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_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__zero_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29,axiom,![A_27t, A_27w]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2EULP_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2EULP_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))))).
fof(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Eabs_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal_2Ereal__lte_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(namespace__tagTheory_2EULP__lt__float__to__real,axiom,![A_27t, A_27w]: ![V0y_2E0]: (~ (p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))))) => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0)))))))))).
