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_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,![A_27b]: ![X0_2E0]: (s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Esum_2EINR_2E0),s(tyop_2Eone_2Eone,X0_2E0))))).
fof(arityeq1_2Ec_2Efinite__map_2Eis__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),c_2Efinite__map_2Eis__fmap_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,![A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X1_2E0),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X2_2E0))))).
fof(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,![A_27b]: ![X0_2E0]: (s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Esum_2EINL_2E0),s(A_27b,X0_2E0))))).
fof(finite__mapTheory_2Eis__fmap__strongind,axiom,![A_27a, A_27b]: ![F0_2E0, F2_2E0, F1_2E0]: (![V1a_2E0]: (s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0),s(A_27a,V1a_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))) => (![V5x_2E0, V3a_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)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0)))) <=> (s(A_27a,V5x_2E0) = s(A_27a,V3a_2E0))) => (![V3a_2E0, V4b_2E0, V2f_2E0, V5x_2E0]: (s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))),s(A_27a,V5x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(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)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V4b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0),s(A_27a,V5x_2E0)))))) => ![V0is__fmap_27_2E0]: ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0)))) & ![V2f_2E0, V3a_2E0, V4b_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))))))) => ![V6a0_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0)))))))))).
