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/Topology/ContinuousOn.lean | Continuous.comp_continuousOn | [] | [
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44
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1
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Mathlib/Data/List/Chain.lean | List.Chain'.cons | [] | [
258,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Order/Extension/Well.lean | toWellOrderExtension_strictMono | [] | [
98,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_map_of_surjective | [
{
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1655,
64
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_pow | [
{
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... | [
1541,
93
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Mathlib/Data/Complex/Exponential.lean | Real.exp_bound_div_one_sub_of_interval | [
{
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},
{
"state_afte... | [
1959,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1955,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_finite_iff_ne_zero | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\n⊢ (if h : φ = 0 then ⊤ else ↑(Nat.find (_ : ∃ n, ↑(coeff R n) φ ≠ 0))).Dom ↔ φ ≠ 0",
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},
{
"state_af... | [
2250,
13
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2241,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_C_mul | [
{
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}
] | [
455,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
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Mathlib/Algebra/CharP/Basic.lean | RingHom.map_frobenius | [] | [
372,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
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Mathlib/RingTheory/Artinian.lean | monotone_stabilizes_iff_artinian | [
{
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202,
50
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199,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_X_add_C_of_degree_le_one | [
{
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"tactic": "simp"
},
{
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449,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
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Mathlib/Topology/Support.lean | image_eq_one_of_nmem_mulTSupport | [] | [
71,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.coe_sup | [] | [
355,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Std/Data/Rat/Lemmas.lean | Rat.mkRat_ne_zero | [] | [
103,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
103,
1
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.toList_formPerm_isRotated_self | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_id | [] | [
749,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.smul_integral_comp_mul_left | [
{
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722,
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Mathlib/Data/Part.lean | Part.not_mem_none | [] | [
132,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/Data/List/Rotate.lean | List.length_rotate' | [
{
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},
{
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77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.isPrime_map_C_iff_isPrime | [
{
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"state_before": "R : Type u\nS : Type ?u.241035\ninst✝ : CommRing R\nP :... | [
721,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
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Mathlib/Data/Finset/Basic.lean | Multiset.disjoint_toFinset | [
{
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3794,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3786,
1
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Mathlib/Logic/Basic.lean | or_iff_not_and_not | [] | [
469,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
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Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.mem_uniformity | [] | [
143,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | IsUnit.mul_left_dvd | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : CommMonoid α\na b : α\nu : αˣ\n⊢ ↑u * a ∣ b ↔ a ∣ b",
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"tactic": "rcases hu with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "... | [
116,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.eqOn_of_isPreconnected_of_isMaxOn_norm | [
{
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292,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
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Mathlib/Data/Seq/Computation.lean | Computation.equiv_of_mem | [
{
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"tactic": "rw [mem_unique ma h... | [
1005,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_left_surjective | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← rpow_mul, _root_.inv_mul_cancel hx, rpow_one]"
}
] | [
251,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.hasBasis_nhds_of_ne_zero | [
{
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"state_before": "α : Type ?u.51011\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂... | [
115,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.forall_of_forall_mem_closedBall | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nX : Type ?u.45555\nι : Type ?u.45558\ninst✝ : PseudoMetricSpace α\nx✝ y✝ z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\np : α → Prop\nx : α\nH : ∃ᶠ (R : ℝ) in atTop, ∀ (y : α), y ∈ closedBall x R → p y\ny : α\nR : ℝ\nhR : R ≥ dist y x\nh : ∀ (z : α), z ∈ closedBall ... | [
679,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
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Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.ext' | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.19949\nσ✝ : Type ?u.19952\nτ : Typ... | [
168,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_smul_left_of_neg | [
{
"state_after": "no goals",
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"tactic": "rw [angle_comm, angle_smul_right_of_neg y x hr, angle_comm]"
}
] | [
178,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasColimits_of_hasColimits_createsColimits | [] | [
218,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.support_uniformOfFintype | [
{
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"tactic": "simp [mem_support_iff]"
}
] | [
129,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.one_coeff | [] | [
598,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_of_differentiableOn_real | [
{
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246,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_one | [
{
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... | [
129,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
11
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_eqOn_of_isPreconnected_of_isMaxOn | [
{
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251,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.ProbabilityMeasure.tendsto_measure_of_null_frontier_of_tendsto' | [] | [
409,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_zero' | [] | [
1486,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Functor.asEquivalence_counit | [] | [
556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_singleton | [] | [
330,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Logic/Basic.lean | Function.mtr | [] | [
382,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
11
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuous_iff_isOpen_preimage | [] | [
260,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Classification.lean | Algebra.IsAlgebraic.cardinal_mk_le_sigma_polynomial | [
{
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Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_zero | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.affine_image | [
{
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381,
98
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376,
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.NullMeasurableSet.fundamentalFrontier | [] | [
647,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
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Mathlib/LinearAlgebra/AffineSpace/Slope.lean | sub_smul_slope_vadd | [
{
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"tactic": "rw [sub_smul_slope, vsub_vadd]"
}
] | [
66,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff_of_sup_le_sup_right | [
{
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"state_before": "ι : Type ?u.142580\nα : Type u_1\nβ : Type ?u.142586\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\nh : a ⊔ c ... | [
734,
31
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732,
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Mathlib/Topology/Separation.lean | ContinuousAt.eventually_ne | [] | [
751,
32
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src/lean/Init/Core.lean | Exists.elim | [] | [
688,
24
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685,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEmbedding.map_apply | [
{
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86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4176,
8
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.iInter₂_smul_subset | [] | [
283,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Data/List/Sort.lean | List.mergeSort_nil | [
{
"state_after": "no goals",
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"tactic": "rw [List.mergeSort]"
}
] | [
468,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
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Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.of.zero_exact_aux2 | [
{
"state_after": "case refine'_1\nR : Type u\ninst✝³ : Ring R\nι : Type v\ndec_ι : DecidableEq ι\ninst✝² : Preorder ι\nG : ι → Type w\ninst✝¹ : (i : ι) → CommRing (G i)\nf : (i j : ι) → i ≤ j → G i → G j\nf' : (i j : ι) → i ≤ j → G i →+* G j\ninst✝ : DirectedSystem G fun i j h => ↑(f' i j h)\nx : FreeCommRing (... | [
513,
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486,
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Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_zero | [
{
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79,
79
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79,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_mul | [
{
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1044,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
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Mathlib/Topology/Sequences.lean | IsCompact.isSeqCompact | [] | [
291,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
11
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Mathlib/Order/Lattice.lean | le_iff_exists_sup | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ≤ b → ∃ c, b = a ⊔ c\n\ncase mpr\nα : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ (∃ c, b = a ⊔ c) → a ≤ b",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ≤ b ... | [
226,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
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Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.star_mul_self_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.42462\nE : Type u_1\nα : Type ?u.42468\ninst✝² : NonUnitalNormedRing E\ninst✝¹ : StarRing E\ninst✝ : CstarRing E\nx : E\n⊢ x⋆ * x ≠ 0 ↔ x ≠ 0",
"tactic": "simp only [Ne.def, star_mul_self_eq_zero_iff]"
}
] | [
144,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_X_right | [] | [
161,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.algebraMap_eq_one_iff | [] | [
218,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_psigma | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort ?u.2642\nβ : Sort ?u.2645\nγ : Sort ?u.2648\nα : Sort u_1\nE : α → Sort u_2\n⊢ IsEmpty (PSigma E) ↔ ∀ (a : α), IsEmpty (E a)",
"tactic": "simp only [← not_nonempty_iff, nonempty_psigma, not_exists]"
}
] | [
161,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/RingTheory/Localization/Integral.lean | IsFractionRing.comap_isAlgebraic_iff | [] | [
174,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.continuousAt_iff_leftLim_eq_rightLim | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : ConditionallyCompleteLinearOrder β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nh : ContinuousAt f x\n⊢ leftLim f x... | [
222,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_bot | [] | [
696,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
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Std/Data/RBMap/WF.lean | Std.RBNode.All.balLeft | [
{
"state_after": "α✝ : Type u_1\np : α✝ → Prop\nl : RBNode α✝\nv : α✝\nr : RBNode α✝\nhl : All p l\nhv : p v\nhr : All p r\n⊢ All p\n (match l with\n | node red a x b => node red (node black a x b) v r\n | l =>\n match r with\n | node black a y b => balance2 l v (node red a y b)\n | node... | [
237,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
235,
11
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_X_add_C_pow | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r✝ : R[X]\nr : R\nn k : ℕ\n⊢ ∑ i in range (n + 1), ↑(lcoeff R k) (X ^ i * ↑C r ^ (n - i) * ↑(Nat.choose n i)) = r ^ (n - k) * ↑(Nat.choose n k)",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring ... | [
319,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_symmDiff_union_symmDiff_right | [] | [
2127,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2126,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_of_subsingleton | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9267\na : α\ninst✝ : Subsingleton α\nthis : Fintype α := Fintype.ofSubsingleton a\n⊢ Nat.card α = 1",
"state_before": "α : Type u_1\nβ : Type ?u.9267\na : α\ninst✝ : Subsingleton α\n⊢ Nat.card α = 1",
"tactic": "letI := Fintype.ofSubsingleton a"
},
{
"... | [
78,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Icc_iff_integrableOn_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4455149\nE : Type u_2\nF : Type ?u.4455155\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ I... | [
699,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.head_stack_ok | [
{
"state_after": "case nil\nq : Λ'\ns : Option Γ'\nL₁ : List ℕ\nL₃ : List Γ'\n⊢ Reaches₁ (TM2.step tr)\n { l := some (head stack q), var := s, stk := elim (trList L₁) [] [] (trList [] ++ Γ'.consₗ :: L₃) }\n { l := some q, var := none, stk := elim (trList (List.headI [] :: L₁)) [] [] L₃ }\n\ncase cons\nq :... | [
1523,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1496,
1
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Mathlib/Data/Nat/Bits.lean | Nat.bit1_bits | [] | [
230,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_prime_pow | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\np : Associates α\nhp : Irreducible p\nk : ℕ\n⊢ p ^ k =\n match som... | [
1682,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1677,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.det | [
{
"state_after": "R : Type u_3\nA : Type u_2\nB : Type ?u.807401\nS : Type ?u.807404\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing B\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R A\ninst✝² : Algebra R B\nf : R →+* S\nn : Type u_1\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nM : Matrix n n A\nh : ∀ (i j... | [
668,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.coe_finset_sum | [] | [
877,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns✝ : Finset α\na : α\ninst✝ : DecidableEq α\ng : γ → α\ns : Finset γ\nH : ∀ (x : γ), x ∈ s → ∀ (y : γ), y ∈ s → g x = g y → x = y\n⊢ fol... | [
74,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.out_one | [] | [
228,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_translationNumber_of_add_le | [] | [
822,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_sub | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : m ≤ n\n⊢ ↑(n - m) = ↑n - ↑m",
"tactic": "match m with\n| 0 => rfl\n| succ m =>\n show ofNat (n - succ m) = subNatNat n (succ m)\n rw [subNatNat, Nat.sub_eq_zero_of_le h]"
},
{
"state_after": "no goals",
"state_before": "m n : Nat... | [
499,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
494,
1
] |
Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.SpecialLinear.eb_val | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.head_val' | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Dfinsupp/Multiset.lean | Multiset.toDfinsupp_toMultiset | [] | [
102,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_update_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np✝ q p : R[X]\nn : ℕ\na : R\ni : ℕ\n⊢ coeff (update p n a) i = if i = n then a else coeff p i",
"tactic": "rw [coeff_update, Function.update_apply]"
}
] | [
1093,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.eq_top_iff_one | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Semiring α\na b : α\n⊢ 1 ∈ ⊤",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b : α\n⊢ I = ⊤ → 1 ∈ I",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiri... | [
97,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Computability/Ackermann.lean | not_nat_primrec_ack_self | [
{
"state_after": "case intro\nh : Nat.Primrec fun n => ack n n\nm : ℕ\nhm : ∀ (n : ℕ), ack n n < ack m n\n⊢ False",
"state_before": "h : Nat.Primrec fun n => ack n n\n⊢ False",
"tactic": "cases' exists_lt_ack_of_nat_primrec h with m hm"
},
{
"state_after": "no goals",
"state_before": "case i... | [
385,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.seq_pre' | [] | [
154,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
151,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_inr | [] | [
992,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_map_eq_C | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝² : CommRing K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nf : K[X]\na : L\nh : map i f = ↑C a\nha : ¬a = 0\ng✝ : L[X]\nhg : Irreducible g✝\nx✝ : g✝ ∣ map i f\np : L[X]\nhp : map i f = g✝ * p\nthis : degree (map i f) = degree (g✝ * p)\n⊢ degree g✝ ... | [
76,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Finset.sum_powerset_neg_one_pow_card | [
{
"state_after": "R : Type ?u.208984\nα : Type u_1\ninst✝ : DecidableEq α\nx : Finset α\n⊢ ∑ m in range (card x + 1), Nat.choose (card x) m • (-1) ^ m = if x = ∅ then 1 else 0",
"state_before": "R : Type ?u.208984\nα : Type u_1\ninst✝ : DecidableEq α\nx : Finset α\n⊢ ∑ m in powerset x, (-1) ^ card m = if x ... | [
172,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_sdiff_dom | [] | [
866,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_bypass_subset | [] | [
1429,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1428,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.map_mod | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.214641\nβ : Type ?u.214644\nn d k N : ℕ\nx : Fin n → ℕ\na : Fin (succ n) → ℕ\n⊢ ↑(map d) a % d = a 0 % d",
"tactic": "rw [map_succ, Nat.add_mul_mod_self_right]"
}
] | [
144,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/GroupTheory/Sylow.lean | Subgroup.sylow_mem_fixedPoints_iff | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\nP : Sylow p G\n⊢ P ∈ fixedPoints { x // x ∈ H } (Sylow p G) ↔ ∀ ⦃x : G⦄, x ∈ H → x • P = P",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\nP : Sylow p G\n⊢ P ∈ fixedPoints { x // x ∈ H } (Sylow p G) ↔ H ≤ normal... | [
279,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/List/Sort.lean | List.sorted_lt_ofFn_iff | [] | [
153,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
9
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_pure_left | [] | [
3070,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3068,
1
] |
Mathlib/Logic/Embedding/Set.lean | subtypeOrEquiv_symm_inr | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_piiUnionInter | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u_1\nι : Type u_2\nπ : ι → Set (Set α)\nhpi : ∀ (x : ι), IsPiSystem (π x)\nS : Set ι\nt1 : Set α\np1 : Finset ι\nhp1S : ↑p1 ⊆ S\nf1 : ι → Set α\nhf1m : ∀ (x : ι), x ∈ p1 → f1 x ∈ π x\nht1_eq : t1 = ⋂ (x : ι) (_ : x ∈ p1), f1 x\nt2 ... | [
463,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongEpi_of_strongEpi | [
{
"state_after": "case sq_hasLift\nC : Type u\ninst✝¹ : Category C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\ninst✝ : StrongEpi (f ≫ g)\nX Y : C\nz : X ⟶ Y\nx✝ : Mono z\n⊢ ∀ {f : Q ⟶ X} {g_1 : R ⟶ Y} (sq : CommSq f g z g_1), CommSq.HasLift sq",
"state_before": "C : Type u\ninst✝¹ : Category C\nP Q R : C\nf : P ⟶ Q\n... | [
127,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_compl_inf_distrib | [
{
"state_after": "ι : Type ?u.164668\nα : Type u_1\nβ : Type ?u.164674\ninst✝ : HeytingAlgebra α\na✝ b✝ c a b : α\n⊢ aᶜᶜ ⊓ bᶜᶜ ≤ (a ⊓ b)ᶜᶜ",
"state_before": "ι : Type ?u.164668\nα : Type u_1\nβ : Type ?u.164674\ninst✝ : HeytingAlgebra α\na✝ b✝ c a b : α\n⊢ (a ⊓ b)ᶜᶜ = aᶜᶜ ⊓ bᶜᶜ",
"tactic": "refine' ((co... | [
933,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
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