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/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.top_rpow_def | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictFDerivAt_exp_smul_const | [] | [
398,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_option_succ | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | ediam_smul_le | [] | [
37,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_add | [
{
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"state_before": "ι : Type u\nγ : Type ... | [
436,
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433,
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Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousWithinAt_left_of_monotoneOn_of_image_mem_nhdsWithin | [] | [
183,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.nonneg_add_neg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.477720\nγ : Type ?u.477723\nδ : Type ?u.477726\ninst✝² : AddCommGroup α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalAddGroup α\nf✝ g : β → α\na a₁ a₂ b : α\nf : ℤ → α\nhnonneg : HasSum (fun n => f ↑n) a\nhneg : HasSum (fun n => f (Int.negSucc n)) b\n⊢ HasSum f (a... | [
1020,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.coe_nnreal_ennreal | [] | [
1793,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1791,
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Mathlib/Order/Bounds/Basic.lean | NoMinOrder.lowerBounds_univ | [] | [
846,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.dist_map | [] | [
274,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_eq_zero_and_zero_of_ae_le_mul_neg | [
{
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1307,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
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Mathlib/ModelTheory/Definability.lean | Set.Definable.mono | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
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Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.OuterRegular.smul | [
{
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301,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
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Mathlib/Order/Filter/Basic.lean | Filter.map_neBot_iff | [
{
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"tactic": "simp only [neBot_iff, Ne, map_eq_bot_i... | [
2453,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2452,
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Mathlib/Algebra/BigOperators/Basic.lean | map_prod | [
{
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209,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
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Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt | [
{
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538,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
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Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | Even.convexOn_pow | [
{
"state_after": "n : ℕ\nhn : Even n\n⊢ ∀ ⦃x : ℝ⦄,\n x ∈ univ →\n ∀ ⦃y : ℝ⦄,\n y ∈ univ →\n ∀ ⦃a b : ℝ⦄,\n 0 ≤ a →\n 0 ≤ b → a + b = 1 → (fun x => x ^ n) (a • x + b • y) ≤ a • (fun x => x ^ n) x + b • (fun x => x ^ n) y",
"state_before": "n : ℕ\nhn : Even n\n⊢... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Analysis/Normed/Field/InfiniteSum.lean | Summable.mul_of_nonneg | [
{
"state_after": "no goals",
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"tactic": "simpa only [hg.tsum_mul_left _] us... | [
37,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Term.relabel_id | [
{
"state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.5062\nP : Type ?u.5065\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.5093\n_a✝ : α\n⊢ relabel id (var _a✝) = var _a✝\n\ncase func\nL : Language\nL' : Language\nM : Typ... | [
116,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.supp_injective | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2138,
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Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_apply_lt' | [] | [
81,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_sum | [
{
"state_after": "α : Type u_1\nβ : Type ?u.203569\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nf : α → ℝ≥0∞\nhf : ∀ (a : α), a ∈ s → f a ≠ ⊤\n⊢ ∑ a in s, ↑(ENNReal.toNNReal (f a)) = ∑ a in s, ENNReal.toReal (f a)",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Iic | [] | [
164,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_diff_Iio_same | [
{
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"tactic": "rw [← Iic_diff_right, diff_diff_cancel_left (singleton_subset_iff.2 right_mem_Iic)]"
}
] | [
842,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.apply_zero | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\n⊢ Quotient.mk (setoid Q) (Over.mk ((Over.mk 0).hom ≫ f)) = 0",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\n⊢ pseudoApply f 0 = 0",
"tactic": "rw [pseudoZero_def, pseudoA... | [
272,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousLinearMap.uncurryLeft_apply | [] | [
1338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.emetric_ball_nnreal | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.164621\nι : Type ?u.164624\ninst✝ : PseudoMetricSpace α\nx : α\nε : ℝ≥0\n⊢ EMetric.ball x ↑ε = EMetric.ball x (ENNReal.ofReal ↑ε)",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.164621\nι : Type ?u.164624\ninst✝ : PseudoMetricSpace α\nx : α\nε : ℝ... | [
1207,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
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Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedHull.balanced | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.26762\ninst✝² : SeminormedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns✝ s : Set E\na : 𝕜\nha : ‖a‖ ≤ 1\n⊢ a • balancedHull 𝕜 s ⊆ balancedHull 𝕜 s",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.26762\ninst✝² : SeminormedRi... | [
154,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_univ | [
{
"state_after": "no goals",
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403,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
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Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.row_ne_zero | [
{
"state_after": "no goals",
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"tactic": "simp [h]"
}
] | [
170,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/Separation.lean | limUnder_nhdsWithin_id | [] | [
1091,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_max | [] | [
170,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image2_iUnion_left | [
{
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1876,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1874,
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Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_div_cancel' | [] | [
194,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_pos_iff | [] | [
174,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.diam_preimage | [
{
"state_after": "no goals",
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"tactic": "rw [← image_symm, diam_image]"
}
] | [
602,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.equivRealProd_symm_apply | [
{
"state_after": "no goals",
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"tactic": "ext <;> simp [Complex.equivRealProd, ofReal']"
}
] | [
356,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd | [] | [
2172,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2170,
1
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Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.tsnd_eq_snd_id | [
{
"state_after": "no goals",
"state_before": "t : Type u → Type u → Type u\ninst✝⁵ : Bitraversable t\nβ✝ : Type u\nF G : Type u → Type u\ninst✝⁴ : Applicative F\ninst✝³ : Applicative G\ninst✝² : IsLawfulBitraversable t\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα β β' : Type u\nf : β → β'\n... | [
124,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_refl' | [] | [
1937,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1936,
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] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.IsCycle.existsUnique_cycle_subtype | [
{
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485,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_strict_mono_of_ae_le_of_frequently_ae_lt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.984332\nγ : Type ?u.984335\nδ : Type ?u.984338\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhg : AEMeasurable g\nhfi : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\nh_le : f ≤ᵐ[μ] g\nh : (∫⁻ (x : α), g x ∂μ) ≤ ∫⁻ (x : α), f x ∂μ\n⊢ ¬∃ᵐ (x : α) ∂μ, f x ≠ g x",
"state_befor... | [
942,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_prod_of_nonneg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.837756\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nf : α → ℝ\nhf : ∀ (i : α), i ∈ s → 0 ≤ f i\n⊢ Real.toNNReal (∏ i in s, f i) = ∏ a in s, Real.toNNReal (f a)",
"state_before": "α : Type u_1\nβ : Type ?u.837756\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nf : α → ℝ... | [
2332,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2329,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left | [] | [
898,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Std/Data/Int/Lemmas.lean | Int.max_eq_right | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : a ≤ b\n⊢ max a b = b",
"tactic": "simp [Int.max_def, h, Int.not_lt.2 h]"
}
] | [
723,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
722,
11
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.mulEquiv_apply | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_inv | [
{
"state_after": "case inl\np q✝ q : ℚ\nhq : q ≤ 0\n⊢ toNNRat q⁻¹ = (toNNRat q)⁻¹\n\ncase inr\np q✝ q : ℚ\nhq : 0 ≤ q\n⊢ toNNRat q⁻¹ = (toNNRat q)⁻¹",
"state_before": "p q✝ q : ℚ\n⊢ toNNRat q⁻¹ = (toNNRat q)⁻¹",
"tactic": "obtain hq | hq := le_total q 0"
},
{
"state_after": "no goals",
"stat... | [
422,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.and_eq_true_eq_eq_true_and_eq_true | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ ((a && b) = true) = (a = true ∧ b = true)",
"tactic": "simp"
}
] | [
87,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_range_const | [] | [
1026,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.comp_add | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y Z : C\nf : X ⟶ Y\ng h : Y ⟶ Z\n⊢ f ≫ (g + h) = f ≫ g + f ≫ h",
"tactic": "rw [add_def, comp_sub, neg_def, comp_sub, comp_zero, add_def, neg_def]"
}
] | [
440,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.im_sq_le_normSq | [] | [
521,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/CategoryTheory/EssentialImage.lean | CategoryTheory.Functor.essImage_eq_of_natIso | [] | [
74,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Std/Data/Range/Lemmas.lean | Std.Range.numElems_le_iff | [
{
"state_after": "no goals",
"state_before": "start stop step i : Nat\nhstep : 0 < step\n⊢ (stop - start + step - 1) / step ≤ i ↔ stop - start + step - 1 < step * i + step",
"tactic": "rw [← Nat.lt_succ (n := i), Nat.div_lt_iff_lt_mul hstep, Nat.mul_comm, ← Nat.mul_succ]"
},
{
"state_after": "no... | [
32,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
23,
9
] |
Mathlib/Algebra/Group/Units.lean | divp_assoc' | [] | [
458,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_map_snd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3282\ns : Multiset α\nl : List α\n⊢ map Prod.snd (antidiagonal (Quotient.mk (isSetoid α) l)) = powerset (Quotient.mk (isSetoid α) l)",
"tactic": "simp [powersetAux']"
}
] | [
68,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_le_iff | [] | [
581,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.units_inv_right | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : Monoid M\na : M\nx y : Mˣ\nh : SemiconjBy a ↑x ↑y\n⊢ a * ↑x⁻¹ = ↑y⁻¹ * (↑y * a) * ↑x⁻¹",
"tactic": "rw [Units.inv_mul_cancel_left]"
},
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : Monoid M\na : M\nx y ... | [
125,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_apply | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.succ_pos | [] | [
1085,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/Algebra/DirectLimit.lean | Field.DirectLimit.exists_inv | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁴ : Ring R\nι : Type v\ndec_ι : DecidableEq ι\ninst✝³ : Preorder ι\nG : ι → Type w\ninst✝² : Nonempty ι\ninst✝¹ : IsDirected ι fun x x_1 => x ≤ x_1\ninst✝ : (i : ι) → Field (G i)\nf : (i j : ι) → i ≤ j → G i → G j\nf' : (i j : ι) → i ≤ j → G i →... | [
719,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.shiftr_to_nat | [
{
"state_after": "case zero\nα : Type ?u.624959\nn : ℕ\n⊢ ↑0 = Nat.shiftr (↑zero) n\n\ncase pos\nα : Type ?u.624959\nn : ℕ\nm : PosNum\n⊢ ↑(PosNum.shiftr m n) = Nat.shiftr (↑(pos m)) n",
"state_before": "α : Type ?u.624959\nm : Num\nn : ℕ\n⊢ ↑(shiftr m n) = Nat.shiftr (↑m) n",
"tactic": "cases' m with m... | [
995,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.sub_one_covby | [
{
"state_after": "no goals",
"state_before": "z : ℤ\n⊢ z - 1 ⋖ z",
"tactic": "rw [Int.covby_iff_succ_eq, sub_add_cancel]"
}
] | [
84,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | AlgHom.restrictScalars_injective | [] | [
207,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_eq_sub_single | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ✝ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β✝ i)\ns : Finset ι\nx : (i : ↑↑s) → β✝ ↑i\ni✝ : ι\nβ : ι → Type u_1\ninst✝ : (i : ι) → AddGroup (β i)\nf : Π₀ (i : ι), β i\ni j : ι\n⊢ ↑(erase i f) j = ↑(f - sing... | [
772,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_eq_cycle_map | [] | [
497,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.mem_antidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nx : ℕ × ℕ\n⊢ x ∈ antidiagonal n ↔ x.fst + x.snd = n",
"tactic": "rw [antidiagonal, mem_coe, List.Nat.mem_antidiagonal]"
}
] | [
40,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Computability/Ackermann.lean | lt_ack_left | [] | [
196,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Analysis/Analytic/RadiusLiminf.lean | FormalMultilinearSeries.radius_eq_liminf | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nthis : ∀ (r : ℝ≥0) {n : ℕ}, 0 < n → (↑r ≤ 1 / ↑(‖p n‖₊ ^ (1 / ↑... | [
67,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_zpow | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.lift_binop_eq | [
{
"state_after": "f : ℚ → ℚ → ℚ\nf₁ f₂ : ℤ → ℤ → ℤ → ℤ → ℤ\nfv :\n ∀ {n₁ : ℤ} {d₁ : ℕ} {h₁ : d₁ ≠ 0} {c₁ : Nat.coprime (Int.natAbs n₁) d₁} {n₂ : ℤ} {d₂ : ℕ} {h₂ : d₂ ≠ 0}\n {c₂ : Nat.coprime (Int.natAbs n₂) d₂}, f (mk' n₁ d₁) (mk' n₂ d₂) = f₁ n₁ (↑d₁) n₂ ↑d₂ /. f₂ n₁ (↑d₁) n₂ ↑d₂\nf0 : ∀ {n₁ d₁ n₂ d₂ : ℤ}, ... | [
151,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.differentiable | [] | [
50,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_iUnionLift | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.92448\nδ : Type ?u.92451\nδ' : Type ?u.92454\nι : Sort uι\ns✝ t✝ u : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nmγ : MeasurableSpace γ\ninst✝ : Countable ι\nt : ι → Set α\nf : (i : ι) → ↑(t i) → β\nhtf :\n ∀ (i j : ι) (x : α) (hxi : x ∈ t i) ... | [
779,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.changeOriginSeries_summable_aux₂ | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.1515814\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np ... | [
1225,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/Algebra/Group/Defs.lean | inv_mul_cancel_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ b✝ c a b : G\n⊢ a⁻¹ * (a * b) = b",
"tactic": "rw [← mul_assoc, mul_left_inv, one_mul]"
}
] | [
1107,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Matrix.det_conj_of_mul_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.33943\ninst✝¹¹ : CommRing R\nM✝ : Type ?u.33949\ninst✝¹⁰ : AddCommGroup M✝\ninst✝⁹ : Module R M✝\nM'✝ : Type ?u.34534\ninst✝⁸ : AddCommGroup M'✝\ninst✝⁷ : Module R M'✝\nι : Type ?u.35076\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ne : Basis ι R M✝\n... | [
104,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_trans_apply | [] | [
2048,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2046,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiable_id | [] | [
1021,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.map_constants | [] | [
797,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | StronglyMeasurable.apply_continuousLinearMap | [] | [
1789,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1786,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_iff_count_le_one | [] | [
185,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | compact_covered_by_mul_left_translates | [
{
"state_after": "no goals",
"state_before": "case intro\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : TopologicalGroup G\nK V : Set G\nhK : IsCompact K\nhV : Set.Nonempty (interior V)\nt : Finset G\nht : K ⊆ ⋃ (x : G) (h : x ∈ t), interior ((fun x_1... | [
1594,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_sdiff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.93853\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt✝ : Finset β\na : α\nb c : β\ninst✝ : DecidableEq α\nf : α → β\ns t : Finset α\nhf : Injective f\n⊢ f '' (↑s \\ ↑t) = f '' ↑s \\ f '' ↑t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : T... | [
535,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.apply_mono | [] | [
324,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_injective | [] | [
171,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.id_apply | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.nonempty_inv | [] | [
247,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.toMeasure_injective | [] | [
149,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_congr_ae | [] | [
376,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Topology/Algebra/Field.lean | Subfield.isClosed_topologicalClosure | [] | [
71,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_traverse | [] | [
2795,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2791,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.toList_ne_nil | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\n⊢ 0 < s.length + 1",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\n⊢ toList s ≠ []",
"tactic": "rw [← List.length_pos_iff_ne_nil, length_to... | [
224,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Prod/TProd.lean | Set.mk_preimage_tprod | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nα : ι → Type v\ni j : ι\nl : List ι\nf : (i : ι) → α i\nt : (i : ι) → Set (α i)\n⊢ TProd.mk [] ⁻¹' Set.tprod [] t = pi {i | i ∈ []} t",
"tactic": "simp [Set.tprod]"
},
{
"state_after": "case h\nι : Type u\nα : ι → Type v\ni✝ j : ι\nl✝ : L... | [
173,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.summable_mul_of_Lp_Lq_of_nonneg | [] | [
622,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_comp_inv | [] | [
273,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_normalizer_iff'' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.379936\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.379945\ninst✝ : AddGroup A\nH K : Subgroup G\ng : G\n⊢ g ∈ normalizer H ↔ ∀ (h : G), h ∈ H ↔ g⁻¹ * h * g ∈ H",
"tactic": "rw [← inv_mem_iff (x := g), mem_normalizer_iff, inv_... | [
2160,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2159,
1
] |
Mathlib/Algebra/GeomSum.lean | zero_geom_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Semiring α\n⊢ ∑ i in range 0, 0 ^ i = if 0 = 0 then 0 else 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Semiring α\n⊢ ∑ i in range 1, 0 ^ i = if 1 = 0 then 0 else 1",
"tactic": ... | [
76,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.le_div_iff | [] | [
531,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
11
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_sSup | [] | [
693,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Order/CompleteLatticeIntervals.lean | subset_sInf_def | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.tendstoUniformlyOn | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.949202\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → F\np pf pg ... | [
824,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
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