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_2Efmapal_2Eassocv_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Eassocv_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Efmapal_2Eassocv_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))))).
fof(arityeq2_2Ec_2Efmapal_2Eincr__sort_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Eincr__sort_2E0),s(tyop_2Etoto_2Etoto(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))))).
fof(namespace__tagTheory_2Eincr__sort__fun,axiom,![A_27a, A_27b]: ![V0cmp_2E0, V1l_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Eassocv_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__sort_2E2(s(tyop_2Etoto_2Etoto(A_27a),V0cmp_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Eassocv_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))).
