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/Data/Set/Lattice.lean | Set.sUnion_eq_compl_sInter_compl | [
{
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1244,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.continuous_from_bounded | [
{
"state_after": "𝕜 : Type ?u.555943\n𝕜₂ : Type ?u.555946\n𝕝 : Type u_1\n𝕝₂ : Type u_4\nE : Type u_2\nF : Type u_5\nG : Type ?u.555961\nι : Type u_3\nι' : Type u_6\ninst✝¹⁷ : NontriviallyNormedField 𝕜\ninst✝¹⁶ : AddCommGroup E\ninst✝¹⁵ : Module 𝕜 E\ninst✝¹⁴ : NormedField 𝕝\ninst✝¹³ : Module 𝕝 E\ninst✝¹²... | [
645,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | Filter.Tendsto.integral_sub_linear_isLittleO_ae | [
{
"state_after": "α : Type u_2\nβ : Type ?u.355571\nE : Type u_1\nF : Type ?u.355577\ninst✝⁴ : MeasurableSpace α\nι : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nμ : MeasureTheory.Measure α\nl : Filter α\ninst✝ : IsMeasurablyGenerated l\nf : α → E\nb : E\nh : Ten... | [
983,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
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Mathlib/Data/Set/Function.lean | Set.EqOn.mono | [] | [
221,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.cos | [] | [
978,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_empty_left | [] | [
412,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.move₂_ok | [
{
"state_after": "p : Γ' → Bool\nk₁ k₂ : K'\nq : Λ'\ns : Option Γ'\nL₁ : List Γ'\no : Option Γ'\nL₂ : List Γ'\nS : K' → List Γ'\nh₁ : k₁ ≠ rev ∧ k₂ ≠ rev ∧ k₁ ≠ k₂\nh₂ : S rev = []\ne : splitAtPred p (S k₁) = (L₁, o, L₂)\n⊢ TransGen (fun a b => b ∈ TM2.step tr a)\n (TM2.stepAux (tr (Λ'.push k₁ id (Λ'.move (f... | [
1413,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
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Mathlib/Algebra/CharP/Algebra.lean | algebraRat.charZero | [] | [
90,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.sum_fin | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : AddCommMonoid S\nf : ℕ → R → S\nhf : ∀ (i : ℕ), f i 0 = 0\nn : ℕ\np : R[X]\nhn : degree p < ↑n\nhp : p = 0\n⊢ ∑ i : Fin n, f (↑i) (coeff p ↑i) = sum p f\n\ncase neg\nR : Type u\nS : Type v\na b... | [
420,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.denseEmbedding | [] | [
302,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | OrderIso.tendsto_atTop | [] | [
422,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Analysis/Convex/Integral.lean | ConvexOn.map_average_le | [] | [
142,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.center_toSubmonoid | [] | [
728,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_le_multiplicity_choose_add | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\nx✝ : ℕ\n⊢ multiplicity p x✝ ≤ multiplicity p (choose x✝ 0) + multiplicity p 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\nn✝ : ℕ\n⊢ multiplicity p 0 ≤ multiplicity p (choose 0 (n✝ ... | [
218,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.Tendsto.isCompact_insert_range_of_cocompact | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.47904\nπ : ι → Type ?u.47909\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nf : α → β\nb : β\nhf : Tendsto f (cocompact α) (𝓝 b)\nhfc : Continuous f\nl : Filter β\nhne : NeBot l\nhle : l ≤ 𝓟 (insert b (range f))\n⊢ ∃ a, a ∈ insert b... | [
568,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.sum_divisors_eq_sum_properDivisors_add_self | [
{
"state_after": "case inl\n\n⊢ ∑ i in divisors 0, i = ∑ i in properDivisors 0, i + 0\n\ncase inr\nn : ℕ\nhn : n ≠ 0\n⊢ ∑ i in divisors n, i = ∑ i in properDivisors n, i + n",
"state_before": "n : ℕ\n⊢ ∑ i in divisors n, i = ∑ i in properDivisors n, i + n",
"tactic": "rcases Decidable.eq_or_ne n 0 with ... | [
289,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_pair_le_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.27664\ninst✝ : EDist α\nx y : α\ns t : Set α\nhxy : x ≠ y\n⊢ einfsep {y, x} ≤ edist y x",
"state_before": "α : Type u_1\nβ : Type ?u.27664\ninst✝ : EDist α\nx y : α\ns t : Set α\nhxy : x ≠ y\n⊢ einfsep {x, y} ≤ edist y x",
"tactic": "rw [pair_comm]"
},
{
... | [
163,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.erase | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ List.eraseP (fun b => decide (a = b)) l₁ <+ List.eraseP (fun b => decide (a = b)) l₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ List.erase l₁ a <+ List.erase l₂ a... | [
1048,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1047,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearEquiv_toAddEquiv | [] | [
884,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.single_eq_lof | [] | [
80,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_sub | [] | [
426,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_dite | [] | [
638,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.toLinearEquiv'_apply | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_le_ofReal_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.806432\nβ : Type ?u.806435\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nh : 0 ≤ q\n⊢ ENNReal.ofReal p ≤ ENNReal.ofReal q ↔ p ≤ q",
"tactic": "rw [ENNReal.ofReal, ENNReal.ofReal, coe_le_coe, Real.toNNReal_le_toNNReal_iff h]"
}
] | [
2094,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2093,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_map_swap | [
{
"state_after": "case nil\nι : Type ?u.491056\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx : α\ny : β\n⊢ (y, x) ∈ map Prod.swap [] ↔ (x, y) ∈ []\n\ncase cons\nι : Type ?u.491056\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx✝ : α\ny : β\nx : α × β\nxs : List (α × β)\nx... | [
4335,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4330,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_erase_of_mem | [] | [
137,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.top_prod | [] | [
1567,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Module.End.ker_pow_eq_ker_pow_finrank_of_le | [
{
"state_after": "case intro.intro\nK : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nm : ℕ\nhm : finrank K V ≤ m\nk : ℕ\nh_k_le : k ≤ finrank K V\nhk : LinearMap.ker (f ^ k) = LinearMap.ker (f ^ Nat.succ k)\n⊢ LinearMap.ke... | [
1518,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_iSup | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nf : ι → Subgraph G\nv : V\n⊢ neighborSet (⨆ (i : ι), f i) v = ⋃ (i : ι), neighborSet (f i) v",
"tactic": "simp [iSup]"
}
] | [
530,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/RingTheory/Artinian.lean | set_has_minimal_iff_artinian | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\n⊢ (∀ (a : Set (Submodule R M)), Set.Nonempty a → ∃ M', M' ∈ a ∧ ∀ (I : Submodule R M), I ∈ a → ¬I < M') ↔ IsArtinian R M",
"tactic": "rw [isArtinian_iff_wellFounded, We... | [
190,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_add_le_of_degree_le | [] | [
652,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
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Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.op_zero | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.411231\nβ : Type u_1\nγ : Type ?u.411237\np q : α → Prop\ninst✝³ : DecidablePred p\ninst✝² : DecidablePred q\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Finset β\nb x✝¹ : β\nx✝ : x✝¹ ∈ s\n⊢ x✝¹ = b ↔ b = x✝¹",
"tactic": "simp_rw [@eq_comm... | [
2935,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2933,
1
] |
Mathlib/Topology/Sequences.lean | IsCompact.tendsto_subseq' | [] | [
297,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.dist_nonneg | [
{
"state_after": "case inl\nE : ℕ → Type u_1\nx : (n : ℕ) → E n\n⊢ 0 ≤ dist x x\n\ncase inr\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nh : x ≠ y\n⊢ 0 ≤ dist x y",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\n⊢ 0 ≤ dist x y",
"tactic": "rcases eq_or_ne x y with (rfl | h)"
},
{
"state_afte... | [
290,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
11
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.hom_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22031\nγ : Type ?u.22034\nM : Type u_2\ninst✝¹ : Monoid M\nN : Type ?u.22043\ninst✝ : Monoid N\nf g : FreeMonoid α →* M\nh : ∀ (x : α), ↑f (of x) = ↑g (of x)\nl : FreeMonoid α\nx : α\nxs : FreeMonoid α\nhxs : ↑f xs = ↑g xs\n⊢ ↑f (of x *... | [
205,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | measurable_inv_iff | [
{
"state_after": "no goals",
"state_before": "G✝ : Type ?u.2420648\nα : Type u_2\ninst✝⁵ : Inv G✝\ninst✝⁴ : MeasurableSpace G✝\ninst✝³ : MeasurableInv G✝\nm : MeasurableSpace α\nf✝ : α → G✝\nμ : MeasureTheory.Measure α\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : MeasurableSpace G\ninst✝ : MeasurableInv G\nf :... | [
472,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_measurable_on_compl_finite | [] | [
618,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.filter_gt_eq_Iio | [
{
"state_after": "case a\nι : Type ?u.67690\nα : Type u_1\ninst✝³ : Preorder α\ninst✝² : LocallyFiniteOrderBot α\na : α\ninst✝¹ : Fintype α\ninst✝ : DecidablePred fun x => x < a\na✝ : α\n⊢ a✝ ∈ filter (fun x => x < a) univ ↔ a✝ ∈ Iio a",
"state_before": "ι : Type ?u.67690\nα : Type u_1\ninst✝³ : Preorder α\... | [
505,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.Rel.addLeft | [
{
"state_after": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X b c\n⊢ Rel R X (b + a) (c + a)",
"state_before": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X b c\n⊢ Rel R X (a + b) (a + c)",
"tactic": "rw [add_comm _ b, add_comm _ c]"
},
{
... | [
96,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_bot | [] | [
554,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.restr_toLocalEquiv' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.53706\nδ : Type ?u.53709\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set α\nhs : IsOpen s\n⊢ (L... | [
716,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Iio | [] | [
502,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isCompact_image_coe_of_bounded_of_weak_closed | [] | [
1641,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | CompleteLattice.iSup_continuous | [] | [
489,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.succ_mod_two_add_mod_two | [
{
"state_after": "no goals",
"state_before": "m✝ n m : ℕ\n⊢ (m + 1) % 2 + m % 2 = 1",
"tactic": "rw [add_comm, mod_two_add_succ_mod_two]"
}
] | [
108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Order/GameAdd.lean | Prod.gameAdd_le_lex | [] | [
88,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Icc | [] | [
121,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries_zero | [] | [
291,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_self | [] | [
1663,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.id_pushforward | [
{
"state_after": "case h_map\nC : Type u\ninst✝ : Category C\nX : TopCat\n⊢ autoParam\n (∀ (X_1 Y : Presheaf C X) (f : X_1 ⟶ Y),\n (pushforward C (𝟙 X)).map f =\n eqToHom (_ : ?F.obj X_1 = ?G.obj X_1) ≫\n (𝟭 (Presheaf C X)).map f ≫ eqToHom (_ : (𝟭 (Presheaf C X)).obj Y = (pushforward ... | [
389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_kunion_eq_some | [] | [
786,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_injective | [
{
"state_after": "R✝ : Type ?u.225297\ninst✝¹ : Semiring R✝\nr✝ : R✝\nf✝ : R✝[X]\nR : Type u_1\ninst✝ : CommRing R\nr : R\nf g : R[X]\nh : ↑(taylor r) f = ↑(taylor r) g\n⊢ f = g",
"state_before": "R✝ : Type ?u.225297\ninst✝¹ : Semiring R✝\nr✝ : R✝\nf : R✝[X]\nR : Type u_1\ninst✝ : CommRing R\nr : R\n⊢ Funct... | [
137,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | dNext_eq_dFrom_fromNext | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_le_of_neg_le | [
{
"state_after": "a b : Int\nh✝ : -a ≤ b\nh : -b ≤ - -a\n⊢ -b ≤ a",
"state_before": "a b : Int\nh : -a ≤ b\n⊢ -b ≤ a",
"tactic": "have h := Int.neg_le_neg h"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : -a ≤ b\nh : -b ≤ - -a\n⊢ -b ≤ a",
"tactic": "rwa [Int.neg_neg] at... | [
908,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
906,
11
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.C_eq_algebraMap | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_pos_of_is_mul_left_invariant | [
{
"state_after": "case this\nG : Type w\ninst✝³ : TopologicalSpace G\nμ : Content G\ninst✝² : T2Space G\ninst✝¹ : Group G\ninst✝ : TopologicalGroup G\nh3 :\n ∀ (g : G) {K : Compacts G},\n (fun s => ↑(toFun μ s)) (Compacts.map (fun b => g * b) (_ : Continuous fun b => g * b) K) =\n (fun s => ↑(toFun μ s... | [
239,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.continuous_compContinuous | [] | [
394,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_comap | [] | [
182,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.meas_preimage_singleton_ne_zero | [] | [
1206,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_map | [] | [
224,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderEmbedding.coe_ofMapLEIff | [] | [
717,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.freeGroupCongr_symm | [] | [
878,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | norm_norm | [] | [
841,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.addBottom_nth_succ_fst | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝² : DecidableEq K\nΓ : K → Type u_2\nΛ : Type ?u.603198\ninst✝¹ : Inhabited Λ\nσ : Type ?u.603204\ninst✝ : Inhabited σ\nL : ListBlank ((k : K) → Option (Γ k))\nn : ℕ\n⊢ (ListBlank.nth (addBottom L) (n + 1)).fst = false",
"tactic": "rw [Lis... | [
2396,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2394,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.map_map | [] | [
219,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.t2Space_iff_one_closed | [
{
"state_after": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nthis : UniformGroup G\n⊢ T2Space G ↔ IsClosed {1}",
"state_before": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\n⊢ T2Space G ↔ IsClosed {1}",
"t... | [
709,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.lcm_order_eq_exponent | [
{
"state_after": "G : Type u\ninst✝¹ : Monoid G\ninst✝ : Fintype G\n⊢ exponent G ∣ Finset.lcm Finset.univ orderOf",
"state_before": "G : Type u\ninst✝¹ : Monoid G\ninst✝ : Fintype G\n⊢ Finset.lcm Finset.univ orderOf = exponent G",
"tactic": "apply Nat.dvd_antisymm (lcm_orderOf_dvd_exponent G)"
},
{
... | [
261,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/Set/Function.lean | StrictAntiOn.congr | [] | [
271,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk_zero | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_sub_Iic | [] | [
227,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.add_of_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhq : Monic q\nhpq : degree p < degree q\n⊢ Monic (p + q)",
"tactic": "rwa [Monic, leadingCoeff_add_of_degree_lt hpq]"
}
] | [
137,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_subset_inter_left | [] | [
1703,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns : Multiset α\na : α\n⊢ lcm 0 ∣ a ↔ ∀ (b : α), b ∈ 0 → b ∣ a",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommM... | [
68,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.16480\nγ : Type ?u.16483\nι : Type ?u.16486\nι' : Type ?u.16489\nr p q : α → α → Prop\nf g : ι → α\ns t u : Set α\na b : α\n⊢ Set.Pairwise univ r ↔ Pairwise r",
"tactic": "simp only [Set.Pairwise, Pairwise, mem_univ, forall_const]"
... | [
204,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.ideal_le_vanishingIdeal_zeroLocus | [] | [
167,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.mono'' | [] | [
442,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pi_sub | [] | [
1019,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/Topology/Order/Lattice.lean | Filter.Tendsto.sup_right_nhds' | [] | [
112,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.range_top_iff_surjective | [] | [
917,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.integrable_inner | [] | [
198,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_right_on_Ioo | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\nhgg' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt g (g' x) x\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → g' x ≠ 0\nhfa : Tendsto f (𝓝[Ioi a] a) (𝓝 0)\nhga : Tendsto g (𝓝[Ioi a] a) (𝓝 0)\nhdiv : Tends... | [
96,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_coe_orderAddMonoidHom | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.principal_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.77623\nι : Sort x\nf g : Filter α\ns✝ t✝ s t : Set α\n⊢ 𝓟 s ≤ 𝓟 t ↔ s ⊆ t",
"tactic": "simp only [le_principal_iff, iff_self_iff, mem_principal]"
}
] | [
654,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | Measurable.congr_ae | [] | [
481,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | MixedCharZero.reduce_to_maximal_ideal | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : CommRing R\np : ℕ\nhp : Nat.Prime p\n⊢ (∃ I, I ≠ ⊤ ∧ CharP (R ⧸ I) p) → ∃ I, Ideal.IsMaximal I ∧ CharP (R ⧸ I) p\n\ncase mpr\nR : Type u_1\ninst✝ : CommRing R\np : ℕ\nhp : Nat.Prime p\n⊢ (∃ I, Ideal.IsMaximal I ∧ CharP (R ⧸ I) p) → ∃ I, I ≠ ⊤ ∧ CharP (R ⧸ I) p",
... | [
140,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.coe_preimage | [] | [
45,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_int_add | [] | [
363,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/List/Sigma.lean | List.nodupKeys_nil | [] | [
102,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.powEquiv_apply | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.bit1_apply | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.diam_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.564058\nβ : Type ?u.564061\nγ : Type ?u.564064\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : a ≤ b\n⊢ Metric.diam (Ioc a b) = b - a",
"tactic": "simp [Metric.diam, ENNReal.toReal_ofReal (sub_nonneg.2 h)]"
}
] | [
1564,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_mono_real | [] | [
418,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_ofSeq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ Computation.pure (Option.map (Prod.fst ∘ fun a => (a, ↑(Seq.tail s))) (Seq.head s)) = Computation.pure (Seq.head s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ head ↑s = Computation.pure (Seq.head s)",
"tactic": "... | [
1362,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.prodZeroIso_hom | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsPreirreducible.subset_irreducible | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι : Type ?u.204765\nπ : ι → Type ?u.204770\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t S U Z : Set α\nhZ : IsPreirreducible Z\nhU' : IsOpen U\nh₁ : U ⊆ S\nh₂ : S ⊆ Z\nz : α\nhz : z ∈ U\n⊢ IsIrreducible S",
"state_before": "α : Type u\nβ... | [
1974,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1960,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | geom_goldConj_isSol_fibRec | [
{
"state_after": "α : Type ?u.59403\ninst✝ : CommSemiring α\n⊢ IsRoot (X ^ 2 - (X + 1)) ψ",
"state_before": "α : Type ?u.59403\ninst✝ : CommSemiring α\n⊢ LinearRecurrence.IsSolution fibRec fun x => ψ ^ x",
"tactic": "rw [fibRec.geom_sol_iff_root_charPoly, fibRec_charPoly_eq]"
},
{
"state_after":... | [
206,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_int_three_mod_four | [
{
"state_after": "n : ℤ\nhn : n % 4 = 3\n⊢ ↑χ₄ ↑3 = -1",
"state_before": "n : ℤ\nhn : n % 4 = 3\n⊢ ↑χ₄ ↑n = -1",
"tactic": "rw [χ₄_int_mod_four, hn]"
},
{
"state_after": "no goals",
"state_before": "n : ℤ\nhn : n % 4 = 3\n⊢ ↑χ₄ ↑3 = -1",
"tactic": "rfl"
}
] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.coe_sInf | [] | [
453,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Logic/Basic.lean | and_symm_right | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b : α\np : Prop\n⊢ p ∧ a = b ↔ p ∧ b = a",
"tactic": "simp [eq_comm]"
}
] | [
320,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
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