{ "707": { "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos707.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos707.lean", "checked": "2026-08-21T13:17:47Z", "built": true, "elaborated": true, "declarations": { "Erdos707.not_erdos_707P": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos707.not_erdos_707H": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos707.not_erdos_707H2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos707.not_erdos_707AM": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "4 theorems on the standard axioms only" } }, "138": { "https://github.com/mo271/formal-conjectures/blob/6ac8d0cbe1a85e71747c62c1391a84788015ebc1/FormalConjectures/ErdosProblems/138.lean#L844": { "url": "https://github.com/mo271/formal-conjectures/blob/6ac8d0cbe1a85e71747c62c1391a84788015ebc1/FormalConjectures/ErdosProblems/138.lean#L844", "checked": "2026-08-21T13:18:48Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: FormalConjectures.Util.ProblemImports" } }, "582": { "https://github.com/plby/lean-proofs/blob/1d7b3f00780b85ed0462e79a1cd5650ee9055655/src/v4.29.1/ErdosProblems/Erdos582.lean": { "url": "https://github.com/plby/lean-proofs/blob/1d7b3f00780b85ed0462e79a1cd5650ee9055655/src/v4.29.1/ErdosProblems/Erdos582.lean", "checked": "2026-08-21T13:22:49Z", "built": true, "elaborated": true, "declarations": { "Erdos582.erdos_582": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos582.exists_H_n_of_exists_H_2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos582.exists_H_2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos582.exists_H_n": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos582.folkman_theorem": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "5 theorems on the standard axioms only" } }, "105": { "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos105.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos105.lean", "checked": "2026-08-21T13:26:56Z", "built": true, "elaborated": true, "declarations": { "Erdos105.not_erdos_105": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "1 theorems on the standard axioms only" } }, "426": { "https://github.com/plby/lean-proofs/blob/68da20b96673899166e94638f5a7fffeb7231d35/src/latest/ErdosProblems/Erdos426.lean": { "url": "https://github.com/plby/lean-proofs/blob/68da20b96673899166e94638f5a7fffeb7231d35/src/latest/ErdosProblems/Erdos426.lean", "checked": "2026-08-21T13:29:34Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "dependencies unavailable", "detail": "info: downloading https://releases.lean-lang.org/lean4/v4.32.0/lean-4.32.0-linux.tar.zst info: installing /home/user/.elan/toolchains/leanprover--lean4---v4.32.0 error: ComparatorChallenges: package directory not found: /tmp/qed-checks/plby-lean-proofs-68da20b9-src_latest/ComparatorChallenges" } }, "94": { "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos94.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos94.lean", "checked": "2026-08-21T13:30:18Z", "built": true, "elaborated": true, "declarations": { "Erdos94.erdos94_convex_no3collinear": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.convexPosition_noThreeCollinear": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.perpBisectorAtMostTwo_of_general_position": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.erdos94": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.erdos94_general_position": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.erdos94_bigO": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.erdos94_bigO_general_position": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos94.erdos94_bigO_convex_no3collinear": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "8 theorems on the standard axioms only" } }, "56": { "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos56.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos56.lean", "checked": "2026-08-21T13:32:00Z", "built": true, "elaborated": true, "declarations": { "Erdos56.erdos_56": [ "propext", "Classical.choice", "Lean.ofReduceBool", "Lean.trustCompiler", "Quot.sound" ] }, "nonstandard_axioms": [ "Lean.ofReduceBool", "Lean.trustCompiler" ], "uses_sorry": false, "verdict": "nonstandard axioms", "detail": "Lean.ofReduceBool, Lean.trustCompiler" } }, "865": { "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/865/Erdos865.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/865/Erdos865.lean", "checked": "2026-08-21T13:34:58Z", "built": true, "elaborated": true, "declarations": { "Erdos865.erdos_865": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.four_card_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_two_sol": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.cast_injOn": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_T1": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_T2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_T3": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_T4": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.union_card_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T1_T2_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T1_T2_odd": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T1_T3_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T2_T3_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T2_T4_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T1_T4_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.inter_T3_T4_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.case2_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.foldedOK_subset": [ "propext", "Quot.sound" ], "Erdos865.lowSums_mono": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.highSums_mono": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.collisions_mono": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.mem_lowSums_lt": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.mem_highSums_lt": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.sum_not_lowSums_erase": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_reflB": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.foldedOK_reflB": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.lowSums_reflB": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.highSums_reflB": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.collisions_reflB_card": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.core_step": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.folded_additive": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.foldedOK_Bset": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.collisions_subset_Eset": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_XY_E": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.folding_lemma": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.card_A_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.gap_empty": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.case1_I_sub": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.even_bound_case1": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.case2_Bset_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.case2_I_sub": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.tripleFree_subset": [ "propext", "Quot.sound" ], "Erdos865.even_bound_case2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.even_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.sharpSet_subset": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.sharpSet_card": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.sharpSet_tripleFree": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.sharpness": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.erdos865_upper_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.erdos865_contains_triple": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos865.erdos865_threshold": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "51 theorems on the standard axioms only" }, "https://github.com/mrricky22/erdos-865-lean/blob/f861539107a7adeaa97462ce7c7171127696b63a/RequestProject/Main.lean#L45": { "url": "https://github.com/mrricky22/erdos-865-lean/blob/f861539107a7adeaa97462ce7c7171127696b63a/RequestProject/Main.lean#L45", "checked": "2026-08-21T13:40:03Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: RequestProject.Sharpness, RequestProject.UpperBound" } }, "512": { "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/512/Erdos512.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/512/Erdos512.lean", "checked": "2026-08-21T13:40:04Z", "built": true, "elaborated": true, "declarations": { "Erdos512.erdos_512": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.log_le_harmonic": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.integrable_fourier_smul": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.continuous": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.integrable": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.coAnalytic": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.const": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.fourier_neg": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.add": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.smul": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.neg": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.mul": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.sum": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.pow": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fourierCoeff_fourier_mul": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.norm_fourierCoeff_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.coAnalytic_of_tendstoUniformly": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.expPartialSum_tendstoUniformly": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.TrigPolyNeg.coAnalytic_exp": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_nonneg": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.sq_L2nrm": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.integral_fourier": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.parseval_trigpoly": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_le_sup": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.integral_norm_mul_le_L2": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.norm_fourierCoeff_mul_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_add_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_sum_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.integral_sq_trigPolyNeg": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.norm_exp_neg_sub_one_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.norm_exp_neg_le_one": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_exp_neg_sub_one_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_le_sqrt2_re": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.exists_completion": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.exists_trigPoly_approx": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.exists_majorant": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.prodexp_self": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.prodexp_succ": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.prodexp_continuous": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.prodexp_coAnalytic": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.Frec_closed": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.exp_calc_ineq": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.Frec_norm_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.Frec_coeff": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.geom_sum_half_Ioc": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.L2nrm_prodexp_sub_one_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.Frec_continuous": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.geom_sum_quarter_Ico": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.re_coeff_ge": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.blk_mono": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.pow_blk_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.card_block_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fpoly_continuous": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.card_blockSet_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fpoly_norm_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fpoly_L2_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fpoly_coeff": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.mem_blockSet_iff": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.blockSet_lt": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.coAnalytic_sub_one": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.fpoly_mul_prodexp_sub_one_vanish": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.sum_eq_sum_enum": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.construction_sum_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.exists_good_F": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.intervalIntegral_eq_circleIntegral": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.pairing_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.hardy_key": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos512.Littlewood.littlewood_L1_lower_bound": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "68 theorems on the standard axioms only" } }, "464": { "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/464/Erdos464.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/464/Erdos464.lean", "checked": "2026-08-21T13:44:17Z", "built": true, "elaborated": true, "declarations": { "Erdos464.erdos_464": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos464.exists_refinement": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos464.Setup.solution_uncountable": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos464.deMathan_not_dense": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "4 theorems on the standard axioms only" } }, "353": { "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/353/Erdos353.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/353/Erdos353.lean", "checked": "2026-08-21T13:47:15Z", "built": true, "elaborated": true, "declarations": { "Erdos353.erdos_353": 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"Erdos353.Kovac.area_lt_one_of_large": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.Kovac.area_lt_one": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.Kovac.thm_congruent": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.erdos_353_isosceles_trapezoid_FC": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.erdos_353_cyclic_quadrilateral_FC": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.erdos_353_congruent_sides_FC": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.erdos_353_isosceles_triangle_FC": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos353.erdos_353_right_triangle_FC": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "32 theorems on the standard axioms only" } }, "403": { "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/403/Erdos403.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/403/Erdos403.lean", "checked": "2026-08-21T13:53:36Z", "built": true, "elaborated": true, "declarations": { "Erdos403.erdos_403": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos403.erdos403_complete": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos403.erdos403": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "3 theorems on the standard axioms only" } }, "328": { "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/328/Erdos328.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/f8a51976fd2e66a52b4928c109fb9ae877a1a507/problems/328/Erdos328.lean", "checked": "2026-08-21T13:58:33Z", "built": true, "elaborated": true, "declarations": { "Erdos328.erdos_328": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos328.additiveRepresentation_finite": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos328.additiveRepresentation_eq_natCard": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos328.erdos_problem_328_disproof": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "4 theorems on the standard axioms only" } }, "209": { "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/209/Erdos209.lean": { "url": "https://github.com/Jayyhk/erdos-lean/blob/110d489ed5c07e5b216453e092e9113127c98c9a/problems/209/Erdos209.lean", "checked": "2026-08-21T14:01:18Z", "built": true, "elaborated": true, "declarations": { "Erdos209.erdos_209": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.complexParametricLine_direction": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.complexParametricLine_isLine": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.mem_complexParametricLine_iff": [ "propext", 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"Classical.choice", "Quot.sound" ], "Erdos209.gallai_vertex_mult2_no_third_line": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.gallai_forces_9nu_equiv": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.no_gallai_number_theory": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.escuderoArrangement_no_gallai_triangle": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.escuderoArrangementForD_card": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.escuderoArrangementForD_pairwiseNonParallel": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.escuderoArrangementForD_mult_le_3": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.escuderoArrangementForD_no_gallai": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.erdos_problem_209_disproof": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos209.erdos_209_of_lineArrangement": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "25 theorems on the standard axioms only" } }, "539": { "https://github.com/KitaKen1/erdos-539-formal-conjectures/blob/79897cf9241390eb168572f4a481e29e0e64b5f7/lean/Erdos539/FC.lean#L282-L296": { "url": "https://github.com/KitaKen1/erdos-539-formal-conjectures/blob/79897cf9241390eb168572f4a481e29e0e64b5f7/lean/Erdos539/FC.lean#L282-L296", "checked": "2026-08-21T14:04:30Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: Erdos539.Main" } }, "619": { "https://github.com/google-deepmind/formal-conjectures/blob/b8c7a76f267c29eaa41d1212c211a920be8b05ea/FormalConjectures/ErdosProblems/619.lean#L6009": { "url": "https://github.com/google-deepmind/formal-conjectures/blob/b8c7a76f267c29eaa41d1212c211a920be8b05ea/FormalConjectures/ErdosProblems/619.lean#L6009", "checked": "2026-08-21T14:04:33Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: FormalConjectures.Util.ProblemImports" }, "https://github.com/nick-kuhn/erdos-619/blob/7f65718b8c1019ecc24e6c9a6b04ec4c66a4e26f/Solution.lean#L5869": { "url": "https://github.com/nick-kuhn/erdos-619/blob/7f65718b8c1019ecc24e6c9a6b04ec4c66a4e26f/Solution.lean#L5869", "checked": "2026-08-21T14:04:43Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: Erdos" } }, "775": { "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos775.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos775.lean", "checked": "2026-08-21T14:04:44Z", "built": true, "elaborated": true, "declarations": { "Erdos775.erdos_problem_775": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.layered_tree_bounded_zero": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.layered_tree_bounded_one": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.first_block_layered": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.sum_rootChildren_le_iterBound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.contractionTree_root_degree_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.full_contraction": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.layered_tree_bounded": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.helly_complete": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.tree_from_many_clique_sizes": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos775.main_theorem": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "11 theorems on the standard axioms only" } }, "762": { 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], "Erdos762.lemma_obs_obvious_lifted_B": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_sets_eq": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_clique_free_structure_A_aux": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_rainbow_clique_free_case_A": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_clique_free_structure_B_aux": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_rainbow_clique_free_case_B": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_rainbow_clique_free": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.clique_new_vertices_card_le_one": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.clique_old_vertices_subset_X": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.old_vertices_form_clique_in_H": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.clique_old_part_size": [ "propext", "Classical.choice", "Quot.sound" ], 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"Erdos762.lemma_H_covered_by_2K_of_disjoint_clique": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_no_cover_3K": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_indep_inter_H_eq_X_implies_v_not_in_I": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_no_cover_3I": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_no_cover_1K_2I": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_clique_inter_H_le_one_of_mem_V_indep": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_H_not_covered_by_small_cliques_and_indep": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_no_cover_2K_1I_nonempty_I": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_no_cover_2K_1I": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_G_not_cochromatic_3": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.G_cochromatic_ge_4": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.main_theorem": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.lemma_H_has_clique_4": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos762.steiner_graph": [ "propext", "Classical.choice", "Quot.sound" ] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "46 theorems on the standard axioms only" } }, "760": { "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos760.lean": { "url": "https://github.com/plby/lean-proofs/blob/main/src/v4.29.1/ErdosProblems/Erdos760.lean", "checked": "2026-08-21T14:10:04Z", "built": true, "elaborated": true, "declarations": { "Erdos760.SimpleGraph.erdos_760": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.cochromPartable_card": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.cochromaticNumber_le_of_cochromPartable": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.CochromPartable_comap_equiv": [ "propext", "Quot.sound" ], "Erdos760.SimpleGraph.cochromaticNumber_comap_equiv": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.colorable_of_cochromPartable_of_cliqueNum_le": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.colorable_of_degenerate": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.cliqueNum_spanSub_le_of_no_large_clique": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.degeneracy_of_no_dense_indep": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.edgeFinset_within_ge_of_min_deg": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.edgesWithin_sub_edgeFinset": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.indep_spanSub_edgesWithin_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.card_edgesWithin_clique": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.per_clique_bad_count": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.per_degen_bad_count": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.card_filter_bexists_le_sum": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.exists_good_edge_subset_of_few_edges": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.clique_bad_total_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.geom_sum_telesc": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.geom_sum_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.clog_ge_five": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.choose_pow_bound": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos760.SimpleGraph.degen_bad_total_bound": [ "propext", "Classical.choice", "Quot.sound" ], 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"https://github.com/mo271/formal-conjectures/blob/6ac8d0cbe1a85e71747c62c1391a84788015ebc1/FormalConjectures/ErdosProblems/138.lean#L844", "checked": "2026-08-21T17:01:36Z", "built": false, "elaborated": false, "declarations": {}, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "not self-contained", "detail": "imports project modules: FormalConjectures.Util.ProblemImports" } }, "erdos:146": { "https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d31d6de640a725c9d43d2b6/CompactnessAndDegeneracy.lean": { "url": "https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d31d6de640a725c9d43d2b6/CompactnessAndDegeneracy.lean", "checked": "2026-08-21T17:01:44Z", "built": true, "elaborated": true, "declarations": { "CompactnessConjecture.FamilyFree.member": [ "propext", "Quot.sound" ], "CompactnessConjecture.edgeFinset_card_eq_natCard": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.degree_eq_natCard_neighborSet": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.booleanCut_adj": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.booleanCut_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.booleanCut_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.flipBooleanColor_self": [ "propext" ], "CompactnessConjecture.booleanCut_deleteIncidence_flip": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.booleanCut_flip_neighborFinset": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.booleanCut_flip_degree_add": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.exists_maximum_booleanCut": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.maximum_booleanCut_degree": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.exists_bipartite_half_edges": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.natCard_support_le_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.natCard_support_deleteIncidence_add_one_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.exists_maximum_sharp_pruning_subgraph": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.maximum_sharp_pruning_subgraph_degree": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.maximum_sharp_pruning_subgraph_edge_positive": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.exists_bipartite_min_degree_supported_subgraph": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.exists_bipartite_min_degree_subgraph": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jQuotients_mem_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kQuotients_mem_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_mem_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_induction": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_cycle_mem_proposedFamily": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_nonempty": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.six_cycle_mem_proposedFamily": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_four_cycle": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_six_cycle": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jQuotient_mem_proposedFamily": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kQuotient_mem_proposedFamily": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_self": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_swap": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_add_left": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_add_right": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_smul_left": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_smul_right": [ "propext", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_nondegenerate_left": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.standardSymplecticForm_nondegenerate_right": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.standardSymplecticBilin_nondegenerate": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.standardSymplecticBilin_isAlt": [ "propext", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_le_orthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointOrthogonal_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointRadical_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointQuotient_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quotient_map_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_le_pointOrthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplectic_two_plane_isotropic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineInPointOrthogonal_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointRadical_le_lineInPointOrthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLinesOnPoint_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointsOnLine_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_sup_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_eq_of_points": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplectic_isotropic_finrank_le_two": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplectic_triangle_points_collinear": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplectic_triangle_lines_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_incidence_adj": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_adjacent_to_point": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_adjacent_to_line": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_common_neighbor_unique": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_four_cycle_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_six_cycle_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticIncidence_card_by_points": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticIncidence_card_by_lines": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticIncidence_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_vertex_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticIncidenceToEdge_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticIncidenceToEdge_surjective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_edge_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_density_certificate": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_rpow_density": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangleVertexCount_mul_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jThetaVertex_mem": [ "propext", "Quot.sound" ], "CompactnessConjecture.not_acyclic_of_eight_cycle_copy": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodeFiniteGraph_not_acyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jTheta_quotient_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jQuotient_not_acyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kGamma_quotient_injective": [ "propext", "Quot.sound" ], "CompactnessConjecture.kQuotient_not_acyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_cycle_not_acyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.six_cycle_not_acyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_isCyclic": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointRelated_symm": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointRelated_iff_orthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointRelated_of_quadrangle_common_neighbor": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionGraph_base_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.subdivisionGraph_center_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.subdivisionPoint_pair_incidence": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPoint_center_of_point_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPoint_base_of_point_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPoint_base_center_related": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPoint_bases_unrelated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPointSpan_orthogonal_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_centers_span_orthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_mem_span_of_two_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticPoint_point_class_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jTemplate_adj_color_ne": [ "propext", "Quot.sound" ], "CompactnessConjecture.kTemplate_adj_color_ne": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_point_jTemplate": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_point_jTemplate_of_bases": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_point_jTemplate_of_first_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_jTemplate_first_base_is_line": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_kTemplate_has_line_gamma": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_pair_incidence": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_center_of_line_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_base_of_line_center": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_base_of_line_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_centers_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionLine_bases_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.free_map_of_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.extremalNumber_monotone_of_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.cycleGraph_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quotientGraph_no_isolated": [ "propext", "Quot.sound" ], "CompactnessConjecture.map_equiv_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodeFiniteGraph_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jTemplate_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kTemplate_no_isolated": [ "propext", "Quot.sound" ], "CompactnessConjecture.encodedJQuotient_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodedKQuotient_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_member_no_isolated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nat_le_pow_of_two_le": [ "propext", "Quot.sound" ], "CompactnessConjecture.quadrangleVertexCount_parameter_lt": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_prime_power_bracketing": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_extremal_lower_of_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_extremal_lower_padded_of_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_manuscript_scaled_density_of_gap": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quadrangle_uniform_lower_of_prime_power_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_cycle_uniform_manuscript_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.six_cycle_uniform_manuscript_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.common_neighbor_unique_of_four_cycle_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.bipartite_coloring_eq_of_common_neighbor": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.common_neighbors_triangle_eq_of_cycle_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.common_second_neighbors_pairwise_unrelated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.card_nonbacktrackingNeighbor": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.fintype_card_sigma_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.card_nonbacktrackingFourPath_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nonbacktrackingFourPath_endpoint_ne": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nonbacktrackingFourPath_endpoint_unrelated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nonbacktrackingFourPathPair_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nonbacktrackingFourPathWitness_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_path_endpoint_witness_count_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.fourPathEndpointWitness_card_eq_sum": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_path_common_second_neighbor_sum_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.commonNeighborIndependent_neighborhood_injective": [ "propext", "Quot.sound" ], "CompactnessConjecture.commonNeighborIndependent_sum_degree_le_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.commonNeighborIndependent_card_mul_degree_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.card_nonbacktrackingThreePath_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.nonbacktrackingThreePathEndpoint_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.girthEight_degree_mul_pred_sq_le_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPairVertex_ne_base": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionPairVertex_ne_center": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionVertexImage_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionVertexImage_map_relation": [ "propext", "Quot.sound" ], "CompactnessConjecture.fiberRepresentative_spec": [ "Classical.choice" ], "CompactnessConjecture.kernelNormalForm_spec": [ "Classical.choice" ], "CompactnessConjecture.kernelNormalForm_eq_iff": [ "Classical.choice" ], "CompactnessConjecture.kernelNormalForm_idempotent": [ "Classical.choice" ], "CompactnessConjecture.kernelNormalForm_fixed": [ "Classical.choice" ], "CompactnessConjecture.kernelNormalForm_jAdmissible": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kernelNormalForm_kAdmissible": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_no_jTemplate": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_no_kTemplate": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricQuadratic_eq_bilinear": [ "propext" ], "CompactnessConjecture.symmetricDet_zero_diagonal_sub": [ "propext" ], "CompactnessConjecture.symmetricQuadratic_char_two": [ "propext", "Quot.sound" ], "CompactnessConjecture.symmetricQuadratic_char_two_eq_square": [ "propext", "Quot.sound" ], "CompactnessConjecture.square_surjective_char_two": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricQuadratic_char_two_diagonal_zero_of_two_independent_roots": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricQuadraticEvaluationMatrix_det": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricQuadratic_no_three_independent_roots": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricQuadratic_no_three_roots_of_det_ne_zero": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricDet_zero_diagonal_sub_ne_zero": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.extremalScale_pos": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.extremalScale_nonneg": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.manuscriptLowerConstant_pos": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.not_compact_of_separation": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_not_compact_of_bounds": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.not_compactnessConjecture_of_bounds": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.finite_heavy_fiber_mass_half": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.unrelated_four_path_endpoint_card_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.common_second_neighbor_pairwise_unrelated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_path_heavy_common_second_neighbor_mass_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_thetaBaseExtensions": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJBase_jBase": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJVertex_jThetaVertex": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.inJCopy_iff_exists_jThetaVertex": [ "propext", "Quot.sound" ], "CompactnessConjecture.theta_base_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.theta_center_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.gluedJVertex_map_relation": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJHom_injOn_marked_copy": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJBase_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.thetaCopy_base_center_color_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.thetaCopy_base_color_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedThetaBase_color_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJBase_color_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJVertex_color_false_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedJHom_color_respecting": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.thetaBaseExtensions_commonNeighborIndependent": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.thetaBaseExtensions_card_mul_degree_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_tripleCommonCenters": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_thetaBaseExtensions_of_girthEightCenters": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_thetaBaseExtensions_of_two_common_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.choose_three_factorial_identity": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.choose_three_cubic_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_path_common_second_neighbor_triple_mass_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_four_path_triple_mass_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.orderedThetaTripleCount_mul_degree_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaGood_of_three_common_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gamma_base_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.gamma_center_pair_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.gammaCopy_vertex_color_false_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.subdivisionRelation_adj": [ "propext", "Quot.sound" ], "CompactnessConjecture.gluedKVertex_map_relation": [ "propext", "Quot.sound" ], "CompactnessConjecture.gluedKHom_injOn_marked_copy": [ "propext", "Quot.sound" ], "CompactnessConjecture.gluedKVertex_color_false_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gluedKHom_color_respecting": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_not_adj_gammaGood": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_gammaBadVertices": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_edge_has_gammaBad": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.edgeFinset_card_le_sum_degree_of_vertex_cover": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_edge_card_le_gammaBad_degree_sum": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.finite_bad_fiber_card_le_two": [ "propext", "Quot.sound" ], "CompactnessConjecture.finite_bad_fiber_mass_le_two": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_commonCenterFinset": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTripleBase_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTripleBase_mem": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTripleBase_surjective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.commonCenterFinset_eq_tripleCommonCenters": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTripleBase_unrelated": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaGood_of_independentThetaTriple_fiber": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTripleOrderedWitness_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.orderedThetaWitness_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.independentThetaTriple_card_le_orderedThetaTripleCount": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gamma_bad_triple_fiber_mass_le_two_orderedTheta": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.mem_commonSecondNeighborFinset": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.commonSecondNeighborFinset_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.fourPathTripleToIndependentThetaTriple_center_mem": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.fourPathTripleToIndependentThetaTriple_endpoint_mem": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.badIndependentThetaTriple_other_center_unique": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.badFourPathTripleToBadIndependentTriple_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.badFourPathTripleWitness_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.badIndependentTripleWitness_card": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaBad_four_path_triple_mass_le_bad_fiber_mass": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaBad_four_path_triple_mass_le_two_orderedTheta": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaBad_card_mul_heavyTripleLower_le_two_orderedTheta": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.gammaBad_card_mul_fourpath_power_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_edge_mul_pred_sq_le_bad_card_mul": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.fourPathHeavyThreshold_low_degree_fourth_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quantitative_minimum_degree_edge_bound": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quantitative_bad_vertex_edge_bound": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quantitative_bad_vertex_heavy_triple_bound": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_minDegree_polynomial_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_minDegree_sixteenth_power_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphVector_orthogonal": [ "propext", "Quot.sound" ], "CompactnessConjecture.coordinateCenterLinearMap_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLinearMap_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphVector_mem_center_span_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_coordinateCenter_intersection_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_coordinateCenter_common_point_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.projectiveDirection_nonzero_left": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.projectiveDirection_nonzero_right": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_odd_no_three_actual_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLines_disjoint_of_difference_det": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_zero_diagonal_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_char_two_diagonal_zero_of_actual_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphism_form": [ "propext", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphism_incidence_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphism_isotropic_iff": [ "propext", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphismLineEquiv_apply": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_orthogonal_eq": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_isCompl_of_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLinePairing_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLinePairing_finrank": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineDualCoordinates_apply": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLinePairing_coordinate_expansion": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineCoordinateEquiv_apply_add": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineCoordinateEquiv_form": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineNormalizer_apply_left": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineNormalizer_apply_right": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticVerticalLinearMap_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineNormalizer_map_left": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineNormalizer_map_right": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticHorizontalProjection_ker": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineHorizontalProjection_injective": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineGraphMap_horizontal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineGraphMap_symmetric": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineGraphMap_coordinate_expansion": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLineGraphMap_graphVector": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_eq_symmetricGraphLine_of_disjoint_vertical": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symmetricGraphLine_det_ne_zero_of_disjoint_horizontal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_eq_invertible_symmetricGraphLine": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticCanonicalLines_disjoint": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticVertical_mem_coordinateCenter_of_orthogonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_eq_coordinateCenterLine_of_common_points": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.coordinateCenterLine_direction_det_ne_zero_of_ne": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphism_disjoint_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticCanonical_line_no_three_common_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_no_three_common_centers": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_line_gamma_of_odd": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_kQuotient_of_odd": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_encodeFiniteGraph_free_iff": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_encoded_kQuotient_of_odd": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jQuotient_free_of_template_avoidance": [ "propext", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_encoded_jQuotient_of_template_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_jTemplate_of_char_two_line_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_char_two_canonical_zero_diagonal": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticAutomorphism_commonPoint": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_char_two_disjoint_of_two_common_center_pairs": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticLine_char_two_pair_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_jTemplate_of_char_two": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.symplecticQuadrangle_no_encoded_jQuotient_of_char_two": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.familyExtremal_real_le_of_forall_free": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.familyLittleO_of_eventual_host_bounds": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.familyFree_of_embedded_subgraph": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.eventually_constant_le_positive_nat_rpow": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.extremalScale_sixteenth_power": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.familyLittleO_of_sixteenth_power_host_bound": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_minDegree_ambient_sixteenth_power_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamilyFree_sixteenth_power_host_bound": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_familyLittleO": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.four_cycle_eventual_manuscript_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.six_cycle_eventual_manuscript_lower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.member_eventual_lower_of_prime_power_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.uniformMemberLower_of_characteristic_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_odd_characteristic_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_even_characteristic_avoidance": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_uniformMemberLower": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_not_compact": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.not_erdos_180": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.jTemplate_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.kTemplate_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quotientGraph_connected_of_colorRespecting": [ "propext", "Quot.sound" ], "CompactnessConjecture.encodeFiniteGraph_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodedJQuotient_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodedKQuotient_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.finiteCycle_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_member_connected": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.colorRespectingQuotient_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodeFiniteGraph_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodedJQuotient_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.encodedKQuotient_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_member_isBipartite": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.finiteNatSup_sixteenth_power_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_familyExtremal_sixteenth_power_le": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.proposedFamily_familyExtremal_isBigO": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.compactnessSharpHostPowerConstant_pos": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.checkedManuscriptCounterexample": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.quantitativeCompactnessCounterexample": [ "propext", "Classical.choice", "Quot.sound" ], "CompactnessConjecture.compactnessCounterexample_bigO": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.twelve_sevenths_lt_sqrt_three": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.log_two_pos": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_nonneg": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_le_one": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_zero": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_one_sub": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_continuous": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_scale_le": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_subadditive": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.abs_binaryEntropy_sub_le_binaryEntropy_abs_sub": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binaryEntropy_mono_on_half": [ "propext", "Classical.choice", "Quot.sound" ], 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"TwoDegenerateGraphs.sqrt_one_add_le": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.normalized_binary_cauchy": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.binary_log_sum_bound": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.entropyTangentSigma_pos": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.entropyTangentRho_pos": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.log_entropyTangentSigma": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.log_entropyTangentRho": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.sqrt_three_mul_entropyTangentRho": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.entropyTangentZeroCoefficient_eq": [ "propext", "Classical.choice", "Quot.sound" ], "TwoDegenerateGraphs.entropyTangentOneCoefficient_eq": [ "propext", "Classical.choice", "Quot.sound" ], 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], "Erdos346.intended_problem_if_limit_exists_of_eventualFiniteSingletonLeastSmallPrefixCover": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos346.intended_problem_if_limit_exists_of_arbitrarilyLargeFiniteSingletonLeastSmallPrefixCover": [ "propext", "Classical.choice", "Quot.sound" ], "Erdos346.strictMono_periodicDeletionSeq_of_pos": [], "Erdos346.strictMono_of_gap_one": [] }, "nonstandard_axioms": [], "uses_sorry": false, "verdict": "verified", "detail": "346 theorems on the standard axioms only" } } }