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_2Efmapal_2Eoptry_2E2_2Emono_2EA_27g,axiom,![A_27g]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27g),X0_2E0),s(tyop_2Eoption_2Eoption(A_27g),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g))),c_2Efmapal_2Eoptry_2E0),s(tyop_2Eoption_2Eoption(A_27g),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27g),X1_2E0))))).
fof(arityeq2_2Ec_2Efmapal_2Eoptry__list_2E2_2Emono_2EA_27g_20mono_2EA_27z,axiom,![A_27g, A_27z]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g))),c_2Efmapal_2Eoptry__list_2E0),s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27z_29,axiom,![A_27z]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)))),c_2Elist_2ECONS_2E0),s(tyop_2Eoption_2Eoption(A_27z),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),X1_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27z,axiom,![A_27z]: ![X0_2E0]: (s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27z),app_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27z)),c_2Eoption_2ESOME_2E0),s(A_27z,X0_2E0))))).
fof(fmapalTheory_2Eoptry__list,axiom,![A_27g, A_27z]: (![V0f_2E0]: (s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V0f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Eoption_2ENONE_2E0)) & (![V1l_2E0, V2f_2E0]: (s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V1l_2E0)))) & ![V3z_2E0, V4l_2E0, V5f_2E0]: (s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),c_2Elist_2ECONS_2E2(s(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(s(A_27z,V3z_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V4l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry_2E2(s(tyop_2Eoption_2Eoption(A_27g),app_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(A_27z,V3z_2E0))),s(tyop_2Eoption_2Eoption(A_27g),c_2Efmapal_2Eoptry__list_2E2(s(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5f_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V4l_2E0))))))))).
