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(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq1_2Ec_2Eextreal_2Eextreal__sup_2E1,axiom,![X0_2E0]: (s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sup_2E1(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__sup_2E0),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Emeasure_2Emeasure__space_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure__space_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq1_2Ec_2Emeasure_2Em__space_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emeasure_2Em__space_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eextreal_2Eextreal_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Esigma__algebra_2Emeasurable_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eextreal_2Eextreal,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),c_2Esigma__algebra_2Emeasurable_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool))),c_2Esigma__algebra_2Emeasurable_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))))).
fof(arityeq1_2Ec_2Emeasure_2Emeasurable__sets_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emeasure_2Emeasurable__sets_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))))).
fof(arityeq2_2Ec_2Eborel_2Ealmost__everywhere_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eborel_2Ealmost__everywhere_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eborel_2Ealmost__everywhere_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,X0_2E0),s(tyop_2Eextreal_2Eextreal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),c_2Eextreal_2Eextreal__le_2E0),s(tyop_2Eextreal_2Eextreal,X0_2E0))),s(tyop_2Eextreal_2Eextreal,X1_2E0))))).
fof(arityeq1_2Ec_2Eextreal_2Eextreal__of__num_2E1,axiom,![X0_2E0]: (s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),c_2Eextreal_2Eextreal__of__num_2E0),s(tyop_2Enum_2Enum,X0_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(arityeq1_2Ec_2Eborel_2Efn__plus_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Eborel_2Efn__plus_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),c_2Eborel_2Efn__plus_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_2E0))))).
fof(arityeq2_2Ec_2Elebesgue_2Epos__fn__integral_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal)),c_2Elebesgue_2Epos__fn__integral_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0))))).
fof(lebesgueTheory_2Elebesgue__monotone__convergence__AE,axiom,![A_27a]: ![F2_2E0, F0_2E0, F1_2E0]: (![V0m_2E0, V2fi_2E0, V8i_2E0]: (s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0))),s(tyop_2Enum_2Enum,V8i_2E0))) = s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Eborel_2Efn__plus_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,V8i_2E0)))))))) => (![V2fi_2E0, V4x_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0))),s(A_27a,V4x_2E0)))) <=> ![V5i_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,V5i_2E0))),s(A_27a,V4x_2E0))),s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5i_2E0))))),s(A_27a,V4x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eextreal_2Eextreal__le_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,V5i_2E0))),s(A_27a,V4x_2E0)))))))) => (![V2fi_2E0, V6x_2E0, V7i_2E0]: (s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0))),s(A_27a,V6x_2E0))),s(tyop_2Enum_2Enum,V7i_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,V7i_2E0))),s(A_27a,V6x_2E0)))) => ![V0m_2E0, V1f_2E0, V2fi_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0)))) & (![V3i_2E0]: p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),c_2Esigma__algebra_2Emeasurable_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasurable__sets_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eborel_2EBorel_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Eborel_2Ealmost__everywhere_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0)))))) & ![V6x_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0)))))) => (s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sup_2E1(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0))),s(A_27a,V6x_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0),s(A_27a,V6x_2E0)))))))) => (s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),c_2Eborel_2Efn__plus_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0))))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sup_2E1(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal))),F2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal))),V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V2fi_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))))))).
