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/LinearAlgebra/Lagrange.lean | Lagrange.degree_nodal | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝ : Field F\nι : Type u_2\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\n⊢ degree (nodal s v) = ↑(card s)",
"tactic": "simp_rw [nodal, degree_prod, degree_X_sub_C, sum_const, Nat.smul_one_eq_coe]"
}
] | [
501,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_mem_smul | [] | [
971,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.toSubsemiring_subtype | [] | [
450,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Finsupp/Antidiagonal.lean | Finsupp.prod_antidiagonal_swap | [] | [
101,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_iInf₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.74343\nγ : Type ?u.74346\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\nS : Set (LowerSet α)\ns t : LowerSet α\na : α\nf : (i : ι) → κ i → LowerSet α\n⊢ ↑(⨅ (i : ι) (j : κ i), f i j) = ⋂ (i : ι) (j : κ i), ↑(f i j)",
"tactic": "simp... | [
718,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | isLUB_of_tendsto_atTop | [
{
"state_after": "case left\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : TopologicalSpace α\ninst✝³ : Preorder α\ninst✝² : OrderClosedTopology α\ninst✝¹ : Nonempty β\ninst✝ : SemilatticeSup β\nf : β → α\na : α\nhf : Monotone f\nha : Tendsto f atTop (𝓝 a)\n⊢ a ∈ upperBounds (range f)\n\ncase right\nα : Type u_1\nβ : T... | [
283,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | uniformContinuous_vsub | [] | [
266,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.charpoly_natDegree_eq_dim | [] | [
130,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.normalize_lcm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns : Multiset α\n⊢ ↑normalize (lcm 0) = lcm 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\n... | [
85,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_empty_codomain | [] | [
268,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometryEquiv.norm_iteratedFDeriv_comp_right | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\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 : Normed... | [
466,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_const_mul_zpow_atTop_nhds_iff | [
{
"state_after": "case refine'_1\n𝕜 : Type u_1\nα : Type ?u.43044\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nn : ℤ\nc d : 𝕜\nhc : c ≠ 0\nh : Tendsto (fun x => c * x ^ n) atTop (𝓝 d)\n⊢ n = 0 ∧ c = d ∨ n < 0 ∧ d = 0\n\ncase refine'_2\n�... | [
206,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | Matrix.isUnit_det_J | [] | [
78,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/String/Lemmas.lean | String.drop_empty | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ drop \"\" n = \"\"",
"tactic": "rw [drop_eq, List.drop_nil]"
}
] | [
1094,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1094,
9
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.le_ndunion_left | [] | [
191,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.one_right | [] | [
323,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.tendsto_add_haar_inter_smul_one_of_density_one | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2289386\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
832,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.agree'_refl | [
{
"state_after": "case succ.f.a\nF : PFunctor\nX : Type ?u.16870\nf : X → Obj F X\nx : M F\nn✝ : ℕ\nn_ih : ∀ (x : M F), Agree' n✝ x x\na✝ : F.A\nf✝ : B F a✝ → M F\n⊢ ∀ (i : B F a✝), Agree' n✝ (f✝ i) (f✝ i)",
"state_before": "F : PFunctor\nX : Type ?u.16870\nf : X → Obj F X\nn : ℕ\nx : M F\n⊢ Agree' n x x",
... | [
405,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Order/Bounds/Basic.lean | lt_isLUB_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝ : LinearOrder α\ns : Set α\na b : α\nh : IsLUB s a\n⊢ b < a ↔ ∃ c, c ∈ s ∧ b < c",
"tactic": "simp_rw [← not_le, isLUB_le_iff h, mem_upperBounds, not_forall, not_le, exists_prop]"
}
] | [
1115,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.hasEqualizer_comp_mono | [] | [
1249,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_le_middle | [
{
"state_after": "case inl\nr n : ℕ\nb : r ≤ n\n⊢ choose n r ≤ choose n (n / 2)\n\ncase inr\nr n : ℕ\nb : r > n\n⊢ choose n r ≤ choose n (n / 2)",
"state_before": "r n : ℕ\n⊢ choose n r ≤ choose n (n / 2)",
"tactic": "cases' le_or_gt r n with b b"
},
{
"state_after": "case inl.inl\nr n : ℕ\nb : ... | [
310,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Std/Data/List/Lemmas.lean | List.cons_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\n⊢ List.diff (a :: l₁) l₂ = if a ∈ l₂ then List.diff l₁ (List.erase l₂ a) else a :: List.diff l₁ l₂",
"tactic": "induction l₂ generalizing l₁ with\n| nil => rfl\n| cons b l₂ ih => by_cases h : a = b ... | [
1510,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1506,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_eq_empty | [] | [
99,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_iff_ultrafilter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nx : α\n⊢ x ∈ closure s ↔ ∃ u, s ∈ u ∧ ↑u ≤ 𝓝 x",
"tactic": "simp [closure_eq_cluster_pts, ClusterPt, ← exists_ultrafilter_iff, and_comm... | [
1362,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.iff_exists_open | [] | [
88,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/List/Count.lean | List.countp_eq_length | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\np q : α → Bool\n⊢ countp p l = length l ↔ ∀ (a : α), a ∈ l → p a = true",
"tactic": "rw [countp_eq_length_filter, filter_length_eq_length]"
}
] | [
113,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iSup_disjoint_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.7410\ninst✝ : Frame α\ns t : Set α\na b : α\nf : ι → α\n⊢ Disjoint (⨆ (i : ι), f i) a ↔ ∀ (i : ι), Disjoint (f i) a",
"tactic": "simp only [disjoint_iff, iSup_inf_eq, iSup_eq_bot]"
}
] | [
133,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/List/Range.lean | List.unzip_enum_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\n⊢ unzip (enum l) = (range (length l), l)",
"tactic": "simp only [enum_eq_zip_range, unzip_zip, length_range]"
}
] | [
187,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.singleton_sigma | [
{
"state_after": "case mp\nι : Type u_1\nι' : Type ?u.6266\nα : ι → Type u_2\nβ : ι → Type ?u.6276\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx✝ : (i : ι) × α i\ni j : ι\na : α i\nx : (i : ι) × α i\n⊢ x ∈ Set.Sigma {i} t → x ∈ Sigma.mk i '' t i\n\ncase mpr\nι : Type u_1\nι' : Type... | [
119,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_pow_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA B✝ C : Finset α\nhA : Finset.Nonempty A\nB : Finset α\nn : ℕ\n⊢ ↑(card (B ^ n)) ≤ (↑(card (A / B)) / ↑(card A)) ^ n * ↑(card A)",
"tactic": "simpa only [_root_.pow_zero, div_one] using card_pow_div... | [
260,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Ring/Defs.lean | neg_mul | [] | [
293,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_det | [
{
"state_after": "X : Type u_3\nα : Type ?u.24141\nl : Type ?u.24144\nm : Type ?u.24147\nn : Type u_1\np : Type ?u.24153\nS : Type ?u.24156\nR : Type u_2\nm' : l → Type ?u.24164\nn' : l → Type ?u.24169\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace R\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ ... | [
201,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Vector.lean | Vector.toList_cons | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nφ : Type w\nn : ℕ\na : α\nval✝ : List α\nproperty✝ : List.length val✝ = n\n⊢ toList (cons a { val := val✝, property := property✝ }) = a :: toList { val := val✝, property := property✝ }",
"state_before": "α : Type u\nβ : Type v\nφ : Type w\nn : ℕ\na : α\nv :... | [
235,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | finiteDimensional_of_isCompact_closedBall | [
{
"state_after": "𝕜 : Type u\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁵ : AddCommGroup F'\ninst✝⁴ : Module 𝕜 F'\ninst✝³ : TopologicalSpace F'\ninst✝² : To... | [
487,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.Equivalent.refl | [] | [
630,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.image_closedBall | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1197004\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nh✝ h : α ≃ᵢ β\nx : α\nr : ℝ\n⊢ ↑h '' Metric.closedBall x r = Metric.closedBall (↑h x) r",
"tactic": "rw [← h.preimage_symm, h.symm.preimage_cl... | [
641,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/GroupTheory/Subgroup/Saturated.lean | Subgroup.saturated_iff_npow | [] | [
39,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_unit | [] | [
885,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Frequently.filter_mono | [] | [
1273,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/Algebra/Ring/CompTypeclasses.lean | RingHomInvPair.comp_apply_eq₂ | [
{
"state_after": "R₁ : Type u_2\nR₂ : Type u_1\nR₃ : Type ?u.4227\ninst✝³ : Semiring R₁\ninst✝² : Semiring R₂\ninst✝¹ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nσ : R₁ →+* R₂\nσ' : R₂ →+* R₁\ninst✝ : RingHomInvPair σ σ'\nx : R₂\n⊢ ↑(RingHom.id R₂) x = x",
"state_before": "R₁ : Type u_... | [
100,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.mul | [] | [
1398,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/Topology/Connected.lean | Sum.isConnected_iff | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Type ?u.42555\nπ : ι → Type ?u.42560\ninst✝¹ : TopologicalSpace α\ns✝ t u v : Set α\ninst✝ : TopologicalSpace β\ns : Set (α ⊕ β)\nhs : IsConnected s\n⊢ (∃ t, IsConnected t ∧ s = inl '' t) ∨ ∃ t, IsConnected t ∧ s = inr '' t\n\ncase refine'_2\nα : Typ... | [
555,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_flip_aux | [] | [
2665,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2664,
9
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_lt_sqrt | [] | [
281,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | homology.π_map | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.105508\nV : Type u\ninst✝¹⁹ : Category V\ninst✝¹⁸ : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ninst✝¹⁷ : HasImage f\ng : B ⟶ C\ninst✝¹⁶ : HasKernel g\nw : f ≫ g = 0\nA' B' C' : V\nf' : A' ⟶ B'\ninst✝¹⁵ : HasImage f'\ng' : B' ⟶ C'\ninst✝¹⁴ : HasKernel ... | [
289,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_zero | [
{
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"tactic": "rw [thickenedIndicator_apply, thickenedIndicatorAux_zero δ_pos E x_out, zero_toNNReal]"
}
] | [
209,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.ClosedUnder.sInf | [] | [
89,
30
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88,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.le_div_iff | [] | [
825,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
8
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Mathlib/Data/Stream/Init.lean | Stream'.drop_append_stream | [
{
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"tactic": "rfl"
},
{
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548,
92
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545,
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Mathlib/Order/Chain.lean | Flag.bot_mem | [] | [
345,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_inversion | [
{
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89,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Computability/Ackermann.lean | ack_zero | [
{
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}
] | [
72,
58
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1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableOn.mono | [] | [
609,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_le_mul_self_iff | [] | [
993,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_submatrix_le | [
{
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113,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Data/ZMod/Basic.lean | ZMod.val_one' | [] | [
73,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Mathlib/Data/Fin/Basic.lean | Fin.coe_castSucc | [] | [
1208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderivWithin_const_add | [
{
"state_after": "no goals",
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316,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.tendsto_measure_biInter_gt | [
{
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568,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_congr_set | [] | [
2934,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2932,
1
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Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_zmodeq | [] | [
534,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
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Mathlib/Data/Bool/Basic.lean | Bool.not_or | [
{
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"tactic": "decide"
}
] | [
311,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_smul_index' | [] | [
1636,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1634,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_mulEquiv_refl | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.subtypeVal_toSubtype' | [
{
"state_after": "case a.h\nn : ℕ\nα : TypeVec n\nr : α ⊗ α ⟹ repeat n Prop\ni : Fin2 n\nx : (fun i => { x // ofRepeat (r i (prod.mk i x.fst x.snd)) }) i\n⊢ (subtypeVal r ⊚ toSubtype' r) i x = prod.mk i (↑x).fst (↑x).snd",
"state_before": "n : ℕ\nα : TypeVec n\nr : α ⊗ α ⟹ repeat n Prop\n⊢ subtypeVal r ⊚ to... | [
828,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
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Mathlib/Analysis/Normed/Group/Basic.lean | Real.ofReal_le_ennnorm | [
{
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1773,
17
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1769,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_sub_cancel | [] | [
554,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.map_neg_atTop | [] | [
834,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
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Mathlib/CategoryTheory/Limits/Preserves/Limits.lean | CategoryTheory.preservesLimitsIso_inv_π | [] | [
72,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.dual_iff | [
{
"state_after": "α : Type u_1\ninst✝ : Preorder α\nt : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : Valid' o₂ (Ordnode.dual t) o₁\nthis : Valid' o₁ (Ordnode.dual (Ordnode.dual t)) o₂\n⊢ Valid' o₁ t o₂",
"state_before": "α : Type u_1\ninst✝ : Preorder α\nt : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : ... | [
1084,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
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Mathlib/Data/Real/Irrational.lean | irrational_add_int_iff | [] | [
553,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.sup_mul_inf | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b : Associates α\n✝ : Nontrivial α\n⊢ FactorSet.prod (factors a ⊔ factors b) * FactorSet.p... | [
1580,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_add_const_left | [] | [
699,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
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Std/Data/Rat/Lemmas.lean | Rat.mkRat_eq_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← normalize_eq_mkRat z₁, ← normalize_eq_mkRat z₂, normalize_eq_iff]"
}
] | [
114,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
112,
1
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Mathlib/Topology/ContinuousOn.lean | continuousOn_id | [] | [
987,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.card_interedges_add_card_interedges_compl | [
{
"state_after": "𝕜 : Type ?u.113206\nι : Type ?u.113209\nκ : Type ?u.113212\nα : Type u_1\nβ : Type ?u.113218\nG : SimpleGraph α\ninst✝¹ : DecidableRel G.Adj\ns s₁ s₂ t t₁ t₂ : Finset α\na b : α\ninst✝ : DecidableEq α\nh : Disjoint s t\n⊢ card (filter (fun e => Adj G e.fst e.snd) (s ×ˢ t)) + card (filter (fun... | [
385,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
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Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.isInteger_mul | [] | [
66,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.PolyCnstr.denote_mul | [
{
"state_after": "case mk\nctx : Context\nk : Nat\neq✝ : Bool\nlhs✝ rhs✝ : Poly\n⊢ denote ctx (mul (k + 1) { eq := eq✝, lhs := lhs✝, rhs := rhs✝ }) = denote ctx { eq := eq✝, lhs := lhs✝, rhs := rhs✝ }",
"state_before": "ctx : Context\nk : Nat\nc : PolyCnstr\n⊢ denote ctx (mul (k + 1) c) = denote ctx c",
... | [
599,
34
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
587,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_sub | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.close_eq_self_of_isClosed | [] | [
125,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.uniformContinuous | [] | [
120,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Order/Monotone/Basic.lean | monotone_lam | [] | [
324,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.ofMulAction_apply | [
{
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... | [
301,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/Algebra/GroupWithZero/Power.lean | zpow_ne_zero_of_ne_zero | [
{
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"state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na : G₀\nha : a ≠ 0\na✝ : ℕ\n⊢ a ^ ↑a✝ ≠ 0",
"tactic": "rw [zpow_ofNat]"
},
{
"state_after": "no goals",
"state_before": "G₀ : Type u... | [
160,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_neighborSet_union_compl_neighborSet | [
{
"state_after": "no goals",
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997,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
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Mathlib/Topology/LocallyFinite.lean | LocallyFinite.comp_injective | [] | [
59,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_of_mem_nhdsWithin_Ioi_aux | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1394071\nγ : Type ?u.1394074\nγ₂ : Type ?u.1394077\nδ : Type ?u.1394080\nι : Sort y\ns✝ t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : BorelSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : BorelSpace β\ninst... | [
1213,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots_sub_C' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\na : R\nhp0 : 0 < degree p\nh : p = 0\n⊢ False",
"tactic": "simp_all [lt_irrefl]"
}
] | [
563,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.eq_single_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.54288\nγ : Type ?u.54291\nι : Type ?u.54294\nM : Type u_2\nM' : Type ?u.54300\nN : Type ?u.54303\nP : Type ?u.54306\nG : Type ?u.54309\nH : Type ?u.54312\nR : Type ?u.54315\nS : Type ?u.54318\ninst✝ : Zero M\na✝ a' : α\nb✝ : M\nf : α →₀ M\na : α\nb : M\n⊢ f.support ⊆ ... | [
401,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_X_mul | [
{
"state_after": "no goals",
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"tactic": "... | [
738,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isSuccLimit_iff' | [
{
"state_after": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\na b : α\nC : α → Sort ?u.8730\ninst✝ : NoMaxOrder α\n⊢ (∃ x, succ x = a) ↔ a ∈ range succ",
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207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Wbtw.angle₁₃₂_eq_zero_of_ne | [] | [
376,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
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Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.submonoid_map_le_is_unit | [
{
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"state_before": "R : Type u_2\n... | [
54,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_prod | [] | [
1553,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_top | [] | [
665,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Algebra/Associated.lean | Associated.dvd_iff_dvd_left | [] | [
572,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.epigraph | [] | [
240,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.lt_tsub_iff_left | [] | [
439,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_zero | [
{
"state_after": "S : Set Ordinal\n⊢ sInf (S ∩ {b | ∀ (c : Ordinal), c < 0 → enumOrd S c < b}) = sInf S",
"state_before": "S : Set Ordinal\n⊢ enumOrd S 0 = sInf S",
"tactic": "rw [enumOrd_def]"
},
{
"state_after": "no goals",
"state_before": "S : Set Ordinal\n⊢ sInf (S ∩ {b | ∀ (c : Ordinal)... | [
2229,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2227,
1
] |
Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.boundaries_le_cycles | [] | [
107,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
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