file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/GroupTheory/OrderOfElement.lean | pow_card_eq_one' | [] | [
936,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.nonempty | [] | [
242,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
11
] |
Mathlib/Data/List/Infix.lean | List.tail_sublist | [] | [
183,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/Computability/Primrec.lean | Primrec.list_getI | [] | [
1097,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
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Mathlib/Data/List/Rdrop.lean | List.rdrop_nil | [
{
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"tactic": "simp [rdrop]"
}
] | [
49,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_eq_norm_mul_iff_div | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.3199819\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\nh₀ h₀' : x ≠ 0\n⊢ inner x y = ↑‖x‖ * ↑‖y‖ ↔ (↑‖y‖ / ↑‖x‖) • x = y"... | [
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Mathlib/Data/Int/Parity.lean | Int.Odd.of_mul_left | [] | [
150,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBy_one | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set R\na : R\nx✝ : M\nh : x✝ = 0\n⊢ x✝ ∈ ⊥",
"state_before": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : Set R\na : R\nx✝ : M\n... | [
307,
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Mathlib/Data/Set/Prod.lean | Set.mk_preimage_prod_right | [
{
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233,
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231,
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Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | one_add_mul_self_lt_rpow_one_add | [
{
"state_after": "case inl\np : ℝ\nhp : 1 < p\nhs : -1 ≤ -1\nhs' : -1 ≠ 0\n⊢ 1 + p * -1 < (1 + -1) ^ p\n\ncase inr\ns : ℝ\nhs✝ : -1 ≤ s\nhs' : s ≠ 0\np : ℝ\nhp : 1 < p\nhs : -1 < s\n⊢ 1 + p * s < (1 + s) ^ p",
"state_before": "s : ℝ\nhs : -1 ≤ s\nhs' : s ≠ 0\np : ℝ\nhp : 1 < p\n⊢ 1 + p * s < (1 + s) ^ p",
... | [
220,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/RingTheory/Ideal/Over.lean | Ideal.comap_lt_comap_of_root_mem_sdiff | [] | [
232,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Std/Data/Int/Lemmas.lean | Int.le_add_of_neg_le_sub_right | [] | [
1022,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1021,
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Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.borel_le_caratheodory | [
{
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"state_before": "G : Type w\ninst✝² : TopologicalSpace G\nμ : Content G\ninst✝¹ : T2Space G\nS : Measura... | [
378,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
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Mathlib/Order/UpperLower/Hom.lean | LowerSet.coe_iicInfHom | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
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Mathlib/Algebra/Order/Floor.lean | Int.sub_one_lt_floor | [] | [
692,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_pow | [
{
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378,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.isClosed_cthickening | [] | [
1051,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc | [
{
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647,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_iUnion_mem_option | [
{
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"tactic": "cases o <;> sim... | [
920,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
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Mathlib/Data/Finset/Basic.lean | Finset.not_nonempty_iff_eq_empty | [] | [
613,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
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Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.min | [] | [
521,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
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] |
Mathlib/Analysis/Calculus/Deriv/Prod.lean | HasStrictDerivAt.prod | [] | [
76,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
8
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.mul_add | [
{
"state_after": "no goals",
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"tactic": "simp only [coeff_mul, mul_add, Finset.sum_add_distrib, LinearMap.map_... | [
278,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.of_measurable_inverse | [] | [
1573,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/CategoryTheory/Grothendieck.lean | CategoryTheory.Grothendieck.id_fiber' | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.14362\nD : Type ?u.14365\ninst✝¹ : Category C\ninst✝ : Category D\nF : C ⥤ Cat\nX : Grothendieck F\n⊢ (F.map (𝟙 X).base).obj X.fiber = X.fiber",
"tactic": "erw [CategoryTheory.Functor.map_id, Functor.id_obj X.fiber]"
}
] | [
133,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_eq_one_iff_dvd | [
{
"state_after": "case intro\nM : Type u_1\nN : Type ?u.1660609\nG : Type ?u.1660612\nR : Type ?u.1660615\nS : Type ?u.1660618\nF : Type ?u.1660621\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk l : ℕ\nζ : M\nf : F\nh : IsPrimitiveRoot ζ k\ni : ℕ\n⊢ ζ ^ (k * i) = 1",
"state_b... | [
364,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_inv_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DivisionRing α\n⊢ (↑1)⁻¹ = ↑1",
"tactic": "simp"
}
] | [
493,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.continuous_equiv_symm | [] | [
467,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.preimage_of_injOn | [] | [
148,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_lt_sum' | [] | [
711,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.BicartesianSq.of_is_biproduct₁ | [] | [
940,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffWithinAt_id | [] | [
178,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_Iio | [] | [
2359,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2358,
1
] |
Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsMaxOn.closure | [] | [
32,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
11
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.pow_left | [
{
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"state_before": "R : Type u\nI : Type v\ninst✝ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\nm n : ℕ\nH : IsCoprime x y\n⊢ IsCoprime ... | [
194,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/Data/Set/Image.lean | Set.preimage_id | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.toAddMonoidHom_injective | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.210329\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.210338\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf✝ g✝ f g : NormedAddGroupHom V₁ V₂\nh : toAddMon... | [
159,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_snd | [] | [
2184,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2182,
1
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src/lean/Init/Data/List/Basic.lean | List.drop_eq_nil_of_le | [
{
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"tactic": "match as, i with\n| [], i => simp\n| _::_, 0 => simp at h\n| _::as, i+1 => simp at h; exact @drop_eq_nil_of_le as i (Nat.le_of_succ_le_succ h)... | [
857,
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853,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_monotone | [] | [
516,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.evalList_sort_loop_swap | [
{
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"tactic": "induction ys generalizing y xs with\n| nil => simp [sort.loop, evalList_inser... | [
223,
37
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.ι_pre | [
{
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"state_before": "J : Type u₁\ninst✝⁴ : Category J\n... | [
976,
6
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974,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.count_support_takeUntil_eq_one | [
{
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93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
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Mathlib/Data/Finset/Basic.lean | Finset.union_val_nd | [] | [
1331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.disjoint_iff_comap_eq_bot | [
{
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Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.exact_of_split | [
{
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58
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Mathlib/Data/Part.lean | Part.some_injective | [] | [
217,
50
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216,
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Mathlib/Data/List/Basic.lean | List.reduceOption_map | [
{
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3440,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3434,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.chebyshev_T_eq_dickson_one_one | [
{
"state_after": "R : Type u_1\nS : Type ?u.201283\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nk : ℕ\na : R\ninst✝ : Invertible 2\nn : ℕ\n⊢ Chebyshev.T R n = ↑C ⅟2 * (↑2 * comp (Chebyshev.T R n) (↑C ⅟2 * (2 * X)))",
"state_before": "R : Type u_1\nS : Type ?u.201283\ninst✝² : CommRing R\ninst✝¹ : CommRing S\n... | [
174,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.exists_eq_range | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nhc : Set.Countable s\nhs : Set.Nonempty s\nf : ℕ → ↑s\nhf : Surjective f\n⊢ ∃ f, s = range f",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nhc : Set.Countable s\nhs : Set.Nonempty s\n⊢ ∃ f... | [
125,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.sInter_sets | [
{
"state_after": "α : Type u_1\nβ : Type ?u.68520\nγ : Type ?u.68523\nι : Sort u_2\nι' : Sort ?u.68529\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nh : HasBasis l p s\n⊢ (⋂ (i : Set α) (_ : i ∈ l.sets), i) = ⋂ (i : ι) (_ : p i), s i",
"state_befo... | [
829,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.omega_le | [
{
"state_after": "o : Ordinal\nH : ∀ (n : ℕ), ↑n ≤ o\na : Ordinal\nh : a < ω\nn : ℕ\ne : a = ↑n\n⊢ a < o",
"state_before": "o : Ordinal\nH : ∀ (n : ℕ), ↑n ≤ o\na : Ordinal\nh : a < ω\n⊢ a < o",
"tactic": "let ⟨n, e⟩ := lt_omega.1 h"
},
{
"state_after": "o : Ordinal\nH : ∀ (n : ℕ), ↑n ≤ o\na : Or... | [
2433,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2429,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.map_isFunc | [] | [
1405,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1396,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | AddMonoidHom.completion_zero | [
{
"state_after": "case h\nM : Type ?u.263181\nR : Type ?u.263184\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : UniformSpace α\ninst✝⁴ : AddGroup α\ninst✝³ : UniformAddGroup α\ninst✝² : UniformSpace β\ninst✝¹ : AddGroup β\ninst✝ : UniformAddGroup β\nx : Completion α\n⊢ ↑(completion 0 (_ : Continuous fun x => AddZeroClas... | [
291,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformCauchySeqOn_iff | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nX : Type ?u.218356\nι : Type ?u.218359\ninst✝² : PseudoMetricSpace α\ninst✝¹ : Nonempty β\ninst✝ : SemilatticeSup β\nγ : Type u_1\nF : β → γ → α\ns : Set γ\n⊢ UniformCauchySeqOn F atTop s →\n ∀ (ε : ℝ), ε > 0 → ∃ N, ∀ (m : β), m ≥ N → ∀ (n : β), n ≥ N → ∀ (x... | [
1534,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1515,
1
] |
Std/Data/String/Lemmas.lean | String.utf8Len_le_of_suffix | [] | [
74,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
73,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_subset_ge_of_subset_image_lift | [
{
"state_after": "α✝ β✝ α : Type u\nβ : Type v\nf : α → β\ns : Set α\nt : Set β\nh : t ⊆ range fun x => f ↑x\n⊢ lift (#↑t) ≤ lift (#↑{x | x ∈ s ∧ f x ∈ t})",
"state_before": "α✝ β✝ α : Type u\nβ : Type v\nf : α → β\ns : Set α\nt : Set β\nh : t ⊆ f '' s\n⊢ lift (#↑t) ≤ lift (#↑{x | x ∈ s ∧ f x ∈ t})",
"t... | [
2212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2207,
1
] |
Mathlib/Topology/OmegaCompletePartialOrder.lean | scottContinuous_of_continuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : OmegaCompletePartialOrder α\ninst✝ : OmegaCompletePartialOrder β\nf : Scott α → Scott β\nhf : ∀ (s : Set (Scott β)), IsOpen s → IsOpen {x | f x ∈ s}\nh : Monotone f\n⊢ Continuous' f",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : OmegaCompletePa... | [
148,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_smul | [
{
"state_after": "R : Type u_3\nA : Type u_2\nB : Type ?u.660893\nS : Type u_1\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\nf : R →+* S\ninst✝² : Algebra S A\ninst✝¹ : Algebra R S\ninst✝ : IsScalarTower R S A\nx : A\nr : R\nhx :... | [
535,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_lt_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.13215\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.13247\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y : (i : ι) → β i\n⊢ hammingDist x y < 1 ↔ x = y",
"tactic": "rw [Nat.lt_one_iff, hammi... | [
127,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.range_id | [] | [
922,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_diagonal_iff | [] | [
477,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.InitialMonoClass.of_initial | [] | [
536,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.empty_subset | [] | [
412,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_fuse | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np : Poly\n⊢ denote ctx (fuse p) = denote ctx p",
"tactic": "match p with\n| [] => rfl\n| (k, v) :: p =>\n have ih := denote_fuse ctx p\n simp\n split\n case _ h => simp [← ih, h]\n case _ k' v' p' h => by_cases he : v == v' <;> simp [he, ... | [
331,
89
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
323,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Module.lean | Summable.smul_const | [] | [
29,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mk'_eq | [] | [
506,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.coe_ker | [] | [
2773,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2772,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_lift | [] | [
727,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_mod | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ↑(m % n) = ↑m % ↑n",
"tactic": "rw [← add_left_cancel, div_add_mod, ← nat_cast_div, ← nat_cast_mul, ← Nat.cast_add,\n Nat.div_add_mod]"
}
] | [
2358,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2356,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.FineSubfamilyOn.index_subset | [] | [
135,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_mul_inv_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a * b⁻¹ < c * d⁻¹ ↔ a * d < c * b",
"tactic": "rw [mul_comm c, mul_inv_lt_inv_mul_iff, mul_comm]"
}
] | [
566,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_commute | [
{
"state_after": "case h\nF : Type ?u.196819\nι : Type ?u.196822\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.196831\nf✝ : α → β → β\nop : α → α → α\ninst✝¹ : Monoid β\ninst✝ : Monoid γ\ns : Finset α\nf : α → β\ncomm : Set.Pairwise ↑s fun a b => Commute (f a) (f b)\ny : β\nh : ∀ (x : α), x ∈ s → Commute y (f x)\n⊢ ... | [
344,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.ext_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14308\nγ : Type ?u.14311\nι : Type ?u.14314\nM : Type u_2\nM' : Type ?u.14320\nN : Type ?u.14323\nP : Type ?u.14326\nG : Type ?u.14329\nH : Type ?u.14332\nR : Type ?u.14335\nS : Type ?u.14338\ninst✝ : Zero M\nf g : α →₀ M\nx✝ : f.suppor... | [
213,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.toFun_eq_coe_aux | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_eq_sep_prod | [] | [
570,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | continuousAt_of_locally_lipschitz | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf : α → β\nx : α\nr : ℝ\nhr : 0 < r\nK : ℝ\nh : ∀ (y : α), dist y x < r → dist (f y) (f x) ≤ K * dist y x\n⊢ Tendsto (fun a => K * dist a x) (𝓝 x) (𝓝 0)",
"state_before": "α : Type ... | [
632,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.isSubterminal_of_mono_isTerminal_from | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nA T : C\nhT : IsTerminal T\ninst✝ : Mono (IsTerminal.from hT A)\nZ : C\nf g : Z ⟶ A\n⊢ f ≫ IsTerminal.from hT A = g ≫ IsTerminal.from hT A",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nA T : C\nhT : IsTerminal T\ninst✝ : Mono (IsTerminal.from hT A)\... | [
76,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_pow | [] | [
80,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Connected.lean | connectedComponentIn_nonempty_iff | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.50542\nπ : ι → Type ?u.50547\ninst✝ : TopologicalSpace α\ns t u v : Set α\nx : α\nF : Set α\n⊢ Set.Nonempty (if h : x ∈ F then Subtype.val '' connectedComponent { val := x, property := h } else ∅) ↔ x ∈ F",
"state_before": "α : Type u\nβ : Type v\nι : Ty... | [
611,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.restrict | [] | [
1247,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
11
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NormedAddCommGroup.tendsto_atTop' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ✝ : Type ?u.395811\nγ : Type ?u.395814\nι : Type ?u.395817\ninst✝³ : Nonempty α\ninst✝² : SemilatticeSup α\ninst✝¹ : NoMaxOrder α\nβ : Type u_2\ninst✝ : SeminormedAddCommGroup β\nf : α → β\nb : β\n⊢ (∀ (ib : ℝ), 0 < ib → ∃ ia, True ∧ ∀ (x : α), x ... | [
862,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.gcd_eq_sup | [] | [
875,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Topology/Order/Basic.lean | Icc_mem_nhds | [] | [
357,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_zero | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.116542\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝ x : 𝕜\n⊢ iteratedDeriv 0 f x = f x",
"state_be... | [
252,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Seq/Parallel.lean | Computation.parallel_congr_lem | [] | [
380,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.apply_eq_iff_eq | [] | [
828,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Std/Data/List/Lemmas.lean | List.mem_insert_self | [] | [
908,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
907,
14
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.continuousAt_tan | [
{
"state_after": "x : ℝ\nhc : ContinuousAt tan x\nh₀ : cos x = 0\n⊢ False",
"state_before": "x : ℝ\n⊢ ContinuousAt tan x ↔ cos x ≠ 0",
"tactic": "refine' ⟨fun hc h₀ => _, fun h => (hasDerivAt_tan h).continuousAt⟩"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhc : ContinuousAt tan ... | [
56,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Std/Data/AssocList.lean | Std.AssocList.modify_toList | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β → β\ninst✝ : BEq α\na : α\nl : AssocList α β\n⊢ toList (modify a f l) =\n List.replaceF\n (fun x =>\n match x.fst == a with\n | true => some (a, f x.fst x.snd)\n | false => none)\n (toList l)",
"state_before": "α : Typ... | [
200,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
195,
9
] |
Mathlib/Data/List/Rotate.lean | List.rotate_eq_self_iff_eq_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u\nhα : Nonempty α\n⊢ (∀ (n : ℕ), rotate [] n = []) ↔ ∃ a, [] = replicate (length []) a",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nhα : Nonempty α\na : α\nl : List α\nh : ∀ (n : ℕ), rotate (a :: l) n ... | [
315,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subsingleton.antitone | [] | [
487,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
11
] |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.closed_range | [
{
"state_after": "case intro.intro\nV : Type u\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : CompleteSpace V\nB : V →L[ℝ] V →L[ℝ] ℝ\ncoercive : IsCoercive B\nw✝ : ℝ≥0\nleft✝ : 0 < w✝\nantilipschitz : AntilipschitzWith w✝ ↑(continuousLinearMapOfBilin B)\n⊢ IsClosed ↑(range (continuousLi... | [
90,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Separation.lean | Bornology.relativelyCompact_eq_inCompact | [] | [
1278,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_injective | [] | [
483,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.mono_set_ae | [] | [
139,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Parity.lean | Even.neg_one_pow | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.24624\nα : Type u_1\nβ : Type ?u.24630\nR : Type ?u.24633\ninst✝¹ : Monoid α\nn : ℕ\na : α\ninst✝ : HasDistribNeg α\nh : Even n\n⊢ (-1) ^ n = 1",
"tactic": "rw [h.neg_pow, one_pow]"
}
] | [
140,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.inl_map_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.148405\nM₆ : Type ?u.148408\nS : Type ?u.148411\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : Semiring S\ninst✝¹⁵ : AddCommMonoid M\n... | [
404,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ringEquivOfRingEquiv_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommSemiring R\nM : Submonoid R\nS : Type u_4\ninst✝⁶ : CommSemiring S\ninst✝⁵ : Algebra R S\nP : Type u_2\ninst✝⁴ : CommSemiring P\ninst✝³ : IsLocalization M S\ng : R →+* P\nhg : ∀ (y : { x // x ∈ M }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ ... | [
704,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteSpanningSetsIn.isCountablySpanning | [] | [
3762,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3761,
11
] |
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