include('Axioms/powser^2.ax').
thf(tp_c_2Etransc_2EDint,type,(c_2Etransc_2EDint:$i)).
thf(mem_c_2Etransc_2EDint,axiom,(mem@c_2Etransc_2EDint@(arr@(ty_2Epair_2Eprod@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(arr@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(arr@ty_2Erealax_2Ereal@bool))))).
thf(tp_c_2Etransc_2Eacs,type,(c_2Etransc_2Eacs:$i)).
thf(mem_c_2Etransc_2Eacs,axiom,(mem@c_2Etransc_2Eacs@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Eacs,type,(fo__c_2Etransc_2Eacs:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Eacs,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Eacs @ X0)) = (ap @ c_2Etransc_2Eacs @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Easn,type,(c_2Etransc_2Easn:$i)).
thf(mem_c_2Etransc_2Easn,axiom,(mem@c_2Etransc_2Easn@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Easn,type,(fo__c_2Etransc_2Easn:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Easn,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Easn @ X0)) = (ap @ c_2Etransc_2Easn @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Eatn,type,(c_2Etransc_2Eatn:$i)).
thf(mem_c_2Etransc_2Eatn,axiom,(mem@c_2Etransc_2Eatn@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Eatn,type,(fo__c_2Etransc_2Eatn:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Eatn,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Eatn @ X0)) = (ap @ c_2Etransc_2Eatn @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Ecos,type,(c_2Etransc_2Ecos:$i)).
thf(mem_c_2Etransc_2Ecos,axiom,(mem@c_2Etransc_2Ecos@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Ecos,type,(fo__c_2Etransc_2Ecos:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Ecos,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Ecos @ X0)) = (ap @ c_2Etransc_2Ecos @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Edivision,type,(c_2Etransc_2Edivision:$i)).
thf(mem_c_2Etransc_2Edivision,axiom,(mem@c_2Etransc_2Edivision@(arr@(ty_2Epair_2Eprod@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(arr@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@bool)))).
thf(tp_c_2Etransc_2Edsize,type,(c_2Etransc_2Edsize:$i)).
thf(mem_c_2Etransc_2Edsize,axiom,(mem@c_2Etransc_2Edsize@(arr@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@ty_2Enum_2Enum))).
thf(tp_c_2Etransc_2Eexp,type,(c_2Etransc_2Eexp:$i)).
thf(mem_c_2Etransc_2Eexp,axiom,(mem@c_2Etransc_2Eexp@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Eexp,type,(fo__c_2Etransc_2Eexp:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Eexp,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Eexp @ X0)) = (ap @ c_2Etransc_2Eexp @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Efine,type,(c_2Etransc_2Efine:$i)).
thf(mem_c_2Etransc_2Efine,axiom,(mem@c_2Etransc_2Efine@(arr@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(arr@(ty_2Epair_2Eprod@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@bool)))).
thf(tp_c_2Etransc_2Egauge,type,(c_2Etransc_2Egauge:$i)).
thf(mem_c_2Etransc_2Egauge,axiom,(mem@c_2Etransc_2Egauge@(arr@(arr@ty_2Erealax_2Ereal@bool)@(arr@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@bool)))).
thf(tp_c_2Etransc_2Eln,type,(c_2Etransc_2Eln:$i)).
thf(mem_c_2Etransc_2Eln,axiom,(mem@c_2Etransc_2Eln@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Eln,type,(fo__c_2Etransc_2Eln:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Eln,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Eln @ X0)) = (ap @ c_2Etransc_2Eln @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Epi,type,(c_2Etransc_2Epi:$i)).
thf(mem_c_2Etransc_2Epi,axiom,(mem@c_2Etransc_2Epi@ty_2Erealax_2Ereal)).
thf(stp_fo_c_2Etransc_2Epi,type,(fo__c_2Etransc_2Epi:tp__ty_2Erealax_2Ereal)).
thf(stp_eq_fo_c_2Etransc_2Epi,axiom,((inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi) = c_2Etransc_2Epi)).
thf(tp_c_2Etransc_2Eroot,type,(c_2Etransc_2Eroot:$i)).
thf(mem_c_2Etransc_2Eroot,axiom,(mem@c_2Etransc_2Eroot@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Etransc_2Eroot,type,(fo__c_2Etransc_2Eroot:(tp__ty_2Enum_2Enum > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Etransc_2Eroot,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Etransc_2Eroot @ X0) @ X1)) = (ap @ (ap @ c_2Etransc_2Eroot @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Etransc_2Erpow,type,(c_2Etransc_2Erpow:$i)).
thf(mem_c_2Etransc_2Erpow,axiom,(mem@c_2Etransc_2Erpow@(arr@ty_2Erealax_2Ereal@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)))).
thf(stp_fo_c_2Etransc_2Erpow,type,(fo__c_2Etransc_2Erpow:(tp__ty_2Erealax_2Ereal > (tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal)))).
thf(stp_eq_fo_c_2Etransc_2Erpow,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ( ! [X1:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ ((fo__c_2Etransc_2Erpow @ X0) @ X1)) = (ap @ (ap @ c_2Etransc_2Erpow @ (inj__ty_2Erealax_2Ereal @ X0)) @ (inj__ty_2Erealax_2Ereal @ X1)))))).
thf(tp_c_2Etransc_2Ersum,type,(c_2Etransc_2Ersum:$i)).
thf(mem_c_2Etransc_2Ersum,axiom,(mem@c_2Etransc_2Ersum@(arr@(ty_2Epair_2Eprod@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@(arr@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@ty_2Erealax_2Ereal)))).
thf(tp_c_2Etransc_2Esin,type,(c_2Etransc_2Esin:$i)).
thf(mem_c_2Etransc_2Esin,axiom,(mem@c_2Etransc_2Esin@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Esin,type,(fo__c_2Etransc_2Esin:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Esin,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Esin @ X0)) = (ap @ c_2Etransc_2Esin @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Esqrt,type,(c_2Etransc_2Esqrt:$i)).
thf(mem_c_2Etransc_2Esqrt,axiom,(mem@c_2Etransc_2Esqrt@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Esqrt,type,(fo__c_2Etransc_2Esqrt:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Esqrt,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Esqrt @ X0)) = (ap @ c_2Etransc_2Esqrt @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Etan,type,(c_2Etransc_2Etan:$i)).
thf(mem_c_2Etransc_2Etan,axiom,(mem@c_2Etransc_2Etan@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))).
thf(stp_fo_c_2Etransc_2Etan,type,(fo__c_2Etransc_2Etan:(tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal))).
thf(stp_eq_fo_c_2Etransc_2Etan,axiom,( ! [X0:tp__ty_2Erealax_2Ereal] : ((inj__ty_2Erealax_2Ereal @ (fo__c_2Etransc_2Etan @ X0)) = (ap @ c_2Etransc_2Etan @ (inj__ty_2Erealax_2Ereal @ X0))))).
thf(tp_c_2Etransc_2Etdiv,type,(c_2Etransc_2Etdiv:$i)).
thf(mem_c_2Etransc_2Etdiv,axiom,(mem@c_2Etransc_2Etdiv@(arr@(ty_2Epair_2Eprod@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(arr@(ty_2Epair_2Eprod@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@bool)))).
thf(ax_thm_2Etransc_2Eexp,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Eseq_2Esuminf@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n)))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n))))))))).
thf(ax_thm_2Etransc_2Ecos,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Eseq_2Esuminf@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2EDIV@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n))))))))).
thf(ax_thm_2Etransc_2Esin,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Eseq_2Esuminf@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2EDIV@(ap@(ap@c_2Earithmetic_2E_2D@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n))))))))).
thf(conj_thm_2Etransc_2EEXP__CONVERGES,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2Esums@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n)))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n)))))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ESIN__CONVERGES,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2Esums@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2EDIV@(ap@(ap@c_2Earithmetic_2E_2D@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n)))))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ECOS__CONVERGES,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2Esums@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2EDIV@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n)))))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EEXP__FDIFF,lemma,((ap@c_2Epowser_2Ediffs@(lam@ty_2Enum_2Enum@(^ [V0n:$i] : (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V0n)))))) = (lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@c_2Erealax_2Einv@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V1n))))))).
thf(conj_thm_2Etransc_2ESIN__FDIFF,lemma,((ap@c_2Epowser_2Ediffs@(lam@ty_2Enum_2Enum@(^ [V0n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V0n))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(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_2Earithmetic_2EDIV@(ap@(ap@c_2Earithmetic_2E_2D@V0n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V0n))))))) = (lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V1n))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@c_2Earithmetic_2EDIV@V1n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V1n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Etransc_2ECOS__FDIFF,lemma,((ap@c_2Epowser_2Ediffs@(lam@ty_2Enum_2Enum@(^ [V0n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V0n))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(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_2Earithmetic_2EDIV@V0n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V0n))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) = (lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@c_2Erealax_2Ereal__neg@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(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_2Earithmetic_2EDIV@(ap@(ap@c_2Earithmetic_2E_2D@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))))@V1n)))))).
thf(conj_thm_2Etransc_2ESIN__NEGLEMMA,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Eseq_2Esuminf@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@c_2Earithmetic_2EEVEN@V2n))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(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_2Earithmetic_2EDIV@(ap@(ap@c_2Earithmetic_2E_2D@V2n)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V2n))))))@V1n))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V1n)))))))))).
thf(conj_thm_2Etransc_2EDIFF__EXP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Eexp)@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x))))).
thf(conj_thm_2Etransc_2EDIFF__SIN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Esin)@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x))))).
thf(conj_thm_2Etransc_2EDIFF__COS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Ecos)@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))@(inj__ty_2Erealax_2Ereal @ V0x))))).
thf(conj_thm_2Etransc_2EDIFF__COMPOSITE,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1l:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3g:$i] : ((mem@V3g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V4m:tp__ty_2Erealax_2Ereal] : ( ! [V5n:tp__ty_2Enum_2Enum] : ((((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) & (~~ ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Erealax_2Ereal @ V2x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V6x:$i] : (ap@c_2Erealax_2Einv@(ap@V0f@V6x)))))@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1l))@(ap@(ap@c_2Ereal_2Epow@(ap@V0f@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V2x)))) & ((((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) & ((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x))) & (~~ ((surj__ty_2Erealax_2Ereal @ (ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V7x:$i] : (ap@(ap@c_2Ereal_2E_2F@(ap@V0f@V7x))@(ap@V3g@V7x)))))@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1l))@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4m))@(ap@V0f@(inj__ty_2Erealax_2Ereal @ V2x)))))@(ap@(ap@c_2Ereal_2Epow@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V2x)))) & ((((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) & (p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x)))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V8x:$i] : (ap@(ap@c_2Erealax_2Ereal__add@(ap@V0f@V8x))@(ap@V3g@V8x)))))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & ((((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) & (p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x)))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V9x:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@V0f@V9x))@(ap@V3g@V9x)))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1l))@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x))))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4m))@(ap@V0f@(inj__ty_2Erealax_2Ereal @ V2x)))))@(inj__ty_2Erealax_2Ereal @ V2x)))) & ((((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) & (p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x)))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V10x:$i] : (ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0f@V10x))@(ap@V3g@V10x)))))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & (((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(inj__ty_2Erealax_2Ereal @ V1l))@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V11x:$i] : (ap@c_2Erealax_2Ereal__neg@(ap@V0f@V11x)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1l)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & (((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V12x:$i] : (ap@(ap@c_2Ereal_2Epow@(ap@V3g@V12x))@(inj__ty_2Enum_2Enum @ V5n)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V5n)))@(ap@(ap@c_2Ereal_2Epow@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V5n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & (((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V13x:$i] : (ap@c_2Etransc_2Eexp@(ap@V3g@V13x)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Eexp@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x))))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & (((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V14x:$i] : (ap@c_2Etransc_2Esin@(ap@V3g@V14x)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Ecos@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x))))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))) & ((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V3g)@(inj__ty_2Erealax_2Ereal @ V4m))@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V15x:$i] : (ap@c_2Etransc_2Ecos@(ap@V3g@V15x)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(ap@V3g@(inj__ty_2Erealax_2Ereal @ V2x)))))@(inj__ty_2Erealax_2Ereal @ V4m)))@(inj__ty_2Erealax_2Ereal @ V2x)))))))))))))))))))))).
thf(conj_thm_2Etransc_2EEXP__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Etransc_2EEXP__LE__X,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(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 @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2EEXP__LT__1,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2EEXP__ADD__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Eexp@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Etransc_2Eexp@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Etransc_2EEXP__NEG__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2EEXP__NEG__MUL2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Eexp@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2EEXP__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2EEXP__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2EEXP__POS__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EEXP__NZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Etransc_2EEXP__POS__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EEXP__N,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(conj_thm_2Etransc_2EEXP__SUB,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2EEXP__MONO__IMP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2EEXP__MONO__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Etransc_2EEXP__MONO__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))))).
thf(conj_thm_2Etransc_2EEXP__INJ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (V0x = V1y))))).
thf(conj_thm_2Etransc_2EEXP__TOTAL__LEMMA,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(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 @ V0y))) => (? [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1x))) = V0y))))))).
thf(conj_thm_2Etransc_2EEXP__TOTAL,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0y))) => (? [V1x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V1x))) = V0y))))).
thf(ax_thm_2Etransc_2Eln,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1u:$i] : (ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Eexp@V1u))@(inj__ty_2Erealax_2Ereal @ V0x))))))))).
thf(conj_thm_2Etransc_2ELN__EXP,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x))).
thf(conj_thm_2Etransc_2EEXP__LN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ELN__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ELN__INJ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (V0x = V1y)))))).
thf(conj_thm_2Etransc_2ELN__1,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ELN__INV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Etransc_2ELN__DIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ELN__MONO__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2ELN__MONO__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1y)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2ELN__POW,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eln@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1x))))))))).
thf(conj_thm_2Etransc_2ELN__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Eln@(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 @ V0x))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ELN__LT__X,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ELN__POS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(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))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(ax_thm_2Etransc_2Eroot,axiom,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Erealax_2Ereal @ V1x))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V2u:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V2u)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@(ap@c_2Ereal_2Epow@V2u)@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x))))))))))).
thf(ax_thm_2Etransc_2Esqrt,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EROOT__LT__LEMMA,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Eexp@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = V1x))))).
thf(conj_thm_2Etransc_2EROOT__LN,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))))))))).
thf(conj_thm_2Etransc_2EROOT__0,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Etransc_2EROOT__1,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2EROOT__POS__LT,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))))))).
thf(conj_thm_2Etransc_2EROOT__POW__POS,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = V1x))))).
thf(conj_thm_2Etransc_2EPOW__ROOT__POS,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n))))) = V1x))))).
thf(conj_thm_2Etransc_2EROOT__POS,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))))))).
thf(conj_thm_2Etransc_2EROOT__POS__UNIQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2y))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))) = V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x))) = V2y)))))).
thf(conj_thm_2Etransc_2EROOT__MUL,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V2y)))))))))).
thf(conj_thm_2Etransc_2EROOT__INV,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V1x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x))))))))).
thf(conj_thm_2Etransc_2EROOT__DIV,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V2y)))))))))).
thf(conj_thm_2Etransc_2EROOT__MONO__LE,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1x))@(inj__ty_2Erealax_2Ereal @ V2y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Etransc_2Eroot@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ V2y))))))))).
thf(conj_thm_2Etransc_2ESQRT__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ESQRT__1,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Etransc_2ESQRT__POS__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESQRT__POS__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESQRT__POW2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ESQRT__POW__2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x)))).
thf(conj_thm_2Etransc_2EPOW__2__SQRT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = V0x)))).
thf(conj_thm_2Etransc_2ESQRT__POS__UNIQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y))) & ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x))) = V1y))))).
thf(conj_thm_2Etransc_2ESQRT__MUL,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ESQRT__INV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Etransc_2ESQRT__DIV,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1y)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ESQRT__MONO__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2ESQRT__EVEN__POW2,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V0n))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(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)))))@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Erealax_2Ereal @ (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_2EDIV@(inj__ty_2Enum_2Enum @ V0n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))).
thf(conj_thm_2Etransc_2EREAL__DIV__SQRT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESQRT__EQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V1y) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x)))) => (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2Etransc_2ESIN__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ECOS__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Etransc_2ESIN__CIRCLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2ESIN__BOUND,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2ESIN__BOUNDS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2ECOS__BOUND,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2ECOS__BOUNDS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2ESIN__COS__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V1y))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V1y))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Etransc_2ESIN__COS__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Etransc_2Esin@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Etransc_2Ecos@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Etransc_2ESIN__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ECOS__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2Etransc_2ESIN__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ESIN__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(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_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2Etransc_2ECOS__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2ESIN__PAIRED,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2Esums@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@V1n))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@V1n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@V1n))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ESIN__POS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__PAIRED,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@c_2Eseq_2Esums@(lam@ty_2Enum_2Enum@(^ [V1n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@V1n))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@V1n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@V1n))))))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ECOS__2,lemma,(p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Ecos@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ECOS__ISZERO,lemma,(p@(ap@(c_2Ebool_2E_3F_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V0x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V0x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V0x)@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Ecos@V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(ax_thm_2Etransc_2Epi,axiom,(fo__c_2Etransc_2Epi = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V0x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V0x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V0x)@(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_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Ecos@V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2Etransc_2EPI2,lemma,((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V0x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V0x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V0x)@(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_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Ecos@V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2Etransc_2ECOS__PI2,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2EPI2__BOUNDS,lemma,((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2EPI__POS,lemma,(p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))).
thf(conj_thm_2Etransc_2ESIN__PI2,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))).
thf(conj_thm_2Etransc_2ECOS__PI,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))).
thf(conj_thm_2Etransc_2ESIN__PI,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ESIN__COS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__SIN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESIN__PERIODIC__PI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__PERIODIC__PI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESIN__PERIODIC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ECOS__PERIODIC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ECOS__NPI,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Enum_2Enum @ V0n)))))).
thf(conj_thm_2Etransc_2ESIN__NPI,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Etransc_2ESIN__POS__PI2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__POS__PI2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__POS__PI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESIN__POS__PI,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__POS__PI2__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__POS__PI__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESIN__POS__PI2__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ESIN__POS__PI__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ECOS__TOTAL,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(c_2Ebool_2E_3F_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V1x)@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Ecos@V1x))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(conj_thm_2Etransc_2ESIN__TOTAL,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(c_2Ebool_2E_3F_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V1x)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(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_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Esin@V1x))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(conj_thm_2Etransc_2ECOS__ZERO__LEMMA,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => (? [V1n:tp__ty_2Enum_2Enum] : ((~~ (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V1n)))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))).
thf(conj_thm_2Etransc_2ESIN__ZERO__LEMMA,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => (? [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V1n))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))).
thf(conj_thm_2Etransc_2ECOS__ZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> ((? [V1n:tp__ty_2Enum_2Enum] : ((~~ (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V1n)))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))) | (? [V2n:tp__ty_2Enum_2Enum] : ((~~ (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V2n)))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V2n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))).
thf(conj_thm_2Etransc_2ESIN__ZERO,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> ((? [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V1n))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))) | (? [V2n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V2n))) & (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V2n)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))).
thf(ax_thm_2Etransc_2Etan,axiom,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ETAN__0,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ETAN__PI,lemma,((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2ETAN__NPI,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V0n)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2Etransc_2ETAN__NEG,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2ETAN__PERIODIC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ETAN__ADD,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : (((~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & ((~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Erealax_2Ereal__mul@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V1y))))))))))).
thf(conj_thm_2Etransc_2ETAN__DOUBLE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2ETAN__POS__PI2,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2Etransc_2EDIFF__TAN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Etan)@(ap@c_2Erealax_2Einv@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2ETAN__TOTAL__LEMMA,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0y))) => (? [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V1x)))))))))).
thf(conj_thm_2Etransc_2ETAN__TOTAL__POS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0y))) => (? [V1x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V1x))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V1x))) = V0y))))))).
thf(conj_thm_2Etransc_2ETAN__TOTAL,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (p@(ap@(c_2Ebool_2E_3F_21@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Erealax_2Ereal__lt@V1x)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(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_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Etan@V1x))@(inj__ty_2Erealax_2Ereal @ V0y)))))))))).
thf(ax_thm_2Etransc_2Easn,axiom,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V1x)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Esin@V1x))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(ax_thm_2Etransc_2Eacs,axiom,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@V1x)@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Ecos@V1x))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(ax_thm_2Etransc_2Eatn,axiom,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y))) = (surj__ty_2Erealax_2Ereal @ (ap@(c_2Emin_2E_40@ty_2Erealax_2Ereal)@(lam@ty_2Erealax_2Ereal@(^ [V1x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@V1x))@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Erealax_2Ereal__lt@V1x)@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(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_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@c_2Etransc_2Etan@V1x))@(inj__ty_2Erealax_2Ereal @ V0y))))))))))).
thf(conj_thm_2Etransc_2EASN,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y)))))).
thf(conj_thm_2Etransc_2EASN__SIN,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y)))).
thf(conj_thm_2Etransc_2EASN__BOUNDS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2EASN__BOUNDS__LT,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2ESIN__ASN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Easn@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x)))).
thf(conj_thm_2Etransc_2EACS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y)))))).
thf(conj_thm_2Etransc_2EACS__COS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y)))).
thf(conj_thm_2Etransc_2EACS__BOUNDS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))))))).
thf(conj_thm_2Etransc_2EACS__BOUNDS__LT,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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 @ V0y))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0y))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0y)))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))))))).
thf(conj_thm_2Etransc_2ECOS__ACS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eacs@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x)))).
thf(conj_thm_2Etransc_2EATN,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y))))).
thf(conj_thm_2Etransc_2EATN__TAN,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Etan@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))) = V0y))).
thf(conj_thm_2Etransc_2EATN__BOUNDS,lemma,( ! [V0y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0y)))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))).
thf(conj_thm_2Etransc_2ETAN__ATN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eatn@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))) = V0x)))).
thf(conj_thm_2Etransc_2ETAN__SEC,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) => ((surj__ty_2Erealax_2Ereal @ (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)))))@(ap@(ap@c_2Ereal_2Epow@(ap@c_2Etransc_2Etan@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2ESIN__COS__SQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2ECOS__SIN__SQ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Erealax_2Ereal__neg@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Ereal_2E_2F@(inj__ty_2Erealax_2Ereal @ fo__c_2Etransc_2Epi))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2ECOS__ATN__NZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Etransc_2Eatn@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Etransc_2ECOS__ASN__NZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Etransc_2ESIN__ACS__NZ,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (~~ ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0x)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Etransc_2ECOS__SIN__SQRT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2ESIN__COS__SQRT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x)))) => ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esin@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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_2Etransc_2Ecos@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2Etransc_2EDIFF__LN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Eln)@(ap@c_2Erealax_2Einv@(inj__ty_2Erealax_2Ereal @ V0x)))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EDIFF__ASN__LEMMA,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Easn)@(ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Ecos@(ap@c_2Etransc_2Easn@(inj__ty_2Erealax_2Ereal @ V0x)))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EDIFF__ASN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Easn)@(ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EDIFF__ACS__LEMMA,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Eacs)@(ap@c_2Erealax_2Einv@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Etransc_2Esin@(ap@c_2Etransc_2Eacs@(inj__ty_2Erealax_2Ereal @ V0x))))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EDIFF__ACS,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Erealax_2Ereal__neg@(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))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Eacs)@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Erealax_2Einv@(ap@c_2Etransc_2Esqrt@(ap@(ap@c_2Ereal_2Ereal__sub@(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@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2Etransc_2EDIFF__ATN,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@c_2Etransc_2Eatn)@(ap@c_2Erealax_2Einv@(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)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))@(inj__ty_2Erealax_2Ereal @ V0x))))).
thf(ax_thm_2Etransc_2Edivision,axiom,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2D:$i] : ((mem@V2D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@V2D)) <=> (((surj__ty_2Erealax_2Ereal @ (ap@V2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0a) & (? [V3N:tp__ty_2Enum_2Enum] : (( ! [V4n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4n))@(inj__ty_2Enum_2Enum @ V3N))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V2D@(inj__ty_2Enum_2Enum @ V4n)))@(ap@V2D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V4n))))))) & ( ! [V5n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Enum_2Enum @ V3N))) => ((surj__ty_2Erealax_2Ereal @ (ap@V2D@(inj__ty_2Enum_2Enum @ V5n))) = V1b)))))))))))).
thf(ax_thm_2Etransc_2Edsize,axiom,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((surj__ty_2Enum_2Enum @ (ap@c_2Etransc_2Edsize@V0D)) = (surj__ty_2Enum_2Enum @ (ap@(c_2Emin_2E_40@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V1N:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(c_2Ebool_2E_21@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@c_2Eprim__rec_2E_3C@V2n)@V1N))@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@V2n))@(ap@V0D@(ap@c_2Enum_2ESUC@V2n))))))))@(ap@(c_2Ebool_2E_21@ty_2Enum_2Enum)@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@(ap@c_2Emin_2E_3D_3D_3E@(ap@(ap@c_2Earithmetic_2E_3E_3D@V3n)@V1N))@(ap@(ap@(c_2Emin_2E_3D@ty_2Erealax_2Ereal)@(ap@V0D@V3n))@(ap@V0D@V1N))))))))))))))).
thf(ax_thm_2Etransc_2Etdiv,axiom,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2D:$i] : ((mem@V2D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V3p:$i] : ((mem@V3p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V2D)@V3p))) <=> ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@V2D)) & ( ! [V4n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@V2D@(inj__ty_2Enum_2Enum @ V4n)))@(ap@V3p@(inj__ty_2Enum_2Enum @ V4n)))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@V3p@(inj__ty_2Enum_2Enum @ V4n)))@(ap@V2D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V4n)))))))))))))))).
thf(ax_thm_2Etransc_2Egauge,axiom,( ! [V0E:$i] : ((mem@V0E@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1g:$i] : ((mem@V1g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@c_2Etransc_2Egauge@V0E)@V1g)) <=> ( ! [V2x:tp__ty_2Erealax_2Ereal] : ((p@(ap@V0E@(inj__ty_2Erealax_2Ereal @ V2x))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@V1g@(inj__ty_2Erealax_2Ereal @ V2x)))))))))))).
thf(ax_thm_2Etransc_2Efine,axiom,( ! [V0g:$i] : ((mem@V0g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1D:$i] : ((mem@V1D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2p:$i] : ((mem@V2p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@c_2Etransc_2Efine@V0g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V1D)@V2p))) <=> ( ! [V3n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Etransc_2Edsize@V1D))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@V1D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V3n))))@(ap@V1D@(inj__ty_2Enum_2Enum @ V3n))))@(ap@V0g@(ap@V2p@(inj__ty_2Enum_2Enum @ V3n))))))))))))))).
thf(ax_thm_2Etransc_2Ersum,axiom,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1p:$i] : ((mem@V1p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Ersum@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V0D)@V1p))@V2f)) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Etransc_2Edsize@V0D)))@(lam@ty_2Enum_2Enum@(^ [V3n:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@V2f@(ap@V1p@V3n)))@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0D@(ap@c_2Enum_2ESUC@V3n)))@(ap@V0D@V3n))))))))))))))).
thf(ax_thm_2Etransc_2EDint,axiom,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V3k:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@(ap@c_2Etransc_2EDint@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@V2f)@(inj__ty_2Erealax_2Ereal @ V3k))) <=> ( ! [V4e:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V4e))) => (? [V5g:$i] : ((mem@V5g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) & ((p@(ap@(ap@c_2Etransc_2Egauge@(lam@ty_2Erealax_2Ereal@(^ [V6x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@V6x))@(ap@(ap@c_2Ereal_2Ereal__lte@V6x)@(inj__ty_2Erealax_2Ereal @ V1b))))))@V5g)) & ( ! [V7D:$i] : ((mem@V7D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V8p:$i] : ((mem@V8p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => (((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V7D)@V8p))) & (p@(ap@(ap@c_2Etransc_2Efine@V5g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V7D)@V8p)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Etransc_2Ersum@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V7D)@V8p))@V2f))@(inj__ty_2Erealax_2Ereal @ V3k))))@(inj__ty_2Erealax_2Ereal @ V4e)))))))))))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__0,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((V0a = V1b) => ((surj__ty_2Enum_2Enum @ (ap@c_2Etransc_2Edsize@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@V2n)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))))) = fo__c_2Enum_2E0))))).
thf(conj_thm_2Etransc_2EDIVISION__1,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) => ((surj__ty_2Enum_2Enum @ (ap@c_2Etransc_2Edsize@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@V2n)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2EDIVISION__SINGLE,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) => (p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(lam@ty_2Enum_2Enum@(^ [V2n:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@(c_2Emin_2E_3D@ty_2Enum_2Enum)@V2n)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))))))))).
thf(conj_thm_2Etransc_2EDIVISION__LHS,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ((surj__ty_2Erealax_2Ereal @ (ap@V0D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V1a))))))).
thf(conj_thm_2Etransc_2EDIVISION__THM,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) <=> (((surj__ty_2Erealax_2Ereal @ (ap@V0D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V1a) & (( ! [V3n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Etransc_2Edsize@V0D))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@(inj__ty_2Enum_2Enum @ V3n)))@(ap@V0D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V3n))))))) & ( ! [V4n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V4n))@(ap@c_2Etransc_2Edsize@V0D))) => ((surj__ty_2Erealax_2Ereal @ (ap@V0D@(inj__ty_2Enum_2Enum @ V4n))) = V2b))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__RHS,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ((surj__ty_2Erealax_2Ereal @ (ap@V0D@(ap@c_2Etransc_2Edsize@V0D))) = V2b))))))).
thf(conj_thm_2Etransc_2EDIVISION__LT__GEN,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ( ! [V3m:tp__ty_2Enum_2Enum] : ( ! [V4n:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3m))@(inj__ty_2Enum_2Enum @ V4n))) & (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V4n))@(ap@c_2Etransc_2Edsize@V0D))))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@(inj__ty_2Enum_2Enum @ V3m)))@(ap@V0D@(inj__ty_2Enum_2Enum @ V4n)))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__LT,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ( ! [V3n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Etransc_2Edsize@V0D))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@V0D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V3n))))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__LE,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b))))))))).
thf(conj_thm_2Etransc_2EDIVISION__GT,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ( ! [V3n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Etransc_2Edsize@V0D))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@(inj__ty_2Enum_2Enum @ V3n)))@(ap@V0D@(ap@c_2Etransc_2Edsize@V0D)))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__EQ,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ((V1a = V2b) <=> ((surj__ty_2Enum_2Enum @ (ap@c_2Etransc_2Edsize@V0D)) = fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Etransc_2EDIVISION__LBOUND,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ( ! [V3r:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1a))@(ap@V0D@(inj__ty_2Enum_2Enum @ V3r))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__LBOUND__LT,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) & (~~ ((surj__ty_2Enum_2Enum @ (ap@c_2Etransc_2Edsize@V0D)) = fo__c_2Enum_2E0))) => ( ! [V3n:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V1a))@(ap@V0D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V3n)))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__UBOUND,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) => ( ! [V3r:tp__ty_2Enum_2Enum] : (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@V0D@(inj__ty_2Enum_2Enum @ V3r)))@(inj__ty_2Erealax_2Ereal @ V2b)))))))))).
thf(conj_thm_2Etransc_2EDIVISION__UBOUND__LT,lemma,( ! [V0D:$i] : ((mem@V0D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ( ! [V3n:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Etransc_2Edivision@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@V0D)) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V3n))@(ap@c_2Etransc_2Edsize@V0D)))) => (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0D@(inj__ty_2Enum_2Enum @ V3n)))@(inj__ty_2Erealax_2Ereal @ V2b)))))))))).
thf(conj_thm_2Etransc_2EDIVISION__APPEND,lemma,( ! [V0g:$i] : ((mem@V0g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : ( ! [V2b:tp__ty_2Erealax_2Ereal] : ( ! [V3c:tp__ty_2Erealax_2Ereal] : (((? [V4D1:$i] : ((mem@V4D1@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & (? [V5p1:$i] : ((mem@V5p1@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & ((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V2b)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V4D1)@V5p1))) & (p@(ap@(ap@c_2Etransc_2Efine@V0g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V4D1)@V5p1)))))))) & (? [V6D2:$i] : ((mem@V6D2@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & (? [V7p2:$i] : ((mem@V7p2@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & ((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2b))@(inj__ty_2Erealax_2Ereal @ V3c)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V6D2)@V7p2))) & (p@(ap@(ap@c_2Etransc_2Efine@V0g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V6D2)@V7p2))))))))) => (? [V8D:$i] : ((mem@V8D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & (? [V9p:$i] : ((mem@V9p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & ((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V3c)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V8D)@V9p))) & (p@(ap@(ap@c_2Etransc_2Efine@V0g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V8D)@V9p))))))))))))))).
thf(conj_thm_2Etransc_2EDIVISION__EXISTS,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2g:$i] : ((mem@V2g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) & (p@(ap@(ap@c_2Etransc_2Egauge@(lam@ty_2Erealax_2Ereal@(^ [V3x:$i] : (ap@(ap@c_2Ebool_2E_2F_5C@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@V3x))@(ap@(ap@c_2Ereal_2Ereal__lte@V3x)@(inj__ty_2Erealax_2Ereal @ V1b))))))@V2g))) => (? [V4D:$i] : ((mem@V4D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & (? [V5p:$i] : ((mem@V5p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) & ((p@(ap@(ap@c_2Etransc_2Etdiv@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V4D)@V5p))) & (p@(ap@(ap@c_2Etransc_2Efine@V2g)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V4D)@V5p)))))))))))))).
thf(conj_thm_2Etransc_2EGAUGE__MIN,lemma,( ! [V0E:$i] : ((mem@V0E@(arr@ty_2Erealax_2Ereal@bool)) => ( ! [V1g1:$i] : ((mem@V1g1@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V2g2:$i] : ((mem@V2g2@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => (((p@(ap@(ap@c_2Etransc_2Egauge@V0E)@V1g1)) & (p@(ap@(ap@c_2Etransc_2Egauge@V0E)@V2g2))) => (p@(ap@(ap@c_2Etransc_2Egauge@V0E)@(lam@ty_2Erealax_2Ereal@(^ [V3x:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V1g1@V3x))@(ap@V2g2@V3x)))@(ap@V1g1@V3x))@(ap@V2g2@V3x)))))))))))))).
thf(conj_thm_2Etransc_2EFINE__MIN,lemma,( ! [V0g1:$i] : ((mem@V0g1@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1g2:$i] : ((mem@V1g2@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V2D:$i] : ((mem@V2D@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ( ! [V3p:$i] : ((mem@V3p@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)) => ((p@(ap@(ap@c_2Etransc_2Efine@(lam@ty_2Erealax_2Ereal@(^ [V4x:$i] : (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Erealax_2Ereal)@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@V0g1@V4x))@(ap@V1g2@V4x)))@(ap@V0g1@V4x))@(ap@V1g2@V4x)))))@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V2D)@V3p))) => ((p@(ap@(ap@c_2Etransc_2Efine@V0g1)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V2D)@V3p))) & (p@(ap@(ap@c_2Etransc_2Efine@V1g2)@(ap@(ap@(c_2Epair_2E_2C@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal)@(arr@ty_2Enum_2Enum@ty_2Erealax_2Ereal))@V2D)@V3p)))))))))))))).
thf(conj_thm_2Etransc_2EDINT__UNIQ,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ( ! [V2f:$i] : ((mem@V2f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V3k1:tp__ty_2Erealax_2Ereal] : ( ! [V4k2:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) & ((p@(ap@(ap@(ap@c_2Etransc_2EDint@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@V2f)@(inj__ty_2Erealax_2Ereal @ V3k1))) & (p@(ap@(ap@(ap@c_2Etransc_2EDint@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b)))@V2f)@(inj__ty_2Erealax_2Ereal @ V4k2))))) => (V3k1 = V4k2))))))))).
thf(conj_thm_2Etransc_2EINTEGRAL__NULL,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1a:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Etransc_2EDint@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V1a))@(inj__ty_2Erealax_2Ereal @ V1a)))@V0f)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2Etransc_2EFTC1,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1f_27:$i] : ((mem@V1f_27@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V2a:tp__ty_2Erealax_2Ereal] : ( ! [V3b:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2a))@(inj__ty_2Erealax_2Ereal @ V3b))) & ( ! [V4x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2a))@(inj__ty_2Erealax_2Ereal @ V4x))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Erealax_2Ereal @ V3b)))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0f)@(ap@V1f_27@(inj__ty_2Erealax_2Ereal @ V4x)))@(inj__ty_2Erealax_2Ereal @ V4x)))))) => (p@(ap@(ap@(ap@c_2Etransc_2EDint@(ap@(ap@(c_2Epair_2E_2C@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)@(inj__ty_2Erealax_2Ereal @ V2a))@(inj__ty_2Erealax_2Ereal @ V3b)))@V1f_27)@(ap@(ap@c_2Ereal_2Ereal__sub@(ap@V0f@(inj__ty_2Erealax_2Ereal @ V3b)))@(ap@V0f@(inj__ty_2Erealax_2Ereal @ V2a))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1diff:$i] : ((mem@V1diff@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))) => ( ! [V2h:tp__ty_2Erealax_2Ereal] : ( ! [V3n:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V2h))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V3n))) & (((ap@V1diff@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) = V0f) & ( ! [V4m:tp__ty_2Enum_2Enum] : ( ! [V5t:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4m))@(inj__ty_2Enum_2Enum @ V3n))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V5t))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V5t))@(inj__ty_2Erealax_2Ereal @ V2h))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(ap@V1diff@(inj__ty_2Enum_2Enum @ V4m)))@(ap@(ap@V1diff@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V4m)))@(inj__ty_2Erealax_2Ereal @ V5t)))@(inj__ty_2Erealax_2Ereal @ V5t))))))))) => (? [V6t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V6t))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6t))@(inj__ty_2Erealax_2Ereal @ V2h))) & ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Erealax_2Ereal @ V2h))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V7m:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@V7m)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V7m))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2h))@V7m))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@(inj__ty_2Enum_2Enum @ V3n))@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V3n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2h))@(inj__ty_2Enum_2Enum @ V3n))))))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__NEG,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1diff:$i] : ((mem@V1diff@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))) => ( ! [V2h:tp__ty_2Erealax_2Ereal] : ( ! [V3n:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2h))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V3n))) & (((ap@V1diff@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) = V0f) & ( ! [V4m:tp__ty_2Enum_2Enum] : ( ! [V5t:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V4m))@(inj__ty_2Enum_2Enum @ V3n))) & ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V2h))@(inj__ty_2Erealax_2Ereal @ V5t))) & (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V5t))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(ap@V1diff@(inj__ty_2Enum_2Enum @ V4m)))@(ap@(ap@V1diff@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V4m)))@(inj__ty_2Erealax_2Ereal @ V5t)))@(inj__ty_2Erealax_2Ereal @ V5t))))))))) => (? [V6t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V2h))@(inj__ty_2Erealax_2Ereal @ V6t))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V6t))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Erealax_2Ereal @ V2h))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V3n)))@(lam@ty_2Enum_2Enum@(^ [V7m:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@V7m)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V7m))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2h))@V7m))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@(inj__ty_2Enum_2Enum @ V3n))@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V3n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2h))@(inj__ty_2Enum_2Enum @ V3n))))))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__ALL__LT,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1diff:$i] : ((mem@V1diff@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))) => ((((ap@V1diff@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) = V0f) & ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(ap@V1diff@(inj__ty_2Enum_2Enum @ V2m)))@(ap@(ap@V1diff@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2m)))@(inj__ty_2Erealax_2Ereal @ V3x)))@(inj__ty_2Erealax_2Ereal @ V3x)))))) => ( ! [V4x:tp__ty_2Erealax_2Ereal] : ( ! [V5n:tp__ty_2Enum_2Enum] : (((~~ (V4x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V5n)))) => (? [V6t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V6t)))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V4x)))) & ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Erealax_2Ereal @ V4x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V5n)))@(lam@ty_2Enum_2Enum@(^ [V7m:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@V7m)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V7m))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V4x))@V7m))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V5n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Enum_2Enum @ V5n)))))))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__ZERO,lemma,( ! [V0diff:$i] : ((mem@V0diff@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))) => ( ! [V1n:tp__ty_2Enum_2Enum] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((V2x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V0diff@V3m)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V3m))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V2x))@V3m)))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@V0diff@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__ALL__LE,lemma,( ! [V0f:$i] : ((mem@V0f@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1diff:$i] : ((mem@V1diff@(arr@ty_2Enum_2Enum@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal))) => ((((ap@V1diff@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)) = V0f) & ( ! [V2m:tp__ty_2Enum_2Enum] : ( ! [V3x:tp__ty_2Erealax_2Ereal] : (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(ap@V1diff@(inj__ty_2Enum_2Enum @ V2m)))@(ap@(ap@V1diff@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2m)))@(inj__ty_2Erealax_2Ereal @ V3x)))@(inj__ty_2Erealax_2Ereal @ V3x)))))) => ( ! [V4x:tp__ty_2Erealax_2Ereal] : ( ! [V5n:tp__ty_2Enum_2Enum] : (? [V6t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V4x)))) & ((surj__ty_2Erealax_2Ereal @ (ap@V0f@(inj__ty_2Erealax_2Ereal @ V4x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V5n)))@(lam@ty_2Enum_2Enum@(^ [V7m:$i] : (ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@V7m)@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V7m))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V4x))@V7m))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@(ap@V1diff@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Erealax_2Ereal @ V6t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V5n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V4x))@(inj__ty_2Enum_2Enum @ V5n)))))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__EXP__LT,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : (((~~ (V0x = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) & (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))) => (? [V2t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2t)))) & ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2t)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V3m))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V3m)))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V2t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V1n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V1n))))))))))))).
thf(conj_thm_2Etransc_2EMCLAURIN__EXP__LE,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : (? [V2t:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V2t)))@(ap@c_2Ereal_2Eabs@(inj__ty_2Erealax_2Ereal @ V0x)))) & ((surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Ereal_2Esum@(ap@(ap@(c_2Epair_2E_2C@ty_2Enum_2Enum@ty_2Enum_2Enum)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V1n)))@(lam@ty_2Enum_2Enum@(^ [V3m:$i] : (ap@(ap@c_2Ereal_2E_2F@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@V3m))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@V3m)))))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@(ap@c_2Ereal_2E_2F@(ap@c_2Etransc_2Eexp@(inj__ty_2Erealax_2Ereal @ V2t)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2EFACT@(inj__ty_2Enum_2Enum @ V1n)))))@(ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Enum_2Enum @ V1n))))))))))).
thf(conj_thm_2Etransc_2EDIFF__LN__COMPOSITE,lemma,( ! [V0g:$i] : ((mem@V0g@(arr@ty_2Erealax_2Ereal@ty_2Erealax_2Ereal)) => ( ! [V1m:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : (((p@(ap@(ap@(ap@c_2Elim_2Ediffl@V0g)@(inj__ty_2Erealax_2Ereal @ V1m))@(inj__ty_2Erealax_2Ereal @ V2x))) & (p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@V0g@(inj__ty_2Erealax_2Ereal @ V2x))))) => (p@(ap@(ap@(ap@c_2Elim_2Ediffl@(lam@ty_2Erealax_2Ereal@(^ [V3x:$i] : (ap@c_2Etransc_2Eln@(ap@V0g@V3x)))))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Einv@(ap@V0g@(inj__ty_2Erealax_2Ereal @ V2x))))@(inj__ty_2Erealax_2Ereal @ V1m)))@(inj__ty_2Erealax_2Ereal @ V2x))))))))).
thf(ax_thm_2Etransc_2Erpow__def,axiom,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1b:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Erealax_2Ereal @ V1b))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Etransc_2Eexp@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1b))@(ap@c_2Etransc_2Eln@(inj__ty_2Erealax_2Ereal @ V0a))))))))).
thf(conj_thm_2Etransc_2EGEN__RPOW,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0a))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Etransc_2ERPOW__SUC__N,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ V1n)))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Epow@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Etransc_2ERPOW__0,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2Etransc_2ERPOW__1,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = V0a)))).
thf(conj_thm_2Etransc_2EONE__RPOW,conjecture,( ! [V0a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0a))) => ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Etransc_2Erpow@(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 @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
