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/NumberTheory/Liouville/LiouvilleWith.lean | forall_liouvilleWith_iff | [
{
"state_after": "x : ℝ\nH : ∀ (p : ℝ), LiouvilleWith p x\nn : ℕ\n⊢ ∃ a b, 1 < b ∧ x ≠ ↑a / ↑b ∧ abs (x - ↑a / ↑b) < 1 / ↑b ^ n",
"state_before": "x : ℝ\n⊢ (∀ (p : ℝ), LiouvilleWith p x) ↔ Liouville x",
"tactic": "refine ⟨fun H n => ?_, Liouville.liouvilleWith⟩"
},
{
"state_after": "case intro.i... | [
392,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.nhds_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.8500\ninst✝ : TopologicalSpace α\n⊢ (⨅ (l : EReal) (_ : l < ⊤), 𝓟 (Ioi l)) = ⨅ (a : EReal) (_ : a ≠ ⊤), 𝓟 (Ioi a)",
"tactic": "simp only [lt_top_iff_ne_top]"
}
] | [
134,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.map_pre | [
{
"state_after": "case w\nJ : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF : J ⥤ C\ninst✝¹ : HasLimitsOfShape J C\nG : J ⥤ C\nα : F ⟶ G\ninst✝ : HasLimitsOfShape K C\nE : K ⥤ J\nj✝ : K\n⊢ (lim.map α ≫ pre G E) ≫ π (E ⋙ G) j✝ = (pre F E ≫ lim.map (whiskerLeft... | [
547,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
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Mathlib/Data/Set/Prod.lean | Antitone.set_prod | [] | [
441,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.inclusion_map_eq_top | [
{
"state_after": "case h\nX : TopCat\nU : Opens ↑X\n⊢ ↑((map (inclusion U)).obj U) = ↑⊤",
"state_before": "X : TopCat\nU : Opens ↑X\n⊢ (map (inclusion U)).obj U = ⊤",
"tactic": "ext1"
},
{
"state_after": "no goals",
"state_before": "case h\nX : TopCat\nU : Opens ↑X\n⊢ ↑((map (inclusion U)).o... | [
347,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | isComplete_of_complete_image | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nm : α → β\ns : Set α\nhm : UniformInducing m\nhs : IsComplete (m '' s)\nf : Filter α\nhf : Cauchy f\nhfs : f ≤ 𝓟 s\n⊢ ∃ x, x ∈ s ∧ f ≤ 𝓝 x",
"state_before": "α : Type u\nβ : Type... | [
282,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Topology/Algebra/GroupCompletion.lean | AddMonoidHom.completion_add | [
{
"state_after": "M : Type ?u.267459\nR : Type ?u.267462\nα : Type u_2\nβ : Type ?u.267468\ninst✝⁸ : UniformSpace α\ninst✝⁷ : AddGroup α\ninst✝⁶ : UniformAddGroup α\ninst✝⁵ : UniformSpace β\ninst✝⁴ : AddGroup β\ninst✝³ : UniformAddGroup β\nγ : Type u_1\ninst✝² : AddCommGroup γ\ninst✝¹ : UniformSpace γ\ninst✝ : ... | [
304,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | strictAnti_mul_right | [] | [
731,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
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Mathlib/Order/Monotone/Basic.lean | monotoneOn_comp_ofDual_iff | [] | [
162,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_smul | [] | [
229,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Order/Lattice.lean | sup_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ⊔ b = b ⊔ a",
"tactic": "apply le_antisymm <;> simp"
}
] | [
248,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableOn_const_add_iff | [
{
"state_after": "no goals",
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301,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toOpen_eq_const | [] | [
438,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
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Mathlib/SetTheory/Game/PGame.lean | PGame.zero_le_add_right_neg | [] | [
1694,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1693,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_of_le_right | [] | [
2929,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2928,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_midpoint_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.64769\nV : Type u_3\nP : Type u_1\nW : Type ?u.64778\nQ : Type ?u.64781\ninst✝⁹ : SeminormedAddCommGroup V\ninst✝⁸ : PseudoMetricSpace P\ninst✝⁷ : NormedAddTorsor V P\ninst✝⁶ : NormedAddCommGroup W\ninst✝⁵ : MetricSpace Q\ninst✝⁴ : NormedAddTorsor W ... | [
194,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Vector3.lean | VectorAllP.imp | [] | [
301,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
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] |
src/lean/Init/SimpLemmas.lean | cond_false | [] | [
146,
65
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
146,
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_self_mul_transpose | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.284550\nm : Type u_1\nn : Type u_2\no : Type ?u.284559\nR : Type u_3\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : Fintype m\ninst✝ : LinearOrderedField R\nA : Matrix m n R\n⊢ rank (A ⬝ Aᵀ) = rank A",
"tactic": "simpa only ... | [
266,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | Set.Finite.nullMeasurableSet_biUnion | [] | [
377,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.single_mem_grade | [] | [
95,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.map_snd | [] | [
724,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.results_pure | [] | [
557,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.empty_right | [] | [
151,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat_primes | [] | [
484,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dite_eq | [
{
"state_after": "case inl\nι : Type ?u.411026\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\ns : Finset α\na : α\nb : (x : α) → a = x → β\nh : a ∈ s\n⊢ (∏ x in s, if h : a = x then b x h else 1) = b a (_ : a = a)\n\ncase inr\nι : Typ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
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] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lift_mk | [] | [
500,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Rel.lean | Rel.inv_id | [
{
"state_after": "case a.h.a\nα : Type u_1\nβ : Type ?u.12137\nγ : Type ?u.12140\nr : Rel α β\nx y : α\n⊢ inv Eq x y ↔ x = y",
"state_before": "α : Type u_1\nβ : Type ?u.12137\nγ : Type ?u.12140\nr : Rel α β\n⊢ inv Eq = Eq",
"tactic": "ext (x y)"
},
{
"state_after": "no goals",
"state_before... | [
122,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns : Set (PrimeSpectrum R)\n⊢ vanishingIdeal s = ⊤ ↔ s = ∅",
"tactic": "rw [← top_le_iff, ← subset_zeroLocus_iff_le_vanishingIdeal, Submodule.top_coe, zeroLocus_univ,\n Set.subset_empty_iff]"
... | [
321,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
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] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_mul_add_pos | [] | [
399,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_sub | [
{
"state_after": "no goals",
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73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.continuousWithinAt | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Typ... | [
447,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Data/Sym/Basic.lean | Sym.coe_cast | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.charpoly_monic | [
{
"state_after": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nα β : Type v\ninst✝ : DecidableEq α\nM✝ M : Matrix n n R\n✝ : Nontrivial R\n⊢ Monic (charpoly M)",
"state_before": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Fin... | [
152,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.sub | [] | [
256,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/Analysis/LocallyConvex/Bounded.lean | NormedSpace.isBounded_iff_subset_smul_ball | [
{
"state_after": "𝕜 : Type u_2\n𝕜' : Type ?u.262092\nE : Type u_1\nE' : Type ?u.262098\nF : Type ?u.262101\nι : Type ?u.262104\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\n⊢ Bornology.IsVonNBounded 𝕜 s ↔ ∃ a, s ⊆ a • Metric.ball 0 1",
"stat... | [
328,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_of_prime | [] | [
436,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_right | [] | [
770,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
21
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_con | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_eq_iff_mul_self_eq | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 ≤ x\nhy : 0 ≤ y\nh : sqrt x = y\n⊢ y * y = x",
"tactic": "rw [← h, mul_self_sqrt hx]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 ≤ x\nhy : 0 ≤ y\nh : y * y = x\n⊢ sqrt x = y",
"tactic": "rw [← h, sqrt_mul... | [
220,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Logic/Denumerable.lean | Denumerable.sigma_ofNat_val | [
{
"state_after": "α : Type u_1\nβ : Type ?u.23484\ninst✝² : Denumerable α\ninst✝¹ : Denumerable β\nγ : α → Type u_2\ninst✝ : (a : α) → Denumerable (γ a)\nn : ℕ\n⊢ (Option.bind (decode (unpair n).fst) fun a => Option.map (Sigma.mk a) (decode (unpair n).snd)) =\n some { fst := ofNat α (unpair n).fst, snd := of... | [
165,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.r_one_pow | [
{
"state_after": "case zero\nn : ℕ\n⊢ r 1 ^ Nat.zero = r ↑Nat.zero\n\ncase succ\nn k : ℕ\nIH : r 1 ^ k = r ↑k\n⊢ r 1 ^ Nat.succ k = r ↑(Nat.succ k)",
"state_before": "n k : ℕ\n⊢ r 1 ^ k = r ↑k",
"tactic": "induction' k with k IH"
},
{
"state_after": "case zero\nn : ℕ\n⊢ r 1 ^ Nat.zero = r 0",
... | [
137,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_nat | [] | [
1238,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.sInf_adj_of_nonempty | [
{
"state_after": "case intro\nι : Sort ?u.21693\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ns : Set (Subgraph G)\nG' : Subgraph G\nhG' : G' ∈ s\n⊢ (∀ (G' : Subgraph G), G' ∈ s → Adj G' a b) → SimpleGraph.Adj G a b",
"state_before": "ι : Sort ?u.21693\nV : Type u\nW : Type v\nG :... | [
413,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_toAlgHom | [] | [
425,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Logic/Basic.lean | not_iff | [] | [
436,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.of_think_terminates | [] | [
399,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_lt_smul_iff_of_neg | [
{
"state_after": "k : Type u_1\nM : Type u_2\nN : Type ?u.26945\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhc : c < 0\n⊢ -c • b < -c • a ↔ b < a",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.26945\ninst✝³ : OrderedRing ... | [
78,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.head_eq_destruct | [
{
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{
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252,
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Mathlib/Topology/Algebra/StarSubalgebra.lean | elementalStarAlgebra.le_of_isClosed_of_mem | [] | [
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Mathlib/Order/Atoms.lean | isSimpleOrder_iff_isSimpleOrder_orderDual | [
{
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442,
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Mathlib/Order/Closure.lean | LowerAdjoint.le_closure_iff | [] | [
375,
39
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374,
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Mathlib/Order/LiminfLimsup.lean | Filter.CompleteLatticeHom.apply_liminf_iterate | [] | [
852,
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850,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_target | [] | [
1055,
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Mathlib/SetTheory/Game/PGame.lean | PGame.leftResponse_spec | [] | [
725,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_mul_right | [
{
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] | [
911,
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910,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.card_support_C_mul_X_pow_le_one | [
{
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Mathlib/RingTheory/Polynomial/Vieta.lean | Finset.prod_X_add_C_coeff | [
{
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87,
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Mathlib/Analysis/Quaternion.lean | Quaternion.normSq_eq_norm_mul_self | [
{
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] | [
70,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_sum' | [
{
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_iInf | [
{
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] | [
737,
48
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Mathlib/GroupTheory/Solvable.lean | solvable_of_surjective | [] | [
163,
90
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162,
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Std/Data/Int/Lemmas.lean | Int.ofNat_one | [] | [
21,
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Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivWithinAt.iterate | [
{
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219,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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Mathlib/Data/List/Basic.lean | List.get_take' | [
{
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},
{
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2008,
55
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2006,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryFinFinset_apply_const | [
{
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1600,
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1594,
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.map_inv | [] | [
702,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/Data/Finset/Basic.lean | Finset.disjiUnion_filter_eq_of_maps_to | [
{
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3504,
34
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3497,
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Mathlib/Order/MinMax.lean | min_lt_of_left_lt | [] | [
108,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_right_eq_zero_iff | [
{
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"tactic": "by_cases hq : q = 0 <;> simp [h.mul_right_ne_zero, hq]"
}
] | [
467,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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Mathlib/Algebra/Algebra/Tower.lean | Submodule.smul_mem_span_smul' | [
{
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308,
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299,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_image_Ico_eq | [
{
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"state_before": "𝕜 : Type u_1\nB : Type ?u.103473\ninst✝³ : LinearO... | [
300,
42
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298,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.algebraMap_apply | [] | [
523,
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522,
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Mathlib/Data/ENat/Basic.lean | ENat.toNat_sub | [
{
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"tactic": "lift n to ℕ using hn"
},
{
"state_after": "case intro.h₁\nm n✝ : ℕ∞\nn : ℕ\n⊢ ↑toNat (⊤ - ↑n) = ↑to... | [
177,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_one_div | [
{
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},
{
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335,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero | [
{
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"tactic": "rw [← FiniteMeasure.mass_nonzero_iff, μ.mass_toFiniteMeasure]"
},
{
"state_after... | [
209,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_left_of_right_le | [
{
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745,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
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Mathlib/LinearAlgebra/DirectSum/TensorProduct.lean | TensorProduct.directSumLeft_symm_lof_tmul | [
{
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174,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_mul_I_antiperiodic | [
{
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"state_before": "⊢ Function.Antiperiodic (fun x => exp (x * I)) ↑π",
"tactic": "simpa only [mul_inv_cancel_right₀ I_ne_zero] using exp_antiperiodic.mul_const I_ne_zero"
}
] | [
1358,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1357,
1
] |
Mathlib/Data/List/Basic.lean | List.removeNth_eq_nthTail | [
{
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"tactic": "cases l <;> rfl"
}
] | [
1530,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1527,
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Mathlib/Data/Finset/Lattice.lean | Multiset.mem_sup | [
{
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1773,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1755,
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_add | [] | [
500,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
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Mathlib/MeasureTheory/Measure/OpenPos.lean | IsOpen.measure_pos_iff | [] | [
53,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/Data/Finset/Basic.lean | Finset.disjoint_biUnion_left | [
{
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3678,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.coe_toList | [] | [
458,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
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Mathlib/Data/Vector3.lean | Vector3.consElim_cons | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Topology/Algebra/Group/Basic.lean | Filter.Tendsto.div_const' | [] | [
1101,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero | [
{
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551,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
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Mathlib/RingTheory/NonZeroDivisors.lean | mul_right_coe_nonZeroDivisors_eq_zero_iff | [] | [
56,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mono | [
{
"state_after": "case intro.intro\np q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nhle : q ≤ p\nC : ℝ\nhC₀ : 0 < C\nhC : ∃ᶠ (n : ℕ) in atTop, 1 ≤ n ∧ ∃ m, x ≠ ↑m / ↑n ∧ abs (x - ↑m / ↑n) < C / ↑n ^ p\n⊢ LiouvilleWith q x",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nh... | [
95,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.isMatching_iff_forall_degree | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\ninst✝ : (v : V) → Fintype ↑(neighborSet M v)\n⊢ IsMatching M ↔ ∀ (v : V), v ∈ M.verts → degree M v = 1",
"tactic": "simp only [degree_eq_one_iff_unique_adj, IsMatching]"
}
] | [
101,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.algebraMap_eq | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Combinatorics/SetFamily/HarrisKleitman.lean | IsLowerSet.le_card_inter_finset | [] | [
102,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | volume_regionBetween_eq_integral' | [
{
"state_after": "α : Type u_1\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\ninst✝ : SigmaFinite μ\nf_int : IntegrableOn f s\ng_int : IntegrableOn g s\nhs : MeasurableSet s\nhfg : f ≤ᶠ[ae (Measure.restrict μ s)] g\nh : g - f =ᶠ[ae (Measure.restrict μ s)] fun x => ↑(Real.toNNR... | [
34,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Mathlib/Algebra/Invertible.lean | div_self_of_invertible | [] | [
409,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Order/Cover.lean | Wcovby.Ico_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17366\ninst✝ : PartialOrder α\na b c : α\nh : a ⩿ b\n⊢ Ico a b ⊆ {a}",
"tactic": "rw [← Icc_diff_right, h.Icc_eq, diff_singleton_subset_iff, pair_comm]"
}
] | [
181,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSets.piiUnionInter_of_not_mem | [
{
"state_after": "case intro.intro.intro.intro\nΩ : Type u_1\nι : Type u_2\nm0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nπ : ι → Set (Set Ω)\na : ι\nS : Finset ι\nhp_ind : iIndepSets π\nhaS : ¬a ∈ S\nt1 t2 : Set Ω\ns : Finset ι\nhs_mem : ↑s ⊆ ↑S\nft1 : ι → Set Ω\nhft1_mem : ∀ (x : ι), x ∈ s → ft1 x ∈ π ... | [
549,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.ennrealToMeasure_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.152330\nm✝ m : MeasurableSpace α\nv : VectorMeasure α ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(ennrealToMeasure v) s = ↑v s",
"tactic": "rw [ennrealToMeasure, ofMeasurable_apply _ hs]"
}
] | [
541,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Logic/Basic.lean | and_iff_not_or_not | [] | [
472,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.reflectsMonomorphisms.iso_iff | [] | [
161,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
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