include('Axioms/HL4001^2.ax').
thf(tp_c_2Emin_2E_3D_3D_3E,type,(c_2Emin_2E_3D_3D_3E:$i)).
thf(mem_c_2Emin_2E_3D_3D_3E,axiom,(mem@c_2Emin_2E_3D_3D_3E@(arr@bool@(arr@bool@bool)))).
thf(ax_imp_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Emin_2E_3D_3D_3E@Q)@R)) <=> ((p@Q) => (p@R)))))))).
thf(tp_ty_2Elist_2Elist,type,( ty_2Elist_2Elist: del >del )).
thf(tp_c_2Elist_2ECONS,type,(c_2Elist_2ECONS:(del>$i))).
thf(mem_c_2Elist_2ECONS,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ECONS@A_27a)@(arr@A_27a@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27a)))))).
thf(tp_ty_2Enum_2Enum,type,( ty_2Enum_2Enum:del )).
thf(stp_ty_2Enum_2Enum,type,(tp__ty_2Enum_2Enum : $tType)).
thf(stp_inj_ty_2Enum_2Enum,type,(inj__ty_2Enum_2Enum : (tp__ty_2Enum_2Enum > $i))).
thf(stp_surj_ty_2Enum_2Enum,type,(surj__ty_2Enum_2Enum : ($i > tp__ty_2Enum_2Enum))).
thf(stp_inj_surj_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X)) = X))).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,( ! [X:tp__ty_2Enum_2Enum] : (mem @ (inj__ty_2Enum_2Enum @ X) @ ty_2Enum_2Enum))).
thf(stp_iso_mem_ty_2Enum_2Enum,axiom,( ! [X:$i] : ((mem @ X @ ty_2Enum_2Enum) => (X = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X)))))).
thf(tp_c_2Earithmetic_2EEVEN,type,(c_2Earithmetic_2EEVEN:$i)).
thf(mem_c_2Earithmetic_2EEVEN,axiom,(mem@c_2Earithmetic_2EEVEN@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Earithmetic_2EODD,type,(c_2Earithmetic_2EODD:$i)).
thf(mem_c_2Earithmetic_2EODD,axiom,(mem@c_2Earithmetic_2EODD@(arr@ty_2Enum_2Enum@bool))).
thf(tp_c_2Eprim__rec_2EPRE,type,(c_2Eprim__rec_2EPRE:$i)).
thf(mem_c_2Eprim__rec_2EPRE,axiom,(mem@c_2Eprim__rec_2EPRE@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Eprim__rec_2EPRE,type,(fo__c_2Eprim__rec_2EPRE:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Eprim__rec_2EPRE @ X0)) = (ap @ c_2Eprim__rec_2EPRE @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enum_2ESUC,type,(c_2Enum_2ESUC:$i)).
thf(mem_c_2Enum_2ESUC,axiom,(mem@c_2Enum_2ESUC@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enum_2ESUC,type,(fo__c_2Enum_2ESUC:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enum_2ESUC,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enum_2ESUC @ X0)) = (ap @ c_2Enum_2ESUC @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2EEXP,type,(c_2Earithmetic_2EEXP:$i)).
thf(mem_c_2Earithmetic_2EEXP,axiom,(mem@c_2Earithmetic_2EEXP@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2EEXP,type,(fo__c_2Earithmetic_2EEXP:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2EEXP @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2EEXP @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2E_2A,type,(c_2Earithmetic_2E_2A:$i)).
thf(mem_c_2Earithmetic_2E_2A,axiom,(mem@c_2Earithmetic_2E_2A@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2A,type,(fo__c_2Earithmetic_2E_2A:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2A @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2A @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Enumeral_2EiZ,type,(c_2Enumeral_2EiZ:$i)).
thf(mem_c_2Enumeral_2EiZ,axiom,(mem@c_2Enumeral_2EiZ@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiZ,type,(fo__c_2Enumeral_2EiZ:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiZ @ X0)) = (ap @ c_2Enumeral_2EiZ @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Ebool_2E_7E,type,(c_2Ebool_2E_7E:$i)).
thf(mem_c_2Ebool_2E_7E,axiom,(mem@c_2Ebool_2E_7E@(arr@bool@bool))).
thf(ax_neg_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ((p@(ap@c_2Ebool_2E_7E@Q)) <=> (~ (p@Q)))))).
thf(tp_c_2Ebool_2EF,type,(c_2Ebool_2EF:$i)).
thf(mem_c_2Ebool_2EF,axiom,(mem@c_2Ebool_2EF@bool)).
thf(ax_false_p,axiom,(~ (p@c_2Ebool_2EF))).
thf(tp_c_2Ebool_2ET,type,(c_2Ebool_2ET:$i)).
thf(mem_c_2Ebool_2ET,axiom,(mem@c_2Ebool_2ET@bool)).
thf(ax_true_p,axiom,(p@c_2Ebool_2ET)).
thf(tp_c_2Enumeral_2EiSUB,type,(c_2Enumeral_2EiSUB:$i)).
thf(mem_c_2Enumeral_2EiSUB,axiom,(mem@c_2Enumeral_2EiSUB@(arr@bool@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))))).
thf(tp_c_2Ebool_2ECOND,type,(c_2Ebool_2ECOND:(del>$i))).
thf(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2ECOND@A_27a)@(arr@bool@(arr@A_27a@(arr@A_27a@A_27a)))))).
thf(tp_c_2Earithmetic_2E_2D,type,(c_2Earithmetic_2E_2D:$i)).
thf(mem_c_2Earithmetic_2E_2D,axiom,(mem@c_2Earithmetic_2E_2D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2D,type,(fo__c_2Earithmetic_2E_2D:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2D @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Earithmetic_2EBIT2,type,(c_2Earithmetic_2EBIT2:$i)).
thf(mem_c_2Earithmetic_2EBIT2,axiom,(mem@c_2Earithmetic_2EBIT2@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT2,type,(fo__c_2Earithmetic_2EBIT2:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT2 @ X0)) = (ap @ c_2Earithmetic_2EBIT2 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Enumeral_2EiDUB,type,(c_2Enumeral_2EiDUB:$i)).
thf(mem_c_2Enumeral_2EiDUB,axiom,(mem@c_2Enumeral_2EiDUB@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Enumeral_2EiDUB,type,(fo__c_2Enumeral_2EiDUB:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Enumeral_2EiDUB @ X0)) = (ap @ c_2Enumeral_2EiDUB @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2E_2B,type,(c_2Earithmetic_2E_2B:$i)).
thf(mem_c_2Earithmetic_2E_2B,axiom,(mem@c_2Earithmetic_2E_2B@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum)))).
thf(stp_fo_c_2Earithmetic_2E_2B,type,(fo__c_2Earithmetic_2E_2B:(tp__ty_2Enum_2Enum > (tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum)))).
thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ( ! [X1:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ ((fo__c_2Earithmetic_2E_2B @ X0) @ X1)) = (ap @ (ap @ c_2Earithmetic_2E_2B @ (inj__ty_2Enum_2Enum @ X0)) @ (inj__ty_2Enum_2Enum @ X1)))))).
thf(tp_c_2Elist_2EAPPEND,type,(c_2Elist_2EAPPEND:(del>$i))).
thf(mem_c_2Elist_2EAPPEND,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2EAPPEND@A_27a)@(arr@(ty_2Elist_2Elist@A_27a)@(arr@(ty_2Elist_2Elist@A_27a)@(ty_2Elist_2Elist@A_27a)))))).
thf(tp_c_2Ebool_2E_3F,type,(c_2Ebool_2E_3F:(del>$i))).
thf(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_3F@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_ex_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_3F@A)@Q)) <=> (? [X:$i] : ((mem@X@A) & (p@(ap@Q@X))))))))).
thf(tp_c_2Earithmetic_2E_3C_3D,type,(c_2Earithmetic_2E_3C_3D:$i)).
thf(mem_c_2Earithmetic_2E_3C_3D,axiom,(mem@c_2Earithmetic_2E_3C_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Enum_2E0,type,(c_2Enum_2E0:$i)).
thf(mem_c_2Enum_2E0,axiom,(mem@c_2Enum_2E0@ty_2Enum_2Enum)).
thf(stp_fo_c_2Enum_2E0,type,(fo__c_2Enum_2E0:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Enum_2E0,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0) = c_2Enum_2E0)).
thf(tp_c_2Earithmetic_2E_3E_3D,type,(c_2Earithmetic_2E_3E_3D:$i)).
thf(mem_c_2Earithmetic_2E_3E_3D,axiom,(mem@c_2Earithmetic_2E_3E_3D@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Earithmetic_2E_3E,type,(c_2Earithmetic_2E_3E:$i)).
thf(mem_c_2Earithmetic_2E_3E,axiom,(mem@c_2Earithmetic_2E_3E@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Elist_2ENIL,type,(c_2Elist_2ENIL:(del>$i))).
thf(mem_c_2Elist_2ENIL,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ENIL@A_27a)@(ty_2Elist_2Elist@A_27a)))).
thf(tp_c_2Earithmetic_2EZERO,type,(c_2Earithmetic_2EZERO:$i)).
thf(mem_c_2Earithmetic_2EZERO,axiom,(mem@c_2Earithmetic_2EZERO@ty_2Enum_2Enum)).
thf(stp_fo_c_2Earithmetic_2EZERO,type,(fo__c_2Earithmetic_2EZERO:tp__ty_2Enum_2Enum)).
thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,((inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)).
thf(tp_c_2Earithmetic_2EBIT1,type,(c_2Earithmetic_2EBIT1:$i)).
thf(mem_c_2Earithmetic_2EBIT1,axiom,(mem@c_2Earithmetic_2EBIT1@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2EBIT1,type,(fo__c_2Earithmetic_2EBIT1:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2EBIT1 @ X0)) = (ap @ c_2Earithmetic_2EBIT1 @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Earithmetic_2ENUMERAL,type,(c_2Earithmetic_2ENUMERAL:$i)).
thf(mem_c_2Earithmetic_2ENUMERAL,axiom,(mem@c_2Earithmetic_2ENUMERAL@(arr@ty_2Enum_2Enum@ty_2Enum_2Enum))).
thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,(fo__c_2Earithmetic_2ENUMERAL:(tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum))).
thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,( ! [X0:tp__ty_2Enum_2Enum] : ((inj__ty_2Enum_2Enum @ (fo__c_2Earithmetic_2ENUMERAL @ X0)) = (ap @ c_2Earithmetic_2ENUMERAL @ (inj__ty_2Enum_2Enum @ X0))))).
thf(tp_c_2Elist_2ELENGTH,type,(c_2Elist_2ELENGTH:(del>$i))).
thf(mem_c_2Elist_2ELENGTH,axiom,( ! [A_27a:del] : (mem@(c_2Elist_2ELENGTH@A_27a)@(arr@(ty_2Elist_2Elist@A_27a)@ty_2Enum_2Enum)))).
thf(tp_c_2Eprim__rec_2E_3C,type,(c_2Eprim__rec_2E_3C:$i)).
thf(mem_c_2Eprim__rec_2E_3C,axiom,(mem@c_2Eprim__rec_2E_3C@(arr@ty_2Enum_2Enum@(arr@ty_2Enum_2Enum@bool)))).
thf(tp_c_2Emin_2E_3D,type,(c_2Emin_2E_3D:(del>$i))).
thf(mem_c_2Emin_2E_3D,axiom,( ! [A_27a:del] : (mem@(c_2Emin_2E_3D@A_27a)@(arr@A_27a@(arr@A_27a@bool))))).
thf(ax_eq_p,axiom,( ! [A:del] : ( ! [X:$i] : ((mem@X@A) => ( ! [Y:$i] : ((mem@Y@A) => ((p@(ap@(ap@(c_2Emin_2E_3D@A)@X)@Y)) <=> (X = Y)))))))).
thf(tp_c_2Ebool_2E_2F_5C,type,(c_2Ebool_2E_2F_5C:$i)).
thf(mem_c_2Ebool_2E_2F_5C,axiom,(mem@c_2Ebool_2E_2F_5C@(arr@bool@(arr@bool@bool)))).
thf(ax_and_p,axiom,( ! [Q:$i] : ((mem@Q@bool) => ( ! [R:$i] : ((mem@R@bool) => ((p@(ap@(ap@c_2Ebool_2E_2F_5C@Q)@R)) <=> ((p@Q) & (p@R)))))))).
thf(tp_c_2Ebool_2E_21,type,(c_2Ebool_2E_21:(del>$i))).
thf(mem_c_2Ebool_2E_21,axiom,( ! [A_27a:del] : (mem@(c_2Ebool_2E_21@A_27a)@(arr@(arr@A_27a@bool)@bool)))).
thf(ax_all_p,axiom,( ! [A:del] : ( ! [Q:$i] : ((mem@Q@(arr@A@bool)) => ((p@(ap@(c_2Ebool_2E_21@A)@Q)) <=> ( ! [X:$i] : ((mem@X@A) => (p@(ap@Q@X))))))))).
thf(ax_thm_2Earithmetic_2EGREATER__DEF,axiom,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2EADD__SYM,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ V0m))))))).
thf(conj_thm_2Earithmetic_2ELESS__EQ,lemma,( ! [V0m:tp__ty_2Enum_2Enum] : ( ! [V1n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0m))@(inj__ty_2Enum_2Enum @ V1n))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V0m)))@(inj__ty_2Enum_2Enum @ V1n))))))).
thf(conj_thm_2Earithmetic_2ESUB__EQUAL__0,lemma,( ! [V0c:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0c))@(inj__ty_2Enum_2Enum @ V0c))) = fo__c_2Enum_2E0))).
thf(conj_thm_2Earithmetic_2EGREATER__EQ,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))))).
thf(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0t:$i] : ((mem@V0t@(arr@A_27a@A_27b)) => ((lam@A_27a@(^ [V1x:$i] : (ap@V0t@V1x))) = V0t)))))).
thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,( ! [V0t1:$i] : ((mem@V0t1@bool) => ( ! [V1t2:$i] : ((mem@V1t2@bool) => (((p@V0t1) => (p@V1t2)) => (((p@V1t2) => (p@V0t1)) => ((p@V0t1) <=> (p@V1t2))))))))).
thf(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a:del]: ( ! [V0t1:$i] : ((mem@V0t1@A_27a) => ( ! [V1t2:$i] : ((mem@V1t2@A_27a) => (((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0t1)@V1t2) = V0t1) & ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0t1)@V1t2) = V1t2)))))))).
thf(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1Q:$i] : ((mem@V1Q@bool) => ((? [V2x:$i] : ((mem@V2x@A_27a) & ((p@(ap@V0P@V2x)) & (p@V1Q)))) <=> ((? [V3x:$i] : ((mem@V3x@A_27a) & (p@(ap@V0P@V3x)))) & (p@V1Q))))))))).
thf(conj_thm_2Ebool_2EUNWIND__THM2,lemma,( ! [A_27a:del]: ( ! [V0P:$i] : ((mem@V0P@(arr@A_27a@bool)) => ( ! [V1a:$i] : ((mem@V1a@A_27a) => ((? [V2x:$i] : ((mem@V2x@A_27a) & ((V2x = V1a) & (p@(ap@V0P@V2x))))) <=> (p@(ap@V0P@V1a))))))))).
thf(ax_thm_2Elist_2EAPPEND,axiom,( ! [A_27a:del]: (( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => ((ap@(ap@(c_2Elist_2EAPPEND@A_27a)@(c_2Elist_2ENIL@A_27a))@V0l) = V0l))) & ( ! [V1l1:$i] : ((mem@V1l1@(ty_2Elist_2Elist@A_27a)) => ( ! [V2l2:$i] : ((mem@V2l2@(ty_2Elist_2Elist@A_27a)) => ( ! [V3h:$i] : ((mem@V3h@A_27a) => ((ap@(ap@(c_2Elist_2EAPPEND@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V3h)@V1l1))@V2l2) = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V3h)@(ap@(ap@(c_2Elist_2EAPPEND@A_27a)@V1l1)@V2l2)))))))))))).
thf(conj_thm_2Elist_2ELENGTH__NIL,lemma,( ! [A_27a:del]: ( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = fo__c_2Enum_2E0) <=> (V0l = (c_2Elist_2ENIL@A_27a))))))).
thf(conj_thm_2Elist_2ELENGTH__EQ__NUM,lemma,( ! [A_27a:del]: (( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = fo__c_2Enum_2E0) <=> (V0l = (c_2Elist_2ENIL@A_27a))))) & (( ! [V1l:$i] : ((mem@V1l@(ty_2Elist_2Elist@A_27a)) => ( ! [V2n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V1l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V2n)))) <=> (? [V3h:$i] : ((mem@V3h@A_27a) & (? [V4l_27:$i] : ((mem@V4l_27@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V4l_27)) = V2n) & (V1l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V3h)@V4l_27))))))))))) & ( ! [V5l:$i] : ((mem@V5l@(ty_2Elist_2Elist@A_27a)) => ( ! [V6n1:tp__ty_2Enum_2Enum] : ( ! [V7n2:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V5l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V6n1))@(inj__ty_2Enum_2Enum @ V7n2)))) <=> (? [V8l1:$i] : ((mem@V8l1@(ty_2Elist_2Elist@A_27a)) & (? [V9l2:$i] : ((mem@V9l2@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V8l1)) = V6n1) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V9l2)) = V7n2) & (V5l = (ap@(ap@(c_2Elist_2EAPPEND@A_27a)@V8l1)@V9l2))))))))))))))))).
thf(conj_thm_2Elist_2ELENGTH__EQ__NUM__compute,lemma,( ! [A_27a:del]: (( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = fo__c_2Enum_2E0) <=> (V0l = (c_2Elist_2ENIL@A_27a))))) & (( ! [V1l:$i] : ((mem@V1l@(ty_2Elist_2Elist@A_27a)) => ( ! [V2n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V1l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n))))) <=> (? [V3h:$i] : ((mem@V3h@A_27a) & (? [V4l_27:$i] : ((mem@V4l_27@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V4l_27)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (V1l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V3h)@V4l_27))))))))))) & (( ! [V5l:$i] : ((mem@V5l@(ty_2Elist_2Elist@A_27a)) => ( ! [V6n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V5l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V6n))))) <=> (? [V7h:$i] : ((mem@V7h@A_27a) & (? [V8l_27:$i] : ((mem@V8l_27@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V8l_27)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V6n))))) & (V5l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V7h)@V8l_27))))))))))) & ( ! [V9l:$i] : ((mem@V9l@(ty_2Elist_2Elist@A_27a)) => ( ! [V10n1:tp__ty_2Enum_2Enum] : ( ! [V11n2:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V9l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V10n1))@(inj__ty_2Enum_2Enum @ V11n2)))) <=> (? [V12l1:$i] : ((mem@V12l1@(ty_2Elist_2Elist@A_27a)) & (? [V13l2:$i] : ((mem@V13l2@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V12l1)) = V10n1) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V13l2)) = V11n2) & (V9l = (ap@(ap@(c_2Elist_2EAPPEND@A_27a)@V12l1)@V13l2)))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__suc,lemma,(((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) & (( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n))))) & ( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V1n))))))))).
thf(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ! [V0n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V0n))) = V0n)) & (( ! [V1n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V1n)) & (( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enumeral_2EiZ@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))) & (( ! [V4n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V4n))) = fo__c_2Enum_2E0)) & (( ! [V5n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V5n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0)) & (( ! [V6n:tp__ty_2Enum_2Enum] : ( ! [V7m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2A@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V6n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V7m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2A@(inj__ty_2Enum_2Enum @ V6n))@(inj__ty_2Enum_2Enum @ V7m))))))) & (( ! [V8n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V8n))) = fo__c_2Enum_2E0)) & (( ! [V9n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V9n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V9n)) & (( ! [V10n:tp__ty_2Enum_2Enum] : ( ! [V11m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V10n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V11m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V10n))@(inj__ty_2Enum_2Enum @ V11m))))))) & (( ! [V12n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V12n))))) = fo__c_2Enum_2E0)) & (( ! [V13n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V13n))))) = fo__c_2Enum_2E0)) & (( ! [V14n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V14n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) & (( ! [V15n:tp__ty_2Enum_2Enum] : ( ! [V16m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2EEXP@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V15n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V16m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2EEXP@(inj__ty_2Enum_2Enum @ V15n))@(inj__ty_2Enum_2Enum @ V16m))))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V17n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Enum_2ESUC@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V17n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Enum_2ESUC@(inj__ty_2Enum_2Enum @ V17n)))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = fo__c_2Enum_2E0) & (( ! [V18n:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Eprim__rec_2EPRE@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V18n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Eprim__rec_2EPRE@(inj__ty_2Enum_2Enum @ V18n)))))) & (( ! [V19n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V19n))) = fo__c_2Enum_2E0) <=> (V19n = fo__c_2Earithmetic_2EZERO))) & (( ! [V20n:tp__ty_2Enum_2Enum] : ((fo__c_2Enum_2E0 = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V20n)))) <=> (V20n = fo__c_2Earithmetic_2EZERO))) & (( ! [V21n:tp__ty_2Enum_2Enum] : ( ! [V22m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V21n))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V22m)))) <=> (V21n = V22m)))) & (( ! [V23n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V23n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $false)) & (( ! [V24n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V24n)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V24n))))) & (( ! [V25n:tp__ty_2Enum_2Enum] : ( ! [V26m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V25n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V26m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V25n))@(inj__ty_2Enum_2Enum @ V26m)))))) & (( ! [V27n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V27n))) <=> $false)) & (( ! [V28n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V28n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V28n))))) & (( ! [V29n:tp__ty_2Enum_2Enum] : ( ! [V30m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V29n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V30m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V30m))@(inj__ty_2Enum_2Enum @ V29n)))))) & (( ! [V31n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V31n))) <=> $true)) & (( ! [V32n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V32n)))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V32n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) & (( ! [V33n:tp__ty_2Enum_2Enum] : ( ! [V34m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V33n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V34m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V33n))@(inj__ty_2Enum_2Enum @ V34m)))))) & (( ! [V35n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ V35n))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> $true)) & (( ! [V36n:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ V36n))) <=> (V36n = fo__c_2Enum_2E0))) & (( ! [V37n:tp__ty_2Enum_2Enum] : ( ! [V38m:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V37n)))@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V38m)))) <=> (p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V38m))@(inj__ty_2Enum_2Enum @ V37n)))))) & (( ! [V39n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EODD@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V39n)))) <=> (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ V39n))))) & (( ! [V40n:tp__ty_2Enum_2Enum] : ((p@(ap@c_2Earithmetic_2EEVEN@(ap@c_2Earithmetic_2ENUMERAL@(inj__ty_2Enum_2Enum @ V40n)))) <=> (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ V40n))))) & ((~ (p@(ap@c_2Earithmetic_2EODD@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (p@(ap@c_2Earithmetic_2EEVEN@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))))))))))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__lt,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) <=> $true) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) <=> $false) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V1m)))) <=> (~ (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n))))) & ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V1m)))) <=> (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))))))))))).
thf(conj_thm_2Enumeral_2EiSUB__THM,lemma,( ! [V0x:tp__ty_2Enum_2Enum] : ( ! [V1b:$i] : ((mem@V1b@bool) => ( ! [V2n:tp__ty_2Enum_2Enum] : ( ! [V3m:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@V1b)@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))@(inj__ty_2Enum_2Enum @ V0x))) = fo__c_2Earithmetic_2EZERO) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = V2n) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V2n)))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & (((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m))))) & ((surj__ty_2Enum_2Enum @ (ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V2n)))@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V3m)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT1@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2EF)@(inj__ty_2Enum_2Enum @ V2n))@(inj__ty_2Enum_2Enum @ V3m)))))))))))))))))))))).
thf(conj_thm_2Enumeral_2Enumeral__sub,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@c_2Earithmetic_2E_2D@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))) = (surj__ty_2Enum_2Enum @ (ap@(ap@(ap@(c_2Ebool_2ECOND@ty_2Enum_2Enum)@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V1m))@(inj__ty_2Enum_2Enum @ V0n)))@(ap@c_2Earithmetic_2ENUMERAL@(ap@(ap@(ap@c_2Enumeral_2EiSUB@c_2Ebool_2ET)@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2Enumeral_2EiDUB__removal,lemma,( ! [V0n:tp__ty_2Enum_2Enum] : (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ V0n))))) & (((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ V0n)))) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ V0n))))) & ((surj__ty_2Enum_2Enum @ (ap@c_2Enumeral_2EiDUB@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))) = fo__c_2Earithmetic_2EZERO))))).
thf(conj_thm_2EquantHeuristics_2ELENGTH__LE__PLUS,lemma,( ! [A_27a:del]: ( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1m:tp__ty_2Enum_2Enum] : ( ! [V2l:$i] : ((mem@V2l@(ty_2Elist_2Elist@A_27a)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V0n))@(inj__ty_2Enum_2Enum @ V1m)))@(ap@(c_2Elist_2ELENGTH@A_27a)@V2l))) <=> (? [V3l1:$i] : ((mem@V3l1@(ty_2Elist_2Elist@A_27a)) & (? [V4l2:$i] : ((mem@V4l2@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V3l1)) = V0n) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1m))@(ap@(c_2Elist_2ELENGTH@A_27a)@V4l2))) & (V2l = (ap@(ap@(c_2Elist_2EAPPEND@A_27a)@V3l1)@V4l2))))))))))))))).
thf(conj_thm_2EquantHeuristics_2ELENGTH__LE__NUM,lemma,( ! [A_27a:del]: ( ! [V0n:tp__ty_2Enum_2Enum] : ( ! [V1l:$i] : ((mem@V1l@(ty_2Elist_2Elist@A_27a)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V0n))@(ap@(c_2Elist_2ELENGTH@A_27a)@V1l))) <=> (? [V2l1:$i] : ((mem@V2l1@(ty_2Elist_2Elist@A_27a)) & (? [V3l2:$i] : ((mem@V3l2@(ty_2Elist_2Elist@A_27a)) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V2l1)) = V0n) & (V1l = (ap@(ap@(c_2Elist_2EAPPEND@A_27a)@V2l1)@V3l2))))))))))))).
thf(conj_thm_2EquantHeuristics_2ELENGTH__NIL__SYM,lemma,( ! [A_27a:del]: ( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => ((fo__c_2Enum_2E0 = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))))))).
thf(conj_thm_2EquantHeuristics_2ELIST__LENGTH__COMPARE__1,lemma,( ! [A_27a:del]: ( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (V0l = (c_2Elist_2ENIL@A_27a)))))))))).
thf(conj_thm_2EquantHeuristics_2ELIST__LENGTH__4,conjecture,( ! [A_27a:del]: ( ! [V0l:$i] : ((mem@V0l@(ty_2Elist_2Elist@A_27a)) => ( ! [V1x:tp__ty_2Enum_2Enum] : ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V2e1:$i] : ((mem@V2e1@A_27a) & (? [V3e2:$i] : ((mem@V3e2@A_27a) & (? [V4e3:$i] : ((mem@V4e3@A_27a) & (? [V5e4:$i] : ((mem@V5e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V2e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V3e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V4e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V5e4)@(c_2Elist_2ENIL@A_27a))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V6e1:$i] : ((mem@V6e1@A_27a) & (? [V7e2:$i] : ((mem@V7e2@A_27a) & (? [V8e3:$i] : ((mem@V8e3@A_27a) & (? [V9e4:$i] : ((mem@V9e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V6e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V7e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V8e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V9e4)@(c_2Elist_2ENIL@A_27a))))))))))))))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V10l_27:$i] : ((mem@V10l_27@(ty_2Elist_2Elist@A_27a)) & (? [V11e1:$i] : ((mem@V11e1@A_27a) & (? [V12e2:$i] : ((mem@V12e2@A_27a) & (? [V13e3:$i] : ((mem@V13e3@A_27a) & (? [V14e4:$i] : ((mem@V14e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V11e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V12e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V13e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V14e4)@V10l_27)))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V15l_27:$i] : ((mem@V15l_27@(ty_2Elist_2Elist@A_27a)) & (? [V16e1:$i] : ((mem@V16e1@A_27a) & (? [V17e2:$i] : ((mem@V17e2@A_27a) & (? [V18e3:$i] : ((mem@V18e3@A_27a) & (? [V19e4:$i] : ((mem@V19e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V16e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V17e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V18e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V19e4)@V15l_27)))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V20l_27:$i] : ((mem@V20l_27@(ty_2Elist_2Elist@A_27a)) & (? [V21e1:$i] : ((mem@V21e1@A_27a) & (? [V22e2:$i] : ((mem@V22e2@A_27a) & (? [V23e3:$i] : ((mem@V23e3@A_27a) & (? [V24e4:$i] : ((mem@V24e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V21e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V22e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V23e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V24e4)@V20l_27)))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V25l_27:$i] : ((mem@V25l_27@(ty_2Elist_2Elist@A_27a)) & (? [V26e1:$i] : ((mem@V26e1@A_27a) & (? [V27e2:$i] : ((mem@V27e2@A_27a) & (? [V28e3:$i] : ((mem@V28e3@A_27a) & (? [V29e4:$i] : ((mem@V29e4@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V26e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V27e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V28e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V29e4)@V25l_27)))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V30l_27:$i] : ((mem@V30l_27@(ty_2Elist_2Elist@A_27a)) & (? [V31e1:$i] : ((mem@V31e1@A_27a) & (? [V32e2:$i] : ((mem@V32e2@A_27a) & (? [V33e3:$i] : ((mem@V33e3@A_27a) & (? [V34e4:$i] : ((mem@V34e4@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V30l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V31e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V32e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V33e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V34e4)@V30l_27))))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V35l_27:$i] : ((mem@V35l_27@(ty_2Elist_2Elist@A_27a)) & (? [V36e1:$i] : ((mem@V36e1@A_27a) & (? [V37e2:$i] : ((mem@V37e2@A_27a) & (? [V38e3:$i] : ((mem@V38e3@A_27a) & (? [V39e4:$i] : ((mem@V39e4@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V35l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V36e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V37e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V38e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V39e4)@V35l_27))))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V40l_27:$i] : ((mem@V40l_27@(ty_2Elist_2Elist@A_27a)) & (? [V41e1:$i] : ((mem@V41e1@A_27a) & (? [V42e2:$i] : ((mem@V42e2@A_27a) & (? [V43e3:$i] : ((mem@V43e3@A_27a) & (? [V44e4:$i] : ((mem@V44e4@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V40l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V41e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V42e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V43e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V44e4)@V40l_27))))))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) <=> (? [V45l_27:$i] : ((mem@V45l_27@(ty_2Elist_2Elist@A_27a)) & (? [V46e1:$i] : ((mem@V46e1@A_27a) & (? [V47e2:$i] : ((mem@V47e2@A_27a) & (? [V48e3:$i] : ((mem@V48e3@A_27a) & (? [V49e4:$i] : ((mem@V49e4@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V45l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V46e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V47e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V48e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V49e4)@V45l_27))))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V50l_27:$i] : ((mem@V50l_27@(ty_2Elist_2Elist@A_27a)) & (? [V51e1:$i] : ((mem@V51e1@A_27a) & (? [V52e2:$i] : ((mem@V52e2@A_27a) & (? [V53e3:$i] : ((mem@V53e3@A_27a) & (? [V54e4:$i] : ((mem@V54e4@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V50l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V51e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V52e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V53e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V54e4)@V50l_27))))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V55l_27:$i] : ((mem@V55l_27@(ty_2Elist_2Elist@A_27a)) & (? [V56e1:$i] : ((mem@V56e1@A_27a) & (? [V57e2:$i] : ((mem@V57e2@A_27a) & (? [V58e3:$i] : ((mem@V58e3@A_27a) & (? [V59e4:$i] : ((mem@V59e4@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V55l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V56e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V57e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V58e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V59e4)@V55l_27))))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) <=> (? [V60l_27:$i] : ((mem@V60l_27@(ty_2Elist_2Elist@A_27a)) & (? [V61e1:$i] : ((mem@V61e1@A_27a) & (? [V62e2:$i] : ((mem@V62e2@A_27a) & (? [V63e3:$i] : ((mem@V63e3@A_27a) & (? [V64e4:$i] : ((mem@V64e4@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V60l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V61e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V62e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V63e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V64e4)@V60l_27))))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V65l_27:$i] : ((mem@V65l_27@(ty_2Elist_2Elist@A_27a)) & (? [V66e1:$i] : ((mem@V66e1@A_27a) & (? [V67e2:$i] : ((mem@V67e2@A_27a) & (? [V68e3:$i] : ((mem@V68e3@A_27a) & (? [V69e4:$i] : ((mem@V69e4@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V65l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V66e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V67e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V68e3)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V69e4)@V65l_27))))))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V70e1:$i] : ((mem@V70e1@A_27a) & (? [V71e2:$i] : ((mem@V71e2@A_27a) & (? [V72e3:$i] : ((mem@V72e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V70e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V71e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V72e3)@(c_2Elist_2ENIL@A_27a)))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V73e1:$i] : ((mem@V73e1@A_27a) & (? [V74e2:$i] : ((mem@V74e2@A_27a) & (? [V75e3:$i] : ((mem@V75e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V73e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V74e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V75e3)@(c_2Elist_2ENIL@A_27a)))))))))))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V76l_27:$i] : ((mem@V76l_27@(ty_2Elist_2Elist@A_27a)) & (? [V77e1:$i] : ((mem@V77e1@A_27a) & (? [V78e2:$i] : ((mem@V78e2@A_27a) & (? [V79e3:$i] : ((mem@V79e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V77e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V78e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V79e3)@V76l_27))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V80l_27:$i] : ((mem@V80l_27@(ty_2Elist_2Elist@A_27a)) & (? [V81e1:$i] : ((mem@V81e1@A_27a) & (? [V82e2:$i] : ((mem@V82e2@A_27a) & (? [V83e3:$i] : ((mem@V83e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V81e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V82e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V83e3)@V80l_27))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V84l_27:$i] : ((mem@V84l_27@(ty_2Elist_2Elist@A_27a)) & (? [V85e1:$i] : ((mem@V85e1@A_27a) & (? [V86e2:$i] : ((mem@V86e2@A_27a) & (? [V87e3:$i] : ((mem@V87e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V85e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V86e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V87e3)@V84l_27))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V88l_27:$i] : ((mem@V88l_27@(ty_2Elist_2Elist@A_27a)) & (? [V89e1:$i] : ((mem@V89e1@A_27a) & (? [V90e2:$i] : ((mem@V90e2@A_27a) & (? [V91e3:$i] : ((mem@V91e3@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V89e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V90e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V91e3)@V88l_27))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V92l_27:$i] : ((mem@V92l_27@(ty_2Elist_2Elist@A_27a)) & (? [V93e1:$i] : ((mem@V93e1@A_27a) & (? [V94e2:$i] : ((mem@V94e2@A_27a) & (? [V95e3:$i] : ((mem@V95e3@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V92l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V93e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V94e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V95e3)@V92l_27)))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V96l_27:$i] : ((mem@V96l_27@(ty_2Elist_2Elist@A_27a)) & (? [V97e1:$i] : ((mem@V97e1@A_27a) & (? [V98e2:$i] : ((mem@V98e2@A_27a) & (? [V99e3:$i] : ((mem@V99e3@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V96l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V97e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V98e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V99e3)@V96l_27)))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V100l_27:$i] : ((mem@V100l_27@(ty_2Elist_2Elist@A_27a)) & (? [V101e1:$i] : ((mem@V101e1@A_27a) & (? [V102e2:$i] : ((mem@V102e2@A_27a) & (? [V103e3:$i] : ((mem@V103e3@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V100l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V101e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V102e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V103e3)@V100l_27)))))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) <=> (? [V104l_27:$i] : ((mem@V104l_27@(ty_2Elist_2Elist@A_27a)) & (? [V105e1:$i] : ((mem@V105e1@A_27a) & (? [V106e2:$i] : ((mem@V106e2@A_27a) & (? [V107e3:$i] : ((mem@V107e3@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V104l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V105e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V106e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V107e3)@V104l_27)))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V108l_27:$i] : ((mem@V108l_27@(ty_2Elist_2Elist@A_27a)) & (? [V109e1:$i] : ((mem@V109e1@A_27a) & (? [V110e2:$i] : ((mem@V110e2@A_27a) & (? [V111e3:$i] : ((mem@V111e3@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V108l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V109e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V110e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V111e3)@V108l_27)))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Enum_2Enum @ V1x))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V112l_27:$i] : ((mem@V112l_27@(ty_2Elist_2Elist@A_27a)) & (? [V113e1:$i] : ((mem@V113e1@A_27a) & (? [V114e2:$i] : ((mem@V114e2@A_27a) & (? [V115e3:$i] : ((mem@V115e3@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V112l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V113e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V114e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V115e3)@V112l_27)))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) <=> (? [V116l_27:$i] : ((mem@V116l_27@(ty_2Elist_2Elist@A_27a)) & (? [V117e1:$i] : ((mem@V117e1@A_27a) & (? [V118e2:$i] : ((mem@V118e2@A_27a) & (? [V119e3:$i] : ((mem@V119e3@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V116l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V117e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V118e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V119e3)@V116l_27)))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V120l_27:$i] : ((mem@V120l_27@(ty_2Elist_2Elist@A_27a)) & (? [V121e1:$i] : ((mem@V121e1@A_27a) & (? [V122e2:$i] : ((mem@V122e2@A_27a) & (? [V123e3:$i] : ((mem@V123e3@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V120l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V121e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V122e2)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V123e3)@V120l_27)))))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V124e1:$i] : ((mem@V124e1@A_27a) & (? [V125e2:$i] : ((mem@V125e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V124e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V125e2)@(c_2Elist_2ENIL@A_27a))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V126e1:$i] : ((mem@V126e1@A_27a) & (? [V127e2:$i] : ((mem@V127e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V126e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V127e2)@(c_2Elist_2ENIL@A_27a))))))))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V128l_27:$i] : ((mem@V128l_27@(ty_2Elist_2Elist@A_27a)) & (? [V129e1:$i] : ((mem@V129e1@A_27a) & (? [V130e2:$i] : ((mem@V130e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V129e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V130e2)@V128l_27)))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V131l_27:$i] : ((mem@V131l_27@(ty_2Elist_2Elist@A_27a)) & (? [V132e1:$i] : ((mem@V132e1@A_27a) & (? [V133e2:$i] : ((mem@V133e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V132e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V133e2)@V131l_27)))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V134l_27:$i] : ((mem@V134l_27@(ty_2Elist_2Elist@A_27a)) & (? [V135e1:$i] : ((mem@V135e1@A_27a) & (? [V136e2:$i] : ((mem@V136e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V135e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V136e2)@V134l_27)))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V137l_27:$i] : ((mem@V137l_27@(ty_2Elist_2Elist@A_27a)) & (? [V138e1:$i] : ((mem@V138e1@A_27a) & (? [V139e2:$i] : ((mem@V139e2@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V138e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V139e2)@V137l_27)))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V140l_27:$i] : ((mem@V140l_27@(ty_2Elist_2Elist@A_27a)) & (? [V141e1:$i] : ((mem@V141e1@A_27a) & (? [V142e2:$i] : ((mem@V142e2@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V140l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V141e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V142e2)@V140l_27))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V143l_27:$i] : ((mem@V143l_27@(ty_2Elist_2Elist@A_27a)) & (? [V144e1:$i] : ((mem@V144e1@A_27a) & (? [V145e2:$i] : ((mem@V145e2@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V143l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V144e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V145e2)@V143l_27))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V146l_27:$i] : ((mem@V146l_27@(ty_2Elist_2Elist@A_27a)) & (? [V147e1:$i] : ((mem@V147e1@A_27a) & (? [V148e2:$i] : ((mem@V148e2@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V146l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V147e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V148e2)@V146l_27))))))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V149l_27:$i] : ((mem@V149l_27@(ty_2Elist_2Elist@A_27a)) & (? [V150e1:$i] : ((mem@V150e1@A_27a) & (? [V151e2:$i] : ((mem@V151e2@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V149l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V150e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V151e2)@V149l_27))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V152l_27:$i] : ((mem@V152l_27@(ty_2Elist_2Elist@A_27a)) & (? [V153e1:$i] : ((mem@V153e1@A_27a) & (? [V154e2:$i] : ((mem@V154e2@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V152l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V153e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V154e2)@V152l_27))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V155l_27:$i] : ((mem@V155l_27@(ty_2Elist_2Elist@A_27a)) & (? [V156e1:$i] : ((mem@V156e1@A_27a) & (? [V157e2:$i] : ((mem@V157e2@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V155l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V156e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V157e2)@V155l_27))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V158l_27:$i] : ((mem@V158l_27@(ty_2Elist_2Elist@A_27a)) & (? [V159e1:$i] : ((mem@V159e1@A_27a) & (? [V160e2:$i] : ((mem@V160e2@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V158l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V159e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V160e2)@V158l_27))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V161l_27:$i] : ((mem@V161l_27@(ty_2Elist_2Elist@A_27a)) & (? [V162e1:$i] : ((mem@V162e1@A_27a) & (? [V163e2:$i] : ((mem@V163e2@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V161l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V162e1)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V163e2)@V161l_27))))))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V164e1:$i] : ((mem@V164e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V164e1)@(c_2Elist_2ENIL@A_27a)))))) & ((((surj__ty_2Enum_2Enum @ (ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V165e1:$i] : ((mem@V165e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V165e1)@(c_2Elist_2ENIL@A_27a)))))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V166l_27:$i] : ((mem@V166l_27@(ty_2Elist_2Elist@A_27a)) & (? [V167e1:$i] : ((mem@V167e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V167e1)@V166l_27))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (? [V168l_27:$i] : ((mem@V168l_27@(ty_2Elist_2Elist@A_27a)) & (? [V169e1:$i] : ((mem@V169e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V169e1)@V168l_27))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V170l_27:$i] : ((mem@V170l_27@(ty_2Elist_2Elist@A_27a)) & (? [V171e1:$i] : ((mem@V171e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V171e1)@V170l_27))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (? [V172l_27:$i] : ((mem@V172l_27@(ty_2Elist_2Elist@A_27a)) & (? [V173e1:$i] : ((mem@V173e1@A_27a) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V173e1)@V172l_27))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V174l_27:$i] : ((mem@V174l_27@(ty_2Elist_2Elist@A_27a)) & (? [V175e1:$i] : ((mem@V175e1@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V174l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V175e1)@V174l_27)))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V176l_27:$i] : ((mem@V176l_27@(ty_2Elist_2Elist@A_27a)) & (? [V177e1:$i] : ((mem@V177e1@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V176l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V177e1)@V176l_27)))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V178l_27:$i] : ((mem@V178l_27@(ty_2Elist_2Elist@A_27a)) & (? [V179e1:$i] : ((mem@V179e1@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V178l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V179e1)@V178l_27)))))))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V180l_27:$i] : ((mem@V180l_27@(ty_2Elist_2Elist@A_27a)) & (? [V181e1:$i] : ((mem@V181e1@A_27a) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(inj__ty_2Enum_2Enum @ V1x))@(ap@(c_2Elist_2ELENGTH@A_27a)@V180l_27))) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V181e1)@V180l_27)))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x)))) <=> (? [V182l_27:$i] : ((mem@V182l_27@(ty_2Elist_2Elist@A_27a)) & (? [V183e1:$i] : ((mem@V183e1@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V182l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V183e1)@V182l_27)))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(inj__ty_2Enum_2Enum @ V1x))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V184l_27:$i] : ((mem@V184l_27@(ty_2Elist_2Elist@A_27a)) & (? [V185e1:$i] : ((mem@V185e1@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V184l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V185e1)@V184l_27)))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = (surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (? [V186l_27:$i] : ((mem@V186l_27@(ty_2Elist_2Elist@A_27a)) & (? [V187e1:$i] : ((mem@V187e1@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V186l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V187e1)@V186l_27)))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(ap@c_2Earithmetic_2E_2B@(inj__ty_2Enum_2Enum @ V1x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (? [V188l_27:$i] : ((mem@V188l_27@(ty_2Elist_2Elist@A_27a)) & (? [V189e1:$i] : ((mem@V189e1@A_27a) & (((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V188l_27)) = V1x) & (V0l = (ap@(ap@(c_2Elist_2ECONS@A_27a)@V189e1)@V188l_27)))))))) & ((((surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l)) = fo__c_2Enum_2E0) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((fo__c_2Enum_2E0 = (surj__ty_2Enum_2Enum @ (ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & (((p@(ap@(ap@c_2Earithmetic_2E_3E_3D@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))) <=> (V0l = (c_2Elist_2ENIL@A_27a))) & ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Elist_2ELENGTH@A_27a)@V0l))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) <=> (V0l = (c_2Elist_2ENIL@A_27a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
