file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bddAbove_iff_small | [] | [
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82
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Mathlib/GroupTheory/GroupAction/Defs.lean | IsScalarTower.of_smul_one_mul | [
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662,
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Mathlib/Algebra/Parity.lean | even_neg_two | [
{
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}
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420,
74
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Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.le_def | [] | [
222,
10
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220,
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Mathlib/Order/LocallyFinite.lean | Set.finite_Iic | [] | [
701,
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700,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.eq_mul_inverse_iff_mul_eq | [
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"tactic": "rw [h1, inverse_mul_cancel_... | [
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.derivWithin_integral_of_tendsto_ae_left | [] | [
968,
76
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963,
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Mathlib/Data/Set/Prod.lean | Set.univ_pi_update_univ | [
{
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"tactic": "rw [univ_pi_update i (fun j => (u... | [
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Mathlib/GroupTheory/Sylow.lean | Sylow.card_eq_multiplicity | [
{
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696,
35
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Mathlib/RingTheory/Congruence.lean | RingCon.coe_nat_cast | [] | [
312,
6
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311,
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_unit_right | [
{
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"tactic": "simp only [cancel_mono]"
}
] | [
387,
80
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.disjoint_supported_supported | [
{
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315,
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Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsSimpleGroup.prime_card | [
{
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539,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.isPell_one | [
{
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}
] | [
227,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_Ioi_iff_Ici | [
{
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329,
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327,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.apply_one | [] | [
637,
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636,
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Mathlib/Data/Rat/Lemmas.lean | Rat.exists | [
{
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},
{
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314,
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Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_iInf | [] | [
1043,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_im | [] | [
83,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Order/Concept.lean | Concept.sInf_snd | [] | [
369,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isAlt_iff_eq_neg_flip | [
{
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305,
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Mathlib/Data/Rel.lean | Rel.mem_image | [] | [
135,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/Topology/MetricSpace/Basic.lean | dist_nndist | [] | [
309,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsCompact.exists_infEdist_eq_edist | [
{
"state_after": "ι : Sort ?u.27190\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx✝ y : α\ns t : Set α\nΦ : α → β\nhs : IsCompact s\nhne : Set.Nonempty s\nx : α\nA : Continuous fun y => edist x y\n⊢ ∃ y, y ∈ s ∧ infEdist x s = edist x y",
"state_before": "ι : Sort ?u... | [
237,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/Data/Rat/Cast.lean | Rat.commute_cast | [] | [
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26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.leftAdjointMate_comp | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Parity.lean | Nat.even_add_one | [
{
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"state_before": "m n : ℕ\n⊢ Even (n + 1) ↔ ¬Even n",
"tactic": "simp [even_add]"
}
] | [
125,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Gauge.lean | gauge_empty | [
{
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"state_before": "𝕜 : Type ?u.33039\nE : Type u_1\nF : Type ?u.33045\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : S... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_zero_iff_ae_nmem | [] | [
394,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.discr_smul | [
{
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"state_before": "S : Type ?u.614314\nR : Type ?u.614317\nR₁ : Type u_1\nM : Type ?u.614323\nn : Type w\ninst✝⁵ : Fintype n\ninst✝⁴ : CommRing R₁\ninst✝³ : DecidableEq n\ninst✝² : Invertible 2\nm : Type w\ninst✝¹ : DecidableEq m\ninst✝ : Fintype m\nQ : QuadraticForm R₁ (n → R₁)\n... | [
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalk_open_algebraMap | [] | [
649,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.localization_away_comap_range | [
{
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"state_before": "R : Type u\nS✝ : Type v\ninst✝⁴ : CommRin... | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
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Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_ofSubring | [] | [
537,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofMkLEMk_refl | [
{
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461,
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459,
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Mathlib/Topology/LocalExtr.lean | isLocalMaxOn_const | [] | [
195,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_le_self | [
{
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"state_before": "b x : Ordinal\nhx : x = 0\n⊢ log b x ≤ x",
"tactic": "simp only [hx, log_zero_right, Ordinal.zero_le]"
},
{
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"state_before": "b x : Ordinal\nhx : ¬x = 0\nhb : ¬1 < b\n⊢ log b x ≤ x",
"tactic": "simp only [log_of_not_... | [
371,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparator_prod_of_isCoseparator_right | [
{
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"tactic": "simp"
}
] | [
609,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.ofExact_map | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_subtype_range | [] | [
267,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensor_left_iff | [
{
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"tactic": "simp"
}
] | [
271,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.of_add_of | [] | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
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Mathlib/Order/GameAdd.lean | Prod.GameAdd.induction | [] | [
143,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.exists_set_sigmaFinite | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.549973\nι : Type ?u.549976\ninst✝³ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace β\nf g✝ : α → β\ninst✝¹ : Zero β\ninst✝ : T2Space β\ng : α → β\nhg : FinStronglyMeasurable g μ\nhfg : f =ᶠ[ae μ] g\n⊢ ∃ t,... | [
1932,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1925,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.star_self_mem_adjoin_singleton | [] | [
456,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
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Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.uncurry_natural_left | [] | [
200,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.rpow_add_rpow_le | [
{
"state_after": "ι : Type u\ns : Finset ι\np q : ℝ\na b : ℝ≥0\nhp_pos : 0 < p\nhpq : p ≤ q\nh_rpow : ∀ (a : ℝ≥0), a ^ q = (a ^ p) ^ (q / p)\n⊢ (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p)",
"state_before": "ι : Type u\ns : Finset ι\np q : ℝ\na b : ℝ≥0\nhp_pos : 0 < p\nhpq : p ≤ q\n⊢ (a ^ q + b ^ q... | [
218,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_eq' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.86870\nα : Type u_1\nβ : Type ?u.86876\nπ : ι → Type ?u.86881\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ∆ b = (a ⊔ b) ⊓ (aᶜ ⊔ bᶜ)",
"tactic": "rw [symmDiff_eq_sup_sdiff_inf, sdiff_eq, compl_inf]"
}
] | [
721,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDerivWithin_univ | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.3042\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝ x : 𝕜\n⊢ iteratedDerivWithin n f univ x = iteratedDe... | [
76,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_le_one_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.52121\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ (∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a = b) ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b",
"state_before": "α : Type u_1\nβ : Type ?u.52121\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ card s ≤ 1 ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b",
... | [
541,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_le_zero | [] | [
1284,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sub_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sin (x - π / 2) = -cos x",
"tactic": "simp [sub_eq_add_neg, sin_add]"
}
] | [
448,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.on_subset | [] | [
117,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_pos_of_le_one | [
{
"state_after": "case h₁.h\nx : ℝ\nhx : abs' x ≤ 1\n⊢ abs' x ^ 4 ≤ 1\n\ncase h₂.h\nx : ℝ\nhx : abs' x ≤ 1\n⊢ x ^ 2 ≤ 1",
"state_before": "x : ℝ\nhx : abs' x ≤ 1\n⊢ abs' x ^ 4 * (5 / 96) + x ^ 2 / 2 ≤ 1 * (5 / 96) + 1 / 2",
"tactic": "gcongr"
},
{
"state_after": "no goals",
"state_before": "... | [
1878,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1867,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.eq_div_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.310360\nβ : Type ?u.310363\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nha' : a ≠ ⊤\nh : b = c / a\n⊢ a * b = c",
"tactic": "rw [h, ENNReal.mul_div_cancel' ha ha']"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.310360\nβ :... | [
1704,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_mk' | [] | [
428,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Set/Basic.lean | Disjoint.inter_right' | [] | [
2973,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2972,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.nonempty | [] | [
133,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_lt_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ -x < 0 ↔ 0 < x",
"tactic": "rw [neg_lt_iff, neg_zero]"
}
] | [
1388,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Reachable.map | [] | [
1905,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1903,
11
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_product_left | [] | [
432,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.map_mk | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.Lp_toLp_restrict_smul | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.322244\nE : Type ?u.322247\nF : Type u_2\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝² : NormedField 𝕜\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : ℝ≥0∞\nμ : Measure α\nc : 𝕜\nf : { x // x ∈ Lp F p }\ns : ... | [
896,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.one_le_dist_inl_inr | [] | [
223,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Limit.lift_π_apply' | [] | [
215,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/List/Prime.lean | mem_list_primes_of_dvd_prod | [
{
"state_after": "case intro.intro\nM : Type u_1\ninst✝¹ : CancelCommMonoidWithZero M\ninst✝ : Unique Mˣ\np : M\nhp : Prime p\nL : List M\nhL : ∀ (q : M), q ∈ L → Prime q\nhpL : p ∣ prod L\nx : M\nhx1 : x ∈ L\nhx2 : p ∣ x\n⊢ p ∈ L",
"state_before": "M : Type u_1\ninst✝¹ : CancelCommMonoidWithZero M\ninst✝ :... | [
58,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_ne_zero_of_pos_of_ne_one_of_base_lt_one | [] | [
339,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.one_mul | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n✝ : σ →₀ ℕ\nφ ψ : MvPowerSeries σ R\nn : σ →₀ ℕ\n⊢ ↑(coeff R n) (1 * φ) = ↑(coeff R n) φ",
"tactic": "simpa using coeff_add_monomial_mul 0 n φ 1"
}
] | [
270,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.preimage_iterate_ae_eq | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.411803\nγ : Type ?u.411806\nδ : Type ?u.411809\nι : Type ?u.411812\nR : Type ?u.411815\nR' : Type ?u.411818\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\nμa μa' : Measure ... | [
2529,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2525,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | edist_div_right | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝⁶ : PseudoEMetricSpace X\ninst✝⁵ : Group G\ninst✝⁴ : MulAction G X\ninst✝³ : IsometricSMul G X\ninst✝² : DivInvMonoid M\ninst✝¹ : PseudoEMetricSpace M\ninst✝ : IsometricSMul Mᵐᵒᵖ M\na b c : M\n⊢ edist (a / c) (b / c) = ed... | [
124,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualAnnihilator_inf_eq | [
{
"state_after": "K : Type u\ninst✝⁴ : Field K\nV₁ : Type v'\nV₂ : Type v''\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nW W' : Subspace K V₁\n⊢ dualAnnihilator (W ⊓ W') ≤ dualAnnihilator W ⊔ dualAnnihilator W'",
"state_before": "K : Type u\ninst✝⁴ : Field ... | [
1430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Order/Bounds/OrderIso.lean | OrderIso.isLUB_image' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α ≃o β\ns : Set α\nx : α\n⊢ IsLUB (↑f '' s) (↑f x) ↔ IsLUB s x",
"tactic": "rw [isLUB_image, f.symm_apply_apply]"
}
] | [
42,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
src/lean/Init/Data/Nat/Log2.lean | Nat.log2_le_self | [
{
"state_after": "n : Nat\n⊢ (if n ≥ 2 then log2 (n / 2) + 1 else 0) ≤ n",
"state_before": "n : Nat\n⊢ log2 n ≤ n",
"tactic": "unfold Nat.log2"
},
{
"state_after": "case inl\nn : Nat\nh✝ : n ≥ 2\n⊢ log2 (n / 2) + 1 ≤ n\n\ncase inr\nn : Nat\nh✝ : ¬n ≥ 2\n⊢ 0 ≤ n",
"state_before": "n : Nat\n⊢ ... | [
37,
46
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
31,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_erase | [
{
"state_after": "case ofFinsupp\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn i : ℕ\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ coeff (erase n { toFinsupp := toFinsupp✝ }) i = if i = n then 0 else coeff { toFinsupp := toFinsupp✝ } i",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Se... | [
1052,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_add_aleph0 | [] | [
132,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_ge_n | [] | [
429,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.nfp_le_of_principal | [] | [
89,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | comp_comp_symm_mem_uniformity_sets | [
{
"state_after": "case intro.intro.intro\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.53210\ninst✝ : UniformSpace α\ns : Set (α × α)\nhs : s ∈ 𝓤 α\nw : Set (α × α)\nw_in : w ∈ 𝓤 α\nleft✝ : SymmetricRel w\nw_sub : w ○ w ⊆ s\n⊢ ∃ t, t ∈ 𝓤 α ∧ SymmetricRel t ∧ t ○ t ○ t ⊆ s",
"state_befo... | [
604,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | MulAction.injective₀ | [] | [
229,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.valid'_nil | [] | [
1060,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1059,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.exists | [] | [
1300,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_sum_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type u_1\ns : Finset ι\nf : ι → R[X]\n⊢ degree (∑ i in ∅, f i) ≤ sup ∅ fun b => degree (f b)",
"tactic": "simp only [sum_empty, sup_empty, degree_zero, le_refl]"
},
{
"... | [
762,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bodd_bit0 | [] | [
47,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_sup_hom | [] | [
1322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_inf_ne_zero | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\nhK : relindex K L ≠ 0\nhH : relindex H (K ⊓ L) ≠ 0\n⊢ relindex (H ⊓ K) L ≠ 0",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\nhH : relindex H L ≠ 0\nhK : relindex K L ≠ 0\n⊢ relindex (H ⊓ K) L ≠ 0",
"tactic": "repl... | [
425,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.eqOnSource_refl | [] | [
829,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | RingHom.map_multiset_sum | [] | [
259,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
11
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_single_neg | [
{
"state_after": "no goals",
"state_before": "ι : 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\np : ι → Prop\ninst✝ : DecidablePred p\ni : ι\nx : β i\nh : ¬p i\n⊢ filter p (single i x) ... | [
716,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableOn.snd | [] | [
312,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
11
] |
Mathlib/Algebra/Support.lean | Function.support_one | [] | [
310,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_mul_single | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.365398\ninst✝¹ : Semiring k\ninst✝ : Mul G\na₁ a₂ : G\nb₁ b₂ : k\n⊢ (sum (single a₂ b₂) fun a₂ b₂ => single (a₁ * a₂) (0 * b₂)) = 0",
"tactic": "simp only [zero_mul, single_zero, sum_zero]"
},
{
"state_after": "n... | [
461,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tendsto_cos_neg_pi_div_two | [
{
"state_after": "case h1\n\n⊢ Tendsto cos (𝓝[Ioi (-(π / 2))] (-(π / 2))) (𝓝 0)\n\ncase h2\n\n⊢ ∀ᶠ (x : ℝ) in 𝓝[Ioi (-(π / 2))] (-(π / 2)), cos x ∈ Ioi 0",
"state_before": "⊢ Tendsto cos (𝓝[Ioi (-(π / 2))] (-(π / 2))) (𝓝[Ioi 0] 0)",
"tactic": "apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_... | [
1087,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.smul_apply | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\n𝓟 : Ideal R\nf : R[X]\nhf✝ : IsWeaklyEisensteinAt f 𝓟\nS : Type v\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\np : R\nx : S\nhx :\n x ^ natDegree (Polynomial.map (algebraMap R S) f) +\n ∑ i : Fin (natDegree (Polynomial.map (algebraMap R S) f)), coeff (Pol... | [
112,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_eq_nat_cast_iff' | [] | [
471,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_principal | [] | [
1232,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toMul_sub | [] | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_monotone | [] | [
350,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | AntitoneOn.inv | [] | [
1305,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_def | [
{
"state_after": "no goals",
"state_before": "b : Ordinal\nh : 1 < b\nx : Ordinal\n⊢ log b x = pred (sInf {o | x < b ^ o})",
"tactic": "simp only [log, dif_pos h]"
}
] | [
267,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_erase_lt_of_mem | [] | [
146,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
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