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_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27c,X1_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Efinite__map_2EFUPDATE_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27c),X1_2E0))))).
fof(arityeq6_2Ec_2Efinite__map_2EfmlfpR_2E6_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0, X5_2E0]: (s(tyop_2Emin_2Ebool,c_2Efinite__map_2EfmlfpR_2E6(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X3_2E0),s(A_27a,X4_2E0),s(A_27a,X5_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))))),c_2Efinite__map_2EfmlfpR_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X3_2E0))),s(A_27a,X4_2E0))),s(A_27a,X5_2E0))))).
fof(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,![A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Efinite__map_2Efdomsub_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(A_27b,X1_2E0))))).
fof(finite__mapTheory_2EfmlfpR__cases,axiom,![A_27a, A_27b, A_27c]: ![V0f_2E0, V1fm0_2E0, V2a0_2E0, V3a1_2E0, V4a2_2E0, V5a3_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EfmlfpR_2E6(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1fm0_2E0),s(A_27a,V2a0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3a1_2E0),s(A_27a,V4a2_2E0),s(A_27a,V5a3_2E0)))) <=> (((s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3a1_2E0) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EFEMPTY_2E0)) & ((s(A_27a,V5a3_2E0) = s(A_27a,V2a0_2E0)) & (s(A_27a,V2a0_2E0) = s(A_27a,V4a2_2E0)))) | (((s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3a1_2E0) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EFEMPTY_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EfmlfpR_2E6(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1fm0_2E0),s(A_27a,V4a2_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1fm0_2E0),s(A_27a,V4a2_2E0),s(A_27a,V5a3_2E0)))) & ~ ((s(A_27a,V2a0_2E0) = s(A_27a,V4a2_2E0))))) | ?[V6fm_2E0, V7k_2E0, V8v_2E0]: ((s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3a1_2E0) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V6fm_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V7k_2E0),s(A_27c,V8v_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EfmlfpR_2E6(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V1fm0_2E0),s(A_27a,V2a0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V6fm_2E0),s(A_27b,V7k_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(A_27b,V7k_2E0))),s(A_27c,V8v_2E0))),s(A_27a,V4a2_2E0))),s(A_27a,V5a3_2E0))))))))).
