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"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", 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"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": 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