{ "paper": "Monotone Local Search with Sample-Dependent Running Times", "checkers": "Mode of ancillary/verify_all.sh that runs each checker: 'quick' runs in both modes, 'full' only with --full. The RSC antinorm certificate (prop:rsc-cert) is verified only by the two checkers marked 'full'.", "lean": { "toolchain": "leanprover/lean4:v4.35.0", "axioms": "axioms.txt" }, "statements": [ { "label": "thm:fw-main", "statement": "Theorem 3.5", "page": "papers/sample-dependent-mls/03-aprime.html#thm:fw-main", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLS.mls_sound", "MaxLeafFormal.MLS.mls_success", "MaxLeafFormal.MLS.mls_budget" ] } }, { "label": "lem:fw-threshold-prob", "statement": "Lemma 3.8", "page": "papers/sample-dependent-mls/03-aprime.html#lem:fw-threshold-prob", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.Budget.integral_twoPowNeg_pos", "MaxLeafFormal.Budget.threshold_prob", "MaxLeafFormal.Budget.threshold_prob_upper" ] } }, { "label": "lem:fw-gf", "statement": "Lemma 3.9", "page": "papers/sample-dependent-mls/03-aprime.html#lem:fw-gf", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLS.star_of_W", "MaxLeafFormal.MLSNec.fw_gf_upper", "MaxLeafFormal.MLSNec.mu_mul_pow_le_W", "MaxLeafFormal.MLSNec.pow_le_choose_mul" ] } }, { "label": "prop:fw-necessary", "statement": "Proposition 3.10", "page": "papers/sample-dependent-mls/03-aprime.html#prop:fw-necessary", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLSNec.mls_necessary", "MaxLeafFormal.MLSNec.Pnec" ] } }, { "label": "thm:fw-budgeted", "statement": "Theorem 3.14", "page": "papers/sample-dependent-mls/03-aprime.html#thm:fw-budgeted", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.Budget.budgeted_sound", "MaxLeafFormal.Budget.budgeted_success", "MaxLeafFormal.Budget.budgeted_success_of_admissible" ] } }, { "label": "thm:co-mean", "statement": "Theorem 4.1", "page": "papers/sample-dependent-mls/04-corollaries.html#thm:co-mean", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLS.mu_ge_of_mean", "MaxLeafFormal.MLS.mls_success_of_mean" ] } }, { "label": "cor:co-linear", "statement": "Corollary 4.3", "page": "papers/sample-dependent-mls/04-corollaries.html#cor:co-linear", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLS.linear_savings_W", "MaxLeafFormal.MLS.one_sample_size" ] } }, { "label": "rem:co-fsigma", "statement": "Remark 4.4", "page": "papers/sample-dependent-mls/04-corollaries.html#rem:co-fsigma", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.MLS.one_sample_size" ] } }, { "label": "lem:cds-maxleaf", "statement": "Lemma 5.1", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-maxleaf", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.CDS.maxLeaf_eq", "MaxLeafFormal.CDS.spanningTree_of_CDS", "MaxLeafFormal.CDS.maxLeaf_small" ] } }, { "label": "lem:cds-first-accepted", "statement": "Lemma 5.2", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-first-accepted", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.Budget.first_accepted" ] } }, { "label": "lem:cv-W", "statement": "Lemma 5.3", "page": "papers/sample-dependent-mls/05-cds.html#lem:cv-W", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.SteinerDir.steinerAlg_eq", "MaxLeafFormal.SteinerDir.bIE_count", "MaxLeafFormal.SteinerDir.bw_count", "MaxLeafFormal.SteinerDir.bw_mem", "MaxLeafFormal.SteinerDir.bw_zero", "MaxLeafFormal.SteinerDir.bw_pos", "MaxLeafFormal.SteinerDir.feasible_of_walk", "MaxLeafFormal.SteinerDir.walk_of_feasible" ] } }, { "label": "lem:cds-dir-steiner", "statement": "Lemma 5.6", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-dir-steiner", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.SteinerCDS.optSt_eq_optDir", "MaxLeafFormal.SteinerCDS.isState_Jb", "MaxLeafFormal.SteinerCDS.optSt_eq_inf_Jb", "MaxLeafFormal.SteinerCDS.stateAlg_eq" ] } }, { "label": "cor:cds-steiner", "statement": "Corollary 5.8", "page": "papers/sample-dependent-mls/05-cds.html#cor:cds-steiner", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.SteinerCDS.aSt_iff_ext", "MaxLeafFormal.SteinerCDS.aSt_iff_extYes", "MaxLeafFormal.SteinerCDS.not_aSt_of_lt", "MaxLeafFormal.SteinerCDS.isSol_JX_iff", "MaxLeafFormal.SteinerCDS.isState_JX", "MaxLeafFormal.SteinerCDS.terminals_JX", "MaxLeafFormal.SteinerCDS.optSt_J0" ] } }, { "label": "lem:cds-tree", "statement": "Lemma 5.9", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-tree", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.CDS.tree_inequality" ] } }, { "label": "lem:cds-pointwise", "statement": "Lemma 5.10", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-pointwise", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CDS.pointwise" ] } }, { "label": "lem:cds-C", "statement": "Lemma 5.11", "page": "papers/sample-dependent-mls/05-cds.html#lem:cds-C", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CDS.mean_terminals" ] } }, { "label": "prop:rs-rate", "statement": "Proposition 6.1", "page": "papers/sample-dependent-mls/06-rs.html#prop:rs-rate", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSRateAB.rs_rate_a", "MaxLeafFormal.RSRateAB.rsfσ_min_eq", "MaxLeafFormal.RSRateAB.rs_rate_b", "MaxLeafFormal.RSRateAB.rs_rate_b_argmin", "MaxLeafFormal.RSRateAB.rs_base_denom", "MaxLeafFormal.RSRateAB.rs_base", "MaxLeafFormal.RSRateAB.rsfσ_eq_fσ", "MaxLeafFormal.RSRateAB.rsTau_eq_τstar", "MaxLeafFormal.RSRate.rs_rate_c", "MaxLeafFormal.RSRate.rsF_one", "MaxLeafFormal.RSRate.rsF_eq_Fstar" ] }, "certificate": { "files": [ "ancillary/rs_closed_form_interval.py" ], "checkers": { "ancillary/rs_closed_form_interval.py": "quick" } } }, { "label": "cor:rs-moments", "statement": "Corollary 6.2", "page": "papers/sample-dependent-mls/06-rs.html#cor:rs-moments", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RateAssembly.rs_moments" ] } }, { "label": "thm:rs", "statement": "Theorem 6.4", "page": "papers/sample-dependent-mls/06-rs.html#thm:rs", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.RateAssembly.rs_star", "MaxLeafFormal.RSRate.rs_constants" ] } }, { "label": "thm:rstheta", "statement": "Theorem 7.2", "page": "papers/sample-dependent-mls/07-rstheta.html#thm:rstheta", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.RSThetaRate.rst_rates" ] } }, { "label": "lem:rst-E", "statement": "Lemma 7.3", "page": "papers/sample-dependent-mls/07-rstheta.html#lem:rst-E", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CDS.tree_reduction", "MaxLeafFormal.CDS.moment_bound_of_tree_bound", "MaxLeafFormal.CDS.rstheta_moment_bound_0", "MaxLeafFormal.CDS.rstheta_moment_bound_1", "MaxLeafFormal.LobsterGraph.tree_reduction_eq" ] } }, { "label": "lem:rst-treerec", "statement": "Lemma 7.4", "page": "papers/sample-dependent-mls/07-rstheta.html#lem:rst-treerec", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.Antinorm3.triple_single", "MaxLeafFormal.Antinorm3.triple_split", "MaxLeafFormal.Antinorm3.treeW_eq_fin" ] } }, { "label": "lem:rst-F", "statement": "Lemma 7.5", "page": "papers/sample-dependent-mls/07-rstheta.html#lem:rst-F", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.Antinorm3.merge_mem_smul_PZ", "MaxLeafFormal.Antinorm3.init_all", "MaxLeafFormal.Antinorm3.triple_D_mem", "MaxLeafFormal.Antinorm3.tree_bound_of_certificate" ] } }, { "label": "prop:rst-certs", "statement": "Proposition 7.7", "page": "papers/sample-dependent-mls/07-rstheta.html#prop:rst-certs", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSThetaCert.cert0_Z", "MaxLeafFormal.RSThetaCert.cert0_pairs", "MaxLeafFormal.RSThetaCert.cert0_inits", "MaxLeafFormal.RSThetaCert.cert1_Z", "MaxLeafFormal.RSThetaCert.cert1_pairs", "MaxLeafFormal.RSThetaCert.cert1_inits", "MaxLeafFormal.Antinorm3.tree_bound_of_checks", "MaxLeafFormal.rstheta_tree_bound_0", "MaxLeafFormal.rstheta_tree_bound_1", "MaxLeafFormal.RSThetaRate.rst_rates", "MaxLeafFormal.RSThetaRate.rst_rates_detail" ] }, "certificate": { "files": [ "ancillary/cert_final_0.json", "ancillary/cert_final_1.json", "ancillary/verify_cert.py", "ancillary/verify_cert_indep.py", "ancillary/v_cert_primal.py", "ancillary/cz_bounds.py", "ancillary/rst_rate_interval.py" ], "checkers": { "ancillary/verify_cert.py": "quick", "ancillary/verify_cert_indep.py": "quick", "ancillary/v_cert_primal.py": "quick", "ancillary/cz_bounds.py": "quick", "ancillary/rst_rate_interval.py": "quick" } } }, { "label": "prop:rst-rate", "statement": "Proposition 7.8", "page": "papers/sample-dependent-mls/07-rstheta.html#prop:rst-rate", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RateAssembly.rst_rate" ] }, "certificate": { "files": [ "ancillary/rst_rate_interval.py" ], "checkers": { "ancillary/rst_rate_interval.py": "quick" } } }, { "label": "prop:rst-caterpillar", "statement": "Proposition 7.9", "page": "papers/sample-dependent-mls/07-rstheta.html#prop:rst-caterpillar", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.Lobster.u_eq", "MaxLeafFormal.Lobster.M_mulVec", "MaxLeafFormal.Lobster.lobster_lower", "MaxLeafFormal.Lobster.lobster_upper", "MaxLeafFormal.LobsterGraph.Lam", "MaxLeafFormal.LobsterGraph.Sstar", "MaxLeafFormal.LobsterGraph.lobW_eq_matrix", "MaxLeafFormal.LobsterGraph.mu_mul_pow_le_W", "MaxLeafFormal.LobsterGraph.pow_le_choose_mul", "MaxLeafFormal.LobsterGraph.lob_moments_upper", "MaxLeafFormal.LobsterGraph.lob_moments_lower", "MaxLeafFormal.LobsterGraph.rst_caterpillar_c", "MaxLeafFormal.LobsterGraph.rst_caterpillar_c_of_agree" ] }, "certificate": { "files": [ "ancillary/lobster_rate_certificate.py" ], "checkers": { "ancillary/lobster_rate_certificate.py": "quick" } } }, { "label": "thm:rsc", "statement": "Theorem 8.1", "page": "papers/sample-dependent-mls/08-rsc.html#thm:rsc", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.RSCHeadline.rsc_success", "MaxLeafFormal.RSCTrials.rsc_success_of_bound", "MaxLeafFormal.RSCCompose.rsc_success_of_data", "MaxLeafFormal.RSCCompose.rsc_maxLeaf_of_data", "MaxLeafFormal.RSCCompose.rsc_rho_lt", "MaxLeafFormal.RSCCompose.Wcl_eq" ] } }, { "label": "lem:rsc-trials", "statement": "Lemma 8.4", "page": "papers/sample-dependent-mls/08-rsc.html#lem:rsc-trials", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.RSCTrials.rsc_trials_T2", "MaxLeafFormal.RSCTrials.rsc_trials_T3", "MaxLeafFormal.RSCTrials.rsc_trials_W" ] } }, { "label": "cor:cds-budgeted", "statement": "Corollary 8.5", "page": "papers/sample-dependent-mls/08-rsc.html#cor:cds-budgeted", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.Budget.cds_budgeted", "MaxLeafFormal.Budget.cds_budgeted_maxLeaf" ] } }, { "label": "prop:rsc-bound", "statement": "Proposition 8.6", "page": "papers/sample-dependent-mls/08-rsc.html#prop:rsc-bound", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_bound_of_data", "MaxLeafFormal.RSCGraph.rsc_bound_of_data'", "MaxLeafFormal.RSCCompose.rsc_bound_trials" ] } }, { "label": "lem:det-cert", "statement": "Lemma 10.1", "page": "papers/sample-dependent-mls/10-det.html#lem:det-cert", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.DetRate.det_cert" ] }, "certificate": { "files": [ "ancillary/rates.py", "ancillary/v_rates.py" ], "checkers": { "ancillary/rates.py": "quick", "ancillary/v_rates.py": "quick" } } }, { "label": "lem:cc-gibbs", "statement": "Lemma 11.2", "page": "papers/sample-dependent-mls/11-cc.html#lem:cc-gibbs", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CCGibbs.cc_gibbs", "MaxLeafFormal.CCGibbs.Zpart_iso", "MaxLeafFormal.CCGibbs.spr_eigen", "MaxLeafFormal.CCGibbs.spr_facts", "MaxLeafFormal.CCGibbs.eIn_eq_induce" ] } }, { "label": "lem:cc-path", "statement": "Lemma 11.3", "page": "papers/sample-dependent-mls/11-cc.html#lem:cc-path", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CCGibbs.cc_path", "MaxLeafFormal.CCGibbs.cc_path_min" ] } }, { "label": "cor:cc-T", "statement": "Corollary 11.5", "page": "papers/sample-dependent-mls/11-cc.html#cor:cc-T", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.CCT.cc_T_a", "MaxLeafFormal.CCT.cc_T_a_of_hasCCBound", "MaxLeafFormal.CCT.cc_T_a_of_gibbs", "MaxLeafFormal.CCT.W_ge_Z" ] } }, { "label": "lem:cc-cert", "statement": "Lemma 11.12", "page": "papers/sample-dependent-mls/11-cc.html#lem:cc-cert", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.CCRate.cc_cert", "MaxLeafFormal.CCRate.spr_root" ] }, "certificate": { "files": [ "ancillary/component_count_rate_interval.py" ], "checkers": { "ancillary/component_count_rate_interval.py": "quick" } } }, { "label": "thm:fa-dst", "statement": "Theorem 12.8", "page": "papers/sample-dependent-mls/12-further.html#thm:fa-dst", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.DSTCert.dst_rates", "MaxLeafFormal.DSTCert.dst_certs_exact", "MaxLeafFormal.DSTGraph.fa_dst_WS_minimum" ] } }, { "label": "thm:fa-pd", "statement": "Theorem 12.10", "page": "papers/sample-dependent-mls/12-further.html#thm:fa-pd", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.PDRate.pd_constants", "MaxLeafFormal.PDGraph.pd_star", "MaxLeafFormal.PDGraph.pd_success" ] } }, { "label": "prop:fa-pd-tight", "statement": "Proposition 12.11", "page": "papers/sample-dependent-mls/12-further.html#prop:fa-pd-tight", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.PDGraph.fa_pd_tight", "MaxLeafFormal.PDGraph.pd_tight_crit", "MaxLeafFormal.PDGraph.pd_tight_min", "MaxLeafFormal.PDGraph.pd_tight_argmin", "MaxLeafFormal.PDGraph.pd_tight_unique", "MaxLeafFormal.PDGraph.Sstar_subset", "MaxLeafFormal.PDGraph.pd_tight_W", "MaxLeafFormal.PDGraph.pd_tight_ratio", "MaxLeafFormal.PDGraph.pd_tight_W_le", "MaxLeafFormal.PDGraph.pd_tight_moments", "MaxLeafFormal.PDGraph.pd_tight_accepts", "MaxLeafFormal.PDGraph.pd_tight_prob" ] } }, { "label": "lem:rst-closure", "statement": "Lemma D.4.1", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rst-closure", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.Antinorm3.merge_Kcum_left", "MaxLeafFormal.Antinorm3.merge_Kcum_right", "MaxLeafFormal.Antinorm3.fin_nonneg_of_Kcum", "MaxLeafFormal.Antinorm3.PZ_add_Kcum", "MaxLeafFormal.Antinorm3.smul_PZ_add_Kcum", "MaxLeafFormal.Antinorm3.smul_PZ_mono" ] } }, { "label": "lem:rsc-mono", "statement": "Lemma D.5.1", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-mono", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_mono" ] } }, { "label": "lem:rsc-model", "statement": "Lemma D.5.2", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-model", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_model", "MaxLeafFormal.RSCTree.monotone_coupling" ] } }, { "label": "lem:rsc-pointwise", "statement": "Lemma D.5.4", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-pointwise", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_pointwise" ] } }, { "label": "lem:rsc-jensen", "statement": "Lemma D.5.6", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-jensen", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_jensen", "MaxLeafFormal.RSCGraph.EQ3", "MaxLeafFormal.RSCGraph.EQ2", "MaxLeafFormal.RSCGraph.EQex", "MaxLeafFormal.RSCGraph.rsc_jensen_nonneg" ] } }, { "label": "lem:rsc-recursion", "statement": "Lemma D.5.8", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-recursion", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCTree.rsc_recursion", "MaxLeafFormal.RSCTree.rsc_recursion_fin" ] } }, { "label": "lem:rsc-messages", "statement": "Lemma D.5.9", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-messages", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCRec.rsc_messages" ] } }, { "label": "lem:rsc-jlemma", "statement": "Lemma D.5.11", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-jlemma", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_jlemma" ] } }, { "label": "lem:rsc-odds", "statement": "Lemma D.5.12", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-odds", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCTree.rsc_odds", "MaxLeafFormal.RSCTree.odds1" ] } }, { "label": "lem:rsc-credit", "statement": "Lemma D.5.13", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-credit", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_credit", "MaxLeafFormal.RSCGraph.rsc_credit_ex" ] } }, { "label": "lem:rsc-leaf", "statement": "Lemma D.5.14", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-leaf", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_leaf" ] } }, { "label": "cor:rsc-reduction", "statement": "Corollary D.5.17", "page": "papers/sample-dependent-mls/18-app-proofs.html#cor:rsc-reduction", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCGraph.rsc_reduction", "MaxLeafFormal.RSCGraph.rsc_reduction_of", "MaxLeafFormal.RSCGraph.exists_ownerOK" ] } }, { "label": "lem:rsc-relaxed", "statement": "Lemma D.5.18", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-relaxed", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCTree.rsc_relaxed" ] } }, { "label": "lem:rsc-cone", "statement": "Lemma D.5.19", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-cone", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCCert.rsc_cone_a", "MaxLeafFormal.RSCCert.rsc_cone_b", "MaxLeafFormal.RSCCert.rsc_cone_c" ] } }, { "label": "lem:rsc-cert", "statement": "Lemma D.5.20", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-cert", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCCert.certificate_conditions", "MaxLeafFormal.RSCCert.certificate_conditions_of", "MaxLeafFormal.RSCCert.C5_of_stages", "MaxLeafFormal.RSCFinal.rsc_tree_bound", "MaxLeafFormal.RSCTree.rsc_relaxed" ] } }, { "label": "lem:rsc-lightpairs", "statement": "Lemma D.5.21", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-lightpairs", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCParams.rsc_lightpairs", "MaxLeafFormal.RSCParams.rsc_C3" ] } }, { "label": "lem:rsc-rsccredits", "statement": "Lemma D.5.22", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:rsc-rsccredits", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCParams.rsc_rsccredits" ] }, "certificate": { "files": [ "ancillary/rsc/rsc-certificate.json.gz", "ancillary/rsc/rsc-verify.py", "ancillary/rsc/rsc_verify_core.py", "ancillary/rsc/rsc_modelg.py", "ancillary/rsc/rsc-credits.py", "ancillary/rsc/rsc-verify-independent.py" ], "checkers": { "ancillary/rsc/rsc-verify.py": "full", "ancillary/rsc/rsc-credits.py": "quick", "ancillary/rsc/rsc-verify-independent.py": "full" } } }, { "label": "prop:rsc-cert", "statement": "Proposition D.5.23", "page": "papers/sample-dependent-mls/18-app-proofs.html#prop:rsc-cert", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.RSCFinal.rsc_cert_full", "MaxLeafFormal.RSCFinal.certZ_cZ_eq", "MaxLeafFormal.RSCFinal.certZ_cZ_digits", "MaxLeafFormal.RSCFinal.rsc_j_one", "MaxLeafFormal.RSCCert.IsStages", "MaxLeafFormal.RSCCert.isStages_C5", "MaxLeafFormal.RSCFinal.rsc_cert", "MaxLeafFormal.RSCFinal.certZ_cZ", "MaxLeafFormal.RSCFinal.certZ_C1", "MaxLeafFormal.RSCFinal.certZ_C2", "MaxLeafFormal.RSCFinal.certZ_C4", "MaxLeafFormal.RSCFinal.certZ_C5" ] }, "certificate": { "files": [ "ancillary/rsc/rsc-certificate.json.gz", "ancillary/rsc/rsc-verify.py", "ancillary/rsc/rsc_verify_core.py", "ancillary/rsc/rsc_modelg.py", "ancillary/rsc/rsc-credits.py", "ancillary/rsc/rsc-verify-independent.py" ], "checkers": { "ancillary/rsc/rsc-verify.py": "full", "ancillary/rsc/rsc-credits.py": "quick", "ancillary/rsc/rsc-verify-independent.py": "full" } } }, { "label": "lem:cc-inf", "statement": "Lemma D.9.8", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:cc-inf", "lean": { "status": "partly proved", "declarations": [ "MaxLeafFormal.CCRate.cc_c3" ] } }, { "label": "lem:fa-dst-point", "statement": "Lemma D.11.14", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:fa-dst-point", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.DSTGraph.fa_dst_point", "MaxLeafFormal.DSTGraph.fa_dst_point_eq", "MaxLeafFormal.DSTGraph.fa_dst_W" ] } }, { "label": "lem:fa-dst-rec", "statement": "Lemma D.11.15", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:fa-dst-rec", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.DSTCert.dst_rec" ] } }, { "label": "lem:fa-dst-cert", "statement": "Lemma D.11.16", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:fa-dst-cert", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.DSTCert.dst_tree_bound_WA", "MaxLeafFormal.DSTCert.dst_tree_bound" ] } }, { "label": "prop:fa-dst-certs", "statement": "Proposition D.11.17", "page": "papers/sample-dependent-mls/18-app-proofs.html#prop:fa-dst-certs", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.DSTCert.dst_certs_exact", "MaxLeafFormal.DSTCert.checkCert_sound", "MaxLeafFormal.DSTCert.dst_rates" ] }, "certificate": { "files": [ "ancillary/dst_certificates.json", "ancillary/dst_certificate_verify.py", "ancillary/cz_bounds.py" ], "checkers": { "ancillary/dst_certificate_verify.py": "quick", "ancillary/cz_bounds.py": "quick" } } }, { "label": "lem:fa-pd-point", "statement": "Lemma D.11.18", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:fa-pd-point", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.PDGraph.pd_point", "MaxLeafFormal.PDGraph.pd_point_factor", "MaxLeafFormal.PDGraph.card_eq_sum_pairs", "MaxLeafFormal.PDGraph.pairing_of_matching", "MaxLeafFormal.PDGraph.matching_of_pairing", "MaxLeafFormal.PDGraph.exists_anchor", "MaxLeafFormal.PDGraph.Ωpair_amgm" ] } }, { "label": "lem:fa-pd-rate", "statement": "Lemma D.11.19", "page": "papers/sample-dependent-mls/18-app-proofs.html#lem:fa-pd-rate", "lean": { "status": "proved", "declarations": [ "MaxLeafFormal.PDRate.pd_rate", "MaxLeafFormal.PDGraph.pd_rate_W" ] }, "certificate": { "files": [ "ancillary/paired_rate_certificate.py" ], "checkers": { "ancillary/paired_rate_certificate.py": "quick" } } } ] }