fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))))).
fof(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))))).
fof(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))))).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27c,axiom,![A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,X0_2E0),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c))),c_2Ellist_2ELCONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))))).
fof(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27c,axiom,![A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))))).
fof(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27c,axiom,![A_27c]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))))).
fof(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,![A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),X1_2E0))))).
fof(llistTheory_2ELTAKE__THM,axiom,![A_27a, A_27b, A_27c]: (![V0l_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (![V1n_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Eoption_2ENONE_2E0)) & ![V2n_2E0, V3h_2E0, V4t_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E1(s(A_27c,V3h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))))))))).
