file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformSpace_edist | [] | [
172,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.linear_eq_linear_isometry | [
{
"state_after": "case h\n𝕜 : Type u_3\nV : Type u_1\nV₁ : Type ?u.130542\nV₂ : Type u_2\nV₃ : Type ?u.130548\nV₄ : Type ?u.130551\nP₁ : Type ?u.130554\nP : Type u_4\nP₂ : Type u_5\nP₃ : Type ?u.130563\nP₄ : Type ?u.130566\ninst✝²⁰ : NormedField 𝕜\ninst✝¹⁹ : SeminormedAddCommGroup V\ninst✝¹⁸ : SeminormedAddCo... | [
333,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
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Mathlib/Computability/NFA.lean | NFA.mem_stepSet | [
{
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}
] | [
58,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.map_integral | [] | [
377,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/Order/Bounds/Basic.lean | upperBounds_mono_mem | [] | [
200,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_shadow_iff_exists_mem_card_add | [
{
"state_after": "case zero\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜✝ : Finset (Finset α)\ns✝ t : Finset α\na : α\nk r : ℕ\n𝒜 : Finset (Finset α)\ns : Finset α\n⊢ s ∈ (∂ ^[zero]) 𝒜 ↔ ∃ t, t ∈ 𝒜 ∧ s ⊆ t ∧ card t = card s + zero\n\ncase succ\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜✝ : Finset (Finset α)\ns✝ t :... | [
172,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_join | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nSS : WSeq (WSeq (WSeq α))\n⊢ ∀ {s t : WSeq α},\n (fun s1 s2 =>\n ∃ s S SS, s1 = append s (join (append S (join SS))) ∧ s2 = append s (append (join S) (join (map join SS))))\n s t →\n Computation.LiftRel\n (LiftRelO (fun x x_1 =... | [
1795,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1765,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_apply₁₂ | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add | [
{
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"tactic": "simp only [rpow_def_of_pos hx, mul_add, exp_add]"
}
] | [
177,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
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Mathlib/Algebra/Group/Units.lean | eq_divp_iff_mul_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b c x : α\nu : αˣ\ny : α\n⊢ x = y /ₚ u ↔ x * ↑u = y",
"tactic": "rw [eq_comm, divp_eq_iff_mul_eq]"
}
] | [
495,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
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Mathlib/Data/PNat/Defs.lean | PNat.mk_le_mk | [] | [
127,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Data/Finmap.lean | Finmap.not_mem_empty | [] | [
229,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
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Mathlib/Data/List/AList.lean | AList.perm_union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁ s₂ s₃ s₄ : AList β\np₁₂ : s₁.entries ~ s₂.entries\np₃₄ : s₃.entries ~ s₄.entries\n⊢ (s₁ ∪ s₃).entries ~ (s₂ ∪ s₄).entries",
"tactic": "simp [p₁₂.kunion s₃.nodupKeys p₃₄]"
}
] | [
448,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
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Mathlib/Algebra/Algebra/Subalgebra/Pointwise.lean | Subalgebra.mul_toSubmodule | [
{
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... | [
68,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | right_mem_affineSpan_pair | [] | [
1304,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
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Mathlib/Order/Filter/Basic.lean | Filter.Eventually.ne_of_lt | [] | [
1694,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.prod_map | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁷ : No... | [
1620,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.adjoinRoot_eq_top | [
{
"state_after": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf : R[X]\nx : AdjoinRoot f\n⊢ x ∈ Algebra.adjoin R {root f}",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf : R[X]\n⊢ Algebra.adjoin R {root f} = ⊤",
"tactic": "refine Algebra.eq_top_iff.2 fun x => ?_"... | [
243,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Mathlib/Data/Finsupp/BigOperators.lean | Finset.support_sum_subset | [
{
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"tactic": "classical convert Multiset.support_sum_subset s.1 ; simp"
},
{
"state_after": "case h.e... | [
59,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_image | [] | [
627,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_continuousMap_mk | [] | [
127,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.pathEquivList_symm_cons | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Std/Logic.lean | forall₂_congr | [] | [
382,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
380,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_nonneg | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : f ≈ 0\n⊢ 0 ≤ norm f",
"tactic": "simp [hf, norm]"
},
{
"state_after": "no goals",
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"tactic"... | [
174,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.continuous_equiv | [] | [
462,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
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] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasFDerivAt | [] | [
159,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
11
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Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_update | [
{
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93,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_pi | [] | [
1829,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1827,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_equivIco_mk_apply | [] | [
352,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsGreatest.csSup_eq | [] | [
547,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.WalkingParallelPairHom.comp_id | [
{
"state_after": "no goals",
"state_before": "X Y : WalkingParallelPair\nf : WalkingParallelPairHom X Y\n⊢ comp f (id Y) = f",
"tactic": "cases f <;> rfl"
}
] | [
104,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.equivBool_apply_right | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsion'_isTorsion' | [] | [
644,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.finiteType | [] | [
164,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.nonempty_iInter_clPrehaar | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nthis : IsCompact (haarProduct ↑K₀)\n⊢ Set.Nonempty (haarProduct ↑K₀ ∩ ⋂ (V : OpenNhdsOf 1), clPrehaar (↑K₀) V)",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : Topol... | [
388,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
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Std/Data/List/Basic.lean | List.headD_eq_head? | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\na : α\n⊢ headD l a = Option.getD (head? l) a",
"tactic": "cases l <;> rfl"
}
] | [
578,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
578,
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Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.ne_zero_of_order_ne_zero | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.const_pow | [] | [
243,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.ofRightExact_map | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.map_setToSimpleFunc | [
{
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Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_inf_map_of_injective | [] | [
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31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Dual.lean | Submodule.le_dualAnnihilator_dualCoannihilator | [] | [
883,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.add | [
{
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Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.HasShift.shift_obj_obj | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.comp | [
{
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Mathlib/Data/Real/CauSeq.lean | CauSeq.le_antisymm | [] | [
771,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.eq_preimage | [
{
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Ico_filter_pow_dvd_eq | [
{
"state_after": "case a\nn p b : ℕ\npp : Prime p\nhn : n ≠ 0\nhb : n ≤ p ^ b\nx : ℕ\n⊢ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Ico 1 n) ↔ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Icc 1 b)",
"state_before": "n p b : ℕ\npp : Prime p\nhn : n ≠ 0\nhb : n ≤ p ^ b\n⊢ Finset.filter (fun i => p ^ i ∣ n) (Ico 1 n) =... | [
745,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Congruence.lean | Con.mul_ker_mk_eq | [] | [
379,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_zero | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.lift.of | [] | [
735,
12
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Mathlib/Topology/Instances/NNReal.lean | tendsto_real_toNNReal | [] | [
128,
46
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126,
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Mathlib/Order/Category/PartOrdCat.lean | PartOrdCat.coe_of | [] | [
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Mathlib/Algebra/Hom/Units.lean | IsUnit.eq_mul_inv_iff_mul_eq | [] | [
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32
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_pure | [
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.coe_pullback | [] | [
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Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_eq_top | [
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.IsUniform.mono | [
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.coe_map | [] | [
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Mathlib/Data/Fin/Basic.lean | Fin.castLE_of_eq | [
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Mathlib/Algebra/Ring/Prod.lean | RingHom.coe_fst | [] | [
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Mathlib/Data/List/Sigma.lean | List.mem_keys_of_mem | [] | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_sub_le' | [
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Mathlib/Algebra/Ring/Commute.lean | Commute.sub_right | [] | [
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Mathlib/Combinatorics/Quiver/Push.lean | Quiver.Push.lift_unique | [
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.carrier_inj | [] | [
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.id_apply | [] | [
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Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.shadow_empty | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.const_sub | [] | [
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Mathlib/Analysis/Convex/Star.lean | starConvex_univ | [] | [
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Mathlib/Data/Nat/Pow.lean | Nat.pow_left_injective | [] | [
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47
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_op_mul | [] | [
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34
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.compLinearMap_inj | [] | [
437,
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Mathlib/Analysis/Convex/Basic.lean | AntitoneOn.convex_ge | [] | [
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54
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Mathlib/LinearAlgebra/TensorProduct/Matrix.lean | TensorProduct.toMatrix_map | [
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_mul_X_zero | [
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.mem_sInf | [] | [
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Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | HasFDerivAtFilter.restrictScalars | [] | [
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Mathlib/Data/Num/Lemmas.lean | PosNum.one_sub' | [
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Mathlib/Algebra/Order/Field/Basic.lean | inv_pow_lt_inv_pow_of_lt | [
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Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.normalClosure_finRotate_five | [
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252,
16
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Mathlib/Topology/ContinuousOn.lean | mem_nhdsWithin_iff_eventuallyEq | [
{
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89
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126,
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Mathlib/Data/Int/Bitwise.lean | Int.bodd_mul | [
{
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Mathlib/Data/Fintype/Card.lean | Infinite.exists_subset_card_eq | [
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_restrict_union | [
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Mathlib/Data/List/Dedup.lean | List.dedup_sublist | [] | [
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Mathlib/Data/Set/Pairwise/Basic.lean | pairwise_disjoint_mono | [] | [
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Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.map_zero | [] | [
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Mathlib/Algebra/Hom/Aut.lean | MulAut.conj_symm_apply | [] | [
162,
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Mathlib/Order/CompleteLattice.lean | sSup_eq_bot | [] | [
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62
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.hom_zero_zero | [
{
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Mathlib/Computability/Partrec.lean | Computable.pair | [
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Mathlib/GroupTheory/Congruence.lean | Con.sInf_toSetoid | [
{
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.pow_subset_pow_of_one_mem | [
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_add | [
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_const_preimage | [
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Mathlib/Algebra/Order/Algebra.lean | algebraMap_monotone | [
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Mathlib/Data/Rat/Defs.lean | Rat.gcd_abs_dvd_left | [] | [
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77
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Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.isOpen_target_of_mem_pretrivializationAtlas_inter | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.isRegular_cof | [] | [
972,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
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