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_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27b,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_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal)),c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Eextreal_2Eextreal,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Eextreal_2Eextreal,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Elebesgue_2Epsfis_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_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_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,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_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),c_2Elebesgue_2Epsfis_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_2Epsfis__sum,axiom,![A_27a, A_27b]: ![F1_2E0, F0_2E0]: (![V1f_2E0, V7t_2E0, V8i_2E0]: (s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0))),s(A_27a,V7t_2E0))),s(A_27b,V8i_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0),s(A_27b,V8i_2E0))),s(A_27a,V7t_2E0)))) => (![V1f_2E0, V3P_2E0, V7t_2E0]: (s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))),s(A_27a,V7t_2E0))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0))),s(A_27a,V7t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))) => ![V0m_2E0, V1f_2E0, V2a_2E0, V3P_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)))) & (![V4i_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))) => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),V2a_2E0),s(A_27b,V4i_2E0))),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_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),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0),s(A_27b,V4i_2E0))))))))) & (![V5i_2E0, V6t_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V5i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))) => ~ ((s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0),s(A_27b,V5i_2E0))),s(A_27a,V6t_2E0))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2ENegInf_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))))))) => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2EEXTREAL__SUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eextreal_2Eextreal),V2a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))))))))))).
