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_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_2Eprobability_2Eprob__space_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Eprobability_2Eprob__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_2Eprobability_2Eprob__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__sub_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sub_2E2(s(tyop_2Eextreal_2Eextreal,X0_2E0),s(tyop_2Eextreal_2Eextreal,X1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),c_2Eextreal_2Eextreal__sub_2E0),s(tyop_2Eextreal_2Eextreal,X0_2E0))),s(tyop_2Eextreal_2Eextreal,X1_2E0))))).
fof(arityeq2_2Ec_2Eprobability_2Ereal__random__variable_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eprobability_2Ereal__random__variable_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_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))),X1_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),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),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_2Eprobability_2Ereal__random__variable_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X0_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))),X1_2E0))))).
fof(arityeq1_2Ec_2Eprobability_2Ealmost__everywhere_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eprobability_2Econvergence__mode(A_27a),c_2Eprobability_2Ealmost__everywhere_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_2Eprobability_2Econvergence__mode(A_27a),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_2Eprobability_2Econvergence__mode(A_27a)),c_2Eprobability_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))))).
fof(arityeq3_2Ec_2Eprobability_2Econverge_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Eprobability_2Econverge_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0),s(tyop_2Eprobability_2Econvergence__mode(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eprobability_2Econvergence__mode(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eprobability_2Econvergence__mode(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(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eprobability_2Econvergence__mode(A_27a),tyop_2Emin_2Ebool))),c_2Eprobability_2Econverge_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0))),s(tyop_2Eprobability_2Econvergence__mode(A_27a),X2_2E0))))).
fof(probabilityTheory_2Econverge__AE__to__zero,axiom,![A_27a]: ![F0_2E0, F1_2E0]: (![V1X_2E0, V2Y_2E0, V4n_2E0, V5x_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,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_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2Y_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V5x_2E0))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__sub_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)),V1X_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V5x_2E0))),s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2Y_2E0),s(A_27a,V5x_2E0)))))) => (![V6x_2E0]: (s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),F1_2E0),s(A_27a,V6x_2E0))) = s(tyop_2Eextreal_2Eextreal,c_2Eextreal_2Eextreal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) => ![V0p_2E0, V1X_2E0, V2Y_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Eprobability_2Eprob__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))),V0p_2E0)))) & (![V3n_2E0]: p(s(tyop_2Emin_2Ebool,c_2Eprobability_2Ereal__random__variable_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)),V1X_2E0),s(tyop_2Enum_2Enum,V3n_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))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprobability_2Ereal__random__variable_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2Y_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))),V0p_2E0)))))) => (s(tyop_2Emin_2Ebool,c_2Eprobability_2Econverge_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2Y_2E0),s(tyop_2Eprobability_2Econvergence__mode(A_27a),c_2Eprobability_2Ealmost__everywhere_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))),V0p_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprobability_2Econverge_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,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_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V2Y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),F1_2E0),s(tyop_2Eprobability_2Econvergence__mode(A_27a),c_2Eprobability_2Ealmost__everywhere_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))),V0p_2E0)))))))))).
