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_2Ebag_2EBAG__INSERT_2E2_2Emono_2EA_27f,axiom,![A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27f,X0_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum))),c_2Ebag_2EBAG__INSERT_2E0),s(A_27f,X0_2E0))),s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),X1_2E0))))).
fof(arityeq2_2Ec_2Econtainer_2EBAG__OF__FMAP_2E2_2Emono_2EA_27f_20mono_2EA_27d_20mono_2EA_27e,axiom,![A_27d, A_27e, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),c_2Econtainer_2EBAG__OF__FMAP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum))),c_2Econtainer_2EBAG__OF__FMAP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X1_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,![A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Efinite__map_2Efmap(A_27d,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Efinite__map_2Efmap(A_27d,A_27e))),c_2Efinite__map_2Efdomsub_2E0),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X0_2E0))),s(A_27d,X1_2E0))))).
fof(arityeq2_2Ec_2Econtainer_2EBAG__OF__FMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Econtainer_2EBAG__OF__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum))),c_2Econtainer_2EBAG__OF__FMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,![A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27d,A_27e),c_2Epair_2E_2C_2E2(s(A_27d,X0_2E0),s(A_27e,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27d,A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27d,A_27e)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27d,A_27e))),c_2Epair_2E_2C_2E0),s(A_27d,X0_2E0))),s(A_27e,X1_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,![A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X0_2E0),s(tyop_2Epair_2Eprod(A_27d,A_27e),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Efinite__map_2Efmap(A_27d,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Efinite__map_2Efmap(A_27d,A_27e))),c_2Efinite__map_2EFUPDATE_2E0),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),X0_2E0))),s(tyop_2Epair_2Eprod(A_27d,A_27e),X1_2E0))))).
fof(containerTheory_2EBAG__OF__FMAP__THM,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e, A_27f]: (![V0f_2E0]: (s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Econtainer_2EBAG__OF__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Enum_2Enum),c_2Ebag_2EEMPTY__BAG_2E0)) & ![V1f_2E0, V2b_2E0, V3k_2E0, V4v_2E0]: (s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),c_2Econtainer_2EBAG__OF__FMAP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),V2b_2E0),s(tyop_2Epair_2Eprod(A_27d,A_27e),c_2Epair_2E_2C_2E2(s(A_27d,V3k_2E0),s(A_27e,V4v_2E0))))))) = s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),c_2Ebag_2EBAG__INSERT_2E2(s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(A_27d,V3k_2E0))),s(A_27e,V4v_2E0))),s(tyop_2Emin_2Efun(A_27f,tyop_2Enum_2Enum),c_2Econtainer_2EBAG__OF__FMAP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27d,A_27e),V2b_2E0),s(A_27d,V3k_2E0)))))))))).
