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| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaSum_aux1" |
| }, |
| { |
| "id": "SmallerImpZero", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/SmallerImpZero" |
| }, |
| { |
| "id": "prop:a-another-integral", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:a-another-integral" |
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| { |
| "id": "lem:chech_is_determined_by_stalks_2", |
| "repo": "M2", |
| "full_id": "M2/lem:chech_is_determined_by_stalks_2" |
| }, |
| { |
| "id": "1-2-1-polyhedral-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-1-polyhedral-cone" |
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| { |
| "id": "ap_in_ff", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/ap_in_ff" |
| }, |
| { |
| "id": "1-2-2-polytope", |
| "repo": "toric", |
| "full_id": "toric/1-2-2-polytope" |
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| { |
| "id": "0-diag-spec", |
| "repo": "toric", |
| "full_id": "toric/0-diag-spec" |
| }, |
| { |
| "id": "bklnw-cor-5-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-cor-5-1" |
| }, |
| { |
| "id": "StandardRepr.dual", |
| "repo": "seymour", |
| "full_id": "seymour/StandardRepr.dual" |
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| { |
| "id": "staysInY", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/staysInY" |
| }, |
| { |
| "id": "def:L2M", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:L2M" |
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| { |
| "id": "E8-defs-equivalent", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/E8-defs-equivalent" |
| }, |
| { |
| "id": "def:rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:rightContinuous" |
| }, |
| { |
| "id": "lem:komlos_ennreal", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:komlos_ennreal" |
| }, |
| { |
| "id": "prop:modif-indep-char", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/prop:modif-indep-char" |
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| { |
| "id": "sum-dilate-I", |
| "repo": "pfr", |
| "full_id": "pfr/sum-dilate-I" |
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| { |
| "id": "multidist-ruzsa-I", |
| "repo": "pfr", |
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| { |
| "id": "LinearTransformation", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/LinearTransformation" |
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| { |
| "id": "mu-pnt-alt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mu-pnt-alt" |
| }, |
| { |
| "id": "lem:covariation_eq_inner", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covariation_eq_inner" |
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| { |
| "id": "eq1491", |
| "repo": "equational_theories", |
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| { |
| "id": "def:s", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/def:s" |
| }, |
| { |
| "id": "lem:tailSigma_eq_iInf", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:tailSigma_eq_iInf" |
| }, |
| { |
| "id": "def:L2Martingales.inner", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:L2Martingales.inner" |
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| { |
| "id": "lem:integral_sup_rpow_dist_le_of_minimal_cover_of_le_one", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_le_of_minimal_cover_of_le_one" |
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| "id": "lemma:Qlim", |
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| "full_id": "Sphere-Packing-Lean/lemma:Qlim" |
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| { |
| "id": "lem:hasLaw_preBrownian_sub", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasLaw_preBrownian_sub" |
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| { |
| "id": "topology_on_affine_variety_computation", |
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| "id": "fundamental_theorem_of_algbra", |
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| "id": "relabeled-entropy", |
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| "id": "ruzsa-diff", |
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| { |
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| { |
| "id": "lem:abadeulmac", |
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| "full_id": "PrimeNumberTheoremAnd/lem:abadeulmac" |
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| { |
| "id": "eq46", |
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| { |
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| "id": "SpherePackingConstant", |
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| { |
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| "id": "MeasureTheory.addEquivAddHaarChar_smul_preimage", |
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| { |
| "id": "lem:dist_nearestPt_le", |
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| { |
| "id": "Dusart_cor_5_3_d", |
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| "id": "GlobalBound", |
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| { |
| "id": "lem:localizingSequence_min", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:localizingSequence_min" |
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| { |
| "id": "Hurwitz.norm_eq_zero", |
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| "id": "lem:ho-preserves-small-products", |
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| { |
| "id": "diss_span", |
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| "id": "law-count", |
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| { |
| "id": "lem:qcat-1-simplex-htpy", |
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| "id": "staysInX", |
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| { |
| "id": "lem:construct_deriv_inverse", |
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| "id": "bklnw-prop-3", |
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| "id": "Skinner_Wiles_CFT_trick", |
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| { |
| "id": "lem:stable_IsMartingale", |
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| "full_id": "brownian-motion/lem:stable_IsMartingale" |
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| { |
| "id": "lem:uniformIntegrableDominatedSingleton", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrableDominatedSingleton" |
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| { |
| "id": "PuQu", |
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| "id": "ch28theorem", |
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| { |
| "id": "lem:M_cal_converges_L1", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:M_cal_converges_L1" |
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| { |
| "id": "0-hopf-ideal", |
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| { |
| "id": "def:A", |
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| "full_id": "brownian-motion/def:A" |
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| { |
| "id": "lem:cesaro_L2", |
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| "full_id": "exchangeability/lem:cesaro_L2" |
| }, |
| { |
| "id": "lem:invertible_comp_form", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:invertible_comp_form" |
| }, |
| { |
| "id": "Dedekind-nonvanishing", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dedekind-nonvanishing" |
| }, |
| { |
| "id": "lem:brown-fact", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:brown-fact" |
| }, |
| { |
| "id": "def:congruence-subgroup", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:congruence-subgroup" |
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| { |
| "id": "lem:isProjectiveMeasureFamily_gaussianProjectiveFamily", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isProjectiveMeasureFamily_gaussianProjectiveFamily" |
| }, |
| { |
| "id": "Conditional-Gibbs", |
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| }, |
| { |
| "id": "0-coquot", |
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| "full_id": "toric/0-coquot" |
| }, |
| { |
| "id": "lem:cesaro_L1", |
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| "full_id": "exchangeability/lem:cesaro_L1" |
| }, |
| { |
| "id": "defn:trivial-fibration", |
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| "full_id": "infinity-cosmos/defn:trivial-fibration" |
| }, |
| { |
| "id": "prop:DeterminantMethod", |
| "repo": "ABC-Exceptions", |
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| }, |
| { |
| "id": "fks2-lemma-20b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-20b" |
| }, |
| { |
| "id": "Matrix.longTableauPivot", |
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| "full_id": "seymour/Matrix.longTableauPivot" |
| }, |
| { |
| "id": "rudin_exp", |
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| "full_id": "LeanAPAP/rudin_exp" |
| }, |
| { |
| "id": "SpherePacking.finiteDensity", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/SpherePacking.finiteDensity" |
| }, |
| { |
| "id": "rhoplus-subgroup", |
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| "full_id": "pfr/rhoplus-subgroup" |
| }, |
| { |
| "id": "Dusart_cor_5_2_d", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_2_d" |
| }, |
| { |
| "id": "lem:predictable_simpleProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictable_simpleProcess" |
| }, |
| { |
| "id": "prop:GeometryBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:GeometryBound" |
| }, |
| { |
| "id": "eq14", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq14" |
| }, |
| { |
| "id": "decay-alt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/decay-alt" |
| }, |
| { |
| "id": "def:non-monochromatic-protocol", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:non-monochromatic-protocol" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.Y", |
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| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.Y" |
| }, |
| { |
| "id": "lem:block_coord_condIndep", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:block_coord_condIndep" |
| }, |
| { |
| "id": "lem:isStable_classD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_classD" |
| }, |
| { |
| "id": "def:hittingAGT", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:hittingAGT" |
| }, |
| { |
| "id": "lem:directingMeasure_isProb", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:directingMeasure_isProb" |
| }, |
| { |
| "id": "fks2-eq-17", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-eq-17" |
| }, |
| { |
| "id": "Matroid.IsSum3of", |
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| "full_id": "seymour/Matroid.IsSum3of" |
| }, |
| { |
| "id": "SpherePacking.scale_density", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/SpherePacking.scale_density" |
| }, |
| { |
| "id": "classical-bound-pi", |
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| "full_id": "PrimeNumberTheoremAnd/classical-bound-pi" |
| }, |
| { |
| "id": "enlarge-S-induct", |
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| "full_id": "equational_theories/enlarge-S-induct" |
| }, |
| { |
| "id": "def:L2Predictable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:L2Predictable" |
| }, |
| { |
| "id": "minimal", |
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| "full_id": "equational_theories/minimal" |
| }, |
| { |
| "id": "lem:elemStochIntegralBilin_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elemStochIntegralBilin_zero" |
| }, |
| { |
| "id": "def:b-definition", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:b-definition" |
| }, |
| { |
| "id": "defn:NaturalModelUnivalentU", |
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| "full_id": "HoTTLean/defn:NaturalModelUnivalentU" |
| }, |
| { |
| "id": "prop:modif-char", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/prop:modif-char" |
| }, |
| { |
| "id": "buthe-theorem-2b", |
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| "full_id": "PrimeNumberTheoremAnd/buthe-theorem-2b" |
| }, |
| { |
| "id": "score-lower-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/score-lower-1" |
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| { |
| "id": "eq45", |
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| "full_id": "equational_theories/eq45" |
| }, |
| { |
| "id": "def:l1Weighted_mul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:l1Weighted_mul" |
| }, |
| { |
| "id": "1-2-5-facet", |
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| "full_id": "toric/1-2-5-facet" |
| }, |
| { |
| "id": "lem:integral_prod_blockAvg", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:integral_prod_blockAvg" |
| }, |
| { |
| "id": "def:FG-definition", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:FG-definition" |
| }, |
| { |
| "id": "ch37theorem1", |
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| }, |
| { |
| "id": "I1-I2-diff", |
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| "full_id": "pfr/I1-I2-diff" |
| }, |
| { |
| "id": "lem:ClassDL.locally_classD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:ClassDL.locally_classD" |
| }, |
| { |
| "id": "quInQu", |
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| "full_id": "BlueprintRep/quInQu" |
| }, |
| { |
| "id": "Matrix.support_Z2", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.support_Z2" |
| }, |
| { |
| "id": "1689_equiv_2", |
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| "full_id": "equational_theories/1689_equiv_2" |
| }, |
| { |
| "id": "lem:map_eq_of_modification", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:map_eq_of_modification" |
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| { |
| "id": "bijpu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/bijpu" |
| }, |
| { |
| "id": "lem:integral_sup_dist_le_sum_rpow_of_le_one", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_dist_le_sum_rpow_of_le_one" |
| }, |
| { |
| "id": "I4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I4" |
| }, |
| { |
| "id": "lem:lemma4", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/lem:lemma4" |
| }, |
| { |
| "id": "SpherePacking.constant_eq_constant_normalized", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/SpherePacking.constant_eq_constant_normalized" |
| }, |
| { |
| "id": "lemma:E2-transform-S", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:E2-transform-S" |
| }, |
| { |
| "id": "score-lower-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/score-lower-2" |
| }, |
| { |
| "id": "MellinOfDeltaSpike", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfDeltaSpike" |
| }, |
| { |
| "id": "def:limitProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:limitProcess" |
| }, |
| { |
| "id": "0-char-torus", |
| "repo": "toric", |
| "full_id": "toric/0-char-torus" |
| }, |
| { |
| "id": "defn:UvPolyEv", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:UvPolyEv" |
| }, |
| { |
| "id": "fact_B", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/fact_B" |
| }, |
| { |
| "id": "bklnw-prop-3-sub-5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-prop-3-sub-5" |
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| { |
| "id": "eq8", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq8" |
| }, |
| { |
| "id": "lemma:Schwartz-summable", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Schwartz-summable" |
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| { |
| "id": "defn:htpy-cat-of-infinity-cat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:htpy-cat-of-infinity-cat" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComapSemialgHom.mapadicCompletionIntegers", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComapSemialgHom.mapadicCompletionIntegers" |
| }, |
| { |
| "id": "S-truncation", |
| "repo": "carleson", |
| "full_id": "carleson/S-truncation" |
| }, |
| { |
| "id": "lem:logSizeRadius_logSizeBallSequence_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:logSizeRadius_logSizeBallSequence_le" |
| }, |
| { |
| "id": "schwartzQuotient", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/schwartzQuotient" |
| }, |
| { |
| "id": "lem:exists-modif-isssd", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:exists-modif-isssd" |
| }, |
| { |
| "id": "cor:ind₁' trivial homology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:ind₁' trivial homology" |
| }, |
| { |
| "id": "HurwitzRatHat.completed_units", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/HurwitzRatHat.completed_units" |
| }, |
| { |
| "id": "enlarge-l0-many", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/enlarge-l0-many" |
| }, |
| { |
| "id": "def:brownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:brownian" |
| }, |
| { |
| "id": "cor:periodic cohomology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:periodic cohomology" |
| }, |
| { |
| "id": "VectorMatroid", |
| "repo": "seymour", |
| "full_id": "seymour/VectorMatroid" |
| }, |
| { |
| "id": "lem:doob_ineq_stop", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:doob_ineq_stop" |
| }, |
| { |
| "id": "prop:H3-fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:H3-fourier" |
| }, |
| { |
| "id": "def:invFourier-L2", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/def:invFourier-L2" |
| }, |
| { |
| "id": "klm-1", |
| "repo": "pfr", |
| "full_id": "pfr/klm-1" |
| }, |
| { |
| "id": "lem:rightContEq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContEq" |
| }, |
| { |
| "id": "lem:elemStochIntegral_linear", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elemStochIntegral_linear" |
| }, |
| { |
| "id": "theorem:CE_Main", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/theorem:CE_Main" |
| }, |
| { |
| "id": "single-fibres", |
| "repo": "pfr", |
| "full_id": "pfr/single-fibres" |
| }, |
| { |
| "id": "lem:chech_preserve_quasi_iso", |
| "repo": "M2", |
| "full_id": "M2/lem:chech_preserve_quasi_iso" |
| }, |
| { |
| "id": "lem:right-of-monoidal-adj-ucats", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:right-of-monoidal-adj-ucats" |
| }, |
| { |
| "id": "prop:FourierBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:FourierBound" |
| }, |
| { |
| "id": "lem:d comp norm", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:d comp norm" |
| }, |
| { |
| "id": "cor:norm_condExp_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:norm_condExp_le" |
| }, |
| { |
| "id": "def:IsLocalSubmartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsLocalSubmartingale" |
| }, |
| { |
| "id": "QHat.rat_join_zHat", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.rat_join_zHat" |
| }, |
| { |
| "id": "lem:tendsto_eLpNorm_stoppedValue_discreteApproxSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:tendsto_eLpNorm_stoppedValue_discreteApproxSequence" |
| }, |
| { |
| "id": "fks-proposition-3-6", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-proposition-3-6" |
| }, |
| { |
| "id": "bklnw-eq_A_14", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_14" |
| }, |
| { |
| "id": "1-1-11-toric-ideal-gen-binomial", |
| "repo": "toric", |
| "full_id": "toric/1-1-11-toric-ideal-gen-binomial" |
| }, |
| { |
| "id": "0-diag-iff-grp-like-span", |
| "repo": "toric", |
| "full_id": "toric/0-diag-iff-grp-like-span" |
| }, |
| { |
| "id": "def:approximableTimeIndex", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:approximableTimeIndex" |
| }, |
| { |
| "id": "lem:Subcase2.1", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Subcase2.1" |
| }, |
| { |
| "id": "pn_pn_plus_one", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/pn_pn_plus_one" |
| }, |
| { |
| "id": "I7", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I7" |
| }, |
| { |
| "id": "lem:pi-product", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:pi-product" |
| }, |
| { |
| "id": "LogDerivZetaLogSquaredBoundSmallt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/LogDerivZetaLogSquaredBoundSmallt" |
| }, |
| { |
| "id": "tau-ref", |
| "repo": "pfr", |
| "full_id": "pfr/tau-ref" |
| }, |
| { |
| "id": "def:Tate long exact sequence", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:Tate long exact sequence" |
| }, |
| { |
| "id": "bklnw-eq_A_12", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_12" |
| }, |
| { |
| "id": "lem:herbrand idele class group", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:herbrand idele class group" |
| }, |
| { |
| "id": "lem:IsLocalSubmartingale.locally_classD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsLocalSubmartingale.locally_classD" |
| }, |
| { |
| "id": "lem:predictable_Ioc_prod", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictable_Ioc_prod" |
| }, |
| { |
| "id": "crude-upper-bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/crude-upper-bound" |
| }, |
| { |
| "id": "SpechtModules", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/SpechtModules" |
| }, |
| { |
| "id": "cor-fibre", |
| "repo": "pfr", |
| "full_id": "pfr/cor-fibre" |
| }, |
| { |
| "id": "tau-min", |
| "repo": "pfr", |
| "full_id": "pfr/tau-min" |
| }, |
| { |
| "id": "cor:disc-pos", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:disc-pos" |
| }, |
| { |
| "id": "fks2-eq-12", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-eq-12" |
| }, |
| { |
| "id": "small-boundary", |
| "repo": "carleson", |
| "full_id": "carleson/small-boundary" |
| }, |
| { |
| "id": "data-process", |
| "repo": "pfr", |
| "full_id": "pfr/data-process" |
| }, |
| { |
| "id": "lem:Filtration.predictable_le_prod", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Filtration.predictable_le_prod" |
| }, |
| { |
| "id": "prop:UvPoly.equiv", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/prop:UvPoly.equiv" |
| }, |
| { |
| "id": "simple-nontangential-operator", |
| "repo": "carleson", |
| "full_id": "carleson/simple-nontangential-operator" |
| }, |
| { |
| "id": "prop:coherent-iso", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:coherent-iso" |
| }, |
| { |
| "id": "lem:localizingSequence_const_top", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:localizingSequence_const_top" |
| }, |
| { |
| "id": "euler_consequence_c", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/euler_consequence_c" |
| }, |
| { |
| "id": "lem:power_sum_invariance", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:power_sum_invariance" |
| }, |
| { |
| "id": "cor:isStoppingTime_leastGE_of_rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:isStoppingTime_leastGE_of_rightContinuous" |
| }, |
| { |
| "id": "lem:elementaryPredictableSet_iff_indicator", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elementaryPredictableSet_iff_indicator" |
| }, |
| { |
| "id": "lem:ho-preserves-finite-products", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:ho-preserves-finite-products" |
| }, |
| { |
| "id": "sound-complete", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/sound-complete" |
| }, |
| { |
| "id": "lem:isPreLocalizingSequence_of_isLocalizingSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isPreLocalizingSequence_of_isLocalizingSequence" |
| }, |
| { |
| "id": "def:lpWeighted", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:lpWeighted" |
| }, |
| { |
| "id": "lem:ind₁ trivial homology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:ind₁ trivial homology" |
| }, |
| { |
| "id": "def:quasi_iso_of_complex_of_k-prsh", |
| "repo": "M2", |
| "full_id": "M2/def:quasi_iso_of_complex_of_k-prsh" |
| }, |
| { |
| "id": "residueAtNegOne", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/residueAtNegOne" |
| }, |
| { |
| "id": "JBlaschkeDerivBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/JBlaschkeDerivBound" |
| }, |
| { |
| "id": "I8Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I8Bound" |
| }, |
| { |
| "id": "goursat", |
| "repo": "pfr", |
| "full_id": "pfr/goursat" |
| }, |
| { |
| "id": "0-full-faithful-spec-hopf", |
| "repo": "toric", |
| "full_id": "toric/0-full-faithful-spec-hopf" |
| }, |
| { |
| "id": "def:H2-H3-H4", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:H2-H3-H4" |
| }, |
| { |
| "id": "bklnw-thm-5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-thm-5" |
| }, |
| { |
| "id": "lem:locally_leftLimit", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_leftLimit" |
| }, |
| { |
| "id": "0-irred-gen", |
| "repo": "toric", |
| "full_id": "toric/0-irred-gen" |
| }, |
| { |
| "id": "eq41", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq41" |
| }, |
| { |
| "id": "thm:Doob_Meyer", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:Doob_Meyer" |
| }, |
| { |
| "id": "lem:eVariationOn_eq_totalVariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:eVariationOn_eq_totalVariation" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComapContinuousAlgEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComapContinuousAlgEquiv" |
| }, |
| { |
| "id": "def:externalCoveringNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:externalCoveringNumber" |
| }, |
| { |
| "id": "lem:dense_simpleProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:dense_simpleProcess" |
| }, |
| { |
| "id": "defn:simplicial-category", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:simplicial-category" |
| }, |
| { |
| "id": "lem:hasLocallyIntegrableSup_of_locally_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasLocallyIntegrableSup_of_locally_classDL" |
| }, |
| { |
| "id": "lem:criterion-reduced", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:criterion-reduced" |
| }, |
| { |
| "id": "def:schema-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:schema-chapter" |
| }, |
| { |
| "id": "Hilbert-strong-2-2", |
| "repo": "carleson", |
| "full_id": "carleson/Hilbert-strong-2-2" |
| }, |
| { |
| "id": "def:IsProjectiveLimit", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsProjectiveLimit" |
| }, |
| { |
| "id": "def:cohomology long exact sequence", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:cohomology long exact sequence" |
| }, |
| { |
| "id": "bohr-size", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/bohr-size" |
| }, |
| { |
| "id": "thm:l1Weighted_Ring", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_Ring" |
| }, |
| { |
| "id": "convergence-for-smooth", |
| "repo": "carleson", |
| "full_id": "carleson/convergence-for-smooth" |
| }, |
| { |
| "id": "lem:rand-eq-test-protocol-eval-valid", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:rand-eq-test-protocol-eval-valid" |
| }, |
| { |
| "id": "eq6", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq6" |
| }, |
| { |
| "id": "score-lowest", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/score-lowest" |
| }, |
| { |
| "id": "def:hasUsualConditions", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:hasUsualConditions" |
| }, |
| { |
| "id": "lem:R", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/lem:R" |
| }, |
| { |
| "id": "eq38", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq38" |
| }, |
| { |
| "id": "lem:isBounded_image_of_isCadlag_of_isCompact", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isBounded_image_of_isCadlag_of_isCompact" |
| }, |
| { |
| "id": "def:broadcast", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:broadcast" |
| }, |
| { |
| "id": "def:trust-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:trust-chapter" |
| }, |
| { |
| "id": "ch32theorem", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch32theorem" |
| }, |
| { |
| "id": "lem:general_poly_neg_implies_contraction", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:general_poly_neg_implies_contraction" |
| }, |
| { |
| "id": "lem:Predictable.progressive", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Predictable.progressive" |
| }, |
| { |
| "id": "thm:l1Weighted_NormedAlgebra", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_NormedAlgebra" |
| }, |
| { |
| "id": "def: h", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def: h" |
| }, |
| { |
| "id": "thm:local Kronecker Weber", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:local Kronecker Weber" |
| }, |
| { |
| "id": "thm:inflation restriction sequence", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:inflation restriction sequence" |
| }, |
| { |
| "id": "defn:NaturalModelId", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:NaturalModelId" |
| }, |
| { |
| "id": "first-dist-sum", |
| "repo": "pfr", |
| "full_id": "pfr/first-dist-sum" |
| }, |
| { |
| "id": "Dirichlet-approximation", |
| "repo": "carleson", |
| "full_id": "carleson/Dirichlet-approximation" |
| }, |
| { |
| "id": "lem:rightContinuousRightCont", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContinuousRightCont" |
| }, |
| { |
| "id": "thm:det-fun-complex-eval-le-corner-color-num", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/thm:det-fun-complex-eval-le-corner-color-num" |
| }, |
| { |
| "id": "ch31theorem1", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch31theorem1" |
| }, |
| { |
| "id": "def:indep-spec", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:indep-spec" |
| }, |
| { |
| "id": "Zero-sum", |
| "repo": "pfr", |
| "full_id": "pfr/Zero-sum" |
| }, |
| { |
| "id": "euler_consequence_b", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/euler_consequence_b" |
| }, |
| { |
| "id": "lem:modif-proper", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:modif-proper" |
| }, |
| { |
| "id": "MellinOfDeltaSpikeAt1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfDeltaSpikeAt1" |
| }, |
| { |
| "id": "lem:UvPolyEvEq", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/lem:UvPolyEvEq" |
| }, |
| { |
| "id": "book.irrational.Theorem_1", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/book.irrational.Theorem_1" |
| }, |
| { |
| "id": "0-ess-image-spec-hopf", |
| "repo": "toric", |
| "full_id": "toric/0-ess-image-spec-hopf" |
| }, |
| { |
| "id": "eq1", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1" |
| }, |
| { |
| "id": "first-fibre", |
| "repo": "pfr", |
| "full_id": "pfr/first-fibre" |
| }, |
| { |
| "id": "cor:Martingale.submartingale_norm", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:Martingale.submartingale_norm" |
| }, |
| { |
| "id": "lemma:Ek-Fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Ek-Fourier" |
| }, |
| { |
| "id": "lem:optionalSampling_discrete_submartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:optionalSampling_discrete_submartingale" |
| }, |
| { |
| "id": "pi_alt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/pi_alt" |
| }, |
| { |
| "id": "lem:Submartingale.le_condExp_of_tendsto", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.le_condExp_of_tendsto" |
| }, |
| { |
| "id": "I4New", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I4New" |
| }, |
| { |
| "id": "lem:cor comp rest", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:cor comp rest" |
| }, |
| { |
| "id": "thm:l1Weighted_NormOneClass", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_NormOneClass" |
| }, |
| { |
| "id": "finitary-Carleson", |
| "repo": "carleson", |
| "full_id": "carleson/finitary-Carleson" |
| }, |
| { |
| "id": "thm:g", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:g" |
| }, |
| { |
| "id": "vertIntBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/vertIntBound" |
| }, |
| { |
| "id": "lem:simplex-yoneda", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:simplex-yoneda" |
| }, |
| { |
| "id": "def:aud-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:aud-chapter" |
| }, |
| { |
| "id": "prop:ABCTrivialBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:ABCTrivialBound" |
| }, |
| { |
| "id": "standardReprSum3", |
| "repo": "seymour", |
| "full_id": "seymour/standardReprSum3" |
| }, |
| { |
| "id": "def:wienerMeasureAux", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:wienerMeasureAux" |
| }, |
| { |
| "id": "lem:norm comm", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:norm comm" |
| }, |
| { |
| "id": "prop:replay-application-layer", |
| "repo": "amatelus", |
| "full_id": "amatelus/prop:replay-application-layer" |
| }, |
| { |
| "id": "eq29", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq29" |
| }, |
| { |
| "id": "lem:internalCoveringNumber_le_volume_div", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:internalCoveringNumber_le_volume_div" |
| }, |
| { |
| "id": "bklnw-eq_A_13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_13" |
| }, |
| { |
| "id": "IsSimpleRing.ringHaarChar_eq_addEquivAddHaarChar_mulRight", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/IsSimpleRing.ringHaarChar_eq_addEquivAddHaarChar_mulRight" |
| }, |
| { |
| "id": "vertIntBoundLeft", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/vertIntBoundLeft" |
| }, |
| { |
| "id": "C4-convex", |
| "repo": "carleson", |
| "full_id": "carleson/C4-convex" |
| }, |
| { |
| "id": "lem:chech_comm_with_exceptional", |
| "repo": "M2", |
| "full_id": "M2/lem:chech_comm_with_exceptional" |
| }, |
| { |
| "id": "1-2-16-simplicial-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-16-simplicial-cone" |
| }, |
| { |
| "id": "def:rand-eq-test-protocol-eval", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:rand-eq-test-protocol-eval" |
| }, |
| { |
| "id": "Dusart_prop_3_2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_prop_3_2" |
| }, |
| { |
| "id": "MainTheorem", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/MainTheorem" |
| }, |
| { |
| "id": "thm:riesz_interpolation", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:riesz_interpolation" |
| }, |
| { |
| "id": "def:isssd-spec", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:isssd-spec" |
| }, |
| { |
| "id": "def:gaussianLimit", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:gaussianLimit" |
| }, |
| { |
| "id": "def:exceptional_pushforward_of_sheaf", |
| "repo": "M2", |
| "full_id": "M2/def:exceptional_pushforward_of_sheaf" |
| }, |
| { |
| "id": "lem:criterion-sufficient", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:criterion-sufficient" |
| }, |
| { |
| "id": "defn:simplicial-conical-limit", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:simplicial-conical-limit" |
| }, |
| { |
| "id": "DerivativeBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/DerivativeBound" |
| }, |
| { |
| "id": "cauchy_rigidity", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/cauchy_rigidity" |
| }, |
| { |
| "id": "lem:IsSquareIntegrable.module", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsSquareIntegrable.module" |
| }, |
| { |
| "id": "cor:power_sums_determine_coefficients", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/cor:power_sums_determine_coefficients" |
| }, |
| { |
| "id": "def:valid-protocol", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:valid-protocol" |
| }, |
| { |
| "id": "lem:rightContinuousMeasurableSet", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContinuousMeasurableSet" |
| }, |
| { |
| "id": "rainbow_triangle", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/rainbow_triangle" |
| }, |
| { |
| "id": "Smooth1ContinuousAt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1ContinuousAt" |
| }, |
| { |
| "id": "initial-factorization-small-prime-ge", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-small-prime-ge" |
| }, |
| { |
| "id": "fks-lemma-5-3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-lemma-5-3" |
| }, |
| { |
| "id": "thm:QuadraticFormsEstimate", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/thm:QuadraticFormsEstimate" |
| }, |
| { |
| "id": "Dusart_thm_5_7", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_thm_5_7" |
| }, |
| { |
| "id": "lem:empty_is_convex", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/lem:empty_is_convex" |
| }, |
| { |
| "id": "def:cond-exp-ker", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:cond-exp-ker" |
| }, |
| { |
| "id": "deriv_conj_conj", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/deriv_conj_conj" |
| }, |
| { |
| "id": "lem:rightContNotIsMax", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContNotIsMax" |
| }, |
| { |
| "id": "387_implies_43", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/387_implies_43" |
| }, |
| { |
| "id": "lem:externalCoveringNumber_le_internalCoveringNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:externalCoveringNumber_le_internalCoveringNumber" |
| }, |
| { |
| "id": "lem:fourier-bounded", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier-bounded" |
| }, |
| { |
| "id": "lem:tendsto_stoppedValue_discreteApproxSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:tendsto_stoppedValue_discreteApproxSequence" |
| }, |
| { |
| "id": "eq4522", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq4522" |
| }, |
| { |
| "id": "lem:modif-premodif", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:modif-premodif" |
| }, |
| { |
| "id": "defn:homotopy-cat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:homotopy-cat" |
| }, |
| { |
| "id": "def:down", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:down" |
| }, |
| { |
| "id": "defn:n-arrow", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:n-arrow" |
| }, |
| { |
| "id": "rev-claim", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/rev-claim" |
| }, |
| { |
| "id": "Matrix.det", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.det" |
| }, |
| { |
| "id": "transitive-boundary", |
| "repo": "carleson", |
| "full_id": "carleson/transitive-boundary" |
| }, |
| { |
| "id": "lem:non-monochromatic-protocol-valid", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:non-monochromatic-protocol-valid" |
| }, |
| { |
| "id": "ruzsa-symm", |
| "repo": "pfr", |
| "full_id": "pfr/ruzsa-symm" |
| }, |
| { |
| "id": "lem:l2_bound_windows", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:l2_bound_windows" |
| }, |
| { |
| "id": "thm:CauchyProduct_smul_mul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_smul_mul" |
| }, |
| { |
| "id": "initial-factorization-large-prime-ge", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-large-prime-ge" |
| }, |
| { |
| "id": "lem:subgroup compatibility", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:subgroup compatibility" |
| }, |
| { |
| "id": "formulaGtOne", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/formulaGtOne" |
| }, |
| { |
| "id": "lem:externalCoveringNumber_mono", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:externalCoveringNumber_mono" |
| }, |
| { |
| "id": "ZHat.commRing", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.commRing" |
| }, |
| { |
| "id": "eq16", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq16" |
| }, |
| { |
| "id": "14_implies_29", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/14_implies_29" |
| }, |
| { |
| "id": "eq206", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq206" |
| }, |
| { |
| "id": "QHat.injective_zHat", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.injective_zHat" |
| }, |
| { |
| "id": "lem:covMatrix_map", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covMatrix_map" |
| }, |
| { |
| "id": "equivalence-relation", |
| "repo": "carleson", |
| "full_id": "carleson/equivalence-relation" |
| }, |
| { |
| "id": "lem:locally_isCadlag", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_isCadlag" |
| }, |
| { |
| "id": "DiffVertRect_eq_UpperLowerUs", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/DiffVertRect_eq_UpperLowerUs" |
| }, |
| { |
| "id": "cor:integral_sup_rpow_dist_le_of_minimal_cover_two", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:integral_sup_rpow_dist_le_of_minimal_cover_two" |
| }, |
| { |
| "id": "Matroid.IsSum3of.isRegular", |
| "repo": "seymour", |
| "full_id": "seymour/Matroid.IsSum3of.isRegular" |
| }, |
| { |
| "id": "MellinOfSmooth1a", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfSmooth1a" |
| }, |
| { |
| "id": "SmoothedChebyshevClose", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevClose" |
| }, |
| { |
| "id": "pfr-projection'", |
| "repo": "pfr", |
| "full_id": "pfr/pfr-projection'" |
| }, |
| { |
| "id": "5-2-char-tor-var-aff-mon", |
| "repo": "toric", |
| "full_id": "toric/5-2-char-tor-var-aff-mon" |
| }, |
| { |
| "id": "QHat.canonicalForm", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.canonicalForm" |
| }, |
| { |
| "id": "thm:holder_modification", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:holder_modification" |
| }, |
| { |
| "id": "def:locally", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:locally" |
| }, |
| { |
| "id": "IsDedekindDomain.FiniteAdeleRing.IntegraltensorProductAlgEquiv_aux1", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.FiniteAdeleRing.IntegraltensorProductAlgEquiv_aux1" |
| }, |
| { |
| "id": "lem:locally_of_isPreLocalizingSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_of_isPreLocalizingSequence" |
| }, |
| { |
| "id": "dirichlet_thm", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/dirichlet_thm" |
| }, |
| { |
| "id": "thm:Poisson-summation-formula", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:Poisson-summation-formula" |
| }, |
| { |
| "id": "three_coloring", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/three_coloring" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.valued_adicCompletionComap", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.valued_adicCompletionComap" |
| }, |
| { |
| "id": "lem:optionalSampling_discrete_supermartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:optionalSampling_discrete_supermartingale" |
| }, |
| { |
| "id": "IsDedekindDomain.FiniteAdeleRing.IntegraltensorProductAlgEquiv_aux2", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.FiniteAdeleRing.IntegraltensorProductAlgEquiv_aux2" |
| }, |
| { |
| "id": "lem:subspace_restriction_is_primspace", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/lem:subspace_restriction_is_primspace" |
| }, |
| { |
| "id": "lem:lim_Exp_A_n_tau_is_Exp_A_tau", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:lim_Exp_A_n_tau_is_Exp_A_tau" |
| }, |
| { |
| "id": "ch22corollary", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch22corollary" |
| }, |
| { |
| "id": "Smooth1Properties_above", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1Properties_above" |
| }, |
| { |
| "id": "diffBddAtZero", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/diffBddAtZero" |
| }, |
| { |
| "id": "lem:local cyclotomic norms", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local cyclotomic norms" |
| }, |
| { |
| "id": "def:concrete_approx", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:concrete_approx" |
| }, |
| { |
| "id": "lem:br-mul-wd", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/lem:br-mul-wd" |
| }, |
| { |
| "id": "thm:local fund class", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:local fund class" |
| }, |
| { |
| "id": "bklnw-thm-14", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-thm-14" |
| }, |
| { |
| "id": "HolomorphicOn.vanishesOnRectangle", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/HolomorphicOn.vanishesOnRectangle" |
| }, |
| { |
| "id": "lem:stoppingTime_approximation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:stoppingTime_approximation" |
| }, |
| { |
| "id": "prop:v_is_h", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/prop:v_is_h" |
| }, |
| { |
| "id": "pfr-9-aux", |
| "repo": "pfr", |
| "full_id": "pfr/pfr-9-aux" |
| }, |
| { |
| "id": "lem:isssd-isIndep", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:isssd-isIndep" |
| }, |
| { |
| "id": "0-ess-image-grp", |
| "repo": "toric", |
| "full_id": "toric/0-ess-image-grp" |
| }, |
| { |
| "id": "fks-proposition-3-14", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-proposition-3-14" |
| }, |
| { |
| "id": "prop:nerve-qcat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:nerve-qcat" |
| }, |
| { |
| "id": "greedy-prop", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/greedy-prop" |
| }, |
| { |
| "id": "bound-score-4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bound-score-4" |
| }, |
| { |
| "id": "prop:b0", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:b0" |
| }, |
| { |
| "id": "fks2-corollary-21", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-21" |
| }, |
| { |
| "id": "lem:isStable_hasIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_hasIntegrableSup" |
| }, |
| { |
| "id": "defn:degeneracy-map", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:degeneracy-map" |
| }, |
| { |
| "id": "cor:scale_change_rpow", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:scale_change_rpow" |
| }, |
| { |
| "id": "fks-proposition-3-11", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-proposition-3-11" |
| }, |
| { |
| "id": "def:pullback_for_chech", |
| "repo": "M2", |
| "full_id": "M2/def:pullback_for_chech" |
| }, |
| { |
| "id": "cor:psiI-near-0-infty", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:psiI-near-0-infty" |
| }, |
| { |
| "id": "RH-up-to", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/RH-up-to" |
| }, |
| { |
| "id": "rho-BSG-triplet", |
| "repo": "pfr", |
| "full_id": "pfr/rho-BSG-triplet" |
| }, |
| { |
| "id": "multidist-chain-rule", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-chain-rule" |
| }, |
| { |
| "id": "Dirichlet-Hilbert", |
| "repo": "carleson", |
| "full_id": "carleson/Dirichlet-Hilbert" |
| }, |
| { |
| "id": "ch26", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch26" |
| }, |
| { |
| "id": "sift_cor", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/sift_cor" |
| }, |
| { |
| "id": "fks2-theorem-6", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-theorem-6" |
| }, |
| { |
| "id": "R-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/R-def" |
| }, |
| { |
| "id": "exceptional-set", |
| "repo": "carleson", |
| "full_id": "carleson/exceptional-set" |
| }, |
| { |
| "id": "cor:up iso", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:up iso" |
| }, |
| { |
| "id": "ra-defn", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/ra-defn" |
| }, |
| { |
| "id": "cs-bound", |
| "repo": "pfr", |
| "full_id": "pfr/cs-bound" |
| }, |
| { |
| "id": "kis-thm", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/kis-thm" |
| }, |
| { |
| "id": "1-1-1-group-hom-torus", |
| "repo": "toric", |
| "full_id": "toric/1-1-1-group-hom-torus" |
| }, |
| { |
| "id": "de-prop-improv", |
| "repo": "pfr", |
| "full_id": "pfr/de-prop-improv" |
| }, |
| { |
| "id": "averaged-construct-good", |
| "repo": "pfr", |
| "full_id": "pfr/averaged-construct-good" |
| }, |
| { |
| "id": "app-ent-pfr", |
| "repo": "pfr", |
| "full_id": "pfr/app-ent-pfr" |
| }, |
| { |
| "id": "ResidueTheoremOnRectangleWithSimplePole", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ResidueTheoremOnRectangleWithSimplePole" |
| }, |
| { |
| "id": "prop:design-philosophy", |
| "repo": "amatelus", |
| "full_id": "amatelus/prop:design-philosophy" |
| }, |
| { |
| "id": "lem:covariance_structure", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:covariance_structure" |
| }, |
| { |
| "id": "ZHat.e", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.e" |
| }, |
| { |
| "id": "def:scaled_poly", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/def:scaled_poly" |
| }, |
| { |
| "id": "lem:fourier2-welldef", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier2-welldef" |
| }, |
| { |
| "id": "compactness-thm", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/compactness-thm" |
| }, |
| { |
| "id": "0-biquot-hom", |
| "repo": "toric", |
| "full_id": "toric/0-biquot-hom" |
| }, |
| { |
| "id": "TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicFormOfLevel", |
| "repo": "FLT_ch12", |
| "full_id": "FLT_ch12/TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicFormOfLevel" |
| }, |
| { |
| "id": "quInv", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/quInv" |
| }, |
| { |
| "id": "def:L2locM", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:L2locM" |
| }, |
| { |
| "id": "kl-div-copy", |
| "repo": "pfr", |
| "full_id": "pfr/kl-div-copy" |
| }, |
| { |
| "id": "bijYu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/bijYu" |
| }, |
| { |
| "id": "thm:localized_holder_modification_sup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:localized_holder_modification_sup" |
| }, |
| { |
| "id": "thm:did-local-resolution", |
| "repo": "amatelus", |
| "full_id": "amatelus/thm:did-local-resolution" |
| }, |
| { |
| "id": "pfr-9", |
| "repo": "pfr", |
| "full_id": "pfr/pfr-9" |
| }, |
| { |
| "id": "lem:fourier-gaussian", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier-gaussian" |
| }, |
| { |
| "id": "lem:dist_le_of_mem_pairSet", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:dist_le_of_mem_pairSet" |
| }, |
| { |
| "id": "conditional-entropy-def", |
| "repo": "pfr", |
| "full_id": "pfr/conditional-entropy-def" |
| }, |
| { |
| "id": "lem:M_cadlag_mg", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:M_cadlag_mg" |
| }, |
| { |
| "id": "lem:abadusepoisson", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:abadusepoisson" |
| }, |
| { |
| "id": "lem:incr_fun_lim_right_cont_lim_eq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:incr_fun_lim_right_cont_lim_eq" |
| }, |
| { |
| "id": "lem:general_poly_alt_form", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:general_poly_alt_form" |
| }, |
| { |
| "id": "lem:cadlag_covariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:cadlag_covariation" |
| }, |
| { |
| "id": "fks-lemma-2-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-lemma-2-1" |
| }, |
| { |
| "id": "thm:StrongZeroFree", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/thm:StrongZeroFree" |
| }, |
| { |
| "id": "lem:discreteApproxSequence_of", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:discreteApproxSequence_of" |
| }, |
| { |
| "id": "lem:uniformIntegrable_stoppedValue_martingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrable_stoppedValue_martingale" |
| }, |
| { |
| "id": "lem:convex_of_submg_is_submg", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:convex_of_submg_is_submg" |
| }, |
| { |
| "id": "lem:hasLaw_brownian_eval", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasLaw_brownian_eval" |
| }, |
| { |
| "id": "fks2-lemma-12", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-12" |
| }, |
| { |
| "id": "Algebra.IsInvariant.charpoly_mem_lifts", |
| "repo": "FLT_ch8", |
| "full_id": "FLT_ch8/Algebra.IsInvariant.charpoly_mem_lifts" |
| }, |
| { |
| "id": "thm:serre-der-modularity", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:serre-der-modularity" |
| }, |
| { |
| "id": "TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.distribMulAction", |
| "repo": "FLT_ch12", |
| "full_id": "FLT_ch12/TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.distribMulAction" |
| }, |
| { |
| "id": "1-1-9-ideal-ya", |
| "repo": "toric", |
| "full_id": "toric/1-1-9-ideal-ya" |
| }, |
| { |
| "id": "lem:proper-ker-lintegral", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:proper-ker-lintegral" |
| }, |
| { |
| "id": "lem:isStable_rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_rightContinuous" |
| }, |
| { |
| "id": "NumberField.InfiniteAdeleRing.baseChangeEquivAux", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfiniteAdeleRing.baseChangeEquivAux" |
| }, |
| { |
| "id": "Matrix.fromBlocks", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.fromBlocks" |
| }, |
| { |
| "id": "lem:sup_stoppedProcess_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:sup_stoppedProcess_le" |
| }, |
| { |
| "id": "Zeta0EqZeta", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Zeta0EqZeta" |
| }, |
| { |
| "id": "a0000000128", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/a0000000128" |
| }, |
| { |
| "id": "Hurwitz.norm_eq_mul_conj", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.norm_eq_mul_conj" |
| }, |
| { |
| "id": "pfr-9-aux'", |
| "repo": "pfr", |
| "full_id": "pfr/pfr-9-aux'" |
| }, |
| { |
| "id": "def:homotopy_k_sheaf", |
| "repo": "M2", |
| "full_id": "M2/def:homotopy_k_sheaf" |
| }, |
| { |
| "id": "Riemann-von-Mangoldt-estimate", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Riemann-von-Mangoldt-estimate" |
| }, |
| { |
| "id": "lem:poincare-lefschetz_duality", |
| "repo": "M2", |
| "full_id": "M2/lem:poincare-lefschetz_duality" |
| }, |
| { |
| "id": "SpherePacking.density", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/SpherePacking.density" |
| }, |
| { |
| "id": "lem:length-broadcast", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:length-broadcast" |
| }, |
| { |
| "id": "rho-subgroup", |
| "repo": "pfr", |
| "full_id": "pfr/rho-subgroup" |
| }, |
| { |
| "id": "correlation-separated-trees", |
| "repo": "carleson", |
| "full_id": "carleson/correlation-separated-trees" |
| }, |
| { |
| "id": "eq43", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq43" |
| }, |
| { |
| "id": "thm:formal_sq_eq_param", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:formal_sq_eq_param" |
| }, |
| { |
| "id": "Hurwitz.quot_rem", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.quot_rem" |
| }, |
| { |
| "id": "calderon-zygmund-weak-1-1", |
| "repo": "carleson", |
| "full_id": "carleson/calderon-zygmund-weak-1-1" |
| }, |
| { |
| "id": "enlarge-S", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/enlarge-S" |
| }, |
| { |
| "id": "0-diag-closed-emb", |
| "repo": "toric", |
| "full_id": "toric/0-diag-closed-emb" |
| }, |
| { |
| "id": "cor:mean_value_inequality", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/cor:mean_value_inequality" |
| }, |
| { |
| "id": "lem:charFun_map_eq_charFunDual_smul", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:charFun_map_eq_charFunDual_smul" |
| }, |
| { |
| "id": "SmoothedChebyshevPull3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevPull3" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.prodAdicCompletionComap_isModuleTopology", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.prodAdicCompletionComap_isModuleTopology" |
| }, |
| { |
| "id": "cor:norm limitiation", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:norm limitiation" |
| }, |
| { |
| "id": "1-2-22-irred-dual-lat", |
| "repo": "toric", |
| "full_id": "toric/1-2-22-irred-dual-lat" |
| }, |
| { |
| "id": "tau-def-multi", |
| "repo": "pfr", |
| "full_id": "pfr/tau-def-multi" |
| }, |
| { |
| "id": "lem:splits in splitting module", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:splits in splitting module" |
| }, |
| { |
| "id": "I5Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I5Bound" |
| }, |
| { |
| "id": "fks_cor_14", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks_cor_14" |
| }, |
| { |
| "id": "prop:sliced-cosmoi", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:sliced-cosmoi" |
| }, |
| { |
| "id": "initial-factorization-waste", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-waste" |
| }, |
| { |
| "id": "pick_theorem", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/pick_theorem" |
| }, |
| { |
| "id": "lem:IsKolmogorovProcess.edist_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsKolmogorovProcess.edist_eq_zero" |
| }, |
| { |
| "id": "prop:cech_of_pure_homotopy_k_sheaf", |
| "repo": "M2", |
| "full_id": "M2/prop:cech_of_pure_homotopy_k_sheaf" |
| }, |
| { |
| "id": "lem:ambient_is_convex", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/lem:ambient_is_convex" |
| }, |
| { |
| "id": "Dedekind-PNT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dedekind-PNT" |
| }, |
| { |
| "id": "def:IsLocalMartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsLocalMartingale" |
| }, |
| { |
| "id": "ent-w", |
| "repo": "pfr", |
| "full_id": "pfr/ent-w" |
| }, |
| { |
| "id": "foursum-bound", |
| "repo": "pfr", |
| "full_id": "pfr/foursum-bound" |
| }, |
| { |
| "id": "1-2-15-cone-hull-min-gen", |
| "repo": "toric", |
| "full_id": "toric/1-2-15-cone-hull-min-gen" |
| }, |
| { |
| "id": "lem:card_pairSet_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:card_pairSet_le" |
| }, |
| { |
| "id": "lem:Tate cohomology is cohomology or homology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:Tate cohomology is cohomology or homology" |
| }, |
| { |
| "id": "lem:isssd-gibbs-meas-existence", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:isssd-gibbs-meas-existence" |
| }, |
| { |
| "id": "0-hopf-quot-hom", |
| "repo": "toric", |
| "full_id": "toric/0-hopf-quot-hom" |
| }, |
| { |
| "id": "thm:neumann_series", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:neumann_series" |
| }, |
| { |
| "id": "953_equiv_2", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/953_equiv_2" |
| }, |
| { |
| "id": "lem:hasBoundedInternalCoveringNumber_subset", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasBoundedInternalCoveringNumber_subset" |
| }, |
| { |
| "id": "ZetaUpperBnd", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaUpperBnd" |
| }, |
| { |
| "id": "def:logSizeBallSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:logSizeBallSequence" |
| }, |
| { |
| "id": "def:Z0_bound", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:Z0_bound" |
| }, |
| { |
| "id": "def:locallyIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:locallyIntegrableSup" |
| }, |
| { |
| "id": "lem:L2Martingales.module", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:L2Martingales.module" |
| }, |
| { |
| "id": "prop:operator_norm_properties", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/prop:operator_norm_properties" |
| }, |
| { |
| "id": "sym-group", |
| "repo": "pfr", |
| "full_id": "pfr/sym-group" |
| }, |
| { |
| "id": "classical-carleson", |
| "repo": "carleson", |
| "full_id": "carleson/classical-carleson" |
| }, |
| { |
| "id": "Matroid.IsGraphic.isRegular", |
| "repo": "seymour", |
| "full_id": "seymour/Matroid.IsGraphic.isRegular" |
| }, |
| { |
| "id": "lem:volume_le_of_isCover", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:volume_le_of_isCover" |
| }, |
| { |
| "id": "first-estimate", |
| "repo": "pfr", |
| "full_id": "pfr/first-estimate" |
| }, |
| { |
| "id": "HomAeMisoeM", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/HomAeMisoeM" |
| }, |
| { |
| "id": "kl-cond", |
| "repo": "pfr", |
| "full_id": "pfr/kl-cond" |
| }, |
| { |
| "id": "thm:ext_of_charFun", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:ext_of_charFun" |
| }, |
| { |
| "id": "cor:norm submodule mono", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:norm submodule mono" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.mul_rows", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.mul_rows" |
| }, |
| { |
| "id": "lem:locally_mono", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_mono" |
| }, |
| { |
| "id": "lem:get-better", |
| "repo": "pfr", |
| "full_id": "pfr/lem:get-better" |
| }, |
| { |
| "id": "mobius-lemma-2-sub-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mobius-lemma-2-sub-1" |
| }, |
| { |
| "id": "def:K_stalk", |
| "repo": "M2", |
| "full_id": "M2/def:K_stalk" |
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| { |
| "id": "QHat.lowestTerms", |
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| "full_id": "FLT_ch5/QHat.lowestTerms" |
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| { |
| "id": "sumset-lower", |
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| { |
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| { |
| "id": "lem:koopman_condexp_comm", |
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| "id": "Matroid.IsSum1of.isRegular", |
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| "id": "ff", |
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| "id": "copy-ent", |
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| { |
| "id": "lem:dist_chainingSequence_le_sum", |
| "repo": "brownian-motion", |
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| { |
| "id": "def:LocallyBoundedVariationOn", |
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| "id": "lem:herbrand S-units", |
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| "id": "bound-score-2", |
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| "id": "lp_ap", |
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| { |
| "id": "lem:internalCoveringNumber_eq_one_of_diam_le", |
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| { |
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| { |
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| { |
| "id": "lem:antidiagonal_weight", |
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| { |
| "id": "correlation-near-tree-parts", |
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| { |
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| { |
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| { |
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| { |
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| { |
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| { |
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| "full_id": "pfr/cond-dist-alt" |
| }, |
| { |
| "id": "thm:l1Weighted_Algebra", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_Algebra" |
| }, |
| { |
| "id": "local-antichain-density", |
| "repo": "carleson", |
| "full_id": "carleson/local-antichain-density" |
| }, |
| { |
| "id": "SmoothedChebyshevPull2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevPull2" |
| }, |
| { |
| "id": "AbstractHeckeOperator.HeckeOperator", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/AbstractHeckeOperator.HeckeOperator" |
| }, |
| { |
| "id": "thm:jy_13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/thm:jy_13" |
| }, |
| { |
| "id": "def:stochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:stochIntegral" |
| }, |
| { |
| "id": "thm:pt_2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/thm:pt_2" |
| }, |
| { |
| "id": "StandardRepr", |
| "repo": "seymour", |
| "full_id": "seymour/StandardRepr" |
| }, |
| { |
| "id": "discrete-Carleson", |
| "repo": "carleson", |
| "full_id": "carleson/discrete-Carleson" |
| }, |
| { |
| "id": "bound-for-tree-projection", |
| "repo": "carleson", |
| "full_id": "carleson/bound-for-tree-projection" |
| }, |
| { |
| "id": "cond-dist-fact", |
| "repo": "pfr", |
| "full_id": "pfr/cond-dist-fact" |
| }, |
| { |
| "id": "def:eval", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:eval" |
| }, |
| { |
| "id": "1-1-10-tor-ideal", |
| "repo": "toric", |
| "full_id": "toric/1-1-10-tor-ideal" |
| }, |
| { |
| "id": "lem:IsKolmogorovProcess.aemeasurable_edist", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsKolmogorovProcess.aemeasurable_edist" |
| }, |
| { |
| "id": "def:norm submodule", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:norm submodule" |
| }, |
| { |
| "id": "prop:convex_hull_is_convex", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/prop:convex_hull_is_convex" |
| }, |
| { |
| "id": "lem:IsLocalMartingale.locally_classD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsLocalMartingale.locally_classD" |
| }, |
| { |
| "id": "Dusart_prop_5_11b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_prop_5_11b" |
| }, |
| { |
| "id": "irred-desc", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/irred-desc" |
| }, |
| { |
| "id": "def:nu", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/def:nu" |
| }, |
| { |
| "id": "lem:density bound", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:density bound" |
| }, |
| { |
| "id": "Hurwitz.norm", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.norm" |
| }, |
| { |
| "id": "ZHat.torsionfree", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.torsionfree" |
| }, |
| { |
| "id": "wiggle-order-2", |
| "repo": "carleson", |
| "full_id": "carleson/wiggle-order-2" |
| }, |
| { |
| "id": "prop:b-double-zeros", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:b-double-zeros" |
| }, |
| { |
| "id": "lem:isssd-gibbs-meas-uniqueness", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:isssd-gibbs-meas-uniqueness" |
| }, |
| { |
| "id": "lem:trivial-fib-representability", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:trivial-fib-representability" |
| }, |
| { |
| "id": "theorem : zero_smul", |
| "repo": "LBPTester", |
| "full_id": "LBPTester/theorem : zero_smul" |
| }, |
| { |
| "id": "lem:A_cal_conv_A_on_D_T", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:A_cal_conv_A_on_D_T" |
| }, |
| { |
| "id": "def:up", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:up" |
| }, |
| { |
| "id": "lem:doob_ineq_stop_exp_val", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:doob_ineq_stop_exp_val" |
| }, |
| { |
| "id": "lem:fourier-cont", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier-cont" |
| }, |
| { |
| "id": "906-3862", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/906-3862" |
| }, |
| { |
| "id": "forest-inner", |
| "repo": "carleson", |
| "full_id": "carleson/forest-inner" |
| }, |
| { |
| "id": "lem:maximal_ineq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:maximal_ineq" |
| }, |
| { |
| "id": "Cotlar-control", |
| "repo": "carleson", |
| "full_id": "carleson/Cotlar-control" |
| }, |
| { |
| "id": "cor:cohomology unramified iso cohomology Z", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:cohomology unramified iso cohomology Z" |
| }, |
| { |
| "id": "approx-hom-pfr", |
| "repo": "pfr", |
| "full_id": "pfr/approx-hom-pfr" |
| }, |
| { |
| "id": "lem:filtrationRightCont", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:filtrationRightCont" |
| }, |
| { |
| "id": "fks2-corollary-22", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-22" |
| }, |
| { |
| "id": "def:l1Weighted_one", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:l1Weighted_one" |
| }, |
| { |
| "id": "mutual-nonneg", |
| "repo": "pfr", |
| "full_id": "pfr/mutual-nonneg" |
| }, |
| { |
| "id": "Qhat.unitsrat_meet_unitszHat", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Qhat.unitsrat_meet_unitszHat" |
| }, |
| { |
| "id": "1729_refute_817", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/1729_refute_817" |
| }, |
| { |
| "id": "thm:periodic-packing-optimal", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:periodic-packing-optimal" |
| }, |
| { |
| "id": "def:covariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:covariation" |
| }, |
| { |
| "id": "puInPu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/puInPu" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.compact_quotient", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.compact_quotient" |
| }, |
| { |
| "id": "cor-multid", |
| "repo": "pfr", |
| "full_id": "pfr/cor-multid" |
| }, |
| { |
| "id": "def:L-function", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:L-function" |
| }, |
| { |
| "id": "bklnw-eq_A_7", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_7" |
| }, |
| { |
| "id": "Matrix.shortTableauPivot_eq", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.shortTableauPivot_eq" |
| }, |
| { |
| "id": "BlaschkeOfZero", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/BlaschkeOfZero" |
| }, |
| { |
| "id": "Frey_curve_hardly_ramified", |
| "repo": "FLT_ch3", |
| "full_id": "FLT_ch3/Frey_curve_hardly_ramified" |
| }, |
| { |
| "id": "total-dist", |
| "repo": "pfr", |
| "full_id": "pfr/total-dist" |
| }, |
| { |
| "id": "initial-factorization-small-prime-le", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-small-prime-le" |
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| { |
| "id": "mutual-w-z2", |
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| "full_id": "pfr/mutual-w-z2" |
| }, |
| { |
| "id": "WeakPNT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/WeakPNT" |
| }, |
| { |
| "id": "1-1-phiA", |
| "repo": "toric", |
| "full_id": "toric/1-1-phiA" |
| }, |
| { |
| "id": "thm:Martingale.exists_cadlag_modification", |
| "repo": "brownian-motion", |
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| { |
| "id": "residuePull1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/residuePull1" |
| }, |
| { |
| "id": "lem:volume_div_le_internalCoveringNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:volume_div_le_internalCoveringNumber" |
| }, |
| { |
| "id": "DiskBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/DiskBound" |
| }, |
| { |
| "id": "eq1661", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1661" |
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| { |
| "id": "phi-second-estimate", |
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| "full_id": "pfr/phi-second-estimate" |
| }, |
| { |
| "id": "hom-pfr", |
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| "full_id": "pfr/hom-pfr" |
| }, |
| { |
| "id": "def:det-fun-complex", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:det-fun-complex" |
| }, |
| { |
| "id": "C-convex", |
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| "full_id": "carleson/C-convex" |
| }, |
| { |
| "id": "thm:hilbertSpace_L2Martingales", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:hilbertSpace_L2Martingales" |
| }, |
| { |
| "id": "cond-indep-exist", |
| "repo": "pfr", |
| "full_id": "pfr/cond-indep-exist" |
| }, |
| { |
| "id": "ch38theorem", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch38theorem" |
| }, |
| { |
| "id": "eq4513", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq4513" |
| }, |
| { |
| "id": "bklnw-sigma_2_def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-sigma_2_def" |
| }, |
| { |
| "id": "lem:norm naturality", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:norm naturality" |
| }, |
| { |
| "id": "costa-pereira-theorem-1b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-theorem-1b" |
| }, |
| { |
| "id": "instComplexLieAlgebraAction", |
| "repo": "FLT_ch7", |
| "full_id": "FLT_ch7/instComplexLieAlgebraAction" |
| }, |
| { |
| "id": "lem:lemma2", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/lem:lemma2" |
| }, |
| { |
| "id": "lem:IsLocalMartingale.isLocalSubmartingale_sq_norm", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsLocalMartingale.isLocalSubmartingale_sq_norm" |
| }, |
| { |
| "id": "0-grp-like-grp-alg-span", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-grp-alg-span" |
| }, |
| { |
| "id": "FLT", |
| "repo": "FLT_ch2", |
| "full_id": "FLT_ch2/FLT" |
| }, |
| { |
| "id": "chebyshev", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/chebyshev" |
| }, |
| { |
| "id": "lem:internalCoveringNumber_closedBall_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:internalCoveringNumber_closedBall_le" |
| }, |
| { |
| "id": "def:multicorner", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:multicorner" |
| }, |
| { |
| "id": "lem:local_induction", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:local_induction" |
| }, |
| { |
| "id": "1-1-7-ya", |
| "repo": "toric", |
| "full_id": "toric/1-1-7-ya" |
| }, |
| { |
| "id": "buthe-theorem-2a", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/buthe-theorem-2a" |
| }, |
| { |
| "id": "def:Tate cohomology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:Tate cohomology" |
| }, |
| { |
| "id": "multidist-chain-rule-iter", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-chain-rule-iter" |
| }, |
| { |
| "id": "IsDedekindDomain.pi_tensorProduct", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.pi_tensorProduct" |
| }, |
| { |
| "id": "tree-projection-estimate", |
| "repo": "carleson", |
| "full_id": "carleson/tree-projection-estimate" |
| }, |
| { |
| "id": "lem:card_logSizeRadius_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:card_logSizeRadius_le" |
| }, |
| { |
| "id": "riemannZeta_conj", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/riemannZeta_conj" |
| }, |
| { |
| "id": "second-exception", |
| "repo": "carleson", |
| "full_id": "carleson/second-exception" |
| }, |
| { |
| "id": "def:IsGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsGaussian" |
| }, |
| { |
| "id": "bound-score-3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bound-score-3" |
| }, |
| { |
| "id": "QuCard", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/QuCard" |
| }, |
| { |
| "id": "mobius-lemma-2-sub-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mobius-lemma-2-sub-2" |
| }, |
| { |
| "id": "29_equiv_14", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/29_equiv_14" |
| }, |
| { |
| "id": "forest-union", |
| "repo": "carleson", |
| "full_id": "carleson/forest-union" |
| }, |
| { |
| "id": "eq4582", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq4582" |
| }, |
| { |
| "id": "score-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/score-def" |
| }, |
| { |
| "id": "multidist-ruzsa-IV", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-ruzsa-IV" |
| }, |
| { |
| "id": "lem:predictable_predictablePart", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictable_predictablePart" |
| }, |
| { |
| "id": "defn:sset-category", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:sset-category" |
| }, |
| { |
| "id": "costa-pereira-sublemma-1-3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-sublemma-1-3" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.longTableauPivot", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.longTableauPivot" |
| }, |
| { |
| "id": "MellinConvolutionSymmetric", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinConvolutionSymmetric" |
| }, |
| { |
| "id": "gcount", |
| "repo": "pfr", |
| "full_id": "pfr/gcount" |
| }, |
| { |
| "id": "riemannZetaResidue", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/riemannZetaResidue" |
| }, |
| { |
| "id": "eq3744", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq3744" |
| }, |
| { |
| "id": "jensen-bound", |
| "repo": "pfr", |
| "full_id": "pfr/jensen-bound" |
| }, |
| { |
| "id": "adjoint-tree-control", |
| "repo": "carleson", |
| "full_id": "carleson/adjoint-tree-control" |
| }, |
| { |
| "id": "def:wienerMeasure", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:wienerMeasure" |
| }, |
| { |
| "id": "lemma:ineqABnew-equiv", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:ineqABnew-equiv" |
| }, |
| { |
| "id": "lem:quadraticVariation_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:quadraticVariation_zero" |
| }, |
| { |
| "id": "lem:hasLaw_brownian_sub", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasLaw_brownian_sub" |
| }, |
| { |
| "id": "bklnw-eq_A_18", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_18" |
| }, |
| { |
| "id": "lem:pq-ratio", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:pq-ratio" |
| }, |
| { |
| "id": "def:a-definition", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:a-definition" |
| }, |
| { |
| "id": "Dusart_cor_5_2_f", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_2_f" |
| }, |
| { |
| "id": "RectangleIntegral_tendsTo_LowerU", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/RectangleIntegral_tendsTo_LowerU" |
| }, |
| { |
| "id": "partial-exist", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/partial-exist" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_prod", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_prod" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_le_of_minimal_cover", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_le_of_minimal_cover" |
| }, |
| { |
| "id": "Zeta_diff_Bnd", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Zeta_diff_Bnd" |
| }, |
| { |
| "id": "dist-sums", |
| "repo": "pfr", |
| "full_id": "pfr/dist-sums" |
| }, |
| { |
| "id": "MellinOfSmooth1c", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfSmooth1c" |
| }, |
| { |
| "id": "GapSize", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/GapSize" |
| }, |
| { |
| "id": "thm:wed-artin-ideal", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/thm:wed-artin-ideal" |
| }, |
| { |
| "id": "E8-is-basis", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/E8-is-basis" |
| }, |
| { |
| "id": "lemma:sp-finite-density-bound", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:sp-finite-density-bound" |
| }, |
| { |
| "id": "lem:cond-exp-proper-ker-bind", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:cond-exp-proper-ker-bind" |
| }, |
| { |
| "id": "lem:first_non_zero_homology_of_homotopy_k_sheaf_is_k_sheaf", |
| "repo": "M2", |
| "full_id": "M2/lem:first_non_zero_homology_of_homotopy_k_sheaf_is_k_sheaf" |
| }, |
| { |
| "id": "lem:stoppingTime_approximationNat", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:stoppingTime_approximationNat" |
| }, |
| { |
| "id": "thm:CauchyProduct_assoc", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_assoc" |
| }, |
| { |
| "id": "models-def", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/models-def" |
| }, |
| { |
| "id": "lem:qi-product", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:qi-product" |
| }, |
| { |
| "id": "ZHat.e_not_in_Int", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.e_not_in_Int" |
| }, |
| { |
| "id": "ZetaBoxEval", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaBoxEval" |
| }, |
| { |
| "id": "thm:log_le_primeCountingReal_add_one", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/thm:log_le_primeCountingReal_add_one" |
| }, |
| { |
| "id": "0-biideal", |
| "repo": "toric", |
| "full_id": "toric/0-biideal" |
| }, |
| { |
| "id": "MatrixSum3.HasCanonicalSigning.toCanonicalSigning", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.HasCanonicalSigning.toCanonicalSigning" |
| }, |
| { |
| "id": "thm:kolmogorovExtension", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:kolmogorovExtension" |
| }, |
| { |
| "id": "I4Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I4Bound" |
| }, |
| { |
| "id": "Lp-orth", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/Lp-orth" |
| }, |
| { |
| "id": "key", |
| "repo": "pfr", |
| "full_id": "pfr/key" |
| }, |
| { |
| "id": "cuspidal_automorphic_representation", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/cuspidal_automorphic_representation" |
| }, |
| { |
| "id": "1-2-12-salient-cone-tfae", |
| "repo": "toric", |
| "full_id": "toric/1-2-12-salient-cone-tfae" |
| }, |
| { |
| "id": "lem:IsKolmogorovProcess.aemeasurable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsKolmogorovProcess.aemeasurable" |
| }, |
| { |
| "id": "euler_consequence_a", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/euler_consequence_a" |
| }, |
| { |
| "id": "standardReprSum1", |
| "repo": "seymour", |
| "full_id": "seymour/standardReprSum1" |
| }, |
| { |
| "id": "sylvester_gallai2", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/sylvester_gallai2" |
| }, |
| { |
| "id": "de-prop-lim-improv", |
| "repo": "pfr", |
| "full_id": "pfr/de-prop-lim-improv" |
| }, |
| { |
| "id": "th-ap-int", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/th-ap-int" |
| }, |
| { |
| "id": "0-grp-like-quot-hopf", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-quot-hopf" |
| }, |
| { |
| "id": "lem:lintegral_sup_cover_eq_of_lt_iInf_dist", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:lintegral_sup_cover_eq_of_lt_iInf_dist" |
| }, |
| { |
| "id": "erdos-sol-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/erdos-sol-1" |
| }, |
| { |
| "id": "lem:C_eq_gramMatrix", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:C_eq_gramMatrix" |
| }, |
| { |
| "id": "thm:infinity_of_primes", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/thm:infinity_of_primes" |
| }, |
| { |
| "id": "manifold_on_algebraic_variety_computation", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/manifold_on_algebraic_variety_computation" |
| }, |
| { |
| "id": "lem:adj_kshv_and_shv", |
| "repo": "M2", |
| "full_id": "M2/lem:adj_kshv_and_shv" |
| }, |
| { |
| "id": "thm:general_radii_poly_theorem", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:general_radii_poly_theorem" |
| }, |
| { |
| "id": "lem:lemma5", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/lem:lemma5" |
| }, |
| { |
| "id": "cor:disc-nonvanishing", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:disc-nonvanishing" |
| }, |
| { |
| "id": "thm:conditionallyIID_of_contractable_L2", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:conditionallyIID_of_contractable_L2" |
| }, |
| { |
| "id": "highlyabundant-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/highlyabundant-def" |
| }, |
| { |
| "id": "lem:Martingale.classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Martingale.classDL" |
| }, |
| { |
| "id": "fixed_of_fixed1_aux1", |
| "repo": "FLT_ch8", |
| "full_id": "FLT_ch8/fixed_of_fixed1_aux1" |
| }, |
| { |
| "id": "lem:elemStochIntegralBilin_const", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elemStochIntegralBilin_const" |
| }, |
| { |
| "id": "bourgain-trick", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/bourgain-trick" |
| }, |
| { |
| "id": "rs-415", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/rs-415" |
| }, |
| { |
| "id": "prop:kan-cosmos", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:kan-cosmos" |
| }, |
| { |
| "id": "lem:l1Weighted_mem", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:l1Weighted_mem" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_trans", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_trans" |
| }, |
| { |
| "id": "adjoint-tree-estimate", |
| "repo": "carleson", |
| "full_id": "carleson/adjoint-tree-estimate" |
| }, |
| { |
| "id": "cor:phi4-bound", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:phi4-bound" |
| }, |
| { |
| "id": "lem:rightContSelf", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContSelf" |
| }, |
| { |
| "id": "lem:eval_zero", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:eval_zero" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_piCongrRight", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_piCongrRight" |
| }, |
| { |
| "id": "thm:fixed_point_radii", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:fixed_point_radii" |
| }, |
| { |
| "id": "Smooth1Properties_below", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1Properties_below" |
| }, |
| { |
| "id": "anti-impl", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/anti-impl" |
| }, |
| { |
| "id": "lem:esymm_invariant", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:esymm_invariant" |
| }, |
| { |
| "id": "SmoothedChebyshevDirichlet_aux_integrable", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevDirichlet_aux_integrable" |
| }, |
| { |
| "id": "estimate-bad-partial", |
| "repo": "carleson", |
| "full_id": "carleson/estimate-bad-partial" |
| }, |
| { |
| "id": "entropy-comm", |
| "repo": "pfr", |
| "full_id": "pfr/entropy-comm" |
| }, |
| { |
| "id": "NumberField.InfinitePlace.Completion.baseChange_surjective", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfinitePlace.Completion.baseChange_surjective" |
| }, |
| { |
| "id": "SpherePacking.scale_finiteDensity", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/SpherePacking.scale_finiteDensity" |
| }, |
| { |
| "id": "lem:Doob_Meyer_Finite_Predictable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Doob_Meyer_Finite_Predictable" |
| }, |
| { |
| "id": "lem:Case1Basic", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Case1Basic" |
| }, |
| { |
| "id": "asterix-obelix", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/asterix-obelix" |
| }, |
| { |
| "id": "L2-antichain", |
| "repo": "carleson", |
| "full_id": "carleson/L2-antichain" |
| }, |
| { |
| "id": "thm:coeff_mul_eq_cauchy", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:coeff_mul_eq_cauchy" |
| }, |
| { |
| "id": "injYu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/injYu" |
| }, |
| { |
| "id": "eq3588", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq3588" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_adeles_rat", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_adeles_rat" |
| }, |
| { |
| "id": "I1New", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I1New" |
| }, |
| { |
| "id": "li-approx", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/li-approx" |
| }, |
| { |
| "id": "lem:scale_change", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:scale_change" |
| }, |
| { |
| "id": "costa-pereira-sublemma-1-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-sublemma-1-2" |
| }, |
| { |
| "id": "bklnw-def-a-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-def-a-2" |
| }, |
| { |
| "id": "Dusart_cor_5_2_a", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_2_a" |
| }, |
| { |
| "id": "lem:Submartingale.classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.classDL" |
| }, |
| { |
| "id": "chebyshev-asymptotic", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/chebyshev-asymptotic" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_smul_integral_comap", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_smul_integral_comap" |
| }, |
| { |
| "id": "ZHat.multiples", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.multiples" |
| }, |
| { |
| "id": "lemma:Gaussian-Fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Gaussian-Fourier" |
| }, |
| { |
| "id": "thm:plancherel", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:plancherel" |
| }, |
| { |
| "id": "prop:DiophantineReduction", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:DiophantineReduction" |
| }, |
| { |
| "id": "I1Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I1Bound" |
| }, |
| { |
| "id": "fks2-proposition-17", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-proposition-17" |
| }, |
| { |
| "id": "lem:enriched-cob-adjunction", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:enriched-cob-adjunction" |
| }, |
| { |
| "id": "cor:finite_set_bound_of_dist_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:finite_set_bound_of_dist_le" |
| }, |
| { |
| "id": "prop:SpecialThue", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:SpecialThue" |
| }, |
| { |
| "id": "push", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/push" |
| }, |
| { |
| "id": "eq2662", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq2662" |
| }, |
| { |
| "id": "lem:IsSquareIntegrable.submartingale_sq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsSquareIntegrable.submartingale_sq" |
| }, |
| { |
| "id": "NumberField.FiniteAdeleRing.DivisionAlgebra.finiteDoubleCoset", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.FiniteAdeleRing.DivisionAlgebra.finiteDoubleCoset" |
| }, |
| { |
| "id": "I3New", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I3New" |
| }, |
| { |
| "id": "Dusart_prop_4_4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_prop_4_4" |
| }, |
| { |
| "id": "5093-nontrivial", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/5093-nontrivial" |
| }, |
| { |
| "id": "ResidueTheoremAtOrigin", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ResidueTheoremAtOrigin" |
| }, |
| { |
| "id": "initial-factorization-large-prime-le", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-large-prime-le" |
| }, |
| { |
| "id": "eq63", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq63" |
| }, |
| { |
| "id": "0-is-diag-bialg-quot", |
| "repo": "toric", |
| "full_id": "toric/0-is-diag-bialg-quot" |
| }, |
| { |
| "id": "thm:tendsto_limitProcess_of_cadlag", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:tendsto_limitProcess_of_cadlag" |
| }, |
| { |
| "id": "lem:radii_poly_alt_form", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:radii_poly_alt_form" |
| }, |
| { |
| "id": "1-1-10-tor-ideal-ya", |
| "repo": "toric", |
| "full_id": "toric/1-1-10-tor-ideal-ya" |
| }, |
| { |
| "id": "main-entropy", |
| "repo": "pfr", |
| "full_id": "pfr/main-entropy" |
| }, |
| { |
| "id": "lem:trivial-fib-conical", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:trivial-fib-conical" |
| }, |
| { |
| "id": "lem:integral_sup_dist_le_sum_rpow", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_dist_le_sum_rpow" |
| }, |
| { |
| "id": "lem:A_increasing", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:A_increasing" |
| }, |
| { |
| "id": "kneser_conjecture", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/kneser_conjecture" |
| }, |
| { |
| "id": "0-char", |
| "repo": "toric", |
| "full_id": "toric/0-char" |
| }, |
| { |
| "id": "1-1-tor-act-alg", |
| "repo": "toric", |
| "full_id": "toric/1-1-tor-act-alg" |
| }, |
| { |
| "id": "1-2-16-reg-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-16-reg-cone" |
| }, |
| { |
| "id": "cor:sset-cat-colimits", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/cor:sset-cat-colimits" |
| }, |
| { |
| "id": "thm:bounds_verified", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:bounds_verified" |
| }, |
| { |
| "id": "lem:IsGaussian.charFun_eq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsGaussian.charFun_eq" |
| }, |
| { |
| "id": "lem:cond-exp-proper-ker-integral", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:cond-exp-proper-ker-integral" |
| }, |
| { |
| "id": "I2New", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I2New" |
| }, |
| { |
| "id": "Dusart_prop_4_3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_prop_4_3" |
| }, |
| { |
| "id": "lem:isStable_locally", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_locally" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_refl", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_refl" |
| }, |
| { |
| "id": "classical-bound-psi", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/classical-bound-psi" |
| }, |
| { |
| "id": "def:herbrand quotient", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:herbrand quotient" |
| }, |
| { |
| "id": "lem:chech_is_determined_by_stalks_1", |
| "repo": "M2", |
| "full_id": "M2/lem:chech_is_determined_by_stalks_1" |
| }, |
| { |
| "id": "lem:Subcase1.1", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Subcase1.1" |
| }, |
| { |
| "id": "ch23theorem2", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch23theorem2" |
| }, |
| { |
| "id": "AnalyticOn_divRemovable_zero_closedBall", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/AnalyticOn_divRemovable_zero_closedBall" |
| }, |
| { |
| "id": "global-tree-control-2", |
| "repo": "carleson", |
| "full_id": "carleson/global-tree-control-2" |
| }, |
| { |
| "id": "0-cochar-diag", |
| "repo": "toric", |
| "full_id": "toric/0-cochar-diag" |
| }, |
| { |
| "id": "entropy-pfr-improv", |
| "repo": "pfr", |
| "full_id": "pfr/entropy-pfr-improv" |
| }, |
| { |
| "id": "def:polar_dual", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/def:polar_dual" |
| }, |
| { |
| "id": "0-embed-aff-mon", |
| "repo": "toric", |
| "full_id": "toric/0-embed-aff-mon" |
| }, |
| { |
| "id": "real-Carleson-operator-measurable", |
| "repo": "carleson", |
| "full_id": "carleson/real-Carleson-operator-measurable" |
| }, |
| { |
| "id": "Matrix.HasTuCanonicalSigning.toCanonicalSigning", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.HasTuCanonicalSigning.toCanonicalSigning" |
| }, |
| { |
| "id": "iteration", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/iteration" |
| }, |
| { |
| "id": "lem:locally_inter", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_inter" |
| }, |
| { |
| "id": "thm:ABCExceptionalBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/thm:ABCExceptionalBound" |
| }, |
| { |
| "id": "thm:fourier-is-l2-linear", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:fourier-is-l2-linear" |
| }, |
| { |
| "id": "ent-z2", |
| "repo": "pfr", |
| "full_id": "pfr/ent-z2" |
| }, |
| { |
| "id": "eq381", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq381" |
| }, |
| { |
| "id": "pn_asymptotic", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/pn_asymptotic" |
| }, |
| { |
| "id": "def:covMatrix", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:covMatrix" |
| }, |
| { |
| "id": "def:disc-definition", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:disc-definition" |
| }, |
| { |
| "id": "lem:tailSigma_le_futureFiltration", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:tailSigma_le_futureFiltration" |
| }, |
| { |
| "id": "IsDedekindDomain.AKLB.surjective_tensorProduct_map", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.AKLB.surjective_tensorProduct_map" |
| }, |
| { |
| "id": "lem:rightLimitFiltration_basic", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightLimitFiltration_basic" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_mul_volume", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_mul_volume" |
| }, |
| { |
| "id": "lem:Doob_Meyer_Finite_Martingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Doob_Meyer_Finite_Martingale" |
| }, |
| { |
| "id": "def:homotopy_colimit", |
| "repo": "M2", |
| "full_id": "M2/def:homotopy_colimit" |
| }, |
| { |
| "id": "C5-convex", |
| "repo": "carleson", |
| "full_id": "carleson/C5-convex" |
| }, |
| { |
| "id": "fks2-corollary-11", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-11" |
| }, |
| { |
| "id": "Wiles_Frey_again", |
| "repo": "FLT_ch3", |
| "full_id": "FLT_ch3/Wiles_Frey_again" |
| }, |
| { |
| "id": "1-2-4-dual-polyhedral-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-4-dual-polyhedral-cone" |
| }, |
| { |
| "id": "partial-Fourier-sums-of-small", |
| "repo": "carleson", |
| "full_id": "carleson/partial-Fourier-sums-of-small" |
| }, |
| { |
| "id": "def:stable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:stable" |
| }, |
| { |
| "id": "lem:internalCoveringNumber_le_packingNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:internalCoveringNumber_le_packingNumber" |
| }, |
| { |
| "id": "prop:simplex-cat-factorization", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:simplex-cat-factorization" |
| }, |
| { |
| "id": "lem:trivial-protocol-valid", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:trivial-protocol-valid" |
| }, |
| { |
| "id": "Dusart_cor_5_2_c", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_2_c" |
| }, |
| { |
| "id": "vanish-entropy", |
| "repo": "pfr", |
| "full_id": "pfr/vanish-entropy" |
| }, |
| { |
| "id": "lemma:theta-slash-invariant", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:theta-slash-invariant" |
| }, |
| { |
| "id": "Dusart_cor_5_3_a", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_3_a" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.C", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.C" |
| }, |
| { |
| "id": "Matrix.shortTableauPivot", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.shortTableauPivot" |
| }, |
| { |
| "id": "Matrix.IsPartiallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsPartiallyUnimodular" |
| }, |
| { |
| "id": "thm:criterion", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/thm:criterion" |
| }, |
| { |
| "id": "lem:isProbabilityMeasure_stdGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isProbabilityMeasure_stdGaussian" |
| }, |
| { |
| "id": "e_pow_2_irrational", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/e_pow_2_irrational" |
| }, |
| { |
| "id": "freemag-exist", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/freemag-exist" |
| }, |
| { |
| "id": "M2.localFullLevel.isOpen", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/M2.localFullLevel.isOpen" |
| }, |
| { |
| "id": "lem:optionalSampling", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:optionalSampling" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_restrictedProduct", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_restrictedProduct" |
| }, |
| { |
| "id": "fks2-lemma-10-substep", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-10-substep" |
| }, |
| { |
| "id": "thm:kernel-approximation", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:kernel-approximation" |
| }, |
| { |
| "id": "lem:trivial-fib-leibniz", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:trivial-fib-leibniz" |
| }, |
| { |
| "id": "lem:classDLOfClassD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:classDLOfClassD" |
| }, |
| { |
| "id": "row-correlation", |
| "repo": "carleson", |
| "full_id": "carleson/row-correlation" |
| }, |
| { |
| "id": "Homeomorph.restrictedProductMatrix", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/Homeomorph.restrictedProductMatrix" |
| }, |
| { |
| "id": "def:serre-der", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:serre-der" |
| }, |
| { |
| "id": "lem:unramified fundamental class", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:unramified fundamental class" |
| }, |
| { |
| "id": "fks2-corollary-24", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-24" |
| }, |
| { |
| "id": "lem:isGaussian_iff_charFun_eq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_iff_charFun_eq" |
| }, |
| { |
| "id": "def:Y0_bound", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:Y0_bound" |
| }, |
| { |
| "id": "cor:H1 H2 cyclic idele class", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:H1 H2 cyclic idele class" |
| }, |
| { |
| "id": "lem:locallyIntegrable_quadraticVariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locallyIntegrable_quadraticVariation" |
| }, |
| { |
| "id": "cor:dist_chainingSequence_pow_two_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:dist_chainingSequence_pow_two_le" |
| }, |
| { |
| "id": "klm-2", |
| "repo": "pfr", |
| "full_id": "pfr/klm-2" |
| }, |
| { |
| "id": "automorphic_form", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/automorphic_form" |
| }, |
| { |
| "id": "lem:premodif-modif", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:premodif-modif" |
| }, |
| { |
| "id": "instDiscreteE8Lattice", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/instDiscreteE8Lattice" |
| }, |
| { |
| "id": "lemma:F-G-phi-psi-identities", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:F-G-phi-psi-identities" |
| }, |
| { |
| "id": "thm:fourier-inversion-L1", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:fourier-inversion-L1" |
| }, |
| { |
| "id": "Hurwitz.norm_mul", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.norm_mul" |
| }, |
| { |
| "id": "0-char-diag", |
| "repo": "toric", |
| "full_id": "toric/0-char-diag" |
| }, |
| { |
| "id": "lem:komlos", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:komlos" |
| }, |
| { |
| "id": "FsigmaThm", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/FsigmaThm" |
| }, |
| { |
| "id": "1-2-10-dual-face", |
| "repo": "toric", |
| "full_id": "toric/1-2-10-dual-face" |
| }, |
| { |
| "id": "lemma:dedekind_eta_transformation", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:dedekind_eta_transformation" |
| }, |
| { |
| "id": "HurwitzRatHat.canonicalForm", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/HurwitzRatHat.canonicalForm" |
| }, |
| { |
| "id": "rs-419", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/rs-419" |
| }, |
| { |
| "id": "def:internalCoveringNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:internalCoveringNumber" |
| }, |
| { |
| "id": "lem:proper-ker-integral", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:proper-ker-integral" |
| }, |
| { |
| "id": "tau-def", |
| "repo": "pfr", |
| "full_id": "pfr/tau-def" |
| }, |
| { |
| "id": "law-count-triv", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/law-count-triv" |
| }, |
| { |
| "id": "R-truncation", |
| "repo": "carleson", |
| "full_id": "carleson/R-truncation" |
| }, |
| { |
| "id": "lem:MixedThueMethods", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:MixedThueMethods" |
| }, |
| { |
| "id": "fks2-eq-11", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-eq-11" |
| }, |
| { |
| "id": "1-1-8-char-ya", |
| "repo": "toric", |
| "full_id": "toric/1-1-8-char-ya" |
| }, |
| { |
| "id": "lem:charFunDual_map", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:charFunDual_map" |
| }, |
| { |
| "id": "def:Mk", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:Mk" |
| }, |
| { |
| "id": "def:phi4-phi2-phi0", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:phi4-phi2-phi0" |
| }, |
| { |
| "id": "rhoMinus_nonneg", |
| "repo": "pfr", |
| "full_id": "pfr/rhoMinus_nonneg" |
| }, |
| { |
| "id": "antichain-tile-count", |
| "repo": "carleson", |
| "full_id": "carleson/antichain-tile-count" |
| }, |
| { |
| "id": "lemma:mod-div-disc-bound", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:mod-div-disc-bound" |
| }, |
| { |
| "id": "automorphic_form_actions", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/automorphic_form_actions" |
| }, |
| { |
| "id": "qu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/qu" |
| }, |
| { |
| "id": "def:quadraticVariationMeasure", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:quadraticVariationMeasure" |
| }, |
| { |
| "id": "integrable-bump-convolution", |
| "repo": "carleson", |
| "full_id": "carleson/integrable-bump-convolution" |
| }, |
| { |
| "id": "thm:CauchyProduct_one_mul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_one_mul" |
| }, |
| { |
| "id": "primorial_bounds", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/primorial_bounds" |
| }, |
| { |
| "id": "I37", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I37" |
| }, |
| { |
| "id": "ShiftOneBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ShiftOneBound" |
| }, |
| { |
| "id": "lem:Submartingale.exists_modifications_limits", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.exists_modifications_limits" |
| }, |
| { |
| "id": "I1NewBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I1NewBound" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_comap", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_comap" |
| }, |
| { |
| "id": "turan_graph", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/turan_graph" |
| }, |
| { |
| "id": "local-dens1-tree-bound", |
| "repo": "carleson", |
| "full_id": "carleson/local-dens1-tree-bound" |
| }, |
| { |
| "id": "frequency-ball-doubling", |
| "repo": "carleson", |
| "full_id": "carleson/frequency-ball-doubling" |
| }, |
| { |
| "id": "automorphic_representation_local_decomposition", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/automorphic_representation_local_decomposition" |
| }, |
| { |
| "id": "lem:limitProcess_elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:limitProcess_elemStochIntegral" |
| }, |
| { |
| "id": "lem:cond-exp-proper-ker-lintegral", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:cond-exp-proper-ker-lintegral" |
| }, |
| { |
| "id": "fks-corollary-2-9", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-corollary-2-9" |
| }, |
| { |
| "id": "thm:existence_condition", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:existence_condition" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.E", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.E" |
| }, |
| { |
| "id": "lem:forbidden-pattern-project-multicorner", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:forbidden-pattern-project-multicorner" |
| }, |
| { |
| "id": "build-magma", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/build-magma" |
| }, |
| { |
| "id": "rhoplus-def", |
| "repo": "pfr", |
| "full_id": "pfr/rhoplus-def" |
| }, |
| { |
| "id": "lem:inner_elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:inner_elemStochIntegral" |
| }, |
| { |
| "id": "0-cochar-torus", |
| "repo": "toric", |
| "full_id": "toric/0-cochar-torus" |
| }, |
| { |
| "id": "def:predictableMeasurableSpace", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:predictableMeasurableSpace" |
| }, |
| { |
| "id": "lem:HasLocallyIntegrableSup.locally_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:HasLocallyIntegrableSup.locally_classDL" |
| }, |
| { |
| "id": "def:itoIsometry", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:itoIsometry" |
| }, |
| { |
| "id": "thm:primeCountingReal_unbounded", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/thm:primeCountingReal_unbounded" |
| }, |
| { |
| "id": "thm:fourier-inversion", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:fourier-inversion" |
| }, |
| { |
| "id": "pos-def-measures", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/pos-def-measures" |
| }, |
| { |
| "id": "lem:choose-qi", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:choose-qi" |
| }, |
| { |
| "id": "lem:integral_id_multivariateGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_id_multivariateGaussian" |
| }, |
| { |
| "id": "def:adj_kprshv_and_prshv", |
| "repo": "M2", |
| "full_id": "M2/def:adj_kprshv_and_prshv" |
| }, |
| { |
| "id": "sum-dilate-II", |
| "repo": "pfr", |
| "full_id": "pfr/sum-dilate-II" |
| }, |
| { |
| "id": "costa-pereira-sublemma-1-6", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-sublemma-1-6" |
| }, |
| { |
| "id": "diffBddAtNegOne", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/diffBddAtNegOne" |
| }, |
| { |
| "id": "thm:det-fun-complex-eval-ge-corner-color-num", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/thm:det-fun-complex-eval-ge-corner-color-num" |
| }, |
| { |
| "id": "lem:sigmaM-lower-final", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:sigmaM-lower-final" |
| }, |
| { |
| "id": "def:restriction map", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:restriction map" |
| }, |
| { |
| "id": "ruzsa-triangle-improved", |
| "repo": "pfr", |
| "full_id": "pfr/ruzsa-triangle-improved" |
| }, |
| { |
| "id": "lem:choose-pi", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:choose-pi" |
| }, |
| { |
| "id": "Smooth1LeOne", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1LeOne" |
| }, |
| { |
| "id": "hardly_ramified_reducible", |
| "repo": "FLT_ch3", |
| "full_id": "FLT_ch3/hardly_ramified_reducible" |
| }, |
| { |
| "id": "cor:up and down trivial cohomology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:up and down trivial cohomology" |
| }, |
| { |
| "id": "smetaniuk_theorem", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/smetaniuk_theorem" |
| }, |
| { |
| "id": "nontangential-from-simple", |
| "repo": "carleson", |
| "full_id": "carleson/nontangential-from-simple" |
| }, |
| { |
| "id": "lem:hausdorff_young_dual", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:hausdorff_young_dual" |
| }, |
| { |
| "id": "MellinOfSmooth1b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfSmooth1b" |
| }, |
| { |
| "id": "borelCaratheodory-closedBall", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/borelCaratheodory-closedBall" |
| }, |
| { |
| "id": "ZetaDerivUpperBnd", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaDerivUpperBnd" |
| }, |
| { |
| "id": "lem:Martingale.congr", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Martingale.congr" |
| }, |
| { |
| "id": "pi_asymp", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/pi_asymp" |
| }, |
| { |
| "id": "I4NewBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I4NewBound" |
| }, |
| { |
| "id": "lem:dist_nearestPt_of_isCover", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:dist_nearestPt_of_isCover" |
| }, |
| { |
| "id": "lemma:theta-modular", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:theta-modular" |
| }, |
| { |
| "id": "prop:52", |
| "repo": "pfr", |
| "full_id": "pfr/prop:52" |
| }, |
| { |
| "id": "Hurwitz.norm_nonneg", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.norm_nonneg" |
| }, |
| { |
| "id": "def:HasBoundedCoveringNumberCover", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:HasBoundedCoveringNumberCover" |
| }, |
| { |
| "id": "cond-multidist-nonneg", |
| "repo": "pfr", |
| "full_id": "pfr/cond-multidist-nonneg" |
| }, |
| { |
| "id": "lem:uniformIntegrable_stoppedValue_martingale_of_countable_range", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrable_stoppedValue_martingale_of_countable_range" |
| }, |
| { |
| "id": "def:key-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:key-chapter" |
| }, |
| { |
| "id": "lem:newton_Y_bound", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:newton_Y_bound" |
| }, |
| { |
| "id": "initial-factorization-card", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-card" |
| }, |
| { |
| "id": "prop:a-double-zeros", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:a-double-zeros" |
| }, |
| { |
| "id": "lem:SpecialGeometry", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:SpecialGeometry" |
| }, |
| { |
| "id": "lem:M_n_cadlag_mg", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:M_n_cadlag_mg" |
| }, |
| { |
| "id": "fks-corollary_2_3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-corollary_2_3" |
| }, |
| { |
| "id": "eq5093", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq5093" |
| }, |
| { |
| "id": "lcm-M-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lcm-M-def" |
| }, |
| { |
| "id": "thm:coefficients_independent", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/thm:coefficients_independent" |
| }, |
| { |
| "id": "Hilbert-kernel-regularity", |
| "repo": "carleson", |
| "full_id": "carleson/Hilbert-kernel-regularity" |
| }, |
| { |
| "id": "cor:MLDE-pos", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:MLDE-pos" |
| }, |
| { |
| "id": "0-is-diag-bialg-iff-span-group-like", |
| "repo": "toric", |
| "full_id": "toric/0-is-diag-bialg-iff-span-group-like" |
| }, |
| { |
| "id": "thm:Cohn-Elkies-periodic", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:Cohn-Elkies-periodic" |
| }, |
| { |
| "id": "E8-Lattice", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/E8-Lattice" |
| }, |
| { |
| "id": "thm:wed", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/thm:wed" |
| }, |
| { |
| "id": "cor:coind₁' invariants trivial cohomology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:coind₁' invariants trivial cohomology" |
| }, |
| { |
| "id": "initial-score", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-score" |
| }, |
| { |
| "id": "eq1659", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1659" |
| }, |
| { |
| "id": "fks-theorem-2-7", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-theorem-2-7" |
| }, |
| { |
| "id": "eq7", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq7" |
| }, |
| { |
| "id": "lem:isStable_left_limit", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_left_limit" |
| }, |
| { |
| "id": "bklnw-eq_A_17", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_17" |
| }, |
| { |
| "id": "global-antichain-density", |
| "repo": "carleson", |
| "full_id": "carleson/global-antichain-density" |
| }, |
| { |
| "id": "lem:uniformIntegrable_stoppedValue_discreteApproxSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrable_stoppedValue_discreteApproxSequence" |
| }, |
| { |
| "id": "theorem : subspace_neg", |
| "repo": "LBPTester", |
| "full_id": "LBPTester/theorem : subspace_neg" |
| }, |
| { |
| "id": "thm:dim-mf-general-level", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:dim-mf-general-level" |
| }, |
| { |
| "id": "lem:closed_ball_complete", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:closed_ball_complete" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.X", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.X" |
| }, |
| { |
| "id": "initial-score-bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-score-bound" |
| }, |
| { |
| "id": "NumberField.AdeleRing.baseChange_moduleTopology", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.AdeleRing.baseChange_moduleTopology" |
| }, |
| { |
| "id": "NumberField.InfinitePlace.Completion.piEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfinitePlace.Completion.piEquiv" |
| }, |
| { |
| "id": "def:rand-protocol-complex", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:rand-protocol-complex" |
| }, |
| { |
| "id": "tile-reach", |
| "repo": "carleson", |
| "full_id": "carleson/tile-reach" |
| }, |
| { |
| "id": "defn:NaturalModelSigma", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:NaturalModelSigma" |
| }, |
| { |
| "id": "def:revoke-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:revoke-chapter" |
| }, |
| { |
| "id": "entropy-pfr", |
| "repo": "pfr", |
| "full_id": "pfr/entropy-pfr" |
| }, |
| { |
| "id": "graph-dual", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/graph-dual" |
| }, |
| { |
| "id": "thm:local_doobMeyer", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:local_doobMeyer" |
| }, |
| { |
| "id": "alt-submodularity", |
| "repo": "pfr", |
| "full_id": "pfr/alt-submodularity" |
| }, |
| { |
| "id": "WienerIkehara2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/WienerIkehara2" |
| }, |
| { |
| "id": "lem:mono-forbidden-pattern-trivial", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:mono-forbidden-pattern-trivial" |
| }, |
| { |
| "id": "lem:map_eq_iff", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:map_eq_iff" |
| }, |
| { |
| "id": "pu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/pu" |
| }, |
| { |
| "id": "def:adapted", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:adapted" |
| }, |
| { |
| "id": "forest-geometry", |
| "repo": "carleson", |
| "full_id": "carleson/forest-geometry" |
| }, |
| { |
| "id": "0-irred-subset-gen", |
| "repo": "toric", |
| "full_id": "toric/0-irred-subset-gen" |
| }, |
| { |
| "id": "prop:fixed_zero_ef", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/prop:fixed_zero_ef" |
| }, |
| { |
| "id": "Pu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/Pu" |
| }, |
| { |
| "id": "lem:htpy-cat-of-qcat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:htpy-cat-of-qcat" |
| }, |
| { |
| "id": "cor:sset-cat-limits", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/cor:sset-cat-limits" |
| }, |
| { |
| "id": "thm:ext_of_charFunDual", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:ext_of_charFunDual" |
| }, |
| { |
| "id": "limiting-cor", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/limiting-cor" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_complex", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_complex" |
| }, |
| { |
| "id": "lem:Integrable.classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Integrable.classDL" |
| }, |
| { |
| "id": "energy_alt", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/energy_alt" |
| }, |
| { |
| "id": "I5NewBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I5NewBound" |
| }, |
| { |
| "id": "lemma:jacobi-identity", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:jacobi-identity" |
| }, |
| { |
| "id": "WienerIkehara", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/WienerIkehara" |
| }, |
| { |
| "id": "defn:nerve-functor", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:nerve-functor" |
| }, |
| { |
| "id": "lem:card_logSizeRadius_ge", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:card_logSizeRadius_ge" |
| }, |
| { |
| "id": "lem:LocallyBoundedVariationOn.exists_cadlag_monotoneOn_sub_monotoneOn", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:LocallyBoundedVariationOn.exists_cadlag_monotoneOn_sub_monotoneOn" |
| }, |
| { |
| "id": "lem:indistinguishable_of_modification_of_continuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:indistinguishable_of_modification_of_continuous" |
| }, |
| { |
| "id": "gInPuQu", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/gInPuQu" |
| }, |
| { |
| "id": "Meissel-Mertens-constant", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Meissel-Mertens-constant" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_of_dist_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_of_dist_le" |
| }, |
| { |
| "id": "John-Nirenberg", |
| "repo": "carleson", |
| "full_id": "carleson/John-Nirenberg" |
| }, |
| { |
| "id": "de-prop", |
| "repo": "pfr", |
| "full_id": "pfr/de-prop" |
| }, |
| { |
| "id": "1485-dual", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/1485-dual" |
| }, |
| { |
| "id": "phi-min-exist", |
| "repo": "pfr", |
| "full_id": "pfr/phi-min-exist" |
| }, |
| { |
| "id": "second-estimate", |
| "repo": "pfr", |
| "full_id": "pfr/second-estimate" |
| }, |
| { |
| "id": "thm:g1", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:g1" |
| }, |
| { |
| "id": "0-is-diag-bialg-group-like-span", |
| "repo": "toric", |
| "full_id": "toric/0-is-diag-bialg-group-like-span" |
| }, |
| { |
| "id": "law-count-sym", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/law-count-sym" |
| }, |
| { |
| "id": "thm:deFinetti", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:deFinetti" |
| }, |
| { |
| "id": "lem:pair_reduction", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:pair_reduction" |
| }, |
| { |
| "id": "1-2-14-dual-rat-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-14-dual-rat-cone" |
| }, |
| { |
| "id": "lem:herbrand log lattice", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:herbrand log lattice" |
| }, |
| { |
| "id": "cuspidal_automorphic_form_decomposition", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/cuspidal_automorphic_form_decomposition" |
| }, |
| { |
| "id": "def:localizingSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:localizingSequence" |
| }, |
| { |
| "id": "lem:isGaussian_multivariateGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_multivariateGaussian" |
| }, |
| { |
| "id": "lem:stable_IsSubmartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:stable_IsSubmartingale" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_real", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_real" |
| }, |
| { |
| "id": "Etheta-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Etheta-def" |
| }, |
| { |
| "id": "lem:L2Predictable.sq_norm_simpleProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:L2Predictable.sq_norm_simpleProcess" |
| }, |
| { |
| "id": "thm:finite_set_bound_of_dist_le_of_diam_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:finite_set_bound_of_dist_le_of_diam_le" |
| }, |
| { |
| "id": "lem:H2 cyclic Z", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:H2 cyclic Z" |
| }, |
| { |
| "id": "def:pushforward_of_sheaf", |
| "repo": "M2", |
| "full_id": "M2/def:pushforward_of_sheaf" |
| }, |
| { |
| "id": "def:unscaled_poly", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/def:unscaled_poly" |
| }, |
| { |
| "id": "adjoint-tile-support", |
| "repo": "carleson", |
| "full_id": "carleson/adjoint-tile-support" |
| }, |
| { |
| "id": "NumberField.InfinitePlace.Completion.baseChangeEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfinitePlace.Completion.baseChangeEquiv" |
| }, |
| { |
| "id": "local-tree-control", |
| "repo": "carleson", |
| "full_id": "carleson/local-tree-control" |
| }, |
| { |
| "id": "VectorMatroid.exists_standardRepr_isBase_isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/VectorMatroid.exists_standardRepr_isBase_isTotallyUnimodular" |
| }, |
| { |
| "id": "def:newton_ef", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:newton_ef" |
| }, |
| { |
| "id": "lem:coind₁' iso coind₁", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:coind₁' iso coind₁" |
| }, |
| { |
| "id": "1-2-10-dual-face-face-dual", |
| "repo": "toric", |
| "full_id": "toric/1-2-10-dual-face-face-dual" |
| }, |
| { |
| "id": "lem:isHolderWith_brownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isHolderWith_brownian" |
| }, |
| { |
| "id": "eq4512", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq4512" |
| }, |
| { |
| "id": "prop:h_is_v", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/prop:h_is_v" |
| }, |
| { |
| "id": "1-1-char-eigenspace", |
| "repo": "toric", |
| "full_id": "toric/1-1-char-eigenspace" |
| }, |
| { |
| "id": "defn:simplex-boundary", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:simplex-boundary" |
| }, |
| { |
| "id": "def:unramified local inv", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:unramified local inv" |
| }, |
| { |
| "id": "lem:contractable_dist_eq", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:contractable_dist_eq" |
| }, |
| { |
| "id": "lemma:lv1-lv2-identities", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:lv1-lv2-identities" |
| }, |
| { |
| "id": "0-ess-image-spec-alg", |
| "repo": "toric", |
| "full_id": "toric/0-ess-image-spec-alg" |
| }, |
| { |
| "id": "lem:M1_komlos", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:M1_komlos" |
| }, |
| { |
| "id": "uvw-s", |
| "repo": "pfr", |
| "full_id": "pfr/uvw-s" |
| }, |
| { |
| "id": "bklnw-cor_15_1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-cor_15_1" |
| }, |
| { |
| "id": "lem:Submartingale.uniformIntegrable_of_antitone_of_ge", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.uniformIntegrable_of_antitone_of_ge" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.fromCols_outer", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.fromCols_outer" |
| }, |
| { |
| "id": "fks-theorem-1-1b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-theorem-1-1b" |
| }, |
| { |
| "id": "lem:IsKolmogorovProcess.lintegral_sup_rpow_edist_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsKolmogorovProcess.lintegral_sup_rpow_edist_eq_zero" |
| }, |
| { |
| "id": "lem:Subcase2.5", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Subcase2.5" |
| }, |
| { |
| "id": "defn:2-truncated-qcat-htpy-cat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:2-truncated-qcat-htpy-cat" |
| }, |
| { |
| "id": "lem:hasBoundedInternalCoveringNumber_unitInterval", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasBoundedInternalCoveringNumber_unitInterval" |
| }, |
| { |
| "id": "def:inflation map", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:inflation map" |
| }, |
| { |
| "id": "MatrixLikeSum3.shortTableauPivot", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixLikeSum3.shortTableauPivot" |
| }, |
| { |
| "id": "lem:kallenberg_chain", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:kallenberg_chain" |
| }, |
| { |
| "id": "1-1-2-char-eigenspace-direct-sum", |
| "repo": "toric", |
| "full_id": "toric/1-1-2-char-eigenspace-direct-sum" |
| }, |
| { |
| "id": "lem:isLocalizingSequence_of_isPreLocalizingSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isLocalizingSequence_of_isPreLocalizingSequence" |
| }, |
| { |
| "id": "IsDedekindDomain.FiniteAdeleRing.baseChangeContinuousAlgEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.FiniteAdeleRing.baseChangeContinuousAlgEquiv" |
| }, |
| { |
| "id": "lem:deltaBounds", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:deltaBounds" |
| }, |
| { |
| "id": "lem:isGaussian_conv", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_conv" |
| }, |
| { |
| "id": "lyusternik_shnirelman", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/lyusternik_shnirelman" |
| }, |
| { |
| "id": "lem:isStable_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_classDL" |
| }, |
| { |
| "id": "mu-pnt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mu-pnt" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.linearIndependent_iff_support_linearIndependent", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.linearIndependent_iff_support_linearIndependent" |
| }, |
| { |
| "id": "thm:CauchyProduct_left_distrib", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_left_distrib" |
| }, |
| { |
| "id": "kis-thm2", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/kis-thm2" |
| }, |
| { |
| "id": "thm:weighted_sums_L1", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:weighted_sums_L1" |
| }, |
| { |
| "id": "lem:isSquareIntegrable_elemStochIntegralBilin", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isSquareIntegrable_elemStochIntegralBilin" |
| }, |
| { |
| "id": "StandardRepr.toMatroid_isRegular_iff_hasTuSigning", |
| "repo": "seymour", |
| "full_id": "seymour/StandardRepr.toMatroid_isRegular_iff_hasTuSigning" |
| }, |
| { |
| "id": "card-bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/card-bound" |
| }, |
| { |
| "id": "borromean", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/borromean" |
| }, |
| { |
| "id": "def:IsGaussianProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsGaussianProcess" |
| }, |
| { |
| "id": "fks2-corollary-8", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-8" |
| }, |
| { |
| "id": "lem:nondecreasing_predictablePart_of_submartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:nondecreasing_predictablePart_of_submartingale" |
| }, |
| { |
| "id": "prop:FourierAnalysis", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:FourierAnalysis" |
| }, |
| { |
| "id": "thm:exists_rightContinuous_modification_of_bounded_elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:exists_rightContinuous_modification_of_bounded_elemStochIntegral" |
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| { |
| "id": "bklnw-prop-3-sub-6", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-prop-3-sub-6" |
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| { |
| "id": "lemma:FG-de", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:FG-de" |
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| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.T", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.T" |
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| { |
| "id": "def:cohomology_of_k-prsh", |
| "repo": "M2", |
| "full_id": "M2/def:cohomology_of_k-prsh" |
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| { |
| "id": "Matrix.IsTotallyUnimodular.linearIndependent_iff_support_linearIndependent_of_finite", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.linearIndependent_iff_support_linearIndependent_of_finite" |
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| { |
| "id": "defn:NaturalModelPi", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:NaturalModelPi" |
| }, |
| { |
| "id": "fks2-lemma-10c", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-10c" |
| }, |
| { |
| "id": "def:modif", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:modif" |
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| { |
| "id": "1-2-3-dual-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-3-dual-cone" |
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| { |
| "id": "def:radii_poly", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:radii_poly" |
| }, |
| { |
| "id": "lem:rightContNeBot", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContNeBot" |
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| { |
| "id": "smaller-boundary", |
| "repo": "carleson", |
| "full_id": "carleson/smaller-boundary" |
| }, |
| { |
| "id": "lem:rightContIsMax", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContIsMax" |
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| { |
| "id": "relation-geometry", |
| "repo": "carleson", |
| "full_id": "carleson/relation-geometry" |
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| { |
| "id": "Matrix.toCanonicalSigning", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.toCanonicalSigning" |
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| { |
| "id": "law-def", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/law-def" |
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| { |
| "id": "prop:chech_is_determined_by_stalks_3", |
| "repo": "M2", |
| "full_id": "M2/prop:chech_is_determined_by_stalks_3" |
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| { |
| "id": "support_eq_support_of_same_matroid_same_X", |
| "repo": "seymour", |
| "full_id": "seymour/support_eq_support_of_same_matroid_same_X" |
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| { |
| "id": "lem:newton_deriv_bound_simple", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:newton_deriv_bound_simple" |
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| { |
| "id": "lem:integral_sup_rpow_dist_le_card_mul_rpow", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_le_card_mul_rpow" |
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| { |
| "id": "hoelder-lifting", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/hoelder-lifting" |
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| { |
| "id": "rho-def", |
| "repo": "pfr", |
| "full_id": "pfr/rho-def" |
| }, |
| { |
| "id": "lem:doob_countable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:doob_countable" |
| }, |
| { |
| "id": "thm:lvl1_dims", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:lvl1_dims" |
| }, |
| { |
| "id": "TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.finiteDimensional", |
| "repo": "FLT_ch12", |
| "full_id": "FLT_ch12/TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.finiteDimensional" |
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| { |
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| "repo": "toric", |
| "full_id": "toric/1-2-7-face-mem-of-add" |
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| { |
| "id": "1-1-aff-tor-var-diag-aff-mon", |
| "repo": "toric", |
| "full_id": "toric/1-1-aff-tor-var-diag-aff-mon" |
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| { |
| "id": "subadditive", |
| "repo": "pfr", |
| "full_id": "pfr/subadditive" |
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| { |
| "id": "non_imp_1659_4315_thm", |
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| "id": "thm:ramanujan-formula", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:ramanujan-formula" |
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| { |
| "id": "valuation_on_reals", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/valuation_on_reals" |
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| { |
| "id": "thm:fourier2-properties", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/thm:fourier2-properties" |
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| { |
| "id": "NumberField.AdeleRing.zero_discrete", |
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| "full_id": "FLT_ch9/NumberField.AdeleRing.zero_discrete" |
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| { |
| "id": "alternative-mutual", |
| "repo": "pfr", |
| "full_id": "pfr/alternative-mutual" |
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| { |
| "id": "ZerosBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZerosBound" |
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| { |
| "id": "RectangleIntegral_tendsTo_VerticalIntegral", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/RectangleIntegral_tendsTo_VerticalIntegral" |
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| { |
| "id": "Hurwitz.ring", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.ring" |
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| { |
| "id": "lem:aachfour", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:aachfour" |
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| { |
| "id": "prop:fixed_point_iff_zero", |
| "repo": "radii-polynomial", |
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| { |
| "id": "1-2-6-face-polyhedral-cone", |
| "repo": "toric", |
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| { |
| "id": "Matrix.support", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.support" |
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| { |
| "id": "C3-convex", |
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| "full_id": "carleson/C3-convex" |
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| { |
| "id": "IsDedekindDomain.FiniteAdeleRing.baseChangeAlgEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.FiniteAdeleRing.baseChangeAlgEquiv" |
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| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComap_isModuleTopology", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComap_isModuleTopology" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_padic", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_padic" |
| }, |
| { |
| "id": "global-tree-control-1", |
| "repo": "carleson", |
| "full_id": "carleson/global-tree-control-1" |
| }, |
| { |
| "id": "lem:condexp_lag_const", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:condexp_lag_const" |
| }, |
| { |
| "id": "scales-impacting-interval", |
| "repo": "carleson", |
| "full_id": "carleson/scales-impacting-interval" |
| }, |
| { |
| "id": "MatrixSum3.HasTuBr.cccAr_isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.HasTuBr.cccAr_isTotallyUnimodular" |
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| { |
| "id": "cor:phi0-near-0-infty", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:phi0-near-0-infty" |
| }, |
| { |
| "id": "lem:local unram inv infl", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local unram inv infl" |
| }, |
| { |
| "id": "lem:integral_process_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_process_eq_zero" |
| }, |
| { |
| "id": "derivation-def", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/derivation-def" |
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| { |
| "id": "prop:a-schwartz", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:a-schwartz" |
| }, |
| { |
| "id": "random_approx_expect", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/random_approx_expect" |
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| { |
| "id": "buthe-theorem-2e", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/buthe-theorem-2e" |
| }, |
| { |
| "id": "prop:a-fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:a-fourier" |
| }, |
| { |
| "id": "0-hopf-alg-equiv-cogrp-alg", |
| "repo": "toric", |
| "full_id": "toric/0-hopf-alg-equiv-cogrp-alg" |
| }, |
| { |
| "id": "valuation", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/valuation" |
| }, |
| { |
| "id": "linearised-metric-Carleson", |
| "repo": "carleson", |
| "full_id": "carleson/linearised-metric-Carleson" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.shortTableauPivot", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.shortTableauPivot" |
| }, |
| { |
| "id": "DeltaRange", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/DeltaRange" |
| }, |
| { |
| "id": "lem:fourier12-cauchy", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier12-cauchy" |
| }, |
| { |
| "id": "lem:ThreeLowerBounds", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:ThreeLowerBounds" |
| }, |
| { |
| "id": "thm:l1Weighted_NormedRing", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_NormedRing" |
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| { |
| "id": "I2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I2" |
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| { |
| "id": "E8Packing-covol", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/E8Packing-covol" |
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| { |
| "id": "thm:CauchyProduct_comm", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_comm" |
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| { |
| "id": "data-process-single", |
| "repo": "pfr", |
| "full_id": "pfr/data-process-single" |
| }, |
| { |
| "id": "lem:IsSquareIntegrable.eLpNorm_two_mono", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsSquareIntegrable.eLpNorm_two_mono" |
| }, |
| { |
| "id": "lem:NlambdatoSstar", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:NlambdatoSstar" |
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| { |
| "id": "Holder-correlation-tree", |
| "repo": "carleson", |
| "full_id": "carleson/Holder-correlation-tree" |
| }, |
| { |
| "id": "symm-lemma", |
| "repo": "pfr", |
| "full_id": "pfr/symm-lemma" |
| }, |
| { |
| "id": "tau-min-exist-multi", |
| "repo": "pfr", |
| "full_id": "pfr/tau-min-exist-multi" |
| }, |
| { |
| "id": "thm:conditionallyIID_of_contractable_Koopman", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:conditionallyIID_of_contractable_Koopman" |
| }, |
| { |
| "id": "defn:homotopy-2-cat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:homotopy-2-cat" |
| }, |
| { |
| "id": "lem:integral_process_injective", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_process_injective" |
| }, |
| { |
| "id": "5-1-aff-tor-var-iso-diag-aff-mon", |
| "repo": "toric", |
| "full_id": "toric/5-1-aff-tor-var-iso-diag-aff-mon" |
| }, |
| { |
| "id": "balance-zero", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/balance-zero" |
| }, |
| { |
| "id": "lem:modif-modif", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:modif-modif" |
| }, |
| { |
| "id": "lem:poly_neg_implies_contraction", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:poly_neg_implies_contraction" |
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| { |
| "id": "prop:b-another-integral", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:b-another-integral" |
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| { |
| "id": "modulated-averaged-projection", |
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| { |
| "id": "score-lower-3", |
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| { |
| "id": "ruz-indep", |
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| "full_id": "pfr/ruz-indep" |
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| { |
| "id": "kl-sums", |
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| "full_id": "pfr/kl-sums" |
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| { |
| "id": "sumset-lower-gen-cond", |
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| { |
| "id": "rs-418", |
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| "full_id": "PrimeNumberTheoremAnd/rs-418" |
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| "id": "RS_theorem_19", |
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| "full_id": "PrimeNumberTheoremAnd/RS_theorem_19" |
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| "id": "fks-proposition-3-8", |
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| "id": "bklnw-thm-1a", |
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| { |
| "id": "ZetaInvBnd", |
| "repo": "PrimeNumberTheoremAnd", |
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| { |
| "id": "defn:simplicial-horn", |
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| "id": "first-tree-pointwise", |
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| "id": "canonical-invariant", |
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| "id": "unif-exist", |
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| "full_id": "pfr/unif-exist" |
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| { |
| "id": "bklnw-prop-3-sub-2", |
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| "full_id": "PrimeNumberTheoremAnd/bklnw-prop-3-sub-2" |
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| { |
| "id": "lem:newton_fderiv", |
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| "id": "L0-antichain", |
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| { |
| "id": "def:psiI-psiT-psiS", |
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| { |
| "id": "deriv_riemannZeta_conj", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/deriv_riemannZeta_conj" |
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| { |
| "id": "bound-conc", |
| "repo": "pfr", |
| "full_id": "pfr/bound-conc" |
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| { |
| "id": "0-bialg-bij-of-span-grp-like", |
| "repo": "toric", |
| "full_id": "toric/0-bialg-bij-of-span-grp-like" |
| }, |
| { |
| "id": "lem:isGaussianProcess_brownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussianProcess_brownian" |
| }, |
| { |
| "id": "0-char-cochar-pairing-perfect", |
| "repo": "toric", |
| "full_id": "toric/0-char-cochar-pairing-perfect" |
| }, |
| { |
| "id": "euler_criterion", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/euler_criterion" |
| }, |
| { |
| "id": "def:param_seq", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:param_seq" |
| }, |
| { |
| "id": "thm:integration_by_parts", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:integration_by_parts" |
| }, |
| { |
| "id": "lem:upcrossing_simpleProcess_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:upcrossing_simpleProcess_le" |
| }, |
| { |
| "id": "conj_riemannZeta_conj", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/conj_riemannZeta_conj" |
| }, |
| { |
| "id": "lem:ClassDL.hasLocallyIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:ClassDL.hasLocallyIntegrableSup" |
| }, |
| { |
| "id": "lem:Martingale.IsLocalMartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Martingale.IsLocalMartingale" |
| }, |
| { |
| "id": "lem:uniformIntegrableIffNorm", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrableIffNorm" |
| }, |
| { |
| "id": "ruzsa-growth", |
| "repo": "pfr", |
| "full_id": "pfr/ruzsa-growth" |
| }, |
| { |
| "id": "instLatticeE8", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/instLatticeE8" |
| }, |
| { |
| "id": "lem:IsGaussian.map_rotation_eq_self", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsGaussian.map_rotation_eq_self" |
| }, |
| { |
| "id": "def:l1Weighted", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:l1Weighted" |
| }, |
| { |
| "id": "Dusart_thm_5_6", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_thm_5_6" |
| }, |
| { |
| "id": "lem:finite_level_factorization", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:finite_level_factorization" |
| }, |
| { |
| "id": "NumberField.AdeleRing.DivisionAlgebra.Aux.X_compact", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.AdeleRing.DivisionAlgebra.Aux.X_compact" |
| }, |
| { |
| "id": "fks2-proposition-13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-proposition-13" |
| }, |
| { |
| "id": "FinalBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/FinalBound" |
| }, |
| { |
| "id": "lem:A_hittingAGT_sub_ge", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:A_hittingAGT_sub_ge" |
| }, |
| { |
| "id": "waste-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/waste-def" |
| }, |
| { |
| "id": "fks2-eq-13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-eq-13" |
| }, |
| { |
| "id": "lem:common-div-alg", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/lem:common-div-alg" |
| }, |
| { |
| "id": "5-3-van-tor-emb", |
| "repo": "toric", |
| "full_id": "toric/5-3-van-tor-emb" |
| }, |
| { |
| "id": "lem:induced' trivial Tate", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:induced' trivial Tate" |
| }, |
| { |
| "id": "constant-impl", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/constant-impl" |
| }, |
| { |
| "id": "lem:exists_cadlag_mod_of_nonneg_submg", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:exists_cadlag_mod_of_nonneg_submg" |
| }, |
| { |
| "id": "bohr-regularity", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/bohr-regularity" |
| }, |
| { |
| "id": "lem:second_term_bound", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:second_term_bound" |
| }, |
| { |
| "id": "kl-div-convex", |
| "repo": "pfr", |
| "full_id": "pfr/kl-div-convex" |
| }, |
| { |
| "id": "lem:invertible-2-cell", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:invertible-2-cell" |
| }, |
| { |
| "id": "defn:equivalence", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:equivalence" |
| }, |
| { |
| "id": "def:did-amt", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:did-amt" |
| }, |
| { |
| "id": "eq1485", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1485" |
| }, |
| { |
| "id": "cor:free-underlying-2-adj", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/cor:free-underlying-2-adj" |
| }, |
| { |
| "id": "lem:IsLocalSubmartingale.submartingale_iff_classDL_of_nonnegative", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsLocalSubmartingale.submartingale_iff_classDL_of_nonnegative" |
| }, |
| { |
| "id": "NumberField.AdeleRing.units_mem_ringHaarCharacter_ker", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/NumberField.AdeleRing.units_mem_ringHaarCharacter_ker" |
| }, |
| { |
| "id": "prelim-decay-3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/prelim-decay-3" |
| }, |
| { |
| "id": "def:trivial cohomology", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:trivial cohomology" |
| }, |
| { |
| "id": "I3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I3" |
| }, |
| { |
| "id": "lem:Indistinguishable.Modification", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Indistinguishable.Modification" |
| }, |
| { |
| "id": "lem:pair_law_eq", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:pair_law_eq" |
| }, |
| { |
| "id": "I9", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I9" |
| }, |
| { |
| "id": "ZetaLowerBnd", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaLowerBnd" |
| }, |
| { |
| "id": "lem:optionalSamplingSubmartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:optionalSamplingSubmartingale" |
| }, |
| { |
| "id": "lem:elemStochIntegralBilin_assoc", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elemStochIntegralBilin_assoc" |
| }, |
| { |
| "id": "lem:centralMoment_two_mul_gaussianReal", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:centralMoment_two_mul_gaussianReal" |
| }, |
| { |
| "id": "classical-bound-theta", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/classical-bound-theta" |
| }, |
| { |
| "id": "score-eq", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/score-eq" |
| }, |
| { |
| "id": "lem:L_lt_top", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:L_lt_top" |
| }, |
| { |
| "id": "theorem:psp-density", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/theorem:psp-density" |
| }, |
| { |
| "id": "lem:extreme_members_equal", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:extreme_members_equal" |
| }, |
| { |
| "id": "lem:continuous_brownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:continuous_brownian" |
| }, |
| { |
| "id": "StrongPNT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/StrongPNT" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_le_sum_of_le_one", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_le_sum_of_le_one" |
| }, |
| { |
| "id": "lem:gluing_pure_homotopy_k_sheaves", |
| "repo": "M2", |
| "full_id": "M2/lem:gluing_pure_homotopy_k_sheaves" |
| }, |
| { |
| "id": "bklnw-eq_A_19", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_19" |
| }, |
| { |
| "id": "Matrix.support_submatrix", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.support_submatrix" |
| }, |
| { |
| "id": "NumberField.AdeleRing.discrete", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.AdeleRing.discrete" |
| }, |
| { |
| "id": "defn:underlying-cat-of-cosmos", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:underlying-cat-of-cosmos" |
| }, |
| { |
| "id": "rs-417", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/rs-417" |
| }, |
| { |
| "id": "lem:locally_classD_of_locally_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_classD_of_locally_classDL" |
| }, |
| { |
| "id": "ZetaBnd_aux1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaBnd_aux1" |
| }, |
| { |
| "id": "lem:isGaussian_iff_gaussian_charFun", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_iff_gaussian_charFun" |
| }, |
| { |
| "id": "lem:Submartingale.classD_iff_uniformIntegrable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.classD_iff_uniformIntegrable" |
| }, |
| { |
| "id": "def:elemStochIntegralLinear", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:elemStochIntegralLinear" |
| }, |
| { |
| "id": "lem:isCentered_stdGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isCentered_stdGaussian" |
| }, |
| { |
| "id": "def:classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:classDL" |
| }, |
| { |
| "id": "lem:isStable_isCadlag", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isStable_isCadlag" |
| }, |
| { |
| "id": "thm:monotone_class", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:monotone_class" |
| }, |
| { |
| "id": "lem:Dirichlet density degree one", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:Dirichlet density degree one" |
| }, |
| { |
| "id": "lem:ind₁' iso ind₁", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:ind₁' iso ind₁" |
| }, |
| { |
| "id": "prop:mitm-defense", |
| "repo": "amatelus", |
| "full_id": "amatelus/prop:mitm-defense" |
| }, |
| { |
| "id": "induced-def", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/induced-def" |
| }, |
| { |
| "id": "Smooth1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_cover_of_dist_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_cover_of_dist_le" |
| }, |
| { |
| "id": "lem:norm_one", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:norm_one" |
| }, |
| { |
| "id": "fks2-lemma-19", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-19" |
| }, |
| { |
| "id": "HomAeM", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/HomAeM" |
| }, |
| { |
| "id": "0-full-faithful-grp-hom", |
| "repo": "toric", |
| "full_id": "toric/0-full-faithful-grp-hom" |
| }, |
| { |
| "id": "thm:impersonation-resistance", |
| "repo": "amatelus", |
| "full_id": "amatelus/thm:impersonation-resistance" |
| }, |
| { |
| "id": "thm:doob_lp", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:doob_lp" |
| }, |
| { |
| "id": "Hurwitz.starRing", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.starRing" |
| }, |
| { |
| "id": "cor:ineqAnew", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:ineqAnew" |
| }, |
| { |
| "id": "linfty_ap", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/linfty_ap" |
| }, |
| { |
| "id": "lemma:der-q-series", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:der-q-series" |
| }, |
| { |
| "id": "lem:isGaussian_stdGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_stdGaussian" |
| }, |
| { |
| "id": "SmoothedChebyshevPull1_aux_integrable", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevPull1_aux_integrable" |
| }, |
| { |
| "id": "lem:fourier-prop", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/lem:fourier-prop" |
| }, |
| { |
| "id": "prop:change-of-base-adjunction", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:change-of-base-adjunction" |
| }, |
| { |
| "id": "fks-theorem-3-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-theorem-3-2" |
| }, |
| { |
| "id": "I3NewBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I3NewBound" |
| }, |
| { |
| "id": "matrix3x3signed", |
| "repo": "seymour", |
| "full_id": "seymour/matrix3x3signed" |
| }, |
| { |
| "id": "fks-theorem-1-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-theorem-1-1" |
| }, |
| { |
| "id": "schwarz-id", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/schwarz-id" |
| }, |
| { |
| "id": "def:martingalePart", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:martingalePart" |
| }, |
| { |
| "id": "lem:sup_dist_le_two_mul_sup_dist_pairSet", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:sup_dist_le_two_mul_sup_dist_pairSet" |
| }, |
| { |
| "id": "0-grp-like-grp-alg", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-grp-alg" |
| }, |
| { |
| "id": "0-coquot-hom", |
| "repo": "toric", |
| "full_id": "toric/0-coquot-hom" |
| }, |
| { |
| "id": "I8I2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I8I2" |
| }, |
| { |
| "id": "Matrix.IsTotallyUnimodular.toMatroid_eq_support_toMatroid", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTotallyUnimodular.toMatroid_eq_support_toMatroid" |
| }, |
| { |
| "id": "0-grp-like-grp-alg-of", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-grp-alg-of" |
| }, |
| { |
| "id": "1571_impl", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/1571_impl" |
| }, |
| { |
| "id": "fks2-theorem-6-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-theorem-6-1" |
| }, |
| { |
| "id": "n-prop", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/n-prop" |
| }, |
| { |
| "id": "lem:Martingale.elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Martingale.elemStochIntegral" |
| }, |
| { |
| "id": "MatrixLikeSum3.isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixLikeSum3.isTotallyUnimodular" |
| }, |
| { |
| "id": "SmoothedChebyshevDirichlet_aux_tsum_integral", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshevDirichlet_aux_tsum_integral" |
| }, |
| { |
| "id": "Matrix.IsTuSigningOf", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.IsTuSigningOf" |
| }, |
| { |
| "id": "eq3", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq3" |
| }, |
| { |
| "id": "WeakPNT-AP-prelim", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/WeakPNT-AP-prelim" |
| }, |
| { |
| "id": "def:continuousSemiMartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:continuousSemiMartingale" |
| }, |
| { |
| "id": "lem:simpleProcess_mem_L2Predictable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:simpleProcess_mem_L2Predictable" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_adeles_units_rat_eq_one", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_adeles_units_rat_eq_one" |
| }, |
| { |
| "id": "eq854", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq854" |
| }, |
| { |
| "id": "lem:cotensor-bifunctor", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:cotensor-bifunctor" |
| }, |
| { |
| "id": "lem:directingMeasure_measurable", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:directingMeasure_measurable" |
| }, |
| { |
| "id": "defn:NaturalModelEq", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:NaturalModelEq" |
| }, |
| { |
| "id": "lem:Submartingale.locallyIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.locallyIntegrableSup" |
| }, |
| { |
| "id": "def:approx_solution", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:approx_solution" |
| }, |
| { |
| "id": "extend", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/extend" |
| }, |
| { |
| "id": "real-line-doubling", |
| "repo": "carleson", |
| "full_id": "carleson/real-line-doubling" |
| }, |
| { |
| "id": "lem:2-truncated-qcat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:2-truncated-qcat" |
| }, |
| { |
| "id": "Matrix.isUnit_2x2", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.isUnit_2x2" |
| }, |
| { |
| "id": "def:IsStoppingTime", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsStoppingTime" |
| }, |
| { |
| "id": "lem:reciprocity formula", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:reciprocity formula" |
| }, |
| { |
| "id": "0-spec-bialg", |
| "repo": "toric", |
| "full_id": "toric/0-spec-bialg" |
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| { |
| "id": "ZetaBnd_aux1p", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaBnd_aux1p" |
| }, |
| { |
| "id": "0-full-faithful-grp-alg", |
| "repo": "toric", |
| "full_id": "toric/0-full-faithful-grp-alg" |
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| { |
| "id": "eq3167", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq3167" |
| }, |
| { |
| "id": "bklnw-inputs", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-inputs" |
| }, |
| { |
| "id": "prop:amatelus-non-scope", |
| "repo": "amatelus", |
| "full_id": "amatelus/prop:amatelus-non-scope" |
| }, |
| { |
| "id": "I2Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I2Bound" |
| }, |
| { |
| "id": "bklnw-thm-13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-thm-13" |
| }, |
| { |
| "id": "cor:doob_ineq_stop", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:doob_ineq_stop" |
| }, |
| { |
| "id": "initial-factorization-medium-prime-le", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-medium-prime-le" |
| }, |
| { |
| "id": "lem:underlying-cat-iso", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:underlying-cat-iso" |
| }, |
| { |
| "id": "gslice", |
| "repo": "pfr", |
| "full_id": "pfr/gslice" |
| }, |
| { |
| "id": "lemma:log-der-inf", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:log-der-inf" |
| }, |
| { |
| "id": "IsFractionRing.stabilizerHom_surjective", |
| "repo": "FLT_ch8", |
| "full_id": "FLT_ch8/IsFractionRing.stabilizerHom_surjective" |
| }, |
| { |
| "id": "lem:predictable_nat_iff", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictable_nat_iff" |
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| { |
| "id": "def:F_map", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:F_map" |
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| { |
| "id": "enlarge-op", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/enlarge-op" |
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| { |
| "id": "cor:abelian norm submodule mono", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:abelian norm submodule mono" |
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| { |
| "id": "Young-convolution", |
| "repo": "carleson", |
| "full_id": "carleson/Young-convolution" |
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| { |
| "id": "lemma:Fourier-transform-is-automorphism", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Fourier-transform-is-automorphism" |
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| { |
| "id": "def:Z1_bound", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:Z1_bound" |
| }, |
| { |
| "id": "ZetaNear1BndExact", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaNear1BndExact" |
| }, |
| { |
| "id": "costa-pereira-sublemma-1-4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-sublemma-1-4" |
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| { |
| "id": "eq5", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq5" |
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| { |
| "id": "def:trivial-protocol", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:trivial-protocol" |
| }, |
| { |
| "id": "prop:Eqn4Point5", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:Eqn4Point5" |
| }, |
| { |
| "id": "def:LocallyBoundedVariationOn.signedMeasure", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:LocallyBoundedVariationOn.signedMeasure" |
| }, |
| { |
| "id": "bklnw-prop-3-sub-8", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-prop-3-sub-8" |
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| { |
| "id": "def:sheaves", |
| "repo": "M2", |
| "full_id": "M2/def:sheaves" |
| }, |
| { |
| "id": "lem:L2Martingales.norm_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:L2Martingales.norm_eq_zero" |
| }, |
| { |
| "id": "Matrix.isUnit_iff_isUnit_det", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.isUnit_iff_isUnit_det" |
| }, |
| { |
| "id": "lem:covMatrix_stdGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covMatrix_stdGaussian" |
| }, |
| { |
| "id": "lem:TrivialBdforS", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:TrivialBdforS" |
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| { |
| "id": "def:K_sheaves", |
| "repo": "M2", |
| "full_id": "M2/def:K_sheaves" |
| }, |
| { |
| "id": "def:elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:elemStochIntegral" |
| }, |
| { |
| "id": "defn:simplicial-cotensors", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:simplicial-cotensors" |
| }, |
| { |
| "id": "Chebotarev-cyclic", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Chebotarev-cyclic" |
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| { |
| "id": "multi-zero", |
| "repo": "pfr", |
| "full_id": "pfr/multi-zero" |
| }, |
| { |
| "id": "thm:toPowerSeries_mul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:toPowerSeries_mul" |
| }, |
| { |
| "id": "DeltaT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/DeltaT" |
| }, |
| { |
| "id": "FermatLastTheorem.of_p_ge_5", |
| "repo": "FLT_ch2", |
| "full_id": "FLT_ch2/FermatLastTheorem.of_p_ge_5" |
| }, |
| { |
| "id": "thm:eval_mul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:eval_mul" |
| }, |
| { |
| "id": "ZHat.e_def", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/ZHat.e_def" |
| }, |
| { |
| "id": "zero-large", |
| "repo": "pfr", |
| "full_id": "pfr/zero-large" |
| }, |
| { |
| "id": "lem:Homotopy_k-sheaf_axioms_for_singular_chain", |
| "repo": "M2", |
| "full_id": "M2/lem:Homotopy_k-sheaf_axioms_for_singular_chain" |
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| { |
| "id": "sheffer", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/sheffer" |
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| { |
| "id": "dens1-antichain", |
| "repo": "carleson", |
| "full_id": "carleson/dens1-antichain" |
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| { |
| "id": "thm:equiv-are-equiv", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/thm:equiv-are-equiv" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComapAlgEquiv_integral", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComapAlgEquiv_integral" |
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| { |
| "id": "lem:isKolmogorovProcess_preBrownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isKolmogorovProcess_preBrownian" |
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| { |
| "id": "defn:IdComp", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:IdComp" |
| }, |
| { |
| "id": "QHat.unitsrat_join_unitszHat", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.unitsrat_join_unitszHat" |
| }, |
| { |
| "id": "Algebra.IsInvariant.isIntegral", |
| "repo": "FLT_ch8", |
| "full_id": "FLT_ch8/Algebra.IsInvariant.isIntegral" |
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| { |
| "id": "MellinOfPsi", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MellinOfPsi" |
| }, |
| { |
| "id": "lem:isGaussianProcess_preBrownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussianProcess_preBrownian" |
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| { |
| "id": "data-process-unc", |
| "repo": "pfr", |
| "full_id": "pfr/data-process-unc" |
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| { |
| "id": "lem:quadraticVariation_brownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:quadraticVariation_brownian" |
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| { |
| "id": "cor:2-truncated-qcat-htpy-comp", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/cor:2-truncated-qcat-htpy-comp" |
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| { |
| "id": "lem:newton_deriv_bound_general", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:newton_deriv_bound_general" |
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| { |
| "id": "fks_cor_13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks_cor_13" |
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| { |
| "id": "instUniversalEnvelopingAlgebraAction", |
| "repo": "FLT_ch7", |
| "full_id": "FLT_ch7/instUniversalEnvelopingAlgebraAction" |
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| { |
| "id": "lem:covMatrix_multivariateGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covMatrix_multivariateGaussian" |
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| { |
| "id": "rho-cts", |
| "repo": "pfr", |
| "full_id": "pfr/rho-cts" |
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| { |
| "id": "Smooth1Nonneg", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Smooth1Nonneg" |
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| { |
| "id": "cor:equiv-invar-fun", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/cor:equiv-invar-fun" |
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| { |
| "id": "lemma:Gamma-2-generators", |
| "repo": "Sphere-Packing-Lean", |
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| { |
| "id": "bohr-reg-def", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/bohr-reg-def" |
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| { |
| "id": "lem:le_volume_of_isSeparated", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:le_volume_of_isSeparated" |
| }, |
| { |
| "id": "lem:A_hittingAGT_le", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:A_hittingAGT_le" |
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| { |
| "id": "ContinuousMulEquiv.restrictedProductUnits", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/ContinuousMulEquiv.restrictedProductUnits" |
| }, |
| { |
| "id": "thm:general_fixed_point", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:general_fixed_point" |
| }, |
| { |
| "id": "lem:rightContExistsGt", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContExistsGt" |
| }, |
| { |
| "id": "zero-density-bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/zero-density-bound" |
| }, |
| { |
| "id": "1-2-13-separation-lemma", |
| "repo": "toric", |
| "full_id": "toric/1-2-13-separation-lemma" |
| }, |
| { |
| "id": "NumberField.InfiniteAdeleRing.baseChangeEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfiniteAdeleRing.baseChangeEquiv" |
| }, |
| { |
| "id": "lem:iSup_comap_simpleProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:iSup_comap_simpleProcess" |
| }, |
| { |
| "id": "thm:l1Weighted_SMulCommClass", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_SMulCommClass" |
| }, |
| { |
| "id": "cor:theta-pos", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:theta-pos" |
| }, |
| { |
| "id": "nolean-compactopen-U1p", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/nolean-compactopen-U1p" |
| }, |
| { |
| "id": "multidist-perm", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-perm" |
| }, |
| { |
| "id": "k-vanish", |
| "repo": "pfr", |
| "full_id": "pfr/k-vanish" |
| }, |
| { |
| "id": "lem:inner_itoIsometry", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:inner_itoIsometry" |
| }, |
| { |
| "id": "prop:qcat-cosmos", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:qcat-cosmos" |
| }, |
| { |
| "id": "lem:aibiciconstraints", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:aibiciconstraints" |
| }, |
| { |
| "id": "lem:IsGaussian.IsProbabilityMeasure", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsGaussian.IsProbabilityMeasure" |
| }, |
| { |
| "id": "1-2-8-inter-facet", |
| "repo": "toric", |
| "full_id": "toric/1-2-8-inter-facet" |
| }, |
| { |
| "id": "Matroid.IsCographic", |
| "repo": "seymour", |
| "full_id": "seymour/Matroid.IsCographic" |
| }, |
| { |
| "id": "FreyPackage.false", |
| "repo": "FLT_ch2", |
| "full_id": "FLT_ch2/FreyPackage.false" |
| }, |
| { |
| "id": "thm:Submartingale.exists_cadlag_modification_iff_rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:Submartingale.exists_cadlag_modification_iff_rightContinuous" |
| }, |
| { |
| "id": "LogDerivZetaHolcLargeT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/LogDerivZetaHolcLargeT" |
| }, |
| { |
| "id": "prop:nerve-fully-faithful", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:nerve-fully-faithful" |
| }, |
| { |
| "id": "rho-increase", |
| "repo": "pfr", |
| "full_id": "pfr/rho-increase" |
| }, |
| { |
| "id": "GL2.restrictedProduct", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/GL2.restrictedProduct" |
| }, |
| { |
| "id": "defn:face-map", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:face-map" |
| }, |
| { |
| "id": "mobius-lemma-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mobius-lemma-1" |
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| { |
| "id": "mobius-lemma-1-sub", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mobius-lemma-1-sub" |
| }, |
| { |
| "id": "lem:L-function bound", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:L-function bound" |
| }, |
| { |
| "id": "distance-lower", |
| "repo": "pfr", |
| "full_id": "pfr/distance-lower" |
| }, |
| { |
| "id": "I2NewBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I2NewBound" |
| }, |
| { |
| "id": "Holder-van-der-Corput", |
| "repo": "carleson", |
| "full_id": "carleson/Holder-van-der-Corput" |
| }, |
| { |
| "id": "lem:cotensor-associativity", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:cotensor-associativity" |
| }, |
| { |
| "id": "def:dep-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:dep-chapter" |
| }, |
| { |
| "id": "construct-good-improv", |
| "repo": "pfr", |
| "full_id": "pfr/construct-good-improv" |
| }, |
| { |
| "id": "brower", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/brower" |
| }, |
| { |
| "id": "Hurwitz.norm_zero", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.norm_zero" |
| }, |
| { |
| "id": "eq42", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq42" |
| }, |
| { |
| "id": "pfr_aux-improv", |
| "repo": "pfr", |
| "full_id": "pfr/pfr_aux-improv" |
| }, |
| { |
| "id": "lem:Dirichlet density top", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:Dirichlet density top" |
| }, |
| { |
| "id": "zero-counting-function", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/zero-counting-function" |
| }, |
| { |
| "id": "def:spec", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:spec" |
| }, |
| { |
| "id": "lem:Submartingale.stoppedProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.stoppedProcess" |
| }, |
| { |
| "id": "lem:abadtoabsum", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:abadtoabsum" |
| }, |
| { |
| "id": "ckl-div", |
| "repo": "pfr", |
| "full_id": "pfr/ckl-div" |
| }, |
| { |
| "id": "reg-conv", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/reg-conv" |
| }, |
| { |
| "id": "theorem : smul_zero", |
| "repo": "LBPTester", |
| "full_id": "LBPTester/theorem : smul_zero" |
| }, |
| { |
| "id": "Matrix.fromBlocks_isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.fromBlocks_isTotallyUnimodular" |
| }, |
| { |
| "id": "thm:main", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/thm:main" |
| }, |
| { |
| "id": "def:chain-chapter", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:chain-chapter" |
| }, |
| { |
| "id": "lem:covInnerBilin_map", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covInnerBilin_map" |
| }, |
| { |
| "id": "def:proper-spec", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:proper-spec" |
| }, |
| { |
| "id": "hilberts_third", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/hilberts_third" |
| }, |
| { |
| "id": "BorelCaratheodoryDeriv", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/BorelCaratheodoryDeriv" |
| }, |
| { |
| "id": "buthe-eq-1-4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/buthe-eq-1-4" |
| }, |
| { |
| "id": "lem:IsGaussian.memLp_id", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsGaussian.memLp_id" |
| }, |
| { |
| "id": "fibring-ineq", |
| "repo": "pfr", |
| "full_id": "pfr/fibring-ineq" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComapSemialgHom'", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComapSemialgHom'" |
| }, |
| { |
| "id": "defn:qcat-equivalence", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:qcat-equivalence" |
| }, |
| { |
| "id": "unique-factorization", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/unique-factorization" |
| }, |
| { |
| "id": "int", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/int" |
| }, |
| { |
| "id": "lem:dist_chainingSequence_add_one", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:dist_chainingSequence_add_one" |
| }, |
| { |
| "id": "lem:predictablePart_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictablePart_zero" |
| }, |
| { |
| "id": "lem:logSizeBallSequence_disjoint_B", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:logSizeBallSequence_disjoint_B" |
| }, |
| { |
| "id": "lem:M-basic", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:M-basic" |
| }, |
| { |
| "id": "0-diag-faithful-flat", |
| "repo": "toric", |
| "full_id": "toric/0-diag-faithful-flat" |
| }, |
| { |
| "id": "maximal", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/maximal" |
| }, |
| { |
| "id": "lem:4p3q3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:4p3q3" |
| }, |
| { |
| "id": "ZetaSum_aux2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaSum_aux2" |
| }, |
| { |
| "id": "def:StoppingTimeGen", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:StoppingTimeGen" |
| }, |
| { |
| "id": "Matrix.support_transpose", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.support_transpose" |
| }, |
| { |
| "id": "thm:serre-der-equiv-action", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:serre-der-equiv-action" |
| }, |
| { |
| "id": "part-sol", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/part-sol" |
| }, |
| { |
| "id": "thm:triviality criterion", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:triviality criterion" |
| }, |
| { |
| "id": "construct-good-prelim", |
| "repo": "pfr", |
| "full_id": "pfr/construct-good-prelim" |
| }, |
| { |
| "id": "pre-order", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/pre-order" |
| }, |
| { |
| "id": "lem:condexp_convergence", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:condexp_convergence" |
| }, |
| { |
| "id": "lem:locally_classD_iff_locally_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_classD_iff_locally_classDL" |
| }, |
| { |
| "id": "LogDerivZetaUniformLogSquaredBoundStrip", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/LogDerivZetaUniformLogSquaredBoundStrip" |
| }, |
| { |
| "id": "defn:underlying-cat", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:underlying-cat" |
| }, |
| { |
| "id": "MatrixSum3.HasTuBr.dddAl_isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.HasTuBr.dddAl_isTotallyUnimodular" |
| }, |
| { |
| "id": "lem:rightContinuous_basic", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContinuous_basic" |
| }, |
| { |
| "id": "prop:a0", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:a0" |
| }, |
| { |
| "id": "MatrixSum3.toCanonicalSigning", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.toCanonicalSigning" |
| }, |
| { |
| "id": "lem:restriction fundamental class generates", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:restriction fundamental class generates" |
| }, |
| { |
| "id": "ruzsa-triangle", |
| "repo": "pfr", |
| "full_id": "pfr/ruzsa-triangle" |
| }, |
| { |
| "id": "greedy-1323", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/greedy-1323" |
| }, |
| { |
| "id": "cor:phi0-bound", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/cor:phi0-bound" |
| }, |
| { |
| "id": "thm:boundary-clarity", |
| "repo": "amatelus", |
| "full_id": "amatelus/thm:boundary-clarity" |
| }, |
| { |
| "id": "gen-ineq", |
| "repo": "pfr", |
| "full_id": "pfr/gen-ineq" |
| }, |
| { |
| "id": "Massias_Robin_thm_Bv", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Massias_Robin_thm_Bv" |
| }, |
| { |
| "id": "FreyCurve", |
| "repo": "FLT_ch2", |
| "full_id": "FLT_ch2/FreyCurve" |
| }, |
| { |
| "id": "lem:locally_classD_iff_locallyIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_classD_iff_locallyIntegrableSup" |
| }, |
| { |
| "id": "residueAtZero", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/residueAtZero" |
| }, |
| { |
| "id": "lemma:disc-cuspform", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:disc-cuspform" |
| }, |
| { |
| "id": "lem:idele class invariants", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:idele class invariants" |
| }, |
| { |
| "id": "sigma_cts_of_normal", |
| "repo": "Junk-Test", |
| "full_id": "Junk-Test/sigma_cts_of_normal" |
| }, |
| { |
| "id": "lem:posSemidef_brownianCov", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:posSemidef_brownianCov" |
| }, |
| { |
| "id": "pfr_aux", |
| "repo": "pfr", |
| "full_id": "pfr/pfr_aux" |
| }, |
| { |
| "id": "bklnw-eq_A_9", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_9" |
| }, |
| { |
| "id": "costa-pereira-sublemma-1-8", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/costa-pereira-sublemma-1-8" |
| }, |
| { |
| "id": "rho-cond-sym", |
| "repo": "pfr", |
| "full_id": "pfr/rho-cond-sym" |
| }, |
| { |
| "id": "1-2-17-dual-lat-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-17-dual-lat-cone" |
| }, |
| { |
| "id": "tau-min-def", |
| "repo": "pfr", |
| "full_id": "pfr/tau-min-def" |
| }, |
| { |
| "id": "fks2-corollary-14", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-14" |
| }, |
| { |
| "id": "SmoothedChebyshev", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SmoothedChebyshev" |
| }, |
| { |
| "id": "fks2-lemma-10-substep-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-10-substep-2" |
| }, |
| { |
| "id": "lem:isLocalizingSequence_ae", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isLocalizingSequence_ae" |
| }, |
| { |
| "id": "AbstractHeckeOperator.comm", |
| "repo": "FLT_ch13", |
| "full_id": "FLT_ch13/AbstractHeckeOperator.comm" |
| }, |
| { |
| "id": "nontangential-operator-bound", |
| "repo": "carleson", |
| "full_id": "carleson/nontangential-operator-bound" |
| }, |
| { |
| "id": "prop:b-schwartz", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:b-schwartz" |
| }, |
| { |
| "id": "dyadic-partition-1", |
| "repo": "carleson", |
| "full_id": "carleson/dyadic-partition-1" |
| }, |
| { |
| "id": "prop:ineq-holds-large-n", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/prop:ineq-holds-large-n" |
| }, |
| { |
| "id": "lem:map2 image", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:map2 image" |
| }, |
| { |
| "id": "conditional-nonneg", |
| "repo": "pfr", |
| "full_id": "pfr/conditional-nonneg" |
| }, |
| { |
| "id": "lem:finite field trivial", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:finite field trivial" |
| }, |
| { |
| "id": "ZetaBnd_aux1b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaBnd_aux1b" |
| }, |
| { |
| "id": "hardly_ramified_mod3_reducible", |
| "repo": "FLT_ch3", |
| "full_id": "FLT_ch3/hardly_ramified_mod3_reducible" |
| }, |
| { |
| "id": "0-grp-like-grp", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-grp" |
| }, |
| { |
| "id": "forest-separation", |
| "repo": "carleson", |
| "full_id": "carleson/forest-separation" |
| }, |
| { |
| "id": "def:M", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:M" |
| }, |
| { |
| "id": "lem:mono-forbidden-pattern-tip", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:mono-forbidden-pattern-tip" |
| }, |
| { |
| "id": "fks2-theorem-3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-theorem-3" |
| }, |
| { |
| "id": "lem:qcat-htpy-cat-equiv", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:qcat-htpy-cat-equiv" |
| }, |
| { |
| "id": "Holder-correlation-tile", |
| "repo": "carleson", |
| "full_id": "carleson/Holder-correlation-tile" |
| }, |
| { |
| "id": "thm:IsLocalMartingale.eq_zero_of_finiteVariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:IsLocalMartingale.eq_zero_of_finiteVariation" |
| }, |
| { |
| "id": "fks2-lemma-10a", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-10a" |
| }, |
| { |
| "id": "thm:trivial cohomology implies trivial Tate", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:trivial cohomology implies trivial Tate" |
| }, |
| { |
| "id": "thm:isGaussian_iff_charFunDual_eq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:isGaussian_iff_charFunDual_eq" |
| }, |
| { |
| "id": "real-Carleson", |
| "repo": "carleson", |
| "full_id": "carleson/real-Carleson" |
| }, |
| { |
| "id": "cond-multidist-lower", |
| "repo": "pfr", |
| "full_id": "pfr/cond-multidist-lower" |
| }, |
| { |
| "id": "MeasureTheory.addHaarScalarFactor_tensor_adeles_eq_one", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addHaarScalarFactor_tensor_adeles_eq_one" |
| }, |
| { |
| "id": "def:leftLimitFiltration", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:leftLimitFiltration" |
| }, |
| { |
| "id": "def:preLocalizingSequence", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:preLocalizingSequence" |
| }, |
| { |
| "id": "standardReprSum2", |
| "repo": "seymour", |
| "full_id": "seymour/standardReprSum2" |
| }, |
| { |
| "id": "fks2-corollary-26", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-corollary-26" |
| }, |
| { |
| "id": "lem:MixedDetMethods", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:MixedDetMethods" |
| }, |
| { |
| "id": "forest-complement", |
| "repo": "carleson", |
| "full_id": "carleson/forest-complement" |
| }, |
| { |
| "id": "lem:2-truncated-qcat-htpy", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:2-truncated-qcat-htpy" |
| }, |
| { |
| "id": "mobius-lemma-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/mobius-lemma-2" |
| }, |
| { |
| "id": "cor:det-fun-complex-eval-ge-corner-free-num", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/cor:det-fun-complex-eval-ge-corner-free-num" |
| }, |
| { |
| "id": "def:pairSet", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:pairSet" |
| }, |
| { |
| "id": "def:v_polytope", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/def:v_polytope" |
| }, |
| { |
| "id": "def:rand-complex", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/def:rand-complex" |
| }, |
| { |
| "id": "0-irred-finite", |
| "repo": "toric", |
| "full_id": "toric/0-irred-finite" |
| }, |
| { |
| "id": "LogDerivZetaBnd", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/LogDerivZetaBnd" |
| }, |
| { |
| "id": "rs-420", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/rs-420" |
| }, |
| { |
| "id": "lem:internalCoveringNumber_closedBall_ge", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:internalCoveringNumber_closedBall_ge" |
| }, |
| { |
| "id": "lem:locally_rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_rightContinuous" |
| }, |
| { |
| "id": "prop:b-fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:b-fourier" |
| }, |
| { |
| "id": "bohr-majorise", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/bohr-majorise" |
| }, |
| { |
| "id": "lemma:slash-negI-even-weight", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:slash-negI-even-weight" |
| }, |
| { |
| "id": "phi-minimizer-zero-distance", |
| "repo": "pfr", |
| "full_id": "pfr/phi-minimizer-zero-distance" |
| }, |
| { |
| "id": "lem:holder_modification_single", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:holder_modification_single" |
| }, |
| { |
| "id": "lem:isLocalizingSequence_hittingAfter_Ici", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isLocalizingSequence_hittingAfter_Ici" |
| }, |
| { |
| "id": "weak-pfr-asymm", |
| "repo": "pfr", |
| "full_id": "pfr/weak-pfr-asymm" |
| }, |
| { |
| "id": "lem:locally_classDL_iff_locallyIntegrableSup", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_classDL_iff_locallyIntegrableSup" |
| }, |
| { |
| "id": "Cotlar-sets", |
| "repo": "carleson", |
| "full_id": "carleson/Cotlar-sets" |
| }, |
| { |
| "id": "two-sided-metric-space-Carleson", |
| "repo": "carleson", |
| "full_id": "carleson/two-sided-metric-space-Carleson" |
| }, |
| { |
| "id": "th-int-gen", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/th-int-gen" |
| }, |
| { |
| "id": "au", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/au" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_pi", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_pi" |
| }, |
| { |
| "id": "thm:large-n-final", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/thm:large-n-final" |
| }, |
| { |
| "id": "lem:empty_is_primspace", |
| "repo": "polytopes-in-LEAN", |
| "full_id": "polytopes-in-LEAN/lem:empty_is_primspace" |
| }, |
| { |
| "id": "0-diag-tors", |
| "repo": "toric", |
| "full_id": "toric/0-diag-tors" |
| }, |
| { |
| "id": "1-2-dual-cone-add", |
| "repo": "toric", |
| "full_id": "toric/1-2-dual-cone-add" |
| }, |
| { |
| "id": "lem:locally_locally", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_locally" |
| }, |
| { |
| "id": "NumberField.FiniteAdeleRing.DivisionAlgebra.units_cocompact", |
| "repo": "FLT_ch11", |
| "full_id": "FLT_ch11/NumberField.FiniteAdeleRing.DivisionAlgebra.units_cocompact" |
| }, |
| { |
| "id": "prop:isofib-define-isofib", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:isofib-define-isofib" |
| }, |
| { |
| "id": "tau-copy", |
| "repo": "pfr", |
| "full_id": "pfr/tau-copy" |
| }, |
| { |
| "id": "lem:trivial-bound-det-fun-complex", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/lem:trivial-bound-det-fun-complex" |
| }, |
| { |
| "id": "lem:hasBoundedCoveringNumberCover_nnreal", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:hasBoundedCoveringNumberCover_nnreal" |
| }, |
| { |
| "id": "lem:Subcase2.2", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Subcase2.2" |
| }, |
| { |
| "id": "divRemovable_zero_of_ne_zero", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/divRemovable_zero_of_ne_zero" |
| }, |
| { |
| "id": "thm:l1Weighted_IsScalarTower", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:l1Weighted_IsScalarTower" |
| }, |
| { |
| "id": "bklnw-eq_A_16", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_16" |
| }, |
| { |
| "id": "Epi-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Epi-def" |
| }, |
| { |
| "id": "lem:limsup_A_n_tau_is_A_tau_ae", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:limsup_A_n_tau_is_A_tau_ae" |
| }, |
| { |
| "id": "thm:power_sum_equality", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/thm:power_sum_equality" |
| }, |
| { |
| "id": "thm:nonpos_wt", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:nonpos_wt" |
| }, |
| { |
| "id": "0-cochar", |
| "repo": "toric", |
| "full_id": "toric/0-cochar" |
| }, |
| { |
| "id": "defn:qcat-isofibration", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:qcat-isofibration" |
| }, |
| { |
| "id": "lem:chebyshev_roots_characterization", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:chebyshev_roots_characterization" |
| }, |
| { |
| "id": "thm:charFun_multivariateGaussian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:charFun_multivariateGaussian" |
| }, |
| { |
| "id": "0-full-faithful-diag", |
| "repo": "toric", |
| "full_id": "toric/0-full-faithful-diag" |
| }, |
| { |
| "id": "thm:ABCExponentNu", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/thm:ABCExponentNu" |
| }, |
| { |
| "id": "lem:Adapted.progMeasurable_of_rightContinuous", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Adapted.progMeasurable_of_rightContinuous" |
| }, |
| { |
| "id": "Dusart_corollary_4_5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_corollary_4_5" |
| }, |
| { |
| "id": "def:corestriction", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/def:corestriction" |
| }, |
| { |
| "id": "lem:local inv fundamental class", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local inv fundamental class" |
| }, |
| { |
| "id": "bound-score-5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bound-score-5" |
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| { |
| "id": "diagonalize_real_symmetric", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/diagonalize_real_symmetric" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_continuous", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_continuous" |
| }, |
| { |
| "id": "3342", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/3342" |
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| { |
| "id": "prop:change-of-base", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:change-of-base" |
| }, |
| { |
| "id": "def:isssd", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:isssd" |
| }, |
| { |
| "id": "lem:local unramified reciprocity", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local unramified reciprocity" |
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| { |
| "id": "eq40", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq40" |
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| { |
| "id": "greedy-iterate", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/greedy-iterate" |
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| { |
| "id": "torsion-dist-shrinking", |
| "repo": "pfr", |
| "full_id": "pfr/torsion-dist-shrinking" |
| }, |
| { |
| "id": "lem:cadlag_elemStochIntegralBilin", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:cadlag_elemStochIntegralBilin" |
| }, |
| { |
| "id": "lem:simpleProcess_map2", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:simpleProcess_map2" |
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| { |
| "id": "lem:monotone_quadraticVariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:monotone_quadraticVariation" |
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| { |
| "id": "5-1-tor-hom", |
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| "full_id": "toric/5-1-tor-hom" |
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| { |
| "id": "thm:serre-der-prod-rule", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/thm:serre-der-prod-rule" |
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| { |
| "id": "SumBoundII", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SumBoundII" |
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| { |
| "id": "thm:IsGaussian.exists_integrable_exp_sq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:IsGaussian.exists_integrable_exp_sq" |
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| { |
| "id": "fks-lemma-5-2", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-lemma-5-2" |
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| { |
| "id": "bklnw-cor-3-1", |
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| { |
| "id": "TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.module", |
| "repo": "FLT_ch12", |
| "full_id": "FLT_ch12/TotallyDefiniteQuaternionAlgebra.WeightTwoAutomorphicForm.module" |
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| { |
| "id": "lem:integral_eq_zero_of_forall_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_eq_zero_of_forall_eq_zero" |
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| { |
| "id": "dist-projection", |
| "repo": "pfr", |
| "full_id": "pfr/dist-projection" |
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| { |
| "id": "QHat.injective_rat", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.injective_rat" |
| }, |
| { |
| "id": "defn:simplicial-cotensor", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/defn:simplicial-cotensor" |
| }, |
| { |
| "id": "lem:herbrand L_S", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:herbrand L_S" |
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| { |
| "id": "prime_between", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/prime_between" |
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| { |
| "id": "add-entropy", |
| "repo": "pfr", |
| "full_id": "pfr/add-entropy" |
| }, |
| { |
| "id": "Hurwitz.surjective_pnat_quotient", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.surjective_pnat_quotient" |
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| { |
| "id": "row-bound", |
| "repo": "carleson", |
| "full_id": "carleson/row-bound" |
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| { |
| "id": "buthe-theorem-2c", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/buthe-theorem-2c" |
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| { |
| "id": "1-2-6-inter-faces", |
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| { |
| "id": "kakeya", |
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| "full_id": "FormalBook/kakeya" |
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| { |
| "id": "dyadic-partition-2", |
| "repo": "carleson", |
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| { |
| "id": "data-process-unc-one", |
| "repo": "pfr", |
| "full_id": "pfr/data-process-unc-one" |
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| { |
| "id": "fixed_of_fixed2", |
| "repo": "FLT_ch8", |
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| { |
| "id": "thm:anti-serre-der-pos", |
| "repo": "Sphere-Packing-Lean", |
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| { |
| "id": "PeriodicSpherePacking", |
| "repo": "Sphere-Packing-Lean", |
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| { |
| "id": "prop:ho-nerve-adjunction", |
| "repo": "infinity-cosmos", |
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| { |
| "id": "WienerIkeharaInterval", |
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| { |
| "id": "lie_group_from_algebraic_group", |
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| { |
| "id": "Dusart_lemma_4_1", |
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| "id": "contourPull3", |
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| "id": "nontangential-operator-boundary", |
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| "id": "lem:homology 1 trivial", |
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| { |
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| "id": "boundary-operator-bound", |
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| { |
| "id": "LogDerivZetaUniformLogSquaredBound", |
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| { |
| "id": "lem:optionalSampling_discrete", |
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| { |
| "id": "estimate-F-set", |
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| { |
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| { |
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| { |
| "id": "lem:leRightCont", |
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| "full_id": "brownian-motion/lem:leRightCont" |
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| { |
| "id": "5-1-tor-var", |
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| { |
| "id": "lem:exists_cadlag_mod_of_local_mg", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:exists_cadlag_mod_of_local_mg" |
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| { |
| "id": "eq28770", |
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| { |
| "id": "residuePull2", |
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| "full_id": "PrimeNumberTheoremAnd/residuePull2" |
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| { |
| "id": "def:det-protocol-complex", |
| "repo": "ChandraFurstLipton", |
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| { |
| "id": "lem:M_cal_cadlag", |
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| "full_id": "brownian-motion/lem:M_cal_cadlag" |
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| { |
| "id": "slowly_increasing_well_defined", |
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| { |
| "id": "second-estimate-aux", |
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| { |
| "id": "lem:l1_mem_iff", |
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| { |
| "id": "lem:totalVariation_signedMeasure", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:totalVariation_signedMeasure" |
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| { |
| "id": "ra-prop", |
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| { |
| "id": "eq387", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq387" |
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| { |
| "id": "1-2-10-dual-face-antitone", |
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| { |
| "id": "chang", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/chang" |
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| { |
| "id": "cor:doob_ineq_norm", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:doob_ineq_norm" |
| }, |
| { |
| "id": "lem:inflation restriction naturality", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:inflation restriction naturality" |
| }, |
| { |
| "id": "lem:IsSquareIntegrable.tendsto_limitProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsSquareIntegrable.tendsto_limitProcess" |
| }, |
| { |
| "id": "IrreductibleRepresentationSn", |
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| "full_id": "BlueprintRep/IrreductibleRepresentationSn" |
| }, |
| { |
| "id": "waste-eq", |
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| "full_id": "PrimeNumberTheoremAnd/waste-eq" |
| }, |
| { |
| "id": "def:L2Martingales", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:L2Martingales" |
| }, |
| { |
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| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_smul_map" |
| }, |
| { |
| "id": "dist-zero", |
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| "full_id": "pfr/dist-zero" |
| }, |
| { |
| "id": "lem:volume_le_externalCoveringNumber_mul", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:volume_le_externalCoveringNumber_mul" |
| }, |
| { |
| "id": "boundary-measure", |
| "repo": "carleson", |
| "full_id": "carleson/boundary-measure" |
| }, |
| { |
| "id": "lem:norm comp d", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:norm comp d" |
| }, |
| { |
| "id": "0-grp-like-map", |
| "repo": "toric", |
| "full_id": "toric/0-grp-like-map" |
| }, |
| { |
| "id": "def:Submartingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:Submartingale" |
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| { |
| "id": "ZeroInequality", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZeroInequality" |
| }, |
| { |
| "id": "lem:herbrand finite", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:herbrand finite" |
| }, |
| { |
| "id": "eq4315", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq4315" |
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| { |
| "id": "lemma:E2-transform-general", |
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| { |
| "id": "thm:global cohomology bound", |
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| "full_id": "ClassFieldTheory/thm:global cohomology bound" |
| }, |
| { |
| "id": "global_class_field_theory", |
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| "full_id": "FLT_ch14/global_class_field_theory" |
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| { |
| "id": "matroidR10", |
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| "full_id": "seymour/matroidR10" |
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| { |
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| { |
| "id": "puqug", |
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| { |
| "id": "lem:Subcase2.3", |
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| "full_id": "ABC-Exceptions/lem:Subcase2.3" |
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| { |
| "id": "conditional-vanish", |
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| "full_id": "pfr/conditional-vanish" |
| }, |
| { |
| "id": "general_hoelder", |
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| "full_id": "LeanAPAP/general_hoelder" |
| }, |
| { |
| "id": "eq1657", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1657" |
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| { |
| "id": "global_dichotomy", |
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| "full_id": "LeanAPAP/global_dichotomy" |
| }, |
| { |
| "id": "lem:chebyshev_angle_sum_odd", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:chebyshev_angle_sum_odd" |
| }, |
| { |
| "id": "lem:chebyshev_angle_sum_even", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:chebyshev_angle_sum_even" |
| }, |
| { |
| "id": "gauss_lemma", |
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| "full_id": "FormalBook/gauss_lemma" |
| }, |
| { |
| "id": "kl-div-inj", |
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| "full_id": "pfr/kl-div-inj" |
| }, |
| { |
| "id": "diss_energy", |
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| "full_id": "LeanAPAP/diss_energy" |
| }, |
| { |
| "id": "grid-existence", |
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| }, |
| { |
| "id": "rs-pre-413", |
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| { |
| "id": "ruzsa-nonneg", |
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| "full_id": "pfr/ruzsa-nonneg" |
| }, |
| { |
| "id": "lem:Submartingale.exists_cadlag_modification_of_rightContinuous", |
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| { |
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| }, |
| { |
| "id": "lem:predictable_covariation", |
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| "full_id": "brownian-motion/lem:predictable_covariation" |
| }, |
| { |
| "id": "lem:omegaUpperBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:omegaUpperBound" |
| }, |
| { |
| "id": "lem:finite_set_bound", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:finite_set_bound" |
| }, |
| { |
| "id": "lem:A_uniform_integrable", |
| "repo": "brownian-motion", |
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| { |
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| { |
| "id": "eq26302", |
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| { |
| "id": "LogDerivZetaBndUnif", |
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| { |
| "id": "rho-sums-sym", |
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| { |
| "id": "lem:Case2Basic2", |
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| { |
| "id": "prop:theta-der", |
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| { |
| "id": "lem:local_martingale_sub_quadraticVariation", |
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| { |
| "id": "cuspidal_automorphic_form", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/cuspidal_automorphic_form" |
| }, |
| { |
| "id": "NumberField.InfiniteAdeleRing.instIsModuleTopology_fLT", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/NumberField.InfiniteAdeleRing.instIsModuleTopology_fLT" |
| }, |
| { |
| "id": "QHat.IsCoprime", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/QHat.IsCoprime" |
| }, |
| { |
| "id": "1-1-16-total-red", |
| "repo": "toric", |
| "full_id": "toric/1-1-16-total-red" |
| }, |
| { |
| "id": "Cotlar-estimate", |
| "repo": "carleson", |
| "full_id": "carleson/Cotlar-estimate" |
| }, |
| { |
| "id": "lemma:Gamma-1-generators", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Gamma-1-generators" |
| }, |
| { |
| "id": "I1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I1" |
| }, |
| { |
| "id": "uniform-entropy-II", |
| "repo": "pfr", |
| "full_id": "pfr/uniform-entropy-II" |
| }, |
| { |
| "id": "fks-proposition-3-4", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-proposition-3-4" |
| }, |
| { |
| "id": "fks-lemma-2-5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-lemma-2-5" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar" |
| }, |
| { |
| "id": "def:Z2_bound", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:Z2_bound" |
| }, |
| { |
| "id": "cond-dist-def", |
| "repo": "pfr", |
| "full_id": "pfr/cond-dist-def" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_cover_rescale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_cover_rescale" |
| }, |
| { |
| "id": "MulSemiringAction.monic_charpoly", |
| "repo": "FLT_ch8", |
| "full_id": "FLT_ch8/MulSemiringAction.monic_charpoly" |
| }, |
| { |
| "id": "lem:isGaussianProcess_of_modification", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussianProcess_of_modification" |
| }, |
| { |
| "id": "fks2-lemma-10b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-lemma-10b" |
| }, |
| { |
| "id": "lem:L2Predictable.inner_eq", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:L2Predictable.inner_eq" |
| }, |
| { |
| "id": "local_class_field_theory", |
| "repo": "FLT_ch14", |
| "full_id": "FLT_ch14/local_class_field_theory" |
| }, |
| { |
| "id": "rhominus-subgroup", |
| "repo": "pfr", |
| "full_id": "pfr/rhominus-subgroup" |
| }, |
| { |
| "id": "xi-z2-w-dist", |
| "repo": "pfr", |
| "full_id": "pfr/xi-z2-w-dist" |
| }, |
| { |
| "id": "lem:StoppingTimeGenMono", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:StoppingTimeGenMono" |
| }, |
| { |
| "id": "WeakPNT-AP", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/WeakPNT-AP" |
| }, |
| { |
| "id": "Hurwitz.left_ideal_princ", |
| "repo": "FLT_ch5", |
| "full_id": "FLT_ch5/Hurwitz.left_ideal_princ" |
| }, |
| { |
| "id": "pointwise-tree-estimate", |
| "repo": "carleson", |
| "full_id": "carleson/pointwise-tree-estimate" |
| }, |
| { |
| "id": "def:Periodic-sphere-packing-constant", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:Periodic-sphere-packing-constant" |
| }, |
| { |
| "id": "FreyPackage.of_not_FermatLastTheorem_p_ge_5", |
| "repo": "FLT_ch2", |
| "full_id": "FLT_ch2/FreyPackage.of_not_FermatLastTheorem_p_ge_5" |
| }, |
| { |
| "id": "lem:isGaussian_map", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:isGaussian_map" |
| }, |
| { |
| "id": "bklnw-lemma_15", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-lemma_15" |
| }, |
| { |
| "id": "lambda-pnt", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lambda-pnt" |
| }, |
| { |
| "id": "maximal-bound-antichain", |
| "repo": "carleson", |
| "full_id": "carleson/maximal-bound-antichain" |
| }, |
| { |
| "id": "monsky_theorem", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/monsky_theorem" |
| }, |
| { |
| "id": "lem:rightContSuccOrder", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContSuccOrder" |
| }, |
| { |
| "id": "lem:IsStoppingTime_hittingAGT", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsStoppingTime_hittingAGT" |
| }, |
| { |
| "id": "def:Gamma-generators", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/def:Gamma-generators" |
| }, |
| { |
| "id": "def:pullback_of_sheaf", |
| "repo": "M2", |
| "full_id": "M2/def:pullback_of_sheaf" |
| }, |
| { |
| "id": "prop:ThueEquations", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/prop:ThueEquations" |
| }, |
| { |
| "id": "real-line-ball-measure", |
| "repo": "carleson", |
| "full_id": "carleson/real-line-ball-measure" |
| }, |
| { |
| "id": "cond-multidist-def", |
| "repo": "pfr", |
| "full_id": "pfr/cond-multidist-def" |
| }, |
| { |
| "id": "lem:csq_of_pure_homotopy_k_sheaf", |
| "repo": "M2", |
| "full_id": "M2/lem:csq_of_pure_homotopy_k_sheaf" |
| }, |
| { |
| "id": "1323-refute-2744", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/1323-refute-2744" |
| }, |
| { |
| "id": "balance-def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/balance-def" |
| }, |
| { |
| "id": "multidist-indep", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-indep" |
| }, |
| { |
| "id": "Dusart_thm_5_1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_thm_5_1" |
| }, |
| { |
| "id": "rowToCol", |
| "repo": "BlueprintRep", |
| "full_id": "BlueprintRep/rowToCol" |
| }, |
| { |
| "id": "first-upper", |
| "repo": "pfr", |
| "full_id": "pfr/first-upper" |
| }, |
| { |
| "id": "lem:covarianceBilin_same_eq_variance", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covarianceBilin_same_eq_variance" |
| }, |
| { |
| "id": "lem:Trivialaibici", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Trivialaibici" |
| }, |
| { |
| "id": "lem:kshv_equiv_shv", |
| "repo": "M2", |
| "full_id": "M2/lem:kshv_equiv_shv" |
| }, |
| { |
| "id": "lem:100pc-self", |
| "repo": "pfr", |
| "full_id": "pfr/lem:100pc-self" |
| }, |
| { |
| "id": "lem:local H2 l*", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local H2 l*" |
| }, |
| { |
| "id": "fks-eq13", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks-eq13" |
| }, |
| { |
| "id": "lem:Mayer_Vietoris", |
| "repo": "M2", |
| "full_id": "M2/lem:Mayer_Vietoris" |
| }, |
| { |
| "id": "defn:NaturalModelRussell", |
| "repo": "HoTTLean", |
| "full_id": "HoTTLean/defn:NaturalModelRussell" |
| }, |
| { |
| "id": "SumBoundI", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/SumBoundI" |
| }, |
| { |
| "id": "lem:lemma1", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/lem:lemma1" |
| }, |
| { |
| "id": "0-full-faithful-spec-bialg", |
| "repo": "toric", |
| "full_id": "toric/0-full-faithful-spec-bialg" |
| }, |
| { |
| "id": "MeasureTheory.ringHaarChar_mul_integral", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.ringHaarChar_mul_integral" |
| }, |
| { |
| "id": "lem:2-truncated-qcat-htpy-comp", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:2-truncated-qcat-htpy-comp" |
| }, |
| { |
| "id": "lem:locally_of_ae", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:locally_of_ae" |
| }, |
| { |
| "id": "lem:stoppedProcess_eq_elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:stoppedProcess_eq_elemStochIntegral" |
| }, |
| { |
| "id": "prop:H4-fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:H4-fourier" |
| }, |
| { |
| "id": "eq65", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq65" |
| }, |
| { |
| "id": "lem:complex_total_of_three_is_acyclic", |
| "repo": "M2", |
| "full_id": "M2/lem:complex_total_of_three_is_acyclic" |
| }, |
| { |
| "id": "lem:IsLocalMartingale.martingale_iff_classDL", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:IsLocalMartingale.martingale_iff_classDL" |
| }, |
| { |
| "id": "0-ess-image-spec-bialg", |
| "repo": "toric", |
| "full_id": "toric/0-ess-image-spec-bialg" |
| }, |
| { |
| "id": "lem:norm_smul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:norm_smul" |
| }, |
| { |
| "id": "con:br", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/con:br" |
| }, |
| { |
| "id": "exceptional-set-carleson", |
| "repo": "carleson", |
| "full_id": "carleson/exceptional-set-carleson" |
| }, |
| { |
| "id": "Dusart_cor_5_3_b", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_3_b" |
| }, |
| { |
| "id": "entropic-bsg", |
| "repo": "pfr", |
| "full_id": "pfr/entropic-bsg" |
| }, |
| { |
| "id": "def:crypto-assumptions", |
| "repo": "amatelus", |
| "full_id": "amatelus/def:crypto-assumptions" |
| }, |
| { |
| "id": "lem:module_simpleProcess", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:module_simpleProcess" |
| }, |
| { |
| "id": "bklnw-sigma_1_def", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-sigma_1_def" |
| }, |
| { |
| "id": "estimate-x-shift", |
| "repo": "carleson", |
| "full_id": "carleson/estimate-x-shift" |
| }, |
| { |
| "id": "multidist-copy", |
| "repo": "pfr", |
| "full_id": "pfr/multidist-copy" |
| }, |
| { |
| "id": "IsDedekindDomain.FiniteAdeleRing.mapSemialgHom", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.FiniteAdeleRing.mapSemialgHom" |
| }, |
| { |
| "id": "def:proper-ker", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/def:proper-ker" |
| }, |
| { |
| "id": "Matroid.IsGood.isRegular", |
| "repo": "seymour", |
| "full_id": "seymour/Matroid.IsGood.isRegular" |
| }, |
| { |
| "id": "thm:analytic_eq_sqrt", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:analytic_eq_sqrt" |
| }, |
| { |
| "id": "1-2-18-aff-tor-var-rat-polyhedral-cone", |
| "repo": "toric", |
| "full_id": "toric/1-2-18-aff-tor-var-rat-polyhedral-cone" |
| }, |
| { |
| "id": "lem:packingNumber_mul_le_volume", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:packingNumber_mul_le_volume" |
| }, |
| { |
| "id": "thm:split-iff-mem-relative", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/thm:split-iff-mem-relative" |
| }, |
| { |
| "id": "product_rule", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/product_rule" |
| }, |
| { |
| "id": "lem:Submartingale.elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.elemStochIntegral" |
| }, |
| { |
| "id": "first-exception", |
| "repo": "carleson", |
| "full_id": "carleson/first-exception" |
| }, |
| { |
| "id": "antichain-operator", |
| "repo": "carleson", |
| "full_id": "carleson/antichain-operator" |
| }, |
| { |
| "id": "lem:martingale_martingalePart", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:martingale_martingalePart" |
| }, |
| { |
| "id": "AutomorphicForm.GLn.AutomorphicFormForGLnOverQ", |
| "repo": "FLT_ch7", |
| "full_id": "FLT_ch7/AutomorphicForm.GLn.AutomorphicFormForGLnOverQ" |
| }, |
| { |
| "id": "natural-central-groupoid", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/natural-central-groupoid" |
| }, |
| { |
| "id": "ShiftZeroBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ShiftZeroBound" |
| }, |
| { |
| "id": "forest-operator", |
| "repo": "carleson", |
| "full_id": "carleson/forest-operator" |
| }, |
| { |
| "id": "rho-BSG-triplet-symmetrized", |
| "repo": "pfr", |
| "full_id": "pfr/rho-BSG-triplet-symmetrized" |
| }, |
| { |
| "id": "lem:coind₁ invariants", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:coind₁ invariants" |
| }, |
| { |
| "id": "thm:condIndep_extension", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:condIndep_extension" |
| }, |
| { |
| "id": "lem:chainingSequence_mem", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:chainingSequence_mem" |
| }, |
| { |
| "id": "information-def", |
| "repo": "pfr", |
| "full_id": "pfr/information-def" |
| }, |
| { |
| "id": "Matrix.det_fromBlocks_zero", |
| "repo": "seymour", |
| "full_id": "seymour/Matrix.det_fromBlocks_zero" |
| }, |
| { |
| "id": "lem:komlos_convex_aux", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:komlos_convex_aux" |
| }, |
| { |
| "id": "def:predictablePart", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:predictablePart" |
| }, |
| { |
| "id": "def:rightLimitFiltration", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:rightLimitFiltration" |
| }, |
| { |
| "id": "lem:cat-of-n-arrows", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/lem:cat-of-n-arrows" |
| }, |
| { |
| "id": "RectangleIntegral_tendsTo_UpperU", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/RectangleIntegral_tendsTo_UpperU" |
| }, |
| { |
| "id": "C2-convex", |
| "repo": "carleson", |
| "full_id": "carleson/C2-convex" |
| }, |
| { |
| "id": "MeasureTheory.addEquivAddHaarChar_eq_addEquivAddHaarChar_of_isOpenEmbedding", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_eq_addEquivAddHaarChar_of_isOpenEmbedding" |
| }, |
| { |
| "id": "ch38lemma1", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/ch38lemma1" |
| }, |
| { |
| "id": "thm:contractable_of_exchangeable", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:contractable_of_exchangeable" |
| }, |
| { |
| "id": "buthe-theorem-2f", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/buthe-theorem-2f" |
| }, |
| { |
| "id": "prop:Qdec", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:Qdec" |
| }, |
| { |
| "id": "lem:aachIBP", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:aachIBP" |
| }, |
| { |
| "id": "eq1701", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/eq1701" |
| }, |
| { |
| "id": "logDerivResidue", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/logDerivResidue" |
| }, |
| { |
| "id": "Matroid.IsSum1of", |
| "repo": "seymour", |
| "full_id": "seymour/Matroid.IsSum1of" |
| }, |
| { |
| "id": "lem:covariation_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:covariation_zero" |
| }, |
| { |
| "id": "lem:local unram rest", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local unram rest" |
| }, |
| { |
| "id": "IsDedekindDomain.HeightOneSpectrum.adicCompletionComapAlgEquiv", |
| "repo": "FLT_ch9", |
| "full_id": "FLT_ch9/IsDedekindDomain.HeightOneSpectrum.adicCompletionComapAlgEquiv" |
| }, |
| { |
| "id": "top-tiles", |
| "repo": "carleson", |
| "full_id": "carleson/top-tiles" |
| }, |
| { |
| "id": "lem:adapted_predictablePart", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:adapted_predictablePart" |
| }, |
| { |
| "id": "lem:sum_cos_phi_vanishes", |
| "repo": "ChebyshevCircles", |
| "full_id": "ChebyshevCircles/lem:sum_cos_phi_vanishes" |
| }, |
| { |
| "id": "lem:rightContIsolated", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:rightContIsolated" |
| }, |
| { |
| "id": "thm:contraction_mapping", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:contraction_mapping" |
| }, |
| { |
| "id": "lem:local abelian classification", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local abelian classification" |
| }, |
| { |
| "id": "lem:eqRightCont", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:eqRightCont" |
| }, |
| { |
| "id": "lem:integral_sup_rpow_dist_le_sum", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:integral_sup_rpow_dist_le_sum" |
| }, |
| { |
| "id": "lem:packingNumber_two_le_externalCoveringNumber", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:packingNumber_two_le_externalCoveringNumber" |
| }, |
| { |
| "id": "prop:nerve-2-coskeletal", |
| "repo": "infinity-cosmos", |
| "full_id": "infinity-cosmos/prop:nerve-2-coskeletal" |
| }, |
| { |
| "id": "Calderon-Zygmund-decomposition", |
| "repo": "carleson", |
| "full_id": "carleson/Calderon-Zygmund-decomposition" |
| }, |
| { |
| "id": "thm:conditionallyIID_of_contractable_martingale", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:conditionallyIID_of_contractable_martingale" |
| }, |
| { |
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| { |
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| { |
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| { |
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| "full_id": "PrimeNumberTheoremAnd/lem:abadeulmac'" |
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| { |
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| { |
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| "full_id": "polytopes-in-LEAN/lem:ambient_is_primspace" |
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| { |
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| { |
| "id": "def:ScaledReal", |
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| "full_id": "radii-polynomial/def:ScaledReal" |
| }, |
| { |
| "id": "lem:hocolim_preserves_homotopy_k_sheaves", |
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| "full_id": "M2/lem:hocolim_preserves_homotopy_k_sheaves" |
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| { |
| "id": "lem:herbrand ses", |
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| "full_id": "ClassFieldTheory/lem:herbrand ses" |
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| { |
| "id": "isIntegrable", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/isIntegrable" |
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| { |
| "id": "estimate-bad", |
| "repo": "carleson", |
| "full_id": "carleson/estimate-bad" |
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| { |
| "id": "ShiftTwoBound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ShiftTwoBound" |
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| { |
| "id": "0-grp-like-lin-indep", |
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| "full_id": "toric/0-grp-like-lin-indep" |
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| { |
| "id": "0-grp-alg-grp-like-gc", |
| "repo": "toric", |
| "full_id": "toric/0-grp-alg-grp-like-gc" |
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| { |
| "id": "eq39", |
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| "full_id": "equational_theories/eq39" |
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| { |
| "id": "def:fourier-L2", |
| "repo": "BonnAnalysis", |
| "full_id": "BonnAnalysis/def:fourier-L2" |
| }, |
| { |
| "id": "cor:cohomology sub Sylow", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/cor:cohomology sub Sylow" |
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| "id": "lem:cohomology S-ideles decomp", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:cohomology S-ideles decomp" |
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| { |
| "id": "lem:logSizeBallSequence_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:logSizeBallSequence_eq_zero" |
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| { |
| "id": "lem:ch_of_empty_is_empty", |
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| "full_id": "polytopes-in-LEAN/lem:ch_of_empty_is_empty" |
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| { |
| "id": "lem:blockAvg_tendsto", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:blockAvg_tendsto" |
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| { |
| "id": "rho-sums", |
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| "full_id": "pfr/rho-sums" |
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| { |
| "id": "bound-score-1", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bound-score-1" |
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| "id": "partial-Fourier-sum-bound", |
| "repo": "carleson", |
| "full_id": "carleson/partial-Fourier-sum-bound" |
| }, |
| { |
| "id": "lem:charFun_gaussianReal", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:charFun_gaussianReal" |
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| { |
| "id": "submodularity", |
| "repo": "pfr", |
| "full_id": "pfr/submodularity" |
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| { |
| "id": "lem:sigmaLn", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:sigmaLn" |
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| { |
| "id": "lem:Submartingale.integrable_stoppedValue", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.integrable_stoppedValue" |
| }, |
| { |
| "id": "lem:doob_Lp_countable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:doob_Lp_countable" |
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| { |
| "id": "lem:posSemidef_gramMatrix", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:posSemidef_gramMatrix" |
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| { |
| "id": "cor:doob_ineq_stop_exp_val", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/cor:doob_ineq_stop_exp_val" |
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| { |
| "id": "thm:wed-artin-algebra", |
| "repo": "BrauerGroup_new", |
| "full_id": "BrauerGroup_new/thm:wed-artin-algebra" |
| }, |
| { |
| "id": "lem:Subcase2.4", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/lem:Subcase2.4" |
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| { |
| "id": "prop:H2-fourier", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/prop:H2-fourier" |
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| { |
| "id": "MeasureTheory.addEquivAddHaarChar_eq", |
| "repo": "FLT_ch10", |
| "full_id": "FLT_ch10/MeasureTheory.addEquivAddHaarChar_eq" |
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| { |
| "id": "lem:komlos_aux", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:komlos_aux" |
| }, |
| { |
| "id": "thm:BdExceptionalBound", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/thm:BdExceptionalBound" |
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| { |
| "id": "def:sq_map", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/def:sq_map" |
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| { |
| "id": "0-diag-hom", |
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| "full_id": "toric/0-diag-hom" |
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| { |
| "id": "thm:BombierSchmidtforThueEqs", |
| "repo": "ABC-Exceptions", |
| "full_id": "ABC-Exceptions/thm:BombierSchmidtforThueEqs" |
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| { |
| "id": "lem:herbrand local units", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:herbrand local units" |
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| { |
| "id": "cayley_formala_proof4", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/cayley_formala_proof4" |
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| { |
| "id": "lower-oscillation-bound", |
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| "id": "1-2-6-face-face", |
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| "id": "fks2-lemma-20a", |
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| "id": "flat-on-bohr", |
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| "id": "non_imp_3994_3588_thm", |
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| "full_id": "equational_theories/non_imp_3994_3588_thm" |
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| { |
| "id": "lem:martingale_integral_of_forall_eq_zero", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:martingale_integral_of_forall_eq_zero" |
| }, |
| { |
| "id": "def:convex_hull", |
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| "full_id": "polytopes-in-LEAN/def:convex_hull" |
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| { |
| "id": "lem:local image inertia", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local image inertia" |
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| "id": "correlation-distant-tree-parts", |
| "repo": "carleson", |
| "full_id": "carleson/correlation-distant-tree-parts" |
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| "id": "neg-ent", |
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| "id": "prop:applem", |
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| "id": "Dusart_prop_5_11a", |
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| "id": "four_proofs_euler_series", |
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| { |
| "id": "lem:norm_pow_le", |
| "repo": "radii-polynomial", |
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| { |
| "id": "0-spec-hopf", |
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| "full_id": "toric/0-spec-hopf" |
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| { |
| "id": "tendsto_rpow_atTop_nhds_zero_of_norm_gt_one", |
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| "full_id": "PrimeNumberTheoremAnd/tendsto_rpow_atTop_nhds_zero_of_norm_gt_one" |
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| { |
| "id": "thm:infinite_primes", |
| "repo": "infinite-primes-via-log", |
| "full_id": "infinite-primes-via-log/thm:infinite_primes" |
| }, |
| { |
| "id": "lem:elemStochIntegral_assoc", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:elemStochIntegral_assoc" |
| }, |
| { |
| "id": "rho-invariant", |
| "repo": "pfr", |
| "full_id": "pfr/rho-invariant" |
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| { |
| "id": "def:reciprocity iso", |
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| "id": "eq3994", |
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| "id": "dens2-antichain", |
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| "id": "1-2-18-dim-aff-tor-var-rat-polyhedral-cone", |
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| "id": "eq374794", |
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| "id": "claim-4", |
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| { |
| "id": "LogDerivZetaFinalBound", |
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| { |
| "id": "prop:ineqB", |
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| "id": "lem:chech_long_exact_sequence", |
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| "full_id": "M2/lem:chech_long_exact_sequence" |
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| { |
| "id": "lem:directing_measure_isProb_L2", |
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| "full_id": "exchangeability/lem:directing_measure_isProb_L2" |
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| { |
| "id": "multidist-chain-rule-cond", |
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| "id": "Hurwitz.norm_one", |
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| "full_id": "FLT_ch5/Hurwitz.norm_one" |
| }, |
| { |
| "id": "lem:lebesgue-cond-exp-char", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:lebesgue-cond-exp-char" |
| }, |
| { |
| "id": "def:Martingale", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:Martingale" |
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| { |
| "id": "3744_implies_3722_381", |
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| "full_id": "equational_theories/3744_implies_3722_381" |
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| { |
| "id": "duality", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/duality" |
| }, |
| { |
| "id": "lem:predictable_quadraticVariation", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictable_quadraticVariation" |
| }, |
| { |
| "id": "def:pushforward_of_K-sheaf", |
| "repo": "M2", |
| "full_id": "M2/def:pushforward_of_K-sheaf" |
| }, |
| { |
| "id": "lem:local H2 upper bound", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:local H2 upper bound" |
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| { |
| "id": "cor:sqrt2_unique", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/cor:sqrt2_unique" |
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| { |
| "id": "477-confl", |
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| "full_id": "equational_theories/477-confl" |
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| { |
| "id": "thm:simple_radii_poly_ef", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:simple_radii_poly_ef" |
| }, |
| { |
| "id": "lem:Submartingale.locally_classD", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:Submartingale.locally_classD" |
| }, |
| { |
| "id": "lem:uniformIntegrableNorm", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:uniformIntegrableNorm" |
| }, |
| { |
| "id": "lem:explicit_inverse", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:explicit_inverse" |
| }, |
| { |
| "id": "hardly_ramified_spreads_out", |
| "repo": "FLT_ch3", |
| "full_id": "FLT_ch3/hardly_ramified_spreads_out" |
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| { |
| "id": "lemma:disc-E4E6", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:disc-E4E6" |
| }, |
| { |
| "id": "lemma:Ek-is-modular-form", |
| "repo": "Sphere-Packing-Lean", |
| "full_id": "Sphere-Packing-Lean/lemma:Ek-is-modular-form" |
| }, |
| { |
| "id": "thm:CauchyProduct_mul_smul", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_mul_smul" |
| }, |
| { |
| "id": "MatrixSum3.IsCanonicalSigning.Al_D_isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.IsCanonicalSigning.Al_D_isTotallyUnimodular" |
| }, |
| { |
| "id": "I3Bound", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/I3Bound" |
| }, |
| { |
| "id": "MatrixSum3.IsCanonicalSigning.isTotallyUnimodular", |
| "repo": "seymour", |
| "full_id": "seymour/MatrixSum3.IsCanonicalSigning.isTotallyUnimodular" |
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| { |
| "id": "Hilbert-kernel-bound", |
| "repo": "carleson", |
| "full_id": "carleson/Hilbert-kernel-bound" |
| }, |
| { |
| "id": "first-cond", |
| "repo": "pfr", |
| "full_id": "pfr/first-cond" |
| }, |
| { |
| "id": "book.irrational.Theorem_2", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/book.irrational.Theorem_2" |
| }, |
| { |
| "id": "first-useful", |
| "repo": "pfr", |
| "full_id": "pfr/first-useful" |
| }, |
| { |
| "id": "lem:tail_factorization", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:tail_factorization" |
| }, |
| { |
| "id": "lem:predictableSet_elementaryPredictableSet", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictableSet_elementaryPredictableSet" |
| }, |
| { |
| "id": "third-exception", |
| "repo": "carleson", |
| "full_id": "carleson/third-exception" |
| }, |
| { |
| "id": "Ramanujan-Soldner-constant", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Ramanujan-Soldner-constant" |
| }, |
| { |
| "id": "lem:sq_norm_elemStochIntegral", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:sq_norm_elemStochIntegral" |
| }, |
| { |
| "id": "tile-uncertainty", |
| "repo": "carleson", |
| "full_id": "carleson/tile-uncertainty" |
| }, |
| { |
| "id": "lem:gibbs-meas-tfae", |
| "repo": "GibbsMeasure", |
| "full_id": "GibbsMeasure/lem:gibbs-meas-tfae" |
| }, |
| { |
| "id": "lem:aachcanc", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/lem:aachcanc" |
| }, |
| { |
| "id": "ZetaLowerBound3", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/ZetaLowerBound3" |
| }, |
| { |
| "id": "mzi_complex", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/mzi_complex" |
| }, |
| { |
| "id": "lem:summable_eval", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/lem:summable_eval" |
| }, |
| { |
| "id": "def:IsCadlag", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsCadlag" |
| }, |
| { |
| "id": "e_pow_4_irrational", |
| "repo": "FormalBook", |
| "full_id": "FormalBook/e_pow_4_irrational" |
| }, |
| { |
| "id": "fks2-def-5", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/fks2-def-5" |
| }, |
| { |
| "id": "Dusart_cor_5_2_e", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/Dusart_cor_5_2_e" |
| }, |
| { |
| "id": "thm:first inequality", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/thm:first inequality" |
| }, |
| { |
| "id": "main-int-count", |
| "repo": "LeanAPAP", |
| "full_id": "LeanAPAP/main-int-count" |
| }, |
| { |
| "id": "MediumPNT", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/MediumPNT" |
| }, |
| { |
| "id": "0-char-cochar-pairing", |
| "repo": "toric", |
| "full_id": "toric/0-char-cochar-pairing" |
| }, |
| { |
| "id": "lem:logSizeBallSequence_V_anti", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:logSizeBallSequence_V_anti" |
| }, |
| { |
| "id": "finite_imp_3994_3588", |
| "repo": "equational_theories", |
| "full_id": "equational_theories/finite_imp_3994_3588" |
| }, |
| { |
| "id": "def:preBrownian", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:preBrownian" |
| }, |
| { |
| "id": "thm:eval-rand-complexity", |
| "repo": "ChandraFurstLipton", |
| "full_id": "ChandraFurstLipton/thm:eval-rand-complexity" |
| }, |
| { |
| "id": "lem:LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn" |
| }, |
| { |
| "id": "thm:mean_value", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:mean_value" |
| }, |
| { |
| "id": "initial-factorization-medium-prime-ge", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/initial-factorization-medium-prime-ge" |
| }, |
| { |
| "id": "thm:birkhoff_condexp", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/thm:birkhoff_condexp" |
| }, |
| { |
| "id": "def:IsSquareIntegrable", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/def:IsSquareIntegrable" |
| }, |
| { |
| "id": "lem:predictablePart_add_one", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/lem:predictablePart_add_one" |
| }, |
| { |
| "id": "thm:finite_set_bound_of_dist_le_of_le_diam", |
| "repo": "brownian-motion", |
| "full_id": "brownian-motion/thm:finite_set_bound_of_dist_le_of_le_diam" |
| }, |
| { |
| "id": "lem:Tate -1 aug", |
| "repo": "ClassFieldTheory", |
| "full_id": "ClassFieldTheory/lem:Tate -1 aug" |
| }, |
| { |
| "id": "lem:indicator_product_bridge_contractable", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:indicator_product_bridge_contractable" |
| }, |
| { |
| "id": "lem:homotpy_k_sheaves_stable_by_extension", |
| "repo": "M2", |
| "full_id": "M2/lem:homotpy_k_sheaves_stable_by_extension" |
| }, |
| { |
| "id": "bklnw-eq_A_21", |
| "repo": "PrimeNumberTheoremAnd", |
| "full_id": "PrimeNumberTheoremAnd/bklnw-eq_A_21" |
| }, |
| { |
| "id": "thm:CauchyProduct_mul_one", |
| "repo": "radii-polynomial", |
| "full_id": "radii-polynomial/thm:CauchyProduct_mul_one" |
| }, |
| { |
| "id": "lem:product_blockAvg_L1", |
| "repo": "exchangeability", |
| "full_id": "exchangeability/lem:product_blockAvg_L1" |
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