ty_2Eone_2Eone,type,(surj__ty_2Eone_2Eone : ($i > tp__ty_2Eone_2Eone))).
thf(stp_inj_surj_ty_2Eone_2Eone,axiom,( ! [X:tp__ty_2Eone_2Eone] : ((surj__ty_2Eone_2Eone @ (inj__ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_ty_2Eone_2Eone,axiom,( ! [X:tp__ty_2Eone_2Eone] : (mem @ (inj__ty_2Eone_2Eone @ X) @ ty_2Eone_2Eone))).
thf(stp_iso_mem_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ ty_2Eone_2Eone) => (X = (inj__ty_2Eone_2Eone @ (surj__ty_2Eone_2Eone @ X)))))).
thf(tp_ty_2Efcp_2Ebit0,type,( ty_2Efcp_2Ebit0: del >del )).
thf(tp_ty_2Efcp_2Ecart,type,( ty_2Efcp_2Ecart: del > del >del )).
thf(stp_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))) => (X = (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))) => (X = (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))) => (X = (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))) => (X = (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))) => (X = (inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit0@ty_2Eone_2Eone)) => (X = (inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(tp_c_2Emachine__ieee_2Efp32__to__real,type,(c_2Emachine__ieee_2Efp32__to__real:$i)).
thf(mem_c_2Emachine__ieee_2Efp32__to__real,axiom,(mem@c_2Emachine__ieee_2Efp32__to__real@(arr@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Emachine__ieee_2Efp32__to__real,type,(fo__c_2Emachine__ieee_2Efp32__to__real:(tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Emachine__ieee_2Efp32__to__real,axiom,( ! [X0:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Emachine__ieee_2Efp32__to__real @ X0)) = (ap @ c_2Emachine__ieee_2Efp32__to__real @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X0))))).
thf(tp_c_2Ebinary__ieee_2Efloat__is__finite,type,(c_2Ebinary__ieee_2Efloat__is__finite:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__is__finite,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__is__finite@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@bool))))).
thf(tp_c_2Ecombin_2Eo,type,(c_2Ecombin_2Eo:(del>(del>(del>$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_c_2Emachine__ieee_2Efp32__isFinite,type,(c_2Emachine__ieee_2Efp32__isFinite:$i)).
thf(mem_c_2Emachine__ieee_2Efp32__isFinite,axiom,(mem@c_2Emachine__ieee_2Efp32__isFinite@(arr@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@bool))).
thf(tp_ty_2Ebinary__ieee_2Eflags,type,( ty_2Ebinary__ieee_2Eflags:del )).
thf(stp_ty_2Ebinary__ieee_2Eflags,type,(tp__ty_2Ebinary__ieee_2Eflags : $tType)).
thf(stp_inj_ty_2Ebinary__ieee_2Eflags,type,(inj__ty_2Ebinary__ieee_2Eflags : (tp__ty_2Ebinary__ieee_2Eflags > $i))).
thf(stp_surj_ty_2Ebinary__ieee_2Eflags,type,(surj__ty_2Ebinary__ieee_2Eflags : ($i > tp__ty_2Ebinary__ieee_2Eflags))).
thf(stp_inj_surj_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : ((surj__ty_2Ebinary__ieee_2Eflags @ (inj__ty_2Ebinary__ieee_2Eflags @ X)) = X))).
thf(stp_inj_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:tp__ty_2Ebinary__ieee_2Eflags] : (mem @ (inj__ty_2Ebinary__ieee_2Eflags @ X) @ ty_2Ebinary__ieee_2Eflags))).
thf(stp_iso_mem_ty_2Ebinary__ieee_2Eflags,axiom,( ! [X:$i] : ((mem @ X @ ty_2Ebinary__ieee_2Eflags) => (X = (inj__ty_2Ebinary__ieee_2Eflags @ (surj__ty_2Ebinary__ieee_2Eflags @ X)))))).
thf(tp_c_2Ebinary__ieee_2Efloat__mul,type,(c_2Ebinary__ieee_2Efloat__mul:(del>(del>$i)))).
thf(mem_c_2Ebinary__ieee_2Efloat__mul,axiom,( ! [A_27t:del] : ( ! [A_27w:del] : (mem@(c_2Ebinary__ieee_2Efloat__mul@A_27t@A_27w)@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(arr@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)@(ty_2Epair_2Eprod@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))))))))).
thf(tp_c_2Epair_2ESND,type,(c_2Epair_2ESND:(del>(del>$i)))).
thf(mem_c_2Epair_2ESND,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2Epair_2ESND@A_27a@A_27b)@(arr@(ty_2Epair_2Eprod@A_27a@A_27b)@A_27b))))).
thf(tp_c_2Emachine__ieee_2Efp32__mul,type,(c_2Emachine__ieee_2Efp32__mul:$i)).
thf(mem_c_2Emachine__ieee_2Efp32__mul,axiom,(mem@c_2Emachine__ieee_2Efp32__mul@(arr@ty_2Ebinary__ieee_2Erounding@(arr@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(arr@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))))))).
thf(tp_ty_2Efcp_2Ebit1,type,( ty_2Efcp_2Ebit1: del >del )).
thf(stp_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))).
thf(stp_iso_mem_c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))) => (X = (inj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))) => (X = (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))) => (X = (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))) => (X = (inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(tp_c_2Emachine__ieee_2Efloat__to__fp32,type,(c_2Emachine__ieee_2Efloat__to__fp32:$i)).
thf(mem_c_2Emachine__ieee_2Efloat__to__fp32,axiom,(mem@c_2Emachine__ieee_2Efloat__to__fp32@(arr@(ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))))).
thf(tp_c_2Emachine__ieee_2Efp32__to__float,type,(c_2Emachine__ieee_2Efp32__to__float:$i)).
thf(mem_c_2Emachine__ieee_2Efp32__to__float,axiom,(mem@c_2Emachine__ieee_2Efp32__to__float@(arr@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$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_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$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:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2EiiSUC,type,(c_2Enumeral_2EiiSUC:$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_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X0)) = (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$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_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_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2B @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
thf(mem_c_2Ebool_2EF,axiom,(mem@c_2Ebool_2EF@bool)).
thf(ax_false_p,axiom,(~ (p@c_2Ebool_2EF))).
thf(tp_c_2Enumeral_2EiSUB,type,(c_2Enumeral_2EiSUB:$i)).
thf(mem_c_2Enumeral_2EiSUB,axiom,(mem@c_2Enumeral_2EiSUB@(arr@bool@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$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_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:(del>$i))).
thf(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2ECOND@A_27a)@(arr@bool@(arr@A_27a@(arr@A_27a@A_27a)))))).
thf(tp_c_2Ebit_2ETIMES__2EXP,type,(c_2Ebit_2ETIMES__2EXP:$i)).
thf(mem_c_2Ebit_2ETIMES__2EXP,axiom,(mem@c_2Ebit_2ETIMES__2EXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Ebit_2ETIMES__2EXP,type,(fo__c_2Ebit_2ETIMES__2EXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Ebit_2ETIMES__2EXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Ebit_2ETIMES__2EXP @ X0) @ X1)) = (ap @ (ap @ c_2Ebit_2ETIMES__2EXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Enumeral__bit_2ESFUNPOW,type,(c_2Enumeral__bit_2ESFUNPOW:$i)).
thf(mem_c_2Enumeral__bit_2ESFUNPOW,axiom,(mem@c_2Enumeral__bit_2ESFUNPOW@(arr@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(tp_c_2Enumeral_2EiDUB,type,(c_2Enumeral_2EiDUB:$i)).
thf(mem_c_2Enumeral_2EiDUB,axiom,(mem@c_2Enumeral_2EiDUB@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiDUB,type,(fo__c_2Enumeral_2EiDUB:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiDUB @ X0)) = (ap @ c_2Enumeral_2EiDUB @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral__bit_2EiSUC,type,(c_2Enumeral__bit_2EiSUC:$i)).
thf(mem_c_2Enumeral__bit_2EiSUC,axiom,(mem@c_2Enumeral__bit_2EiSUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral__bit_2EiSUC,type,(fo__c_2Enumeral__bit_2EiSUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral__bit_2EiSUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral__bit_2EiSUC @ X0)) = (ap @ c_2Enumeral__bit_2EiSUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral__bit_2EFDUB,type,(c_2Enumeral__bit_2EFDUB:$i)).
thf(mem_c_2Enumeral__bit_2EFDUB,axiom,(mem@c_2Enumeral__bit_2EFDUB@(arr@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$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_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Epair_2E_2C,type,(c_2Epair_2E_2C:(del>(del>$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_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:$i] : ((mem@X@A) & (p@(ap@Q@X))))))))).
thf(tp_c_2Epred__set_2EGSPEC,type,(c_2Epred__set_2EGSPEC:(del>(del>$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_c_2Ebool_2EIN,type,(c_2Ebool_2EIN:(del>$i))).
thf(mem_c_2Ebool_2EIN,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2EIN@A_27a)@(arr@A_27a@(arr@(arr@A_27a@bool)@bool))))).
thf(tp_c_2Ereal_2Ereal__of__num,type,(c_2Ereal_2Ereal__of__num:$i)).
thf(mem_c_2Ereal_2Ereal__of__num,axiom,(mem@c_2Ereal_2Ereal__of__num@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Ereal_2Ereal__of__num,type,(fo__c_2Ereal_2Ereal__of__num:(tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Ereal_2Ereal__of__num @ X0)) = (ap @ c_2Ereal_2Ereal__of__num @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ereal_2E_2F,type,(c_2Ereal_2E_2F:$i)).
thf(mem_c_2Ereal_2E_2F,axiom,(mem@c_2Ereal_2E_2F@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Ereal_2E_2F,type,(fo__c_2Ereal_2E_2F:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Ereal_2E_2F,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Ereal_2E_2F @ X0) @ X1)) = (ap @ (ap @ c_2Ereal_2E_2F @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Erealax_2Einv,type,(c_2Erealax_2Einv:$i)).
thf(mem_c_2Erealax_2Einv,axiom,(mem@c_2Erealax_2Einv@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Erealax_2Einv,type,(fo__c_2Erealax_2Einv:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Erealax_2Einv,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Erealax_2Einv @ X0)) = (ap @ c_2Erealax_2Einv @ (inj__ty_2Erealax_2Ereal @ X0))))).
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:$i] : ((mem@X@A) => (p@(ap@Q@X))))))))).
thf(tp_c_2Efcp_2Edimindex,type,(c_2Efcp_2Edimindex:(del>$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_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EEXP @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EEXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Ewords_2EUINT__MAX,type,(c_2Ewords_2EUINT__MAX:(del>$i))).
thf(mem_c_2Ewords_2EUINT__MAX,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2EUINT__MAX@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
thf(mem_c_2Earithmetic_2EBIT1,axiom,(mem@c_2Earithmetic_2EBIT1@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X0)) = (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$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_2Ewords_2EINT__MAX,type,(c_2Ewords_2EINT__MAX:(del>$i))).
thf(mem_c_2Ewords_2EINT__MAX,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2EINT__MAX@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Ewords_2EINT__MIN,type,(c_2Ewords_2EINT__MIN:(del>$i))).
thf(mem_c_2Ewords_2EINT__MIN,axiom,( ! [A_27a:del] : (mem@(c_2Ewords_2EINT__MIN@A_27a)@(arr@(ty_2Ebool_2Eitself@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$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_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X0)) = (ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$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_2Ebool_2Ethe__value,type,(c_2Ebool_2Ethe__value:(del>$i))).
thf(mem_c_2Ebool_2Ethe__value,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2Ethe__value@A_27a)@(ty_2Ebool_2Eitself@A_27a)))).
thf(tp_c_2Ewords_2Edimword,type,(c_2Ewords_2Edimword:(del>$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_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(conj_thm_2Earithmetic_2ENORM__0,lemma,((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Enum_2E0)).
thf(conj_thm_2Earithmetic_2EMULT__LEFT__1,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ((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))).
thf(conj_thm_2Earithmetic_2ETIMES2,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V0n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(ax_thm_2Ebinary__ieee_2Ethreshold__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ((surj__ty_2Erealax_2Ereal @ (ap@(c_2Ebinary__ieee_2Ethreshold@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2EUINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Ewords_2EINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Enum_2ESUC@(ap@(c_2Efcp_2Edimindex@A_27t)@(c_2Ebool_2Ethe__value@A_27t)))))))))))).
thf(ax_thm_2Ebit_2ETIMES__2EXP__def,axiom,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Ebit_2ETIMES__2EXP@(inj__ty_2Enum_2Enum @ V0x))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V1n))@(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 @ V0x)))))))).
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:$i] : (ap@V0t@V1x))) = V0t)))))).
thf(conj_thm_2Ebool_2ETRUTH,lemma,$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_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_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) <=> $false) & (((p@V0t) & (p@V0t)) <=> (p@V0t))))))))).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,( ! [V0t:$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)) <=> $true)))).
thf(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,( ! [V0t:$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:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,( ! [V0t1:$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_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_2Efcp_2Eindex__bit0,lemma,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Efcp_2Edimindex@(ty_2Efcp_2Ebit0@A_27a))@(c_2Ebool_2Ethe__value@(ty_2Efcp_2Ebit0@A_27a)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a)))@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(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)))))))).
thf(conj_thm_2Efcp_2Efinite__bit0,lemma,( ! [A_27a:del]: ((p@(ap@(c_2Epred__set_2EFINITE@(ty_2Efcp_2Ebit0@A_27a))@(c_2Epred__set_2EUNIV@(ty_2Efcp_2Ebit0@A_27a)))) <=> (p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a)))))).
thf(conj_thm_2Efcp_2Eindex__bit1,lemma,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Efcp_2Edimindex@(ty_2Efcp_2Ebit1@A_27a))@(c_2Ebool_2Ethe__value@(ty_2Efcp_2Ebit1@A_27a)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a)))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(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)))))))).
thf(conj_thm_2Efcp_2Efinite__bit1,lemma,( ! [A_27a:del]: ((p@(ap@(c_2Epred__set_2EFINITE@(ty_2Efcp_2Ebit1@A_27a))@(c_2Epred__set_2EUNIV@(ty_2Efcp_2Ebit1@A_27a)))) <=> (p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a)))))).
thf(conj_thm_2Efcp_2Eindex__one,lemma,((surj__ty_2Enum_2Enum @ (ap@(c_2Efcp_2Edimindex@ty_2Eone_2Eone)@(c_2Ebool_2Ethe__value@ty_2Eone_2Eone))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))).
thf(conj_thm_2Efcp_2Efinite__one,lemma,(p@(ap@(c_2Epred__set_2EFINITE@ty_2Eone_2Eone)@(c_2Epred__set_2EUNIV@ty_2Eone_2Eone)))).
thf(ax_thm_2Elift__ieee_2Enormalizes__def,axiom,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@(c_2Elift__ieee_2Enormalizes@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))@(inj__ty_2Erealax_2Ereal @ V0x))) <=> ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Ewords_2EINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2EINT__MAX@A_27w)@(c_2Ebool_2Ethe__value@A_27w)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(c_2Ebinary__ieee_2Ethreshold@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))))))))))).
thf(conj_thm_2Elift__ieee_2Efloat__mul__relative,lemma,( ! [A_27t:del]: ( ! [A_27w:del]: ( ! [V0a:$i] : ((mem@V0a@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => ( ! [V1b:$i] : ((mem@V1b@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w)) => (((p@(ap@(c_2Ebinary__ieee_2Efloat__is__finite@A_27t@A_27w)@V0a)) & ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__finite@A_27t@A_27w)@V1b)) & (p@(ap@(ap@(c_2Elift__ieee_2Enormalizes@A_27t@A_27w)@(c_2Ebool_2Ethe__value@(ty_2Epair_2Eprod@A_27t@A_27w)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@V0a))@(ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@V1b)))))) => ((p@(ap@(c_2Ebinary__ieee_2Efloat__is__finite@A_27t@A_27w)@(ap@(c_2Epair_2ESND@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__mul@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven))@V0a)@V1b)))) & (? [V2e:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2e)))@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(c_2Efcp_2Edimindex@A_27t)@(c_2Ebool_2Ethe__value@A_27t)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@(ap@(c_2Epair_2ESND@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@A_27t@A_27w))@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__mul@A_27t@A_27w)@(inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven))@V0a)@V1b)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@V0a))@(ap@(c_2Ebinary__ieee_2Efloat__to__real@A_27t@A_27w)@V1b)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V2e)))))))))))))))).
thf(ax_thm_2Elift__machine__ieee_2Einterval__def,axiom,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((ap@(ap@c_2Elift__machine__ieee_2Einterval@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)) = (ap@(c_2Epred__set_2EGSPEC@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V2x:$i] : (ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@bool)@V2x)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@V2x))@(ap@(ap@c_2Erealax_2Ereal__lt@V2x)@(inj__ty_2Erealax_2Ereal @ V1b))))))))))).
thf(ax_thm_2Emachine__ieee_2Efp32__to__real__def,axiom,(c_2Emachine__ieee_2Efp32__to__real = (ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@ty_2Erealax_2Ereal@(ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@(c_2Ebinary__ieee_2Efloat__to__real@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@c_2Emachine__ieee_2Efp32__to__float))).
thf(ax_thm_2Emachine__ieee_2Efp32__isFinite__def,axiom,(c_2Emachine__ieee_2Efp32__isFinite = (ap@(ap@(c_2Ecombin_2Eo@(ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@bool@(ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@(c_2Ebinary__ieee_2Efloat__is__finite@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@c_2Emachine__ieee_2Efp32__to__float))).
thf(ax_thm_2Emachine__ieee_2Efp32__mul__def,axiom,( ! [V0mode:tp__ty_2Ebinary__ieee_2Erounding] : ( ! [V1a:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( ! [V2b:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(ap@(ap@c_2Emachine__ieee_2Efp32__mul@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1a))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V2b))) = (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@c_2Emachine__ieee_2Efloat__to__fp32@(ap@(c_2Epair_2ESND@ty_2Ebinary__ieee_2Eflags@(ty_2Ebinary__ieee_2Efloat@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@(ap@(ap@(ap@(c_2Ebinary__ieee_2Efloat__mul@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__ty_2Ebinary__ieee_2Erounding @ V0mode))@(ap@c_2Emachine__ieee_2Efp32__to__float@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1a)))@(ap@c_2Emachine__ieee_2Efp32__to__float@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V2b))))))))))).
thf(conj_thm_2Emachine__ieee_2Efp32__to__float__float__to__fp32,lemma,( ! [V0x:tp__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@c_2Emachine__ieee_2Efp32__to__float@(ap@c_2Emachine__ieee_2Efloat__to__fp32@(inj__c_ty_2Ebinary__ieee_2Efloat_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x)))) = V0x))).
thf(conj_thm_2Enumeral_2Enumeral__suc,lemma,(((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
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))) <=> $false) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(ax_thm_2Enumeral_2EiDUB,axiom,( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0x))@(inj__ty_2Enum_2Enum @ V0x)))))).
thf(conj_thm_2Enumeral_2EiSUB__THM,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@V1b)@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0x))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = V2n) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__sub,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Enumeral_2EiDUB__removal,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0n))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) & ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO))))).
thf(conj_thm_2Enumeral__bit_2EiDUB__NUMERAL,lemma,( ! [V0i:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V0i)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0i))))))).
thf(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Ebit_2ETIMES__2EXP@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Ebit_2ETIMES__2EXP@(inj__ty_2Enum_2Enum @ V1n))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V2x)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@c_2Enumeral_2EiDUB)@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V2x))))))))).
thf(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB,lemma,(( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@c_2Enumeral_2EiDUB)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0x))) = V0x)) & (( ! [V1y:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@c_2Enumeral_2EiDUB)@(inj__ty_2Enum_2Enum @ V1y))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@c_2Enumeral_2EiDUB)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n))))@(inj__ty_2Enum_2Enum @ V3x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@c_2Enumeral_2EiDUB))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V3x))))))) & ( ! [V4n:tp__ty_2Enum_2Enum] : ( ! [V5x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@c_2Enumeral_2EiDUB)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V4n))))@(inj__ty_2Enum_2Enum @ V5x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@c_2Enumeral_2EiDUB))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V4n)))@(ap@c_2Enumeral_2EiDUB@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V5x)))))))))))).
thf(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)) => (( ! [V1x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1x))) = V1x)) & (( ! [V2y:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(inj__ty_2Enum_2Enum @ V2y))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V3n:tp__ty_2Enum_2Enum] : ( ! [V4x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3n))))@(inj__ty_2Enum_2Enum @ V4x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V3n)))@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(inj__ty_2Enum_2Enum @ V4x))))))) & ( ! [V5n:tp__ty_2Enum_2Enum] : ( ! [V6x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V5n))))@(inj__ty_2Enum_2Enum @ V6x))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral__bit_2ESFUNPOW@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V5n)))@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(inj__ty_2Enum_2Enum @ V6x)))))))))))))).
thf(conj_thm_2Enumeral__bit_2EFDUB__iDUB,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@c_2Enumeral_2EiDUB)@(inj__ty_2Enum_2Enum @ V0x))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0x))))))).
thf(conj_thm_2Enumeral__bit_2EFDUB__FDUB,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)) => (((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO) & (( ! [V1x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(ap@c_2Enumeral__bit_2EiSUC@(inj__ty_2Enum_2Enum @ V1x)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@c_2Enumeral__bit_2EiSUC@(inj__ty_2Enum_2Enum @ V1x))))))) & (( ! [V2x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2x)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2x))))))) & ( ! [V3x:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@(ap@c_2Enumeral__bit_2EFDUB@V0f))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3x)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@(ap@c_2Enumeral__bit_2EFDUB@V0f)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3x))))))))))))).
thf(conj_thm_2Epair_2EPAIR__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(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_2Ereal_2EREAL__INV__1OVER,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(ax_thm_2Ewords_2EINT__MIN__def,axiom,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2EINT__MIN@A_27a)@(c_2Ebool_2Ethe__value@A_27a))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(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))))))))).
thf(ax_thm_2Ewords_2EUINT__MAX__def,axiom,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2EUINT__MAX@A_27a)@(c_2Ebool_2Ethe__value@A_27a))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(ax_thm_2Ewords_2EINT__MAX__def,axiom,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2EINT__MAX@A_27a)@(c_2Ebool_2Ethe__value@A_27a))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@(c_2Ewords_2EINT__MIN@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Ewords_2Edimword__IS__TWICE__INT__MIN,lemma,( ! [A_27a:del]: ((surj__ty_2Enum_2Enum @ (ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Ewords_2EINT__MIN@A_27a)@(c_2Ebool_2Ethe__value@A_27a))))))).
thf(conj_thm_2Elift__machine__ieee_2Efp32__float__mul__relative,conjecture,( ! [V0a:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( ! [V1b:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (((p@(ap@c_2Emachine__ieee_2Efp32__isFinite@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0a))) & ((p@(ap@c_2Emachine__ieee_2Efp32__isFinite@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1b))) & (p@(ap@(ap@(c_2Ebool_2EIN@ty_2Erealax_2Ereal)@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Emachine__ieee_2Efp32__to__real@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0a)))@(ap@c_2Emachine__ieee_2Efp32__to__real@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1b)))))@(ap@(ap@c_2Elift__machine__ieee_2Einterval@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))) => ((p@(ap@c_2Emachine__ieee_2Efp32__isFinite@(ap@(ap@(ap@c_2Emachine__ieee_2Efp32__mul@(inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0a))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1b)))) & (? [V2e:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2e)))@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Emachine__ieee_2Efp32__to__real@(ap@(ap@(ap@c_2Emachine__ieee_2Efp32__mul@(inj__ty_2Ebinary__ieee_2Erounding @ fo__c_2Ebinary__ieee_2EroundTiesToEven))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0a))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1b)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Emachine__ieee_2Efp32__to__real@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0a)))@(ap@c_2Emachine__ieee_2Efp32__to__real@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V1b))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V2e)))))))))))).
