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/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_div_swap | [] | [
408,
63
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406,
1
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Mathlib/Algebra/Periodic.lean | Function.Periodic.neg_eq | [] | [
266,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
11
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Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_apply | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/Computability/Partrec.lean | Partrec.fix_aux | [
{
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850,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
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Mathlib/Data/Nat/Choose/Sum.lean | Commute.add_pow' | [
{
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"tactic": "simp_rw [Finset.Nat.sum_antidiagonal_eq_sum_range_succ fun m p ↦ choose n m • (x ^ m * y ^... | [
79,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/Topology/Instances/EReal.lean | EReal.continuousOn_toReal | [] | [
96,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_eq_of_brange_eq | [] | [
1940,
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1937,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.comp_continuous_iff | [] | [
1908,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1906,
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Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd | [
{
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"state_before": "C : Type u... | [
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703,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_zero | [] | [
1055,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Submodule.eq_top_of_finrank_eq | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.w | [
{
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26
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Ioo | [] | [
454,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Mathlib/Data/Sigma/Basic.lean | PSigma.subtype_ext | [] | [
257,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBiproduct.bicone_snd | [] | [
1311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
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Mathlib/Topology/UniformSpace/Basic.lean | map_uniformity_set_coe | [
{
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"tactic": "rw [uniformity_setCoe, map_comap, range_prod_map, Subtype.range_val]... | [
1487,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/Taylor.lean | taylorWithinEval_self | [
{
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114,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Nilpotent.lean | CommGroup.nilpotencyClass_le_one | [
{
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697,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
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Mathlib/Computability/TuringMachine.lean | Turing.reaches₁_eq | [
{
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"tactic": "rw [h]"
}
] | [
760,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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src/lean/Init/Core.lean | id.def | [] | [
527,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
527,
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.mul | [
{
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178,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_succ_iff_fderiv | [
{
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1674,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.ext | [] | [
118,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/Topology/TietzeExtension.lean | ContinuousMap.exists_extension_of_closedEmbedding | [] | [
394,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
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] |
Mathlib/RingTheory/Congruence.lean | RingCon.trans | [] | [
116,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Basic.lean | Filter.NeBot.of_map | [] | [
2461,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/NAry.lean | Finset.mem_image₂ | [
{
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Mathlib/Data/Part.lean | Part.getOrElse_some | [] | [
288,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coe_mk | [] | [
383,
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381,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_eq_false | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
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Mathlib/Data/Fin/Basic.lean | Fin.succAbove_ne | [
{
"state_after": "n m : ℕ\np : Fin (n + 1)\ni : Fin n\neq : ↑(succAbove p) i = p\n⊢ False",
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},
{
"state_after": "case pos\nn m : ℕ\np : Fin (n + 1)\ni : Fin n\neq : ↑(succAbove p) i = p\nH : ↑cast... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2117,
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Basic.lean | Filter.HasBasis.uniformContinuous_iff | [
{
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Mathlib/Algebra/BigOperators/Basic.lean | MonoidHom.finset_prod_apply | [] | [
288,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
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Mathlib/Data/Set/UnionLift.lean | Set.iUnionLift_of_mem | [
{
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Iio | [] | [
51,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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Mathlib/Order/BooleanAlgebra.lean | eq_of_sdiff_eq_sdiff | [
{
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"tactic": "rw [← sdiff_sdiff_eq_self hxz, h, sdiff_sdiff_eq_self hyz]"
}
] | [
397,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
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Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.natDegree_hasseDeriv_le | [
{
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214,
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.map_bind₂ | [
{
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262,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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Mathlib/Order/Filter/Pointwise.lean | Filter.pow_mem_pow | [
{
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44
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674,
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Mathlib/Topology/UniformSpace/Basic.lean | Sum.uniformity | [] | [
1822,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_zero_of_non_prime | [
{
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}
] | [
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69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/Order/SuccPred/Basic.lean | Order.Ioi_pred_of_not_isMin | [] | [
668,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.map_lift_kernelComparison | [
{
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Mathlib/Analysis/Convex/Independent.lean | convexIndependent_iff_finset | [
{
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197,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_mono' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.47838\nι' : Type ?u.47841\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.47850\ninst✝ : Preorder β\nl : Filter α\nf₁ f₂ : α → β\nh : f₁ ≤ᶠ[l] f₂\nh₁ : Tendsto f₁ l atTop\nb : β\n⊢ ∀ᶠ (a : α) in l, b ≤ f₂ a",
"tactic": "filter_upwards [tendsto_atTop.1 h... | [
375,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | PolishSpace.secondCountable_of_polish | [] | [
730,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
9
] |
Mathlib/Data/Nat/Cast/Field.lean | Nat.cast_div | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : DivisionSemiring α\nn : ℕ\nn_nonzero : ↑n ≠ 0\nk : ℕ\n⊢ ↑(n * k / n) = ↑(n * k) / ↑n",
"state_before": "α : Type u_1\ninst✝ : DivisionSemiring α\nm n : ℕ\nn_dvd : n ∣ m\nn_nonzero : ↑n ≠ 0\n⊢ ↑(m / n) = ↑m / ↑n",
"tactic": "rcases n_dvd with ⟨k, rfl⟩"
... | [
38,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.mk_symm | [] | [
612,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Topology/MetricSpace/CantorScheme.lean | CantorScheme.VanishingDiam.dist_lt | [
{
"state_after": "β : Type u_1\nα : Type u_2\nA : List β → Set α\ninst✝ : PseudoMetricSpace α\nε : ℝ\nε_pos : 0 < ε\nx : ℕ → β\nhA : Tendsto (fun n => EMetric.diam (A (res x n))) atTop (𝓝 0)\n⊢ ∃ n, ∀ (y : α), y ∈ A (res x n) → ∀ (z : α), z ∈ A (res x n) → dist y z < ε",
"state_before": "β : Type u_1\nα : ... | [
146,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Order/Bounds/Basic.lean | image2_upperBounds_lowerBounds_subset_upperBounds_image2 | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Monotone (swap f b)\nh₁ : ∀ (a : α), Antitone (f a)\na : α\nb : β\nha : a ∈ upperBoun... | [
1418,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.prime_divisors_eq_to_filter_divisors_prime | [
{
"state_after": "case inl\nn : ℕ\n⊢ List.toFinset (factors 0) = filter Prime (divisors 0)\n\ncase inr\nn✝ n : ℕ\nhn : n > 0\n⊢ List.toFinset (factors n) = filter Prime (divisors n)",
"state_before": "n✝ n : ℕ\n⊢ List.toFinset (factors n) = filter Prime (divisors n)",
"tactic": "rcases n.eq_zero_or_pos ... | [
490,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxOn.iSup_eq | [] | [
693,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.diff | [] | [
449,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
11
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjointAux_inner_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.251441\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : InnerProduc... | [
86,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.subset_adjoin | [] | [
46,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_map_inl_inr | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.vecMul_fromBlocks | [
{
"state_after": "case h\nl : Type u_4\nm : Type u_5\nn : Type u_1\no : Type u_2\np : Type ?u.78326\nq : Type ?u.78329\nm' : o → Type ?u.78334\nn' : o → Type ?u.78339\np' : o → Type ?u.78344\nR : Type ?u.78347\nS : Type ?u.78350\nα : Type u_3\nβ : Type ?u.78356\ninst✝² : Fintype n\ninst✝¹ : Fintype o\ninst✝ : N... | [
275,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_of_map_pow_eq_add_int | [
{
"state_after": "f g : CircleDeg1Lift\nx : ℝ\nn : ℕ\nm : ℤ\nh : ↑(f ^ n) x = x + ↑m\nhn : 0 < n\nthis : τ (f ^ n) = ↑m\n⊢ τ f = ↑m / ↑n",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nn : ℕ\nm : ℤ\nh : ↑(f ^ n) x = x + ↑m\nhn : 0 < n\n⊢ τ f = ↑m / ↑n",
"tactic": "have := (f ^ n).translationNumber_of_eq... | [
897,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.intersecting_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderBot α\ns t : Set α\na b c : α\n⊢ Intersecting {a} ↔ a ≠ ⊥",
"tactic": "simp [Intersecting]"
}
] | [
64,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subsingleton.eq_empty_or_singleton | [] | [
2366,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2365,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_le_of_sum_range_le | [] | [
1262,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.map_fun | [] | [
792,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.ssubset_cons | [] | [
415,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean | Complex.contDiffAt_tan | [] | [
79,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Antichain.lean | Symmetric.compl | [] | [
39,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
11
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.mclosure_preimage_le | [] | [
799,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_mk_eq_multiplicity | [
{
"state_after": "case pos\nα : Type u_1\ninst✝² : CommMonoidWithZero α\ninst✝¹ : DecidableRel fun x x_1 => x ∣ x_1\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nh : Finite a b\n⊢ multiplicity (Associates.mk a) (Associates.mk b) = multiplicity a b\n\ncase neg\nα : Type u_1\ninst✝² : CommMonoidWithZero α\... | [
395,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_star | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Data/List/Range.lean | List.finRange_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\n⊢ finRange n = [] ↔ n = 0",
"tactic": "rw [← length_eq_zero, length_finRange]"
}
] | [
157,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.quotientMap_mk | [] | [
421,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_append | [
{
"state_after": "case nil\nα : Type u\ninst✝ : DecidableEq α\nl₂ : List α\n⊢ dedup ([] ++ l₂) = [] ∪ dedup l₂\n\ncase cons\nα : Type u\ninst✝ : DecidableEq α\nl₂ : List α\na : α\nl₁ : List α\nIH : dedup (l₁ ++ l₂) = l₁ ∪ dedup l₂\n⊢ dedup (a :: l₁ ++ l₂) = a :: l₁ ∪ dedup l₂",
"state_before": "α : Type u\n... | [
98,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_one_div_one_add_sq | [
{
"state_after": "case refine'_1\na b : ℝ\nn : ℕ\nf : ℝ → ℝ\nμ ν : MeasureTheory.Measure ℝ\ninst✝ : IsLocallyFiniteMeasure μ\nc d : ℝ\n⊢ Continuous fun x => 1 + x ^ 2\n\ncase refine'_2\na b : ℝ\nn : ℕ\nf : ℝ → ℝ\nμ ν : MeasureTheory.Measure ℝ\ninst✝ : IsLocallyFiniteMeasure μ\nc d x : ℝ\n⊢ 1 + x ^ 2 ≠ 0",
"... | [
237,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.smul_negPart | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.mul_def | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.c_of_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.286917\nF : Type ?u.286920\nK : Type ?u.286923\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nh : toPoly P = toPoly Q\n⊢ P.c = Q.c",
"tactic": "rw [← coeff_eq_c, h, coeff_eq_c]"
}
] | [
130,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Combinatorics/SimpleGraph/Partition.lean | SimpleGraph.Partition.mem_partOfVertex | [
{
"state_after": "case intro.intro\nV : Type u\nG : SimpleGraph V\nP : Partition G\nv : V\n_h3 : ∀ (y : Set V), (fun b => ∃! x, v ∈ b) y → y = Exists.choose (_ : ∃! b x, v ∈ b)\nh1 : Exists.choose (_ : ∃! b x, v ∈ b) ∈ P.parts\nh2 :\n (fun x => v ∈ Exists.choose (_ : ∃! b x, v ∈ b)) h1 ∧\n ∀ (y : Exists.cho... | [
98,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.nonempty_iUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.81842\nγ : Type ?u.81845\nι : Sort u_2\nι' : Sort ?u.81851\nι₂ : Sort ?u.81854\nκ : ι → Sort ?u.81859\nκ₁ : ι → Sort ?u.81864\nκ₂ : ι → Sort ?u.81869\nκ' : ι' → Sort ?u.81874\ns : ι → Set α\n⊢ Set.Nonempty (⋃ (i : ι), s i) ↔ ∃ i, Set.No... | [
721,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/CategoryTheory/Closed/FunctorCategory.lean | CategoryTheory.Functor.ihom_coev_app | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_inj | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.111180\nβ : Type ?u.111183\nγ : Type ?u.111186\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\n⊢ lift a = lift b ↔ a = b",
"tactic": "simp only [le_antisymm_iff, lift_le]"
}
] | [
773,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_eq_fun | [
{
"state_after": "α : Type u_2\nβ : Type ?u.341986\nγ : Type ?u.341989\nι : Type ?u.341992\ninst✝⁴ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\nf✝ g✝ : α → β\nE : Type u_1\ninst✝¹ : TopologicalSpace E\ninst✝ : MetrizableSpace E\nf g : α → E\nhf :... | [
1517,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1509,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.row_empty | [
{
"state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ni✝ : Unit\nx✝ : Fin 0\n⊢ row ![] i✝ x✝ = ![]",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\n⊢ row ![] = fun x => ![]",
"tactic": "ext"
},
{
"state_a... | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.IsClique.card_le_of_colorable | [
{
"state_after": "case h.e'_4\nV : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ns : Finset V\nh : IsClique G ↑s\nn : ℕ\nhc : Colorable G n\n⊢ n = Fintype.card (Fin n)",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ns : Finset V\nh : IsClique G ↑s\nn : ℕ\nhc : Colo... | [
436,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.apply_one | [] | [
697,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.differentiable_cos | [] | [
615,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Topology/ContinuousOn.lean | closure_pi_set | [] | [
420,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.differentiableWithinAt | [] | [
87,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Topology/Connected.lean | ConnectedComponents.coe_eq_coe' | [] | [
1455,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Continuous.borel_measurable | [] | [
188,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.left_U_subset_right_C | [] | [
123,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.ofHamming_symm_eq | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_eq_iInf | [] | [
742,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.linearProjOfIsCompl_range | [] | [
169,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.braiding_map_braiding | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nP Q : C\ninst✝ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\n⊢ (braiding X W).hom ≫ map f g ≫ (braiding Y Z).hom = map g f",
"tactic": "aesop_cat"
}
] | [
1844,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1842,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.le_sub_one_iff | [] | [
119,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.edist_lt_of_edist_lt_div | [] | [
517,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
src/lean/Init/Prelude.lean | id_eq | [] | [
284,
51
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
284,
9
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_cast_of_lt | [
{
"state_after": "no goals",
"state_before": "n a : ℕ\nh : a < n\n⊢ val ↑a = a",
"tactic": "rw [val_nat_cast, Nat.mod_eq_of_lt h]"
}
] | [
875,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Order/CountableDenseLinearOrder.lean | Order.PartialIso.exists_across | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : LinearOrder β\ninst✝³ : DenselyOrdered β\ninst✝² : NoMinOrder β\ninst✝¹ : NoMaxOrder β\ninst✝ : Nonempty β\nf : PartialIso α β\na : α\nh : ∃ b, (a, b) ∈ ↑f\n⊢ ∃ b, ∀ (p : α × β), p ∈ ↑f → cmp p.fst a = cmp p.snd b\n\ncase n... | [
125,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_log2_self | [] | [
827,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
827,
1
] |
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