file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange_smul | [
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.add_divMonomial | [] | [
76,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousCore.gc | [] | [
494,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_union_sdiff_cancel | [] | [
2295,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2294,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.repr_apply_apply | [
{
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400,
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396,
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Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Valuation.by_cases | [] | [
137,
25
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133,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.le_multiplicity_iff_replicate_le_normalizedFactors | [
{
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972,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
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Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_sSup_image_eq | [] | [
228,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_mono | [] | [
380,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.isRadical | [] | [
912,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
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Std/Data/Int/Lemmas.lean | Int.lt.dest | [
{
"state_after": "no goals",
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"tactic": "rwa [Int.add_comm, Int.add_left_comm] at h"
}
] | [
597,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
596,
1
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Mathlib/Algebra/Group/Basic.lean | mul_right_surjective | [] | [
623,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
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Mathlib/Order/Filter/ModEq.lean | Nat.frequently_odd | [
{
"state_after": "no goals",
"state_before": "⊢ ∃ᶠ (m : ℕ) in atTop, Odd m",
"tactic": "simpa only [odd_iff] using frequently_mod_eq one_lt_two"
}
] | [
40,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
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Mathlib/Analysis/Analytic/Basic.lean | hasFPowerSeriesAt_const | [] | [
526,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.self_subset_thickening | [] | [
1161,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
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src/lean/Init/Control/Lawful.lean | StateT.seqLeft_eq | [
{
"state_after": "case h\nm : Type u_1 → Type u_2\nσ α β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : StateT σ m α\ny : StateT σ m β\n⊢ ∀ (s : σ), run (SeqLeft.seqLeft x fun x => y) s = run (Seq.seq (const β <$> x) fun x => y) s",
"state_before": "m : Type u_1 → Type u_2\nσ α β : Type u_1\ninst✝... | [
296,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
294,
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Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_ofRestrict | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nU : TopCat\nX : PresheafedSpace C\nf : U ⟶ ↑X\nh : OpenEmbedding ((CategoryTheory.forget TopCat).map f)\nx : ↑U\nV : (OpenNhds ((CategoryTheory.forget TopCat).map f x))ᵒᵖ\n⊢ colimit.ι\n (((whiskeringLeft (OpenNhds ((CategoryTheory.... | [
116,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.toLp_norm_eq_toLp_norm_coe | [] | [
1767,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1764,
1
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Mathlib/Analysis/Convex/Topology.lean | Convex.combo_self_interior_subset_interior | [
{
"state_after": "ι : Type ?u.70178\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\na b : 𝕜\nha : 0 ≤ a\nhb : 0 < b\nhab : a +... | [
153,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasDerivWithinAt_lineMap | [] | [
71,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_lt_prod_of_ne_nil | [] | [
332,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_eq_one_iff | [] | [
361,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.neg_left | [
{
"state_after": "α : Type u_2\nβ : Type ?u.626718\nm : MeasurableSpace α\nL : Type ?u.626724\nM✝ : Type ?u.626727\nN : Type u_3\ninst✝⁸ : AddCommMonoid L\ninst✝⁷ : TopologicalSpace L\ninst✝⁶ : AddCommMonoid M✝\ninst✝⁵ : TopologicalSpace M✝\ninst✝⁴ : AddCommMonoid N\ninst✝³ : TopologicalSpace N\nv✝ : VectorMeas... | [
1117,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
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Mathlib/Algebra/GroupPower/Identities.lean | sq_add_mul_sq_mul_sq_add_mul_sq | [
{
"state_after": "no goals",
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"tactic": "ring"
}
] | [
37,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutationsAux2_comp_append | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type u_2\nt : α\nts : List α\nr : List β\nf✝ f : List α → β\n⊢ (permutationsAux2 t [] r [] fun x => f (x ++ ts)).snd = (permutationsAux2 t ts r [] f).snd\n\ncase cons\nα : Type u_1\nβ : Type u_2\nt : α\nts : List α\nr : List β\nf✝ : List α → β\nys_hd : α\ntail✝ : Li... | [
88,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.not_isLittleO | [] | [
597,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.Monic.degree_mul | [
{
"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.658581\nhq : Monic q\nhp : p = 0\n⊢ degree (p * q) = degree p + degree q",
"tactic": "simp [hp]"
},
{
"state_after": "no goals",
"state_before": "R : Type u... | [
941,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.not_dvd_iff_between_consec_multiples | [
{
"state_after": "a✝ b m n✝ k n a : ℕ\nha : 0 < a\nhan : ¬a ∣ n\n⊢ a * (n / a) ≠ n",
"state_before": "a✝ b m n✝ k n a : ℕ\nha : 0 < a\n⊢ (∃ k, a * k < n ∧ n < a * (k + 1)) ↔ ¬a ∣ n",
"tactic": "refine'\n ⟨fun ⟨k, hk1, hk2⟩ => not_dvd_of_between_consec_multiples hk1 hk2, fun han =>\n ⟨n / a, ⟨lt_of_l... | [
238,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_congr | [] | [
1227,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Order/Chain.lean | IsMaxChain.bot_mem | [] | [
150,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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] |
Mathlib/Algebra/Order/Floor.lean | Nat.cast_ceil_eq_cast_int_ceil | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.311700\nα : Type u_1\nβ : Type ?u.311706\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\na : α\nha : 0 ≤ a\n⊢ ↑⌈a⌉₊ = ↑⌈a⌉",
"tactic": "rw [← Nat.cast_ceil_eq_int_ceil ha, Int.cast_ofNat]"
}
] | [
1615,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1614,
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Mathlib/Algebra/Group/Basic.lean | div_mul_cancel'' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.72204\nβ : Type ?u.72207\nG : Type u_1\ninst✝ : CommGroup G\na✝ b✝ c d a b : G\n⊢ a / (a * b) = b⁻¹",
"tactic": "rw [← inv_div, mul_div_cancel''']"
}
] | [
974,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_ediv_assoc | [
{
"state_after": "no goals",
"state_before": "a c d : Int\ncz : c = 0\n⊢ a * (c * d) / c = a * (c * d / c)",
"tactic": "simp [cz, Int.mul_zero]"
},
{
"state_after": "no goals",
"state_before": "a c d : Int\ncz : ¬c = 0\n⊢ a * (c * d) / c = a * (c * d / c)",
"tactic": "rw [Int.mul_left_co... | [
720,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
717,
11
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_left_inj | [] | [
201,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂_compl₁₂ | [
{
"state_after": "case a.h\nR : Type u_1\nR₁ : Type ?u.1503183\nR₂ : Type ?u.1503186\nM : Type ?u.1503189\nM₁ : Type u_2\nM₂ : Type u_3\nM₁' : Type u_4\nM₂' : Type u_5\nn : Type u_9\nm : Type u_8\nn' : Type u_6\nm' : Type u_7\nι : Type ?u.1503216\ninst✝¹⁶ : CommRing R\ninst✝¹⁵ : AddCommMonoid M₁\ninst✝¹⁴ : Modu... | [
465,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
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] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.739707\nG : Type ?u.739710\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : Inner... | [
169,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | lt_tsub_iff_right | [] | [
420,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/LinearAlgebra/GeneralLinearGroup.lean | LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv | [] | [
81,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsOpen.lowerSemicontinuousAt_indicator | [] | [
219,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.some_removeNone_iff | [
{
"state_after": "case none\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.6621\ne : Option α ≃ Option β\nx : α\nh : ↑e (some x) = none\n⊢ some (↑(removeNone e) x) = ↑e none ↔ ↑e.symm none = some x\n\ncase some\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.6621\ne : Option α ≃ Option β\nx : α\na : β\nh : ↑e (some x) = som... | [
158,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/Bounds/Basic.lean | Antitone.image_lowerBounds_subset_upperBounds_image | [] | [
1318,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_smul_right_of_neg | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nr : ℝ\nhr : r < 0\n⊢ angle x (r • y) = angle x (-y)",
"tactic": "rw [← neg_neg r, neg_smul, angle_neg_right, angle_smul_right_of_pos x y (neg_pos_of_neg hr),\n angle_... | [
172,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/VonNeumannAlgebra/Basic.lean | VonNeumannAlgebra.centralizer_centralizer | [] | [
120,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_map | [] | [
257,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_toIcoMod | [] | [
731,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
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Mathlib/Topology/SubsetProperties.lean | exists_subset_nhds_of_isCompact' | [
{
"state_after": "case intro.intro.intro\nα : Type u\nβ : Type v\nι✝ : Type ?u.36248\nπ : ι✝ → Type ?u.36253\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\nι : Type u_1\ninst✝ : Nonempty ι\nV : ι → Set α\nhV : Directed (fun x x_1 => x ⊇ x_1) V\nhV_cpct : ∀ (i : ι), IsCompact (V i)\nhV_c... | [
481,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.coe_comap | [
{
"state_after": "X : Type u_3\nY : Type u_1\nZ : Type u_2\nα : Type ?u.31928\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf : X → Y\ng : LocallyConstant Y Z\nhf : Continuous f\n⊢ ↑{ toFun := ↑g ∘ f, isLocallyConstant := (_ : IsLocallyConstant (g.toFun ∘ f)) } = ↑g ∘ f",
"state_before": "X : Ty... | [
480,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_image_left_anticomm | [] | [
422,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.of_le | [] | [
350,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
346,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.hasSum_integral_measure | [
{
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1464,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasStrictDerivAt_id | [] | [
649,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_lt_rpow_of_pos_of_lt_one_of_neg | [
{
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"state_before": "x y z : ℝ\nhx1 : 0 < x\nhx2 : x < 1\nhz : z < 0\n⊢ 1 < x ^ z",
"tactic": "convert rpow_lt_rpow_of_exponent_gt hx1 hx2 hz"
},
{
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"state_before": "case h.e'_... | [
547,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
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Std/Data/Nat/Gcd.lean | Nat.dvd_gcd_iff | [] | [
56,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
54,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_some_of_head_tail_some | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nh : some a ∈ head (tail s)\n⊢ ∃ a', some a' ∈ head s",
"... | [
860,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_induction | [] | [
1136,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableAt.exp | [] | [
300,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
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Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.Presieve.in_coverByImage | [
{
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... | [
89,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d | [
{
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312,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.mul_apply | [] | [
1036,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
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Mathlib/Order/Filter/Basic.lean | Filter.map_swap_eq_comap_swap | [] | [
2546,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2545,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_ofSet | [
{
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870,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.nonneg_of_eventually_pow_nonneg | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
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Mathlib/Data/Set/Lattice.lean | Set.injective_iff_injective_of_iUnion_eq_univ | [
{
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1505,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Icc_zsmul | [
{
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"tactic": "simpa only [zero_add] using iUnion_Icc_add_zsmul hp 0"
}
] | [
1083,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.congr | [] | [
704,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.hasStrictFDerivAt_iff | [
{
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1
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Mathlib/Data/Fintype/Card.lean | Finite.exists_infinite_fiber | [
{
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"tactic": "classical\n by_contra' hf\n cases nonempty_fintype β\n haveI := fun y => fintypeOfNotInfinite <| hf y\n let key : F... | [
1176,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
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Std/Data/String/Lemmas.lean | Substring.Valid.prevn | [
{
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"state_before": "m₂ m₁ : List Char\nx✝ : Sub... | [
1014,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1010,
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Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₂Γ₂_toKaroubi | [
{
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129,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/Topology/Algebra/UniformGroup.lean | DenseInducing.extend_Z_bilin_aux | [
{
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815,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
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] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_zero | [
{
"state_after": "no goals",
"state_before": "⊢ aleph 0 = ℵ₀",
"tactic": "rw [aleph, add_zero, aleph'_omega]"
}
] | [
273,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/Combinatorics/Pigeonhole.lean | Nat.exists_lt_modEq_of_infinite | [] | [
468,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
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] |
Mathlib/Data/Option/Basic.lean | Option.iget_mem | [] | [
305,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map_map₂_right_anticomm | [
{
"state_after": "no goals",
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209,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.zero_coeff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑(aeval (Function.uncurry fun i => ![].coeff)) (wittZero p n) = 0",
"tactic": "simp only [wittZero_eq_zero, AlgHom.map_zero]"
}
] | [
337,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ediam_of_unbounded | [] | [
2681,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2681,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | min_mul_distrib' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : CanonicallyLinearOrderedMonoid α\na b c : α\n⊢ min (a * b) c = min (min a c * min b c) c",
"tactic": "simpa [min_comm _ c] using min_mul_distrib c a b"
}
] | [
370,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.exists_of_update | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nself : Bucket α β\ni : USize\nd : AssocList α β\nh : USize.toNat i < Array.size self.val\n⊢ ∃ l₁ l₂,\n self.val.data = l₁ ++ List.get self.val.data { val := USize.toNat i, isLt := h } :: l₂ ∧\n List.length l₁ = USize.toNat i ∧ (update self i d h).val.data = ... | [
27,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.Prime.divisors | [
{
"state_after": "case a\nn p : ℕ\npp : Prime p\na✝ : ℕ\n⊢ a✝ ∈ Nat.divisors p ↔ a✝ ∈ {1, p}",
"state_before": "n p : ℕ\npp : Prime p\n⊢ Nat.divisors p = {1, p}",
"tactic": "ext"
},
{
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318,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.not_not | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (!!b) = b",
"tactic": "cases b <;> rfl"
}
] | [
123,
74
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
123,
9
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_of_im_pos | [] | [
296,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | HasDerivWithinAt.div | [
{
"state_after": "case h.e'_6\n𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter 𝕜\n𝕜' : Type u_1\... | [
193,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.gcd_a_modEq | [
{
"state_after": "m n a✝ b✝ c d : ℤ\na b : ℕ\n⊢ ↑a * Nat.gcdA a b + 0 ≡ ↑a * Nat.gcdA a b + ↑b * Nat.gcdB a b [ZMOD ↑b]",
"state_before": "m n a✝ b✝ c d : ℤ\na b : ℕ\n⊢ ↑a * Nat.gcdA a b ≡ ↑(Nat.gcd a b) [ZMOD ↑b]",
"tactic": "rw [← add_zero ((a : ℤ) * _), Nat.gcd_eq_gcd_ab]"
},
{
"state_after":... | [
282,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | infEdist_smul₀ | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NormedDivisionRing 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : BoundedSMul 𝕜 E\nc : 𝕜\nhc : c ≠ 0\ns : Set E\nx : E\n⊢ (⨅ (y : E) (_ : y ∈ c • s), edist (c • x) y) = ‖c‖₊ • ⨅ (y : E) (_ : y ∈ s), edist x y",
"state_before": "... | [
72,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.ext | [
{
"state_after": "no goals",
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518,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eq_sInf_of_mem_iff_exists_mem | [] | [
786,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Algebra/Algebra/RestrictScalars.lean | RestrictScalars.addEquiv_symm_map_smul_smul | [
{
"state_after": "R : Type u_2\nS : Type u_3\nM : Type u_1\nA : Type ?u.72538\ninst✝⁴ : AddCommMonoid M\ninst✝³ : CommSemiring R\ninst✝² : Semiring S\ninst✝¹ : Algebra R S\ninst✝ : Module S M\nr : R\ns : S\nx : M\n⊢ ↑(AddEquiv.symm (addEquiv R S M)) (↑(algebraMap R S) r • s • x) = r • ↑(AddEquiv.symm (addEquiv ... | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sumAddHom_comm | [
{
"state_after": "case mk'.mk.mk.mk'.mk.mk\nι : Type u\nγ✝ : Type w\nβ : ι → Type v\nβ₁✝ : ι → Type v₁\nβ₂✝ : ι → Type v₂\ndec : DecidableEq ι\nι₁ : Type u_1\nι₂ : Type u_2\nβ₁ : ι₁ → Type u_3\nβ₂ : ι₂ → Type u_4\nγ : Type u_5\ninst✝⁴ : DecidableEq ι₁\ninst✝³ : DecidableEq ι₂\ninst✝² : (i : ι₁) → AddZeroClass (... | [
2008,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2000,
1
] |
Std/Data/String/Lemmas.lean | String.find_of_valid | [
{
"state_after": "no goals",
"state_before": "p : Char → Bool\ns : String\n⊢ find s p = { byteIdx := utf8Len (List.takeWhile (fun x => !p x) s.data) }",
"tactic": "simpa using findAux_of_valid p [] s.1 []"
}
] | [
337,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
336,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.measurable | [] | [
602,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
11
] |
Mathlib/Logic/Equiv/Fin.lean | finRotate_last' | [
{
"state_after": "m n : ℕ\n⊢ ↑(finCongr (_ : 1 + n = n + 1)) (↑finAddFlip { val := n, isLt := (_ : n < n + 1) }) = 0",
"state_before": "m n : ℕ\n⊢ ↑(finRotate (n + 1)) { val := n, isLt := (_ : n < n + 1) } = { val := 0, isLt := (_ : 0 < Nat.succ n) }",
"tactic": "dsimp [finRotate_succ]"
},
{
"st... | [
409,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.measure_inv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.499171\nG : Type u_1\nH : Type ?u.499177\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableSpace H\ninst✝² : InvolutiveInv G\ninst✝¹ : MeasurableInv G\nμ : Measure G\ninst✝ : IsInvInvariant μ\nA : Set G\n⊢ ↑↑μ A⁻¹ = ↑↑μ A",
"tactic": "rw [← inv_ap... | [
414,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.coe_equivInteger_apply | [] | [
237,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.le_last | [] | [
533,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.natCast_pow | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nm n : ℕ\n⊢ ↑(m ^ n) = ↑m ^ ↑n",
"tactic": "induction n <;> simp [pow_succ', power_add, *, Pow.pow]"
}
] | [
1344,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.519553\nG : Type ?u.519556\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : Comp... | [
152,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.iSup_ord | [
{
"state_after": "α : Type ?u.302906\nβ : Type ?u.302909\nγ : Type ?u.302912\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Sort u_1\nf : ι → Cardinal\nhf : BddAbove (range f)\n⊢ ord (sSup (range f)) = sSup (range fun i => ord (f i))",
"state_before": "α : Type ?u.302906\nβ : Type ?u.302909\nγ :... | [
1412,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.hasFDerivAt | [] | [
78,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
11
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_neg | [] | [
195,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_limsup_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.68947\nγ : Type ?u.68950\nδ : Type ?u.68953\nι : Type ?u.68956\nR : Type ?u.68959\nR' : Type ?u.68962\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ : Set α\ns : ℕ → Set α\nhs : (∑' (i : ℕ), ↑↑μ (s i)) ≠ ⊤\nt : ℕ → Set α := fun n => toMeasurable μ (s n)\n⊢ ↑... | [
599,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
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