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/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_closure_pair | [
{
"state_after": "M : Type ?u.264602\nA✝ : Type ?u.264605\nB : Type ?u.264608\nA : Type u_1\ninst✝ : CommMonoid A\na b c : A\n⊢ (∃ y, y ∈ closure {a} ∧ ∃ z, z ∈ closure {b} ∧ y * z = c) ↔ ∃ m n, a ^ m * b ^ n = c",
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689,
56
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686,
1
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Std/Logic.lean | Or.comm | [] | [
261,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
261,
1
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Mathlib/Data/PEquiv.lean | PEquiv.symm_symm | [
{
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138,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Algebra/GroupPower/Order.lean | one_lt_sq_iff_one_lt_abs | [
{
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"tactic": "simpa only [one_pow, abs_one] using @sq_lt_sq _ _ 1 x"
}
] | [
746,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
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Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_inv_π_π | [
{
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343,
7
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335,
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Mathlib/Algebra/Order/Field/Basic.lean | lt_div_iff_of_neg | [] | [
745,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
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Mathlib/Data/List/Basic.lean | List.head?_map | [
{
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"tactic": "cases l <;> rfl"
}
] | [
933,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
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Mathlib/Analysis/SpecialFunctions/Sqrt.lean | DifferentiableWithinAt.sqrt | [] | [
135,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_image | [] | [
205,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
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Mathlib/Data/Quot.lean | Quotient.inductionOn' | [] | [
670,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
11
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Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_comp_continuousOrderHom | [] | [
319,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
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Mathlib/Data/Real/NNReal.lean | NNReal.le_div_iff_mul_le | [] | [
805,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_set_le | [] | [
294,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app | [
{
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141,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Data/Set/Basic.lean | Set.compl_ne_eq_singleton | [] | [
1705,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1704,
1
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Std/Data/List/Lemmas.lean | List.length_take_of_le | [
{
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"tactic": "simp [Nat.min_eq_left h]"
}
] | [
699,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
699,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_pow_card | [] | [
1447,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_spec' | [
{
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"tactic": "rw [mul_comm, mk'... | [
748,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
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Mathlib/RingTheory/EisensteinCriterion.lean | Polynomial.EisensteinCriterionAux.le_natDegree_of_map_eq_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nP : Ideal R\nhP : Ideal.IsPrime P\nq : R[X]\nc : (R ⧸ P)[X]\nhq : map (mk P) q = c * X ^ n\nhc0 : degree c = 0\n⊢ ↑n = degree (map (mk P) q)",
"tactic": "rw [hq, degree_mul, hc0, zero_add, degree_pow, degree_X, nsmul_... | [
64,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.of_isRightAdjoint | [] | [
324,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/CategoryTheory/EssentialImage.lean | CategoryTheory.Functor.obj_mem_essImage | [] | [
79,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_right_cancel_iff | [] | [
65,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
64,
11
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.tendsto_symm | [
{
"state_after": "no goals",
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363,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ dual (dual (node s l x r)) = node s l x r",
"tactic": "rw [dual, dual, dual_dual l, dual_dual r]"
}
] | [
155,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
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Mathlib/Topology/Constructions.lean | Subtype.dense_iff | [
{
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1063,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
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Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_isEmpty | [
{
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176,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_self | [
{
"state_after": "α : Type u_1\ninst✝² : CanonicallyLinearOrderedAddMonoid α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nha : AddLECancellable a\nh₁ : 0 < a\nh₂ : 0 < b\nh : a - b = a\n⊢ False",
"state_before": "α : Type u_1\ninst✝² : CanonicallyLinearOrderedAddMonoid α\ninst✝¹ : Sub α\ninst✝ : Orde... | [
449,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
11
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete | [] | [
903,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
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Mathlib/Algebra/Order/UpperLower.lean | UpperSet.coe_div | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.const_mul' | [] | [
1084,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.domDomCongr_eq_iff | [] | [
766,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
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Mathlib/Topology/SubsetProperties.lean | locallyCompactSpace_of_hasBasis | [] | [
1103,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/Data/Set/Finite.lean | Set.not_injOn_infinite_finite_image | [
{
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"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → β\ns : Set α\nh_inf : Set.Infinite s\nh_fin : Set.Fini... | [
1399,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
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Mathlib/Analysis/Convex/Integral.lean | Convex.set_average_mem | [
{
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104,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Data/Int/Parity.lean | Int.not_even_iff | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ ¬Even n ↔ n % 2 = 1",
"tactic": "rw [even_iff, emod_two_ne_zero]"
}
] | [
50,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_compl_le_add_iff | [] | [
3077,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3074,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sub_int | [
{
"state_after": "no goals",
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"tactic": "simpa using rpow_add_int hx y (-n)"
}
] | [
338,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
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] |
Mathlib/Analysis/SpecificLimits/Basic.lean | Set.Countable.exists_pos_hasSum_le | [
{
"state_after": "α : Type ?u.472618\nβ : Type ?u.472621\nι✝ : Type ?u.472624\nι : Type u_1\ns : Set ι\nhs : Set.Countable s\nε : ℝ\nhε : 0 < ε\nthis : Encodable ↑s\n⊢ ∃ ε', (∀ (i : ι), 0 < ε' i) ∧ ∃ c, HasSum (fun i => ε' ↑i) c ∧ c ≤ ε",
"state_before": "α : Type ?u.472618\nβ : Type ?u.472621\nι✝ : Type ?u... | [
474,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.eq_top_of_forall_nnreal_le | [] | [
1683,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1682,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_prod_symm | [
{
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483,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.piCongr_apply_apply | [
{
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"state_before": "α : Sort u_1\nβ : Sort u_2\nW : α ... | [
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12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1796,
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] |
Mathlib/RingTheory/Noetherian.lean | IsNoetherian.induction | [] | [
361,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
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Mathlib/RingTheory/Subring/Pointwise.lean | Subring.pointwise_smul_le_iff₀ | [] | [
173,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.le_mul_withDensity | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.4937781\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
665,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
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Mathlib/Data/Int/GCD.lean | Int.gcd_mul_left | [
{
"state_after": "i j k : ℤ\n⊢ Nat.gcd (natAbs i * natAbs j) (natAbs i * natAbs k) = natAbs i * Nat.gcd (natAbs j) (natAbs k)",
"state_before": "i j k : ℤ\n⊢ gcd (i * j) (i * k) = natAbs i * gcd j k",
"tactic": "rw [Int.gcd, Int.gcd, natAbs_mul, natAbs_mul]"
},
{
"state_after": "no goals",
"... | [
303,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.trans_apply | [
{
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262,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | QuotientAddGroup.btw_coe_iff | [
{
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Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.rightInverse_of_surjective | [] | [
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Mathlib/Algebra/Algebra/Basic.lean | Algebra.mem_algebraMapSubmonoid_of_mem | [] | [
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44
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.adjoin_eq_top_of_gen_mem_adjoin | [
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Mathlib/Order/Filter/CountableInter.lean | eventually_countable_forall | [
{
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_C_of_natDegree_le_zero | [] | [
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.zero_mul | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.prod_eq_bot_iff | [
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.prod_roots_eq_coeff_zero_of_monic_of_split | [
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Mathlib/Analysis/Convex/Between.lean | Wbtw.trans_sbtw_right | [
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Mathlib/Order/Bounds/Basic.lean | isGLB_empty | [] | [
892,
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Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.continuous | [] | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofRealClm_apply | [] | [
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Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_seven | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_smulRightL_apply | [] | [
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Mathlib/Data/Part.lean | Part.append_mem_append | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.relabelAux_sum_inl | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_zsmul_add | [
{
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.card_support_swap_mul | [
{
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612,
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Mathlib/Order/Lattice.lean | inf_right_idem | [] | [
520,
28
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519,
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Mathlib/CategoryTheory/Bicategory/Functor.lean | CategoryTheory.Pseudofunctor.to_oplax_obj | [] | [
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Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_add_zspan | [
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Mathlib/Order/Bounds/Basic.lean | BddBelow.inter_of_left | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_lt_cos_of_nonneg_of_le_pi | [
{
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564,
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.summable | [] | [
308,
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306,
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_div_iff_forall_mul_mem | [] | [
690,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | GaloisConnection.u_ciInf | [] | [
1310,
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Mathlib/Order/BoundedOrder.lean | not_isMax_iff_ne_top | [] | [
144,
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143,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_le_of_lt_one' | [] | [
752,
78
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750,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.sub_of_right | [
{
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_add_pi | [] | [
389,
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388,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | inv_closedBall | [] | [
100,
48
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.exists_left | [] | [
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20
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162,
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Mathlib/Data/Real/NNReal.lean | NNReal.iSup_empty | [] | [
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82
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Mathlib/Data/Finset/Card.lean | Finset.card_image_iff | [] | [
238,
48
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237,
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Mathlib/Order/LocallyFinite.lean | Multiset.mem_Iio | [
{
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95
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_apply | [] | [
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6
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.infinite_of_exists_right | [] | [
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81
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.id_f | [] | [
227,
6
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226,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_finset_biUnion_apply | [
{
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Mathlib/Data/Pi/Lex.lean | Pi.toLex_apply | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.exists_mem_of_measure_ne_zero_of_ae | [
{
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Std/Data/List/Lemmas.lean | List.get?_modifyNth | [
{
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735,
93
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.coe_zero | [] | [
565,
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Std/Data/Int/Lemmas.lean | Int.add_le_add_iff_right | [] | [
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59
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Mathlib/Analysis/Convex/Segment.lean | left_mem_segment | [
{
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118,
84
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_toIocMod_zero | [
{
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785,
49
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784,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuousWithinAt_of_dominated_interval | [] | [
1084,
97
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.copy_eq | [] | [
555,
27
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554,
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Mathlib/Data/Finset/Image.lean | Function.Semiconj.finset_image | [] | [
432,
15
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430,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.lowerCentralSeries_zero | [] | [
87,
6
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Std/Data/String/Lemmas.lean | String.extract_of_valid | [
{
"state_after": "l m r : List Char\n⊢ (if utf8Len l ≥ utf8Len l + utf8Len m then \"\"\n else { data := extract.go₁ (l ++ m ++ r) 0 { byteIdx := utf8Len l } { byteIdx := utf8Len l + utf8Len m } }) =\n { data := m }",
"state_before": "l m r : List Char\n⊢ extract { data := l ++ m ++ r } { byteIdx := ut... | [
450,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
444,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measure_closure_of_null_frontier | [] | [
429,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Analysis/Convex/Function.lean | concaveOn_iff_div | [] | [
1059,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
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