file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.pointwise_smul_toAddSubgroup | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_zero_singleton | [
{
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428,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.codRestrict_top | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.index_defined | [
{
"state_after": "case intro\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK V : Set G\nhK : IsCompact K\nhV : Set.Nonempty (interior V)\nt : Finset G\nht : K ⊆ ⋃ (g : G) (_ : g ∈ t), (fun h => g * h) ⁻¹' V\n⊢ ∃ n, n ∈ Finset.card '' {t | K ⊆ ⋃ (g : G) (_ : g ∈ t), (f... | [
176,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideEqualizer.lift_ι | [] | [
628,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
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Mathlib/Analysis/Normed/Group/Basic.lean | lipschitzWith_one_norm' | [
{
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1105,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
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Std/Data/Int/DivMod.lean | Int.emod_add_cancel_right | [
{
"state_after": "m n k i : Int\nH : (m + i) % n = (k + i) % n\nthis : (m + i + -i) % n = (k + i + -i) % n\n⊢ m % n = k % n",
"state_before": "m n k i : Int\nH : (m + i) % n = (k + i) % n\n⊢ m % n = k % n",
"tactic": "have := add_emod_eq_add_emod_right (-i) H"
},
{
"state_after": "no goals",
... | [
442,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
438,
1
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Mathlib/Order/Filter/Extr.lean | Filter.EventuallyLE.isMinFilter | [] | [
658,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
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Std/Data/List/Lemmas.lean | List.all_eq_true | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\n⊢ all l p = true ↔ ∀ (x : α), x ∈ l → p x = true",
"tactic": "induction l <;> simp [*]"
}
] | [
869,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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9
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.cauchy_iff | [] | [
937,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.473341\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\nj : Set α\nhj : MeasurableSet j\nhij : j ⊆ i\n... | [
707,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
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Mathlib/Data/Stream/Init.lean | Stream'.nth_const | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod | [] | [
683,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
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Mathlib/Topology/Connected.lean | IsPreconnected.subset_of_closure_inter_subset | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.31786\nπ : ι → Type ?u.31791\ninst✝ : TopologicalSpace α\ns t u v : Set α\nhs : IsPreconnected s\nhu : IsOpen u\nh'u : Set.Nonempty (s ∩ u)\nh : closure u ∩ s ⊆ u\nA : s ⊆ u ∪ closure uᶜ\n⊢ Disjoint u (closure uᶜ)",
"state_before": "α : Type u\nβ : Type ... | [
464,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/Algebra/Order/Field/Basic.lean | div_nonpos_of_nonneg_of_nonpos | [
{
"state_after": "ι : Type ?u.11809\nα : Type u_1\nβ : Type ?u.11815\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a * b⁻¹ ≤ 0",
"state_before": "ι : Type ?u.11809\nα : Type u_1\nβ : Type ?u.11815\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 ≤ a\nh... | [
108,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_one | [
{
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1984,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.totallyBounded_ball | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nx ε : ℝ\n⊢ TotallyBounded (Ioo (x - ε) (x + ε))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nx ε : ℝ\n⊢ TotallyBounded (ball x ε)",
"tactic": "rw [Real.ball_eq_Ioo]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ... | [
156,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.frontier | [] | [
598,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
11
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.Tendsto.div_div | [] | [
911,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
11
] |
Std/Data/RBMap/WF.lean | Std.RBNode.balance1_All | [
{
"state_after": "α : Type u_1\np : α → Prop\nl : RBNode α\nv : α\nr : RBNode α\n⊢ All p\n (match l, v, r with\n | node red (node red a x b) y c, z, d => node red (node black a x b) y (node black c z d)\n | node red a x (node red b y c), z, d => node red (node black a x b) y (node black c z d)\n ... | [
60,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
58,
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Mathlib/Data/Countable/Basic.lean | nonempty_embedding_nat | [] | [
42,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_compl | [] | [
550,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.sup_coe | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Set.EquicontinuousAt.mono | [] | [
194,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
11
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.stepSet_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ σ' : Type v\nM : εNFA α σ\nS : Set σ\nx : List α\ns : σ\na✝ a : α\n⊢ stepSet M ∅ a = ∅",
"tactic": "simp_rw [stepSet, mem_empty_iff_false, iUnion_false, iUnion_empty]"
}
] | [
86,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.xor_false | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ xor b false = b",
"tactic": "cases b <;> simp"
}
] | [
56,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.coe_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.39229\nδ : Type ?u.39232\np : α → Prop\ninst✝² : PartialOrder α\ninst✝¹ : OrderBot α\ninst✝ : OrderBot (Subtype p)\nhbot : p ⊥\nx : { x // p x }\n⊢ ↑x = ⊥ ↔ x = ⊥",
"tactic": "rw [← coe_bot hbot, ext_iff]"
}
] | [
782,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_left_right_iff | [] | [
348,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_eq_univ | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.169171\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.169180\ninst✝ : AddGroup A\nH✝ K H : Subgroup G\n⊢ ↑H = ↑⊤ ↔ ↑H = Set.univ",
"tactic": "rfl"
}
] | [
918,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_comp_apply | [] | [
88,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Basic.lean | image_closure_subset_closure_image | [] | [
1756,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1754,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.prod_ext | [] | [
1572,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_of_shell' | [
{
"state_after": "case pos\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.371221\nE : Type u_3\nEₗ : Type ?u.371227\nF : Type u_4\nFₗ : Type ?u.371233\nG : Type ?u.371236\nGₗ : Type ?u.371239\n𝓕 : Type ?u.371242\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : SeminormedAddCom... | [
257,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.st_id_real | [] | [
364,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.invRev_surjective | [] | [
590,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.sup_aux | [
{
"state_after": "R : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.162242\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf g : E →ₗ.[R] F\nh : ∀ (x : { x // x ∈ f.domain }) (y : { x // x ∈ g.domain }... | [
329,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
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] |
Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.Final.cofinal_of_colimit_comp_coyoneda_iso_pUnit | [
{
"state_after": "C : Type v\ninst✝² : Category C\nD : Type v\ninst✝¹ : Category D\nF : C ⥤ D\ninst✝ : Final F\nI : (d : D) → colimit (F ⋙ coyoneda.obj d.op) ≅ PUnit\nd : D\nthis : Nonempty (StructuredArrow d F)\n⊢ IsConnected (StructuredArrow d F)",
"state_before": "C : Type v\ninst✝² : Category C\nD : Typ... | [
429,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsGroupHom.one_ker_inv | [
{
"state_after": "G : Type u_1\nH : Type u_2\nA : Type ?u.69287\na✝ a₁ a₂ b✝ c : G\ninst✝¹ : Group G\ninst✝ : Group H\nf : G → H\nhf : IsGroupHom f\na b : G\nh : f a * (f b)⁻¹ = 1\n⊢ f a = f b",
"state_before": "G : Type u_1\nH : Type u_2\nA : Type ?u.69287\na✝ a₁ a₂ b✝ c : G\ninst✝¹ : Group G\ninst✝ : Grou... | [
349,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_join | [
{
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"state_before": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr : α → α → Prop\na b : α\nL : List (List α)\n⊢ Nodup (join L) ↔ (∀ (l : List α), l ∈ L → Nodup l) ∧ Pairwise Disjoint L",
"tactic": "simp only [Nodup, pairwise_join, disjoint_left.symm, forall_mem_ne]"
}
] | [
334,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Asymptotics.IsBigO.hasFDerivAt | [
{
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688,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.isPwo_iUnion_support_powers | [
{
"state_after": "Γ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedCancelAddCommMonoid Γ\ninst✝¹ : Ring R\ninst✝ : IsDomain R\nx : HahnSeries Γ R\nhx : 0 < ↑(addVal Γ R) x\n⊢ ∀ (x_1 : Γ), x_1 ∈ support x → 0 ≤ x_1\n\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedCancelAddCommMonoid Γ\ninst✝¹ : Ring R\ninst... | [
1394,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/Analysis/Calculus/ParametricIntervalIntegral.lean | intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nμ : MeasureTheory.Measure ℝ\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type ?u.526446\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\na b ε : ℝ\nbound : ℝ → ℝ\nF :... | [
93,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
8
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.sub | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.39565\nE : Type u_2\nι : Sort ?u.39571\nκ : ι → Sort ?u.39576\ninst✝² : SeminormedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns s₁ s₂ t t₁ t₂ : Set E\nh₁ : Absorbs 𝕜 s₁ t₁\nh₂ : Absorbs 𝕜 s₂ t₂\n⊢ Absorbs 𝕜 (s₁ + -s₂) (t₁ + -t₂)",
"state_before": "... | [
243,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.nontrivial_of_einfsep_lt_top | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.14614\ninst✝ : EDist α\nx y : α\ns t : Set α\nhs : einfsep s < ⊤\nw✝¹ : α\nhx : w✝¹ ∈ s\nw✝ : α\nhy : w✝ ∈ s\nhxy : w✝¹ ≠ w✝\nh✝ : edist w✝¹ w✝ < ⊤\n⊢ Set.Nontrivial s",
"state_before": "α : Type u_1\nβ : Type ?u.14614\ninst✝ : ... | [
93,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_ne_zero | [] | [
146,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.add_factorial_lt_factorial_add | [
{
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"state_before": "m n✝ i n : ℕ\nhi : 2 ≤ i\nhn : 1 ≤ n\n⊢ i + n ! < (i + n)!",
"tactic": "cases hn"
},
{
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182,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/Topology/Filter.lean | Filter.nhds_principal | [] | [
127,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Antitone.map_liminf_of_continuousAt | [] | [
379,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/Topology/SubsetProperties.lean | Filter.hasBasis_coclosedCompact | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.51065\nπ : ι → Type ?u.51070\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\n⊢ HasBasis (⨅ (s : Set α) (_ : IsClosed s ∧ IsCompact s), 𝓟 (sᶜ)) (fun s => IsClosed s ∧ IsCompact s) compl",
"state_before": "α : Type u\nβ : Type v\nι ... | [
595,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
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Mathlib/Order/ModularLattice.lean | inf_strictMonoOn_Icc_sup | [] | [
314,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/Data/PFun.lean | PFun.prodMap_id_id | [
{
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"tactic": "simp [eq_comm]"
}
] | [
701,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_toOrderIso_symm | [] | [
242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_zero | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM0to1.tr_respects | [
{
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2048,
10
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2027,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | deriv_sinh | [] | [
907,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.mem_ker | [] | [
1186,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.ctor_eq_zero | [] | [
424,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
423,
1
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_summable_nnnorm | [] | [
159,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.mk_inr | [] | [
860,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryRightEquiv_apply | [] | [
1567,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
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Mathlib/Order/Concept.lean | Concept.snd_ssubset_snd_iff | [
{
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"tactic": "rw [ssubset_iff_subset_not_subset, lt_iff_le_not_le, snd_subse... | [
255,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/RingTheory/Valuation/Integral.lean | Valuation.Integers.integrallyClosed | [] | [
70,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_of_ne_zero | [] | [
158,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_isTrail_iff | [
{
"state_after": "case mpr\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nh : IsTrail p\n⊢ IsTrail (reverse p)",
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940,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.blsub_eq | [] | [
568,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.homQuotientZPowOfHom_comp | [] | [
518,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/LinearAlgebra/Span.lean | Submodule.prod_mono | [] | [
796,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
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Mathlib/Init/CcLemmas.lean | iff_eq_of_eq_true_left | [] | [
13,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
12,
1
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Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.comp.get_mk | [
{
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}
] | [
148,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Std/Logic.lean | not_of_iff_false | [] | [
57,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
57,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.toOuterMeasure_eq_inducedOuterMeasure | [] | [
177,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/GroupTheory/Congruence.lean | Con.mk'_ker | [] | [
857,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_eq_integral | [
{
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831,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
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Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq | [
{
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149,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Analysis/Fourier/FourierTransform.lean | VectorFourier.fourier_integral_convergent_iff | [
{
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152,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.supported_eq_vars_subset | [] | [
90,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.coe_comp | [] | [
745,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.subset_range | [] | [
757,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
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] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | wittStructureInt_rename | [
{
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355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
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Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_im_ge | [] | [
51,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/Data/List/Lattice.lean | List.sublist_suffix_of_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₂ : List α\n⊢ [] <+ []",
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},
{
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109,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node' | [] | [
1118,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.even_iff_not_odd | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ Even n ↔ ¬Odd n",
"tactic": "rw [not_odd_iff, even_iff]"
}
] | [
60,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.injective_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : Group α\ninst✝ : Group β\nf✝ : α → β\nhf✝ : IsGroupHom f✝\nf : α → β\nhf : IsGroupHom f\nh : Function.Injective f\nx✝ : α\n⊢ f x✝ = f 1 → x✝ = 1",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Group α\ninst✝ : Group β\nf✝ : α → β\nhf✝ : IsGroupHom f✝\nf... | [
334,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prime_X | [
{
"state_after": "case h.e'_3\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\n⊢ X = X - ↑C 0",
"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 : R[X]\n⊢ Prime X",
"tactic": "conver... | [
413,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
src/lean/Init/SimpLemmas.lean | false_implies | [] | [
97,
84
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
97,
9
] |
Mathlib/Data/Fintype/Basic.lean | Finset.mem_univ_val | [] | [
81,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.dvd_div_of_mul_dvd | [
{
"state_after": "case inl\nR : Type u\ninst✝ : EuclideanDomain R\nb c : R\nh : 0 * b ∣ c\n⊢ b ∣ c / 0\n\ncase inr\nR : Type u\ninst✝ : EuclideanDomain R\na b c : R\nh : a * b ∣ c\nha : a ≠ 0\n⊢ b ∣ c / a",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na b c : R\nh : a * b ∣ c\n⊢ b ∣ c / a",
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131,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.conj_inv_apply | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.tendsto_exp_nhds_zero_iff | [
{
"state_after": "α : Type u_1\nl : Filter α\nf : α → ℂ\n⊢ Tendsto (re ∘ f) l atBot ↔ Tendsto (fun x => (f x).re) l atBot",
"state_before": "α : Type u_1\nl : Filter α\nf : α → ℂ\n⊢ Tendsto (fun x => exp (f x)) l (𝓝 0) ↔ Tendsto (fun x => (f x).re) l atBot",
"tactic": "simp_rw [←comp_apply (f := exp), ... | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_zero_iff | [
{
"state_after": "R : Type u_2\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nx : P\nx✝ : x ∈ 0\nx' : R\nx'_mem_zero : x' ∈ ↑0\nx'_eq_x : ↑(Algebra.linearMap R P) x' = x\nx'_eq_zero : x' = 0\n⊢ x = 0",
"state_before": "R : Type u_2\ni... | [
285,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerLeft_id | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Theory.model_iff_subset_completeTheory | [] | [
863,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_subsingleton | [] | [
904,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_mono | [] | [
77,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_iff_le_one_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19428\ninst✝³ : MulOneClass α\ninst✝² : LE α\ninst✝¹ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : ContravariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ a * b ≤ b ↔ a * b ≤ ... | [
426,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.equivCongrLeft_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type v\ndec_ι : DecidableEq ι\nβ : ι → Type w\ninst✝¹ : (i : ι) → AddCommMonoid (β i)\nγ : Type u₁\ninst✝ : AddCommMonoid γ\nκ : Type u_1\nh : ι ≃ κ\nf : ⨁ (i : ι), β i\nk : κ\n⊢ ↑(↑(equivCongrLeft h) f) k = ↑f (↑h.symm k)",
"tactic": "exact Dfinsupp.com... | [
293,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | Complex.hasStrictFDerivAt_log_real | [] | [
64,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.mem_toConvexCone | [] | [
523,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.changeOrigin_eval | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type u_3\nG : Type ?u.2255633\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : CompleteSpa... | [
1326,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
1
] |
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