file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | Antitone.intervalIntegrable | [] | [
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Std/Data/List/Lemmas.lean | List.getLast_append | [
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Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_aux | [
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Mathlib/NumberTheory/Padics/Hensel.lean | hensels_lemma | [
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.w | [
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Mathlib/Algebra/RingQuot.lean | RingQuot.Rel.neg | [
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Mathlib/Data/PNat/Xgcd.lean | PNat.gcd_det_eq | [] | [
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.sec_spec | [] | [
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Mathlib/Data/Fin/Basic.lean | Fin.mk_lt_of_lt_val | [] | [
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.apply_le_nfpFamily | [
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_sSup_of_mem | [
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Mathlib/GroupTheory/Torsion.lean | IsTorsionFree.quotient_torsion | [
{
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Mathlib/Data/Finset/Basic.lean | Finset.erase_idem | [
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Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_iInf_principal_finite | [
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Mathlib/Algebra/BigOperators/Basic.lean | Multiset.sup_powerset_len | [
{
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.topologyOfClosureOperator_close | [
{
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.algHom_ext' | [] | [
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36
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.bot_parallel_iff_eq_bot | [
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.naturality_2' | [
{
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_zero_left_of_mono | [
{
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Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.finrank_add_inf_finrank_orthogonal | [
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_neg | [] | [
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_add | [] | [
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.elim_set | [] | [
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Mathlib/Analysis/Convex/Function.lean | convexOn_of_convex_epigraph | [] | [
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Mathlib/Computability/Reduce.lean | toNat_manyOneReducible | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.empty_not_mem | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_div | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_add | [] | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_bit1 | [] | [
778,
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Mathlib/Algebra/GroupPower/Order.lean | one_le_pow_of_one_le | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_smul_dirac | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_zsmul_add | [
{
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Mathlib/Init/Data/Prod.lean | Prod.mk.eta | [] | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.isHomogeneous_iff_subset_iInter | [] | [
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Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_eq_iSup_biInf_of_nat | [] | [
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Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_and_degree_eq_and_monic | [
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Mathlib/Logic/Equiv/LocalEquiv.lean | Equiv.symm_toLocalEquiv | [] | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasStrictDerivAt_const | [] | [
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Mathlib/Data/Set/Prod.lean | Set.preimage_prod_map_prod | [] | [
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Mathlib/Data/Seq/Computation.lean | Computation.eq_thinkN' | [] | [
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_neg | [] | [
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_id_rename | [
{
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Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_iterate_pred | [] | [
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodalWeight_ne_zero | [
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Mathlib/Data/Set/Function.lean | Set.EqOn.cancel_left | [] | [
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Mathlib/Data/Int/ModEq.lean | Int.ModEq.neg | [
{
"state_after": "m n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ 0 ≡ 0 [ZMOD n]",
"state_before": "m n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ a + -a ≡ b + -b [ZMOD n]",
"tactic": "simp_rw [← sub_eq_add_neg, sub_self]"
},
{
"state_after": "no goals",
"state_before": "m n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n... | [
181,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
21
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Mathlib/Logic/Encodable/Basic.lean | ULower.up_eq_up | [] | [
535,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_mul_monomial | [
{
"state_after": "no goals",
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449,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.congr_fun | [] | [
133,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_unit_right_assoc' | [
{
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421,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.sup_apply | [] | [
535,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.compRightAlgHom_continuous | [] | [
485,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Nat/Pairing.lean | iSup_unpair | [
{
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"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nf : ℕ → ℕ → α\n⊢ (⨆ (n : ℕ), f (unpair n).fst (unpair n).snd) = ⨆ (i : ℕ) (j : ℕ), f i j",
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}
] | [
191,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | Filter.tendsto_mul_right_cobounded | [] | [
619,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_distrib_right | [] | [
1050,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_mul_eq_mk'_of_mul | [
{
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857,
39
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856,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_to_nat | [] | [
428,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
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Mathlib/Data/Matrix/DMatrix.lean | DMatrix.map_map | [
{
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64,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_self | [] | [
1814,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
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Mathlib/Order/WellFoundedSet.lean | Finset.isWf_bUnion | [] | [
600,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
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Mathlib/Data/Finset/Basic.lean | Finset.biUnion_biUnion | [
{
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3598,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3593,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.mem_range_self | [] | [
843,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.ofReal | [] | [
972,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.mkPiRing_apply | [] | [
1063,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
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Mathlib/RingTheory/IsTensorProduct.lean | TensorProduct.isTensorProduct | [
{
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75,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_eq_bot | [] | [
90,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.top_toNNReal | [] | [
221,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
9
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.coe_toHom | [] | [
823,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean | AlgebraicGeometry.Polynomial.isOpen_imageOfDf | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nf : R[X]\n⊢ IsOpen (⋃ (i : ℕ), {x | ¬coeff f i ∈ x.asIdeal})",
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"tactic": "rw [imageOfDf, setOf_exists fun i (x : PrimeSpectrum R) => coeff f i ∉ x.asIdeal]"
},
{
... | [
43,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/Algebra/Order/Group/Defs.lean | Right.inv_lt_self | [] | [
504,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.mk₂_apply | [] | [
252,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_mul_monomial_zero | [] | [
286,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.lintegral_lt_top_of_boundedContinuous_to_nnreal | [
{
"state_after": "case f_bdd\nΩ : Type u_1\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.44593\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nf : Ω →ᵇ ℝ≥0\n⊢ ∃ c, ∀ (x : Ω), ↑(↑f... | [
333,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_lt_nat | [] | [
1572,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.neg_pi_div_two_le_arcsin | [] | [
56,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.toZModPow_eq_iff_ext | [
{
"state_after": "case mp\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\ng g' : R →+* ℤ_[p]\n⊢ (∀ (n : ℕ), RingHom.comp (toZModPow n) g = RingHom.comp (toZModPow n) g') → g = g'\n\ncase mpr\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\ng g' : ... | [
690,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.rotateL_lemma₁ | [
{
"state_after": "no goals",
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"tactic": "linarith"
}
] | [
1220,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/Data/Set/Function.lean | Function.invFunOn_apply_eq | [] | [
1236,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/Logic/Basic.lean | xor_iff_iff_not | [
{
"state_after": "no goals",
"state_before": "a b : Prop\n⊢ Xor' a b ↔ (a ↔ ¬b)",
"tactic": "simp only [← @xor_not_right a, not_not]"
}
] | [
480,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.as_ideal_le_as_ideal | [] | [
489,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_mul | [] | [
357,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_le_of_liminf_slope_right_le_deriv_boundary | [
{
"state_after": "E : Type ?u.11278\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.11374\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → ℝ\na b : ℝ\nhf : ContinuousOn f (Icc a b)\nB B' : ℝ → ℝ\nha : f a ≤ B a\nhB : ContinuousOn B (Icc a b)\nhB' : ∀ (x : ℝ), x ∈ Ico a b → ... | [
178,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.append_right | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
149,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.norm | [] | [
1466,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1464,
11
] |
Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean | TopCat.Presheaf.SheafConditionEqualizerProducts.fork_ι | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.sup_apply | [] | [
349,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.self_add_star' | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.308044\nT : Type ?u.308047\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ a + star a = ↑(2 * a.re)",
"tactic": "ext <;> simp [two_mul]"
}
] | [
649,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.mulHead_prod | [
{
"state_after": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.619397\ninst✝ : Monoid N\ni j : ι\nw : NeWord M i j\nx : M i\nhnotone : x * head w ≠ 1\n⊢ prod (replaceHead (x * head w) hnotone w) = ↑of x * prod w",
"state_before": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i :... | [
665,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.strictAnti_iff_succ_lt | [] | [
1898,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1896,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.coePNat_ofPrime | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_zipWith_right | [] | [
312,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_succ_right | [] | [
382,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eqOn_quadrant_IV | [] | [
671,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.mem_facets | [] | [
197,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.MeasurePreserving.integral_comp | [] | [
1574,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.elementarilyEquivalent | [] | [
123,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.diagramNatTrans_zero | [
{
"state_after": "case w.h\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP✝ : Cᵒᵖ ⥤ D\ninst✝ : Preadditive D\nX : C\nP Q : Cᵒᵖ ⥤ D\nx✝ : (Cover J X)ᵒᵖ\n⊢ (diagramNatTrans J 0 X... | [
91,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.binaryCoproductIso_inr_comp_inv | [] | [
254,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.mem_restrict_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.814135\nδ : Type ?u.814138\ninst✝¹ : MeasurableSpace α\nK : Type ?u.814144\ninst✝ : Zero β\nr : β\ns : Set α\nf : α →ₛ β\nhs : MeasurableSet s\n⊢ r ∈ SimpleFunc.range (restrict f s) ↔ r = 0 ∧ s ≠ univ ∨ r ∈ ↑f '' s",
"... | [
799,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
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