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/Algebra/Ring/Prod.lean | NonUnitalRingHom.coe_prodMap | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_mul_swap_right | [] | [
380,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_nonempty_iff_nonempty | [] | [
740,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Int.cast_finsupp_sum | [] | [
413,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_mul | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.isUnit_mul_iff | [] | [
287,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_le_rpow_iff | [] | [
574,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_empty | [] | [
362,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Function.Surjective.le_map_cofinite | [] | [
193,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | pow_bit1_neg_iff | [] | [
716,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nndist_eq_nnnorm_div | [] | [
906,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_const_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.5974976\nF : Type u_2\nG : Type ?u.5974982\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\n𝕜 : Type u_3\ninst✝⁴ : NormedDivisionR... | [
1565,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
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Mathlib/Logic/Basic.lean | forall_of_ball | [] | [
1065,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
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Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.map_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_1\ninst✝² : Ring R\ninst✝¹ : OrderedCommRing S\nabv : AbsoluteValue R S\ninst✝ : NoZeroDivisors S\na b : R\n⊢ ↑abv (a - b) = ↑abv (b - a)",
"tactic": "rw [← neg_sub, abv.map_neg]"
}
] | [
244,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_singleton | [] | [
665,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Ioc_of_monotone_surjective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Monotone f\nh_surj : Surjective f\na b : α\n⊢ SurjOn f (Ioc a b) (Ioc (f a) (f b))",
"tactic": "simpa using surjOn_Ico_of_monotone_surjective h_mono.dual h_surj (... | [
53,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.right_eq_id | [] | [
335,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.range_finite | [] | [
379,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.fst_prod | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type u_3\nC : Type u_4\ninst✝⁹ : Monoid R\ninst✝⁸ : NonUnitalNonAssocSemiring A\ninst✝⁷ : DistribMulAction R A\ninst✝⁶ : Star A\ninst✝⁵ : NonUnitalNonAssocSemiring B\ninst✝⁴ : DistribMulAction R B\ninst✝³ : Star B\ninst✝² : NonUnitalNonAssocSemiring C\ni... | [
534,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
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Mathlib/Algebra/Star/Basic.lean | star_id_of_comm | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_strictMono | [] | [
239,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Topology/Algebra/StarSubalgebra.lean | StarSubalgebra.isClosed_topologicalClosure | [] | [
92,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mul_div_root_cancel | [] | [
428,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Init/Algebra/Order.lean | compare_lt_iff_lt | [
{
"state_after": "α : Type u\ninst✝ : LinearOrder α\na b : α\n⊢ (if a < b then Ordering.lt else if a = b then Ordering.eq else Ordering.gt) = Ordering.lt ↔ a < b",
"state_before": "α : Type u\ninst✝ : LinearOrder α\na b : α\n⊢ compare a b = Ordering.lt ↔ a < b",
"tactic": "rw [LinearOrder.compare_eq_com... | [
426,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.pmap_eq_map | [] | [
1514,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.apply_eq_of_preconnectedSpace | [] | [
389,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.subtype_injective | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝¹ : Group G\nP✝ : Sylow p G\nK : Type ?u.48738\ninst✝ : Group K\nϕ : K →* G\nN : Subgroup G\nP Q : Sylow p G\nhP : ↑P ≤ N\nhQ : ↑Q ≤ N\nh✝ : Sylow.subtype P hP = Sylow.subtype Q hQ\nh : ∀ (x : { x // x ∈ N }), x ∈ Sylow.subtype P hP ↔ x ∈ Sylow.subtype Q hQ\n⊢ ∀ (x : ... | [
143,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Data/Rat/Defs.lean | Rat.pos | [] | [
41,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_eq_bot | [] | [
2911,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2910,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_zero | [
{
"state_after": "no goals",
"state_before": "⊢ arg 0 = 0",
"tactic": "simp [arg, le_refl]"
}
] | [
123,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_reindex | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.175068\nm : Type u_1\nn : Type u_2\no : Type ?u.175077\nR : Type u_3\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : CommRing R\ninst✝ : Fintype m\ne₁ e₂ : m ≃ n\nA : Matrix m m R\n⊢ rank (↑(reindex e₁ e₂) A) = rank A",
"tact... | [
119,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isCompact_iff_isClosed_bounded | [] | [
2530,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2528,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousMul β\nhf : SuperpolynomialDecay l k f\nhg : SuperpolynomialDecay l k g\nz : ℕ\n⊢ Tendsto (fun a => k a ^ z * (f * g) a) l (𝓝 0)"... | [
94,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_singleton_default_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.502615\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : α\nxs : List α\nd : α\nn✝ n : ℕ\n⊢ getD [d] n d = d",
"tactic": "cases n <;> simp"
}
] | [
4417,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4417,
1
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Std/Data/String/Lemmas.lean | String.get'_eq | [] | [
309,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
309,
9
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.pre_post | [
{
"state_after": "J : Type u₁\ninst✝⁶ : Category J\nK : Type u₂\ninst✝⁵ : Category K\nC : Type u\ninst✝⁴ : Category C\nF✝ : J ⥤ C\nD : Type u'\ninst✝³ : Category D\nE : K ⥤ J\nF : J ⥤ C\nG : C ⥤ D\ninst✝² : HasLimit F\ninst✝¹ : HasLimit (E ⋙ F)\ninst✝ : HasLimit (F ⋙ G)\nh : HasLimit ((E ⋙ F) ⋙ G)\nthis : HasLi... | [
496,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Pairwise.forall | [] | [
115,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/MinMax.lean | max_le_max | [] | [
76,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Down.mem_compression_of_insert_mem_compression | [
{
"state_after": "case pos\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\nh : insert a s ∈ 𝓓 a 𝒜\nha : a ∈ s\n⊢ s ∈ 𝓓 a 𝒜\n\ncase neg\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\nh : insert a s ∈ 𝓓 a 𝒜\nha : ¬a ∈ s\n⊢ s ∈ 𝓓 a �... | [
194,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_orderOf_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y✝ : G\na b : A\nn m : ℕ\ninst✝² : Monoid G\ninst✝¹ : AddMonoid A\nH : Type u_1\ninst✝ : Monoid H\ny : H\n⊢ orderOf x = orderOf y ↔ ∀ (n : ℕ), x ^ n = 1 ↔ y ^ n = 1",
"tactic": "simp_rw [← isPeriodicPt_mul_iff_pow_eq_one, ← minimalP... | [
328,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_preimage_ofDual_iff | [] | [
175,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.IsBilimit.binary_total | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nb : BinaryBicone X Y\ni : BinaryBicone.IsBilimit b\nj : Discrete WalkingPair\n⊢ (b.fst ≫ b.inl + b.snd ≫ b.inr) ≫ (BinaryBicone.toCone b).π.app j = 𝟙 b.pt ≫ (BinaryBi... | [
324,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
src/lean/Init/SimpLemmas.lean | true_and | [] | [
84,
88
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
84,
9
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.isBigO_sub_exp_exp | [
{
"state_after": "E : Type u_1\ninst✝ : NormedAddCommGroup E\na : ℝ\nf g : ℂ → E\nl : Filter ℂ\nu : ℂ → ℝ\nhBf : ∃ c, c < a ∧ ∃ B, f =O[l] fun z => expR (B * expR (c * Abs.abs (u z)))\nhBg : ∃ c, c < a ∧ ∃ B, g =O[l] fun z => expR (B * expR (c * Abs.abs (u z)))\nthis :\n ∀ {c₁ c₂ B₁ B₂ : ℝ},\n c₁ ≤ c₂ →\n ... | [
81,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isLinearOrder | [] | [
375,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
11
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ring.DimensionLeOne.prime_le_prime_iff_eq | [] | [
1200,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1198,
1
] |
Mathlib/Computability/Language.lean | Language.mem_mul | [] | [
117,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | PreErgodic.of_iterate | [] | [
79,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Computability/Encoding.lean | Computability.encodePosNum_nonempty | [] | [
133,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.ρ_one | [
{
"state_after": "V : Type (u + 1)\ninst✝ : LargeCategory V\nG : MonCat\nA : Action V G\n⊢ 1 = 𝟙 A.V",
"state_before": "V : Type (u + 1)\ninst✝ : LargeCategory V\nG : MonCat\nA : Action V G\n⊢ ↑A.ρ 1 = 𝟙 A.V",
"tactic": "rw [MonoidHom.map_one]"
},
{
"state_after": "no goals",
"state_before... | [
67,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_multiset_prod | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.471246\nr : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\ns : Multiset (MvPolynomial σ R)\nl : List (MvPolynomial σ R)\n⊢ totalDegree (Multiset.prod (Quotient.mk (List.isSetoid (MvPolynomial σ R)) l)) ≤\n Mu... | [
740,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_congr | [
{
"state_after": "R✝ : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R✝\nm n : ℕ\ninst✝³ : Semiring R✝\np q r : R✝[X]\ninst✝² : Semiring S✝\nf✝ : R✝ →+* S✝\nx : S✝\nR : Type u_1\nS : Type u_2\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nf : R →+* S\ns : S\nφ : R[X]\n⊢ eval₂ f s φ = eval₂ f s φ",
"state_be... | [
58,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.coe_algebraMap | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_sub | [] | [
198,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq_of_eq | [] | [
444,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.constr_range | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.531644\nR : Type u_3\nR₂ : Type ?u.531650\nK : Type ?u.531653\nM : Type u_4\nM' : Type u_2\nM'' : Type ?u.531662\nV : Type u\nV' : Type ?u.531667\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\ninst✝⁵ : AddCommMono... | [
653,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_prod | [] | [
1659,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_vecAlt1 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.52150\nn' : Type ?u.52153\no' : Type ?u.52156\nh : m + 1 + 1 = n + 1 + (n + 1)\nx y : α\nu : Fin m → α\n⊢ m = n + n",
"tactic": "rwa [add_assoc n, add_comm 1, ← add_assoc, ← add_assoc, add_right_cancel_iff,\n add_right_ca... | [
419,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/Set/Finite.lean | Set.iSup_iInf_of_antitone | [] | [
1507,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.induce_spanningCoe | [] | [
1321,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_right_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_5\nβ : Type u_6\nγ : Type u_4\nf✝ : α → β → γ\na : Option α\nb : Option β\nc : Option γ\nδ : Type u_1\nε : Type u_2\nδ' : Type u_3\nf : δ → γ → ε\ng : α → β → δ\nf' : α → γ → δ'\ng' : δ' → β → ε\nh_right_comm : ∀ (a : α) (b : β) (c : γ), f (g a b) c =... | [
143,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_gcd_self_left_left | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd (gcd m n) m = gcd m n",
"tactic": "rw [gcd_comm m n, gcd_gcd_self_left_right]"
}
] | [
171,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
170,
9
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_ne_zero | [] | [
531,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | split_equalCharZero_mixedCharZero | [
{
"state_after": "case pos\nR : Type u_1\ninst✝¹ : CommRing R\nP : Prop\ninst✝ : CharZero R\nh_equal : Algebra ℚ R → P\nh_mixed : ∀ (p : ℕ), Nat.Prime p → MixedCharZero R p → P\nh : ∃ p, p > 0 ∧ MixedCharZero R p\n⊢ P\n\ncase neg\nR : Type u_1\ninst✝¹ : CommRing R\nP : Prop\ninst✝ : CharZero R\nh_equal : Algebr... | [
337,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.coe_pointwise_smul | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_neg | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b : X ⟶ Y\n⊢ a + -b = a - b",
"tactic": "rw [add_def, neg_neg]"
}
] | [
400,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/UInt.lean | UInt8.toChar_aux | [
{
"state_after": "n : ℕ\nh : n < size\n⊢ Nat.isValidChar n\n\nn : ℕ\nh : n < size\n⊢ n < UInt32.size",
"state_before": "n : ℕ\nh : n < size\n⊢ Nat.isValidChar ↑(UInt32.ofNat n).val",
"tactic": "rw [UInt32.val_eq_of_lt]"
},
{
"state_after": "n : ℕ\nh : n < size\n⊢ n < UInt32.size",
"state_bef... | [
124,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Ico | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\nthis : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)\n⊢ (fun x => a - x) '' Ico b c = Ioc (a - c) (a - b)",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : ... | [
353,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.mk_ι_app_left | [] | [
840,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Combinatorics/Hall/Basic.lean | Fintype.all_card_le_filter_rel_iff_exists_injective | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : Fintype β\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\nthis : DecidableEq β\n⊢ (∀ (A : Finset α), Finset.card A ≤ Finset.card (filter (fun b => ∃ a, a ∈ A ∧ r a b) univ)) ↔\n ∃ f, Function.Injective f ∧ ∀ (x : α), r x (f x)",
"state_before":... | [
228,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.tsum_eq_add_tsum_ite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.330764\nγ : Type ?u.330767\nf : α → ℝ≥0\nhf : Summable f\ni i' : α\n⊢ update (fun x => f x) i 0 i' ≤ f i'",
"state_before": "α : Type u_1\nβ : Type ?u.330764\nγ : Type ?u.330767\nf : α → ℝ≥0\nhf : Summable f\ni : α\n⊢ (∑' (x : α), f x) = f i + ∑' (x : α), if x = i... | [
1234,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/Order/MinMax.lean | le_max_iff | [] | [
42,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | Continuous.exists_forall_ge | [] | [
333,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Filter.EventuallyEq.trans_isLittleO | [] | [
383,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_mul | [
{
"state_after": "case pos\na b c : Ordinal\nb0 : b = 0\n⊢ a ^ (b * c) = (a ^ b) ^ c\n\ncase neg\na b c : Ordinal\nb0 : ¬b = 0\n⊢ a ^ (b * c) = (a ^ b) ^ c",
"state_before": "a b c : Ordinal\n⊢ a ^ (b * c) = (a ^ b) ^ c",
"tactic": "by_cases b0 : b = 0"
},
{
"state_after": "case pos\na b c : Ord... | [
248,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.insert'_eq_insertWith | [
{
"state_after": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (match cmpLE x y with\n | Ordering.lt => balanceL (insert' x l) y r\n | Ordering.eq => node size✝ l y r\n | Ordering.gt => balanceR l y (insert' x r))... | [
1556,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.tendsto_comap_nhds_nhds | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_4\nδ : Type u_3\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ni : α → β\ndi✝ : DenseInducing i\ninst✝ : TopologicalSpace δ\nf : γ → α\ng : γ → δ\nh : δ → β\nd : δ\na : α\ndi : DenseInducing i\nH : Tendsto h (𝓝 d) (𝓝 (i a))\ncomm : h ∘ g = i... | [
128,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.eq_mk_of_mem | [] | [
66,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Order/Lattice.lean | inf_left_comm | [] | [
524,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_unit | [] | [
415,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Closed.lean | ModuleCat.ihom_map_apply | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nndist_le_two_nnnorm | [] | [
1011,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Finset.infsep_pos_iff_nontrivial | [] | [
570,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.congr | [] | [
146,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.map_polynomial_aeval_of_degree_pos | [
{
"state_after": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : IsAlgClosed 𝕜\na : A\np : 𝕜[X]\nhdeg : 0 < degree p\nk : 𝕜\nhk : k ∈ σ (↑(aeval a) p)\n⊢ k ∈ (fun x => eval x p) '' σ a",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Rin... | [
122,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_symm | [
{
"state_after": "no goals",
"state_before": "n k : ℕ\nhk : k ≤ n\n⊢ choose n (n - k) = choose n k",
"tactic": "rw [choose_eq_factorial_div_factorial hk, choose_eq_factorial_div_factorial (Nat.sub_le _ _),\n tsub_tsub_cancel_of_le hk, mul_comm]"
}
] | [
197,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_X_left | [] | [
1459,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.abs_integral_mono_interval | [] | [
1418,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.Ioc_succ_singleton | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Ioc b (b + 1) = {b + 1}",
"tactic": "rw [← Nat.Icc_succ_left, Icc_self]"
}
] | [
195,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_singleton | [] | [
354,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ici | [] | [
73,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.iso_symm_comp | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type ?u.700210\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\nins... | [
841,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Init/Classical.lean | Classical.cases | [] | [
31,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_coe_nnreal_restrict | [] | [
780,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_not_not | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a b : Bool), (xor (!a) !b) = xor a b",
"tactic": "decide"
}
] | [
282,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.coe_add_get | [
{
"state_after": "no goals",
"state_before": "x : ℕ\ny : PartENat\nh : (↑x + y).Dom\n⊢ Part.get (↑x + y) h = x + Part.get y (_ : y.Dom)",
"tactic": "rfl"
}
] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_add_measure_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.400090\nι : Type ?u.400093\ninst✝³ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\nf g : α → β\ninst✝ : PseudoMetrizableSpace β\nν : Measure α\n⊢ AEStronglyMeasurable f (bif true then μ else ... | [
1694,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/Logic/Basic.lean | Decidable.or_not_of_imp | [] | [
366,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
11
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsUnit.tendsto_const_smul_iff | [] | [
404,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
8
] |
Mathlib/RepresentationTheory/Action.lean | Action.associator_inv_hom | [
{
"state_after": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX Y Z : Action V G\n⊢ ((𝟙 X.V ⊗ 𝟙 (Y.V ⊗ Z.V)) ≫ (α_ X.V Y.V Z.V).inv) ≫ (𝟙 (X.V ⊗ Y.V) ⊗ 𝟙 Z.V) = (α_ X.V Y.V Z.V).inv",
"state_before": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ :... | [
522,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
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