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/Polynomial/EraseLead.lean | Polynomial.eraseLead_add_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\n⊢ eraseLead f + ↑C (leadingCoeff f) * X ^ natDegree f = f",
"tactic": "rw [C_mul_X_pow_eq_monomial, eraseLead_add_monomial_natDegree_leadingCoeff]"
}
] | [
74,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_eq_right_inv | [] | [
151,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Quot.lean | Setoid.ext | [
{
"state_after": "α✝ : Sort ?u.8\nβ : Sort ?u.11\nα : Sort u_1\nr : α → α → Prop\niseqv✝¹ : Equivalence r\np : α → α → Prop\niseqv✝ : Equivalence p\nEq : ∀ (a b : α), Setoid.r a b ↔ Setoid.r a b\nthis : r = p\n⊢ { r := r, iseqv := iseqv✝¹ } = { r := p, iseqv := iseqv✝ }",
"state_before": "α✝ : Sort ?u.8\nβ ... | [
33,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.getRight_swap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.23345\nδ : Type ?u.23348\nx : α ⊕ β\n⊢ getRight (swap x) = getLeft x",
"tactic": "cases x <;> rfl"
}
] | [
381,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_of_le | [
{
"state_after": "case zero\ni j : Fin (Nat.succ Nat.zero)\nh : j ≤ i\n⊢ ↑(cycleRange i) j = if j = i then 0 else j + 1\n\ncase succ\nn✝ : ℕ\ni j : Fin (Nat.succ (Nat.succ n✝))\nh : j ≤ i\n⊢ ↑(cycleRange i) j = if j = i then 0 else j + 1",
"state_before": "n : ℕ\ni j : Fin (Nat.succ n)\nh : j ≤ i\n⊢ ↑(cycle... | [
187,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictDerivAt_exp_zero | [] | [
212,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.ball_infDist_compl_subset | [] | [
546,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.choose_spec | [] | [
592,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_right_on_Ico | [
{
"state_after": "case refine'_1\na 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\nhcf : ContinuousOn f (Ico a b)\nhcg : ContinuousOn g (Ico a b)\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → g' x ≠ 0\nhfa : f ... | [
108,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.boxProd_neighborSet | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9830\nG : SimpleGraph α\nH : SimpleGraph β\nx : α × β\na' : α\nb' : β\n⊢ (a', b') ∈ neighborSet (G □ H) x ↔ (a', b') ∈ neighborSet G x.fst ×ˢ {x.snd} ∪ {x.fst} ×ˢ neighborSet H x.snd",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ... | [
75,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.elim_nhds_subcover | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.14579\nπ : ι → Type ?u.14584\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t✝ : Set α\nhs : IsCompact s\nU : α → Set α\nhU : ∀ (x : α), x ∈ s → U x ∈ 𝓝 x\nt : Finset ↑s\nht : s ⊆ ⋃ (x : ↑s) (_ : x ∈ t), U ↑x\n⊢ ... | [
213,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.transpose_eq_iff_eq_transpose | [
{
"state_after": "case mpr\nν : YoungDiagram\n⊢ transpose (transpose ν) = ν",
"state_before": "case mpr\nμ ν : YoungDiagram\n⊢ μ = transpose ν → transpose μ = ν",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_before": "case mpr\nν : YoungDiagram\n⊢ transpose (transpose ν) = ν... | [
231,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.lift_unique | [
{
"state_after": "case w.a\nR : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr✝ : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\nf : R →+* T\nr : R → R → Prop\nw : ∀ ⦃x y : R⦄, r x y → ↑f x = ↑f y\ng : RingQuot r →+* T\nh : RingHom.c... | [
470,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.reLm_coe | [] | [
266,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/Convex/Between.lean | mem_vsub_const_affineSegment | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nV : Type u_1\nV' : Type ?u.55686\nP : Type u_2\nP' : Type ?u.55692\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx y z p : P\n... | [
139,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_eq_of_le | [] | [
297,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.coeff_eq_c | [] | [
116,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_def_of_nonpos | [
{
"state_after": "case inr\nx : ℝ\nhx : x ≤ 0\ny : ℝ\nh : ¬x = 0\n⊢ (↑x ^ ↑y).re = exp (log x * y) * cos (y * π)",
"state_before": "x : ℝ\nhx : x ≤ 0\ny : ℝ\n⊢ x ^ y = if x = 0 then if y = 0 then 1 else 0 else exp (log x * y) * cos (y * π)",
"tactic": "split_ifs with h <;> simp [rpow_def, *]"
},
{
... | [
92,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C | [] | [
1125,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.top_mem | [] | [
125,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.exists_intermediate_set | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.43518\ns t : Finset α\nf : α → β\nn : ℕ\nA B : Finset α\ni : ℕ\nh₁ : i + card B ≤ card A\nh₂ : B ⊆ A\nk : ℕ\nh : i + card B + k = card A\n⊢ ∃ C, B ⊆ C ∧ C ⊆ A ∧ card C = i + card B",
"state_before": "α : Type u_1\nβ : Type ?u.43518\ns t : Finset α\nf :... | [
486,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.coe_injective | [] | [
77,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.neg_fst | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/List/Basic.lean | List.splitOn_intercalate | [
{
"state_after": "ι : Type ?u.310123\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nxs ys : List α\nls : List (List α)\nf : List α → List α\ninst✝ : DecidableEq α\nx : α\nhx : ∀ (l : List α), l ∈ ls → ¬x ∈ l\nhls : ls ≠ []\n⊢ splitOn x (join (intersperse [x] ls)) = ls",
"stat... | [
3024,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3000,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.empty_card | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\n⊢ card Language.empty = 0",
"tactic": "simp [card_eq_card_functions_add_card_relations]"
}
] | [
240,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.toDeleteEdges_cons | [] | [
1795,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1791,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_dirac | [
{
"state_after": "α : Type u_1\nα' : Type ?u.4489185\nβ : Type u_2\nβ' : Type ?u.4489191\nγ : Type ?u.4489194\nE : Type ?u.4489197\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
558,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.const_lintegral | [
{
"state_after": "α : Type u_1\nβ : Type ?u.889363\nγ : Type ?u.889366\nδ : Type ?u.889369\nm : MeasurableSpace α\nμ ν : Measure α\nc : ℝ≥0∞\n⊢ ∑ x in SimpleFunc.range (const α c), x * ↑↑μ (↑(const α c) ⁻¹' {x}) = c * ↑↑μ univ",
"state_before": "α : Type u_1\nβ : Type ?u.889363\nγ : Type ?u.889366\nδ : Type... | [
1094,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.SchurZassenhausInduction.step1 | [
{
"state_after": "G : Type u\ninst✝² : Group G\ninst✝¹ : Fintype G\nN : Subgroup G\ninst✝ : Normal N\nh1 : Nat.coprime (Fintype.card { x // x ∈ N }) (index N)\nh2 :\n ∀ (G' : Type u) [inst : Group G'] [inst_1 : Fintype G'],\n Fintype.card G' < Fintype.card G →\n ∀ {N' : Subgroup G'} [inst_2 : Normal N'... | [
196,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
9
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.as_sum_range | [] | [
429,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.prodEquivOfIsCompl_symm_apply_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.90945\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.91461\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.92424\ni... | [
130,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_mul_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.252386\nβ : Type ?u.252389\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh0 : a ≠ 0\nhI : a ≠ ⊤\n⊢ b / a * a = b",
"tactic": "rw [div_eq_mul_inv, mul_assoc, ENNReal.inv_mul_cancel h0 hI, mul_one]"
}
] | [
1392,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
11
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_empty | [] | [
422,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.symm_one | [
{
"state_after": "no goals",
"state_before": "⊢ ↑(σ 1) = ↑0",
"tactic": "simp [symm]"
}
] | [
116,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Field/Basic.lean | toLex_rat_cast | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lsingle_apply | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.mapₗ_apply_of_measurable | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.176472\nδ : Type ?u.176475\nι : Type ?u.176478\nR : Type ?u.176481\nR' : Type ?u.176484\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nf : α → β\nhf : Measurable f\nμ : ... | [
1167,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | continuousWithinAt_const_smul_iff₀ | [] | [
306,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | MulEquiv.map_finsupp_prod | [] | [
232,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
11
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | WfDvdMonoid.iff_wellFounded_associates | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\n⊢ WfDvdMonoid α → WellFounded fun x x_1 => x < x_1",
"tactic": "apply WfDvdMonoid.wellFounded_associates"
}
] | [
151,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/RingTheory/Localization/Module.lean | LinearIndependent.iff_fractionRing | [] | [
159,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Computability/Partrec.lean | Computable.subtype_mk | [] | [
712,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_const | [] | [
239,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePullback.π_arrow | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type u_1\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → objs j ⟶ B\ninst✝ : HasWidePullback B objs arrows\nj : J\n⊢ π arrows j ≫ arrows j = base arrows",
"tactic": "apply limit.w (WidePullbackSh... | [
326,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atTop_iff | [
{
"state_after": "case inl\nι : Type ?u.233433\nι' : Type ?u.233436\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.233445\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nhr : r < 0\n⊢ Tendsto (fun x => r * f x) l atTop ↔ 0 < r ∧ Tendsto f l atTop ∨ r < 0 ∧ Tendsto f l atBot\n\ncase in... | [
1124,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.zero_inter | [] | [
1759,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1758,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientKerAlgEquivOfRightInverse.apply | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_eq_sum | [
{
"state_after": "no goals",
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"tactic": "simp [expand, eval₂]"
}
] | [
50,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.liftPred_const_iff | [] | [
308,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
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Mathlib/LinearAlgebra/Basic.lean | Submodule.range_subtype | [
{
"state_after": "no goals",
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1622,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
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Mathlib/Data/List/Sigma.lean | List.mem_keys_kunion | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl l₁ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl₂ : List (Sigma β)\n⊢ a ∈ keys (kunion [] l₂) ↔ a ∈ keys [] ∨ a ∈ keys l₂\n\ncase cons\nα : Type u\nβ : α → Type v\nl l₁ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nhead✝ : Sigma β\ntail✝ : ... | [
706,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_diff_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61989\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioi a \\ Ici b = Ioo a b",
"tactic": "rw [diff_eq, compl_Ici, Ioi_inter_Iio]"
}
] | [
1092,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
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Mathlib/Topology/UniformSpace/Basic.lean | uniformity_prod | [] | [
1571,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
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Mathlib/Analysis/LocallyConvex/StrongTopology.lean | ContinuousLinearMap.strongTopology.locallyConvexSpace | [
{
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62,
47
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53,
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Mathlib/Topology/UniformSpace/Basic.lean | Filter.Tendsto.uniformity_symm | [] | [
496,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Std/Data/Rat/Lemmas.lean | Rat.divInt_mul_left | [
{
"state_after": "no goals",
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"tactic": "if d0 : d = 0 then simp [d0] else\nsimp [divInt_eq_iff (Int.mul_ne_zero a0 d0) d0, Int.mul_assoc, Int.mul_left_comm]"
},
{
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145,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.iInf_mul | [
{
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"state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ iInf f * a = ⨅ (i : ι), f i * a",
"tactic": "rw [← NNReal.coe_eq, NNReal.coe_mul, coe_iInf, coe_iInf]"
},
{
"state_after": "no g... | [
955,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Normalized.lean | AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex | [
{
"state_after": "no goals",
"state_before": "A : Type u_2\ninst✝¹ : Category A\ninst✝ : Abelian A\nX✝ X : SimplicialObject A\n⊢ PInfty ≫ PInftyToNormalizedMooreComplex X = PInftyToNormalizedMooreComplex X",
"tactic": "aesop_cat"
}
] | [
93,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/List/Zip.lean | List.lt_length_right_of_zipWith | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.19964\nε : Type ?u.19967\nf : α → β → γ\ni : ℕ\nl : List α\nl' : List β\nh : i < length l ∧ i < length l'\n⊢ i < length l'",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.19964\nε : Type ?u.19967\nf : α → β → γ\ni :... | [
100,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.smul_apply | [] | [
60,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.element_of_chain_not_isUnit_of_index_ne_zero | [] | [
92,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Category/TopCat/EpiMono.lean | TopCat.epi_iff_surjective | [
{
"state_after": "X Y : TopCat\nf : X ⟶ Y\n⊢ Epi f ↔ Epi ((forget TopCat).map f)",
"state_before": "X Y : TopCat\nf : X ⟶ Y\n⊢ Epi f ↔ Function.Surjective ((forget TopCat).map f)",
"tactic": "suffices Epi f ↔ Epi ((forget TopCat).map f) by\n rw [this, CategoryTheory.epi_iff_surjective]"
},
{
"s... | [
36,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsRat.neg_to_eq | [
{
"state_after": "no goals",
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"tactic": "simp [div_eq_mul_inv]"
}
] | [
167,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | weightedVSub_mem_vectorSpan_pair | [
{
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522,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.cons_ndinter_of_mem | [
{
"state_after": "no goals",
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"tactic": "simp [ndinter, h]"
}
] | [
234,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Init/Function.lean | Function.comp_const_right | [] | [
60,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.mem_closed_iff | [] | [
369,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_comm | [] | [
823,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.Rel.mono | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.439427\nδ : Type ?u.439430\nr✝ : α → β → Prop\np✝ : γ → δ → Prop\nr p : α → β → Prop\ns : Multiset α\nt : Multiset β\nh : ∀ (a : α), a ∈ 0 → ∀ (b : β), b ∈ 0 → r a b → p a b\n⊢ Rel p 0 0\n\ncase cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.43... | [
2699,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2692,
1
] |
Mathlib/Topology/Separation.lean | regularSpace_sInf | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α\na : α\ns : Set α\nX : Type u_1\nT : Set (TopologicalSpace X)\nh : ∀ (t : TopologicalSpace X), t ∈ T → RegularSpace X\nx✝ : TopologicalSpace X := sInf T\n⊢ RegularSpace X",
"state_before": "α : Type u\nβ : Type v\n... | [
1617,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | abs_add_eq_add_abs_le | [
{
"state_after": "case inl.inl\nα : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : LinearOrderedAddCommGroup α\na b : α\nhle : a ≤ b\na0 : 0 ≤ a\nb0 : 0 ≤ b\n⊢ abs (a + b) = abs a + abs b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0\n\ncase inl.inr\nα : Ty... | [
483,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.ext' | [] | [
527,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_node4L | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nP : α → Prop\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ All P (node4L l x m y r) ↔ All P l ∧ P x ∧ All P m ∧ P y ∧ All P r",
"tactic": "cases m <;> simp [node4L, all_node', All, all_node3L, and_assoc]"
}
] | [
509,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bodd_add_div2 | [
{
"state_after": "n : ℕ\n⊢ (bif bodd n then 0 else 1) + (bif bodd n then succ (div2 n) else div2 n) * 2 = succ n",
"state_before": "n : ℕ\n⊢ (bif bodd (succ n) then 1 else 0) + 2 * div2 (succ n) = succ n",
"tactic": "simp"
},
{
"state_after": "n : ℕ\n⊢ (bif bodd n then 0 else 1) + (bif bodd n th... | [
137,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.out_nonempty_iff_ne_zero | [] | [
285,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.range_val | [] | [
508,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_add_le_of_le_one | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2557321\nG : Type ?u.2557324\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : AEStronglyMeasurable f μ\nhq0 : 0 ≤ q\nhq1 : q ≤ 1\n⊢ ... | [
766,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Order/Circular.lean | Set.compl_cIoo | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : CircularOrder α\na b x✝ : α\n⊢ x✝ ∈ cIoo a bᶜ ↔ x✝ ∈ cIcc b a",
"state_before": "α : Type u_1\ninst✝ : CircularOrder α\na b : α\n⊢ cIoo a bᶜ = cIcc b a",
"tactic": "ext"
},
{
"state_after": "case h\nα : Type u_1\ninst✝ : CircularOrder α\na b x✝ : α... | [
381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.filter_mono_ae | [] | [
4125,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4124,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Module.algebraMap_end_apply | [] | [
631,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.zero | [] | [
1111,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.typevecCasesNil₂_appendFun | [] | [
381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.on_preimage | [] | [
416,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.continuousAt_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.127935\nι : Type ?u.127938\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\n⊢ ContinuousAt f b ↔ ∀ (ε : ℝ), ε > 0 → ∀ᶠ (x : β) in 𝓝 b, dist (f x) (f b) < ε",
... | [
1080,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Order/BoundedOrder.lean | OrderBot.ext | [
{
"state_after": "case mk\nα✝ : Type u\nβ : Type v\nγ : Type ?u.25434\nδ : Type ?u.25437\nα : Type u_1\ninst✝ : PartialOrder α\nB : OrderBot α\ntoBot✝ : Bot α\nha : ∀ (a : α), ⊥ ≤ a\n⊢ mk ha = B",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type ?u.25434\nδ : Type ?u.25437\nα : Type u_1\ninst✝ : PartialOr... | [
447,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.eventually_lt_of_limsup_lt | [] | [
1134,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.norm_image_sub_le_of_norm_deriv_le | [] | [
672,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.mul_lt_top' | [
{
"state_after": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : Zero α\ninst✝¹ : Mul α\ninst✝ : LT α\na b : WithTop α\nha : a ≠ ⊤\nhb : b ≠ ⊤\n⊢ a * b ≠ ⊤",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : Zero α\ninst✝¹ : Mul α\ninst✝ : LT α\na b : WithTop α\nha : a < ⊤\nhb : b < ⊤\n⊢ a * b... | [
72,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.le_vanishingIdeal_zeroLocus | [] | [
218,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.HasBasis.smallSets | [] | [
50,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Topology/Order/Basic.lean | countable_of_isolated_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n⊢ Set.Countable {x | ∃ y, y < x ∧ Ioo y x = ∅}",
"tactic": "simpa only [← covby_iff_Ioo_eq] using countable_... | [
1432,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure | [
{
"state_after": "case h₁\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nt : Set (ProjectiveSpectrum 𝒜)\n⊢ zeroLocus 𝒜 ↑(vanishingIdeal t) ⊆ closure t\n\ncase h₂\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiri... | [
371,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_optimalGHDist_le | [] | [
438,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
9
] |
Mathlib/Topology/Order/Basic.lean | exists_Ico_subset_of_mem_nhds | [] | [
1245,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_log_mul_rpow_nhds_zero | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nhr : 0 < r\nx : ℝ\nhx : x ∈ Set.Ioi 0\n⊢ log x / x ^ (-r) = (fun x => log x * x ^ r) x",
"tactic": "rw [rpow_neg hx.out.le, div_inv_eq_mul]"
}
] | [
336,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.insert_symm_apply_inr | [] | [
296,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.self_mem_compactConvNhd | [] | [
106,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.tendstoLocallyUniformlyOn_iff | [] | [
650,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_mul_add | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14872189\n𝕜 : Type ?u.14872192\nE : Type u_1\nF : Type ?u.14872198\nA : Type ?u.14872201\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nhc : c ≠ 0\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (c * x + ... | [
755,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Superset.trans | [] | [
359,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
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