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_2Epatricia_2EIN__PTREE_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Epatricia_2EIN__PTREE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Epatricia_2EIN__PTREE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0))))).
fof(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2ETHE__PTREE_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X0_2E0))))).
fof(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))))).
fof(arityeq2_2Ec_2Epatricia__casts_2EIN__PTREEw_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),c_2Epatricia__casts_2EIN__PTREEw_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0))))).
fof(patricia__castsTheory_2EIN__PTREEw__def,axiom,![A_27a]: ![V0w_2E0, V1t_2E0]: (s(tyop_2Emin_2Ebool,c_2Epatricia__casts_2EIN__PTREEw_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0),s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2EIN__PTREE_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0w_2E0))),s(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E1(s(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1t_2E0))))))).
