file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_prod_of_mulSupport_subset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.176909\nι : Type ?u.176912\nG : Type ?u.176915\nM : Type u_2\nN : Type ?u.176921\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\ns : Finset α\nh : mulSupport f ⊆ ↑s\nA : mulSupport (f ∘ PLift.down) = ↑Equiv.plift.symm '' mulSupport f\n⊢ (∏ᶠ (i : α), f i) = ∏ ... | [
392,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_zero | [] | [
509,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
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Std/Logic.lean | Decidable.not_iff | [
{
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"tactic": "by_cases h : b <;> simp [h, iff_true, iff_false]"
}
] | [
583,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/Set/Basic.lean | Set.Nontrivial.not_subset_singleton | [] | [
2552,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2551,
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.comp_aemeasurable | [] | [
161,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/CategoryTheory/Preadditive/Yoneda/Projective.lean | CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nP : C\n⊢ Functor.PreservesEpimorphisms (coyoneda.obj P.op) ↔ Functor.PreservesEpimorphisms (preadditiveCoyoneda.obj P.op)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nP : C\n⊢ Projective P ↔ Functor.Prese... | [
54,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/FieldTheory/Tower.lean | FiniteDimensional.finrank_linear_map' | [] | [
167,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/LinearAlgebra/Basis.lean | LinearMap.exists_leftInverse_of_injective | [
{
"state_after": "ι : Type ?u.1179439\nι' : Type ?u.1179442\nR : Type ?u.1179445\nR₂ : Type ?u.1179448\nK : Type u_1\nM : Type ?u.1179454\nM' : Type ?u.1179457\nM'' : Type ?u.1179460\nV : Type u\nV' : Type u_2\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module K V\ninst... | [
1584,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
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Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_univ | [] | [
333,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
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Mathlib/Order/Cover.lean | Covby.le | [] | [
273,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.edist_le_infEdist_add_ediam | [
{
"state_after": "ι : Sort ?u.8332\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t : Set α\nΦ : α → β\nhy : y ∈ s\n⊢ edist x y ≤ ⨅ (i : α) (_ : i ∈ s), edist x i + diam s",
"state_before": "ι : Sort ?u.8332\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpa... | [
124,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_diff_Ioo_same | [
{
"state_after": "α : Type u_1\nβ : Type ?u.44269\ninst✝ : PartialOrder α\na b c : α\nh : a ≤ b\n⊢ {a, b} ⊆ Icc a b",
"state_before": "α : Type u_1\nβ : Type ?u.44269\ninst✝ : PartialOrder α\na b c : α\nh : a ≤ b\n⊢ Icc a b \\ Ioo a b = {a, b}",
"tactic": "rw [← Icc_diff_both, diff_diff_cancel_left]"
... | [
832,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.Seminorm.isLUB_sSup | [
{
"state_after": "case refine'_1\nR : Type ?u.778047\nR' : Type ?u.778050\n𝕜 : Type u_2\n𝕜₂ : Type ?u.778056\n𝕜₃ : Type ?u.778059\n𝕝 : Type ?u.778062\nE : Type u_1\nE₂ : Type ?u.778068\nE₃ : Type ?u.778071\nF : Type ?u.778074\nG : Type ?u.778077\nι : Type ?u.778080\ninst✝² : NormedField 𝕜\ninst✝¹ : AddComm... | [
600,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
9
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_angle_of_angle_eq_pi | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 p3 p4 : P\nh : InnerProductGeometry.angle (p2 -ᵥ p3) (p4 -ᵥ p3) = π\n⊢ InnerProductGeometry.angle (p1 -ᵥ p2) (p3 -ᵥ p2) = InnerProductGeometry.a... | [
187,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Complex/RemovableSingularity.lean | Complex.differentiableOn_update_limUnder_insert_of_isLittleO | [] | [
103,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_neg_linearMap | [] | [
432,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_mul' | [
{
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"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r ... | [
422,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Algebra/Module/Basic.lean | two_nsmul_eq_zero | [
{
"state_after": "α : Type ?u.276095\nR : Type ?u.276098\nk : Type ?u.276101\nS : Type ?u.276104\nM : Type u_1\nM₂ : Type ?u.276110\nM₃ : Type ?u.276113\nι : Type ?u.276116\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : NoZeroSMulDivisors R M\ninst✝ : CharZero R\nv : M\nthis : NoZ... | [
648,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
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Mathlib/Data/List/Cycle.lean | List.next_nthLe | [] | [
312,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.image_mem_functorPushforward | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
236,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_mul_sqrt_lt_succ | [] | [
183,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.pure_def | [] | [
878,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_of_empty | [] | [
1511,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
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Std/Data/Int/Lemmas.lean | Int.le_min | [
{
"state_after": "a b c : Int\nx✝ : a ≤ b ∧ a ≤ c\nh₁ : a ≤ b\nh₂ : a ≤ c\n⊢ a ≤ if b ≤ c then b else c",
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"tactic": "rw [Int.min_def]"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nx✝ : ... | [
701,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
699,
11
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.oreDiv_add_char | [] | [
614,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_smul | [
{
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47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.equalizer_ext | [
{
"state_after": "no goals",
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"tactic": "rw [s.app_one_eq_ι_comp_left, this]"
},
{
"state_afte... | [
409,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
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Mathlib/Combinatorics/Composition.lean | compositionAsSet_card | [
{
"state_after": "n✝ n : ℕ\nthis : Fintype.card (Finset (Fin (n - 1))) = 2 ^ (n - 1)\n⊢ Fintype.card (CompositionAsSet n) = 2 ^ (n - 1)",
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"tactic": "have : Fintype.card (Finset (Fin (n - 1))) = 2 ^ (n - 1) := by simp"
},
... | [
870,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mk_uniformity_basis_le | [
{
"state_after": "α : Type u\nβ✝ : Type v\nX : Type ?u.17483\ninst✝ : PseudoEMetricSpace α\nβ : Type u_1\np : β → Prop\nf : β → ℝ≥0∞\nhf₀ : ∀ (x : β), p x → 0 < f x\nhf : ∀ (ε : ℝ≥0∞), 0 < ε → ∃ x, p x ∧ f x ≤ ε\ns : Set (α × α)\n⊢ (∃ i, 0 < i ∧ {p | edist p.fst p.snd < i} ⊆ s) ↔ ∃ i, p i ∧ {p | edist p.fst p.s... | [
215,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
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Mathlib/CategoryTheory/Limits/ColimitLimit.lean | CategoryTheory.Limits.ι_colimitLimitToLimitColimit_π_apply | [
{
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108,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Antitone.Ioc | [] | [
156,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
11
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Mathlib/Algebra/Regular/Basic.lean | IsRightRegular.of_mul | [
{
"state_after": "R : Type u_1\ninst✝ : Semigroup R\na b : R\nab : IsRightRegular (b * a)\nx y : R\nxy : (fun x => x * b) x = (fun x => x * b) y\n⊢ x * (b * a) = y * (b * a)",
"state_before": "R : Type u_1\ninst✝ : Semigroup R\na b : R\nab : IsRightRegular (b * a)\n⊢ IsRightRegular b",
"tactic": "refine... | [
142,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_zero_apply | [] | [
782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableAt.smul_const | [] | [
251,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.toFreimanHom_injective | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_atBot | [] | [
1291,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1289,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_smulRight_apply | [
{
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1846,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1830,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.tendsto_setToFun_approxOn_of_measurable_of_range_subset | [
{
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1561,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_dropUntil_subset | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nh : u ∈ support p\nx : V\nhx : x ∈ support (dropUntil p u h)\n⊢ x ∈ support (takeUntil p u h) ∨ x ∈ support (dropUntil p u h)",
"state_bef... | [
1142,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Order/WithBot.lean | WithTop.toDual_lt_toDual_iff | [] | [
896,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | piecewise_ae_eq_restrict_compl | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4342311\nδ : Type ?u.4342314\nι : Type ?u.4342317\nR : Type ?u.4342320\nR' : Type ?u.4342323\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t : Set α\nf g : α → β\nhs : MeasurableSet s\n⊢ piecewise s f g =ᶠ[ae μ ⊓ 𝓟 (sᶜ)] g",
"state_befo... | [
4619,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4616,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofMul_eq_zero | [] | [
223,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.mulVecLin_mul | [] | [
257,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.corec_unique | [
{
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786,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_zero_iff_remainder | [
{
"state_after": "p r i : ℕ\npp : Prime p\nhr0 : r ≠ 0\nh : ↑(factorization (p * i + r)) p = 0\n⊢ ¬p ∣ r",
"state_before": "p r i : ℕ\npp : Prime p\nhr0 : r ≠ 0\n⊢ ¬p ∣ r ↔ ↑(factorization (p * i + r)) p = 0",
"tactic": "refine' ⟨factorization_eq_zero_of_remainder i, fun h => _⟩"
},
{
"state_aft... | [
208,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_ofWithBot | [] | [
420,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_of_subseq_tendsto | [
{
"state_after": "ι✝ : Type ?u.372453\nι' : Type ?u.372456\nα✝ : Type ?u.372459\nβ : Type ?u.372462\nγ : Type ?u.372465\nα : Type u_1\nι : Type u_2\nx : ι → α\nf : Filter α\nl : Filter ι\ninst✝ : IsCountablyGenerated l\nhxy : ∀ (ns : ℕ → ι), Tendsto ns atTop l → ∃ ms, Tendsto (fun n => x (ns (ms n))) atTop f\nh... | [
1912,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1893,
1
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.copy_eq | [] | [
417,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_mul_right | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\nH : 0 < m\n⊢ n * m / (k * m) = n / k",
"tactic": "rw [Nat.mul_comm, Nat.mul_comm k, Nat.mul_div_mul_left _ _ H]"
}
] | [
642,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
641,
11
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_of_injective_forall_mem | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : Infinite α\ns : Set β\nf : α → β\nhi : Injective f\nhf : (range fun x => f x) ⊆ s\n⊢ Set.Infinite s",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : Infinite α\ns : Set β\nf : α → β\nhi : Injective f\nhf : ∀ ... | [
1381,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf g : R[X]\n⊢ f ∣ g - 0 ↔ f ∣ g",
"tactic": "rw [sub_zero]"
}
] | [
197,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_singleton | [] | [
629,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.eventually_hasFDerivAt | [] | [
300,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.toL1_eq_toL1_iff | [] | [
1376,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_symm_comp_coe | [] | [
2078,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2076,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_le_card_fintype | [] | [
212,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.comp_monotone_on_left | [] | [
188,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_pos_and_lt_one | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type ?u.228787\nn : ℕ\nx : α\ninst✝ : StrictOrderedRing α\nhx : x < 0\nhx' : 0 < x + 1\nhn : 1 < n\n⊢ 0 < ∑ i in range 2, x ^ i ∧ ∑ i in range 2, x ^ i < 1\n\ncase refine'_2\nα : Type u\nβ : Type ?u.228787\nn : ℕ\nx : α\ninst✝ : StrictOrderedRing α\nhx : x < 0\n... | [
470,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_lt_iff_lt_rpow | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ logb b x < y ↔ x < b ^ y",
"tactic": "rw [← rpow_lt_rpow_left_iff hb, rpow_logb (b_pos hb) (b_ne_one' hb) hx]"
}
] | [
168,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_toDual | [] | [
3257,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3257,
9
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_eq' | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_mk | [] | [
188,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Pullback.continuous_totalSpaceMk | [
{
"state_after": "B : Type u\nF : Type v\nE : B → Type w₁\nB' : Type w₂\nf✝ : B' → B\ninst✝⁵ : TopologicalSpace B'\ninst✝⁴ : TopologicalSpace (TotalSpace E)\ninst✝³ : TopologicalSpace F\ninst✝² : TopologicalSpace B\ninst✝¹ : (x : B) → TopologicalSpace (E x)\ninst✝ : FiberBundle F E\nf : B' → B\nx : B'\n⊢ instFo... | [
347,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | indicator_ae_eq_of_ae_eq_set | [] | [
4691,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4690,
1
] |
Std/Data/List/Lemmas.lean | List.isInfix.sublist | [] | [
1601,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1600,
11
] |
Mathlib/Algebra/Order/Group/Abs.lean | neg_le_of_abs_le | [] | [
244,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.top_rpow_of_neg | [
{
"state_after": "no goals",
"state_before": "y : ℝ\nh : y < 0\n⊢ ⊤ ^ y = 0",
"tactic": "simp [top_rpow_def, asymm h, ne_of_lt h]"
}
] | [
320,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ne_one_of_mem_unit_sphere | [] | [
720,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_point_open | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.61842\nE : Type u_1\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : TopologicalAddGroup E\ninst✝¹ : Module ℝ E\ninst✝ : ContinuousSMul ℝ E\ns t : Set E\nx y : E\nht₁ : Convex ℝ t\nht₂ : IsOpen t\ndisj : ¬x ∈ t\nf : E →L[ℝ] ℝ\nhf : ∀ ... | [
128,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.one_def | [] | [
673,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Data/Set/BoolIndicator.lean | Set.preimage_boolIndicator_true | [] | [
41,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Analysis/Normed/Order/UpperLower.lean | IsLowerSet.thickening' | [
{
"state_after": "α : Type u_1\nι : Type ?u.557\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsLowerSet s\nε : ℝ\n⊢ IsLowerSet (ball 1 ε * s)",
"state_before": "α : Type u_1\nι : Type ?u.557\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsLowerSet s\nε : ℝ\n⊢ IsLowerSet (thickening ε s)",
"tactic": "... | [
48,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
11
] |
Mathlib/Data/List/AList.lean | AList.lookup_union_right | [] | [
462,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mkHom_f_succ_succ | [
{
"state_after": "ι : Type ?u.203118\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nP Q : ChainComplex V ℕ\nzero : HomologicalComplex.X P 0 ⟶ HomologicalComplex.X Q 0\none : HomologicalComplex.X P 1 ⟶ HomologicalComplex.X Q 1\none_zero_comm : one ≫ HomologicalComplex.d Q 1 0 = HomologicalComplex.... | [
865,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.coe_ideal_le_self_mul_inv | [] | [
112,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.iff_symm_preimage_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.40463\nδ : Type ?u.40466\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set α\nt : Set β\nx : α\ny... | [
528,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | le_tsub_iff_left | [] | [
234,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Std/WF.lean | Acc.rec_eq_recC | [
{
"state_after": "case h.h.h.h.h.h\nα : Sort u_1\nr : α → α → Prop\nmotive : (a : α) → Acc r a → Sort u_2\nintro :\n (x : α) → (h : ∀ (y : α), r y x → Acc r y) → ((y : α) → (a : r y x) → motive y (_ : Acc r y)) → motive x (_ : Acc r x)\na : α\nt : Acc r a\n⊢ rec intro t = Acc.recC intro t",
"state_before":... | [
68,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
63,
18
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.orderOf_units_dvd_card_sub_one | [] | [
440,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.congr_reverse | [
{
"state_after": "case intro.step\nV : Type u\ninst✝ : Quiver V\nX✝¹ Y✝ X Y : Paths (Quiver.Symmetrify V)\nX✝ Z : Quiver.Symmetrify V\nf : X✝ ⟶ Z\nXW : X✝¹ ⟶ Paths.of.obj X✝\nWY : Paths.of.obj X✝ ⟶ Y✝\n⊢ Quotient.CompClosure redStep (Quiver.Path.reverse (XW ≫ 𝟙 (Paths.of.obj X✝) ≫ WY))\n (Quiver.Path.revers... | [
93,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.eq_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7392\ninst✝ : Preorder α\na b : α\nh✝ : Compares lt a b\nh : lt = eq\n⊢ a = b",
"tactic": "injection h"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7392\ninst✝ : Preorder α\na b : α\nh✝ : C... | [
100,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Logic/Pairwise.lean | Set.Pairwise.imp | [] | [
73,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.isCycleOn | [] | [
813,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
11
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.revzip_powersetAux_perm_aux' | [
{
"state_after": "α : Type u_1\nl : List α\nthis : DecidableEq α\n⊢ revzip (powersetAux l) ~ revzip (powersetAux' l)",
"state_before": "α : Type u_1\nl : List α\n⊢ revzip (powersetAux l) ~ revzip (powersetAux' l)",
"tactic": "haveI := Classical.decEq α"
},
{
"state_after": "α : Type u_1\nl : Lis... | [
161,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_eq_closure_mul_set | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.247712\nG : Type ?u.247715\nM✝ : Type ?u.247718\nR : Type u_1\nA : Type ?u.247724\ninst✝² : Monoid M✝\ninst✝¹ : AddMonoid A\ninst✝ : NonUnitalNonAssocSemiring R\nM N : AddSubmonoid R\n⊢ M * N = closure (↑M * ↑N)",
"tactic": "rw [← closure_mul_clo... | [
570,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Data/Fin/SuccPred.lean | Fin.pred_apply | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_right_cancel' | [] | [
177,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | Algebra.lmul_algebraMap | [] | [
50,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_midpoint_left | [] | [
832,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.Γ_map | [] | [
289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.map_of_continuousAt | [] | [
374,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_apply_left | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a < a + p ∧ ∃ z, a = a + p + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ ... | [
213,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/CategoryTheory/Preadditive/InjectiveResolution.lean | CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d | [] | [
107,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.lt_singleton_iff_mem_lt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nr : α\ns : Finset α\n⊢ (∀ {x : α}, r < x → (x ∈ s ↔ x = r)) ∧ ¬r ∈ s ↔ ∀ (x : α), x ∈ s → x < r",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nr : α\ns : Finset α\n⊢ toColex s < toColex {r} ↔ ∀ (x : α), x ∈ s → x < r",
"tactic": "simp only ... | [
287,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/MeasureTheory/Group/GeometryOfNumbers.lean | MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure | [
{
"state_after": "E : Type u_1\nL✝ : Type ?u.6123\ninst✝⁶ : MeasurableSpace E\nμ : Measure E\nF s : Set E\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsAddHaarMeasure μ\nL : AddSubgroup E\ninst✝ : Countable { x // x ∈ L }\nfund : IsAd... | [
86,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.tendsto_smallSets_iff | [] | [
61,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.nextn_stop | [
{
"state_after": "no goals",
"state_before": "x✝ : Substring\nh✝ : Valid x✝\nn : Nat\nl m r : List Char\nh : ValidFor l m r x✝\n⊢ nextn x✝ n { byteIdx := Substring.bsize x✝ } = { byteIdx := Substring.bsize x✝ }",
"tactic": "simp [h.bsize, h.nextn_stop]"
}
] | [
1002,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1001,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_mul_sub_add_iff | [] | [
441,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_empty_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.21155\nι : Type ?u.21158\nκ : Type ?u.21161\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ns : Finset α\n⊢ edgeDens... | [
159,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atBot_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.232588\nι' : Type ?u.232591\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.232600\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x => f x * r) l atBot ↔ Tendsto f l atTop",
"tactic": "simpa only [mul_comm] usi... | [
1114,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
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