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/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.from_eq | [] | [
82,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atTop_prod_self' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.302627\nι' : Type ?u.302630\nα : Type u_1\nβ : Type ?u.302636\nγ : Type ?u.302639\ninst✝¹ : SemilatticeSup α\ninst✝ : Nonempty α\np : α × α → Prop\n⊢ (∀ᶠ (x : α × α) in atTop, p x) ↔ ∃ a, ∀ (k : α), k ≥ a → ∀ (l : α), l ≥ a → p (k, l)",
"tactic":... | [
1485,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1483,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.neg_le_neg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.548949\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : OrderedAddCommGroup M\ninst✝ : TopologicalAddGroup M\nv w : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\nh : restrict v i ≤ restrict w i\nj : Set α\nhj₁ : MeasurableSet j\n⊢ ↑(re... | [
930,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
8
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.eq_sqrt' | [
{
"state_after": "no goals",
"state_before": "n q : ℕ\n⊢ q = sqrt n ↔ q ^ 2 ≤ n ∧ n < (q + 1) ^ 2",
"tactic": "simpa only [pow_two] using eq_sqrt"
}
] | [
127,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_add | [
{
"state_after": "case a.h\nl : Type u_3\nm : Type u_4\nn : Type u_2\no : Type u_5\np : Type ?u.36919\nq : Type ?u.36922\nm' : o → Type ?u.36927\nn' : o → Type ?u.36932\np' : o → Type ?u.36937\nR : Type ?u.36940\nS : Type ?u.36943\nα : Type u_1\nβ : Type ?u.36949\ninst✝ : Add α\nA : Matrix n l α\nB : Matrix n m... | [
247,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Order/GaloisConnection.lean | sSup_image2_eq_sInf_sInf | [] | [
400,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/Algebra/Star.lean | Continuous.star | [] | [
62,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.fac_lift | [] | [
358,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.coe_mul | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_neighborFinset_eq_degree | [] | [
1379,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1379,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.takeUntil_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v' w' : V\np : Walk G v' w'\nh : u ∈ support (Walk.copy p (_ : v' = v') (_ : w' = w'))\n⊢ u ∈ support p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG... | [
1122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_source_mem_nhdsWithin | [] | [
823,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Topology/Inseparable.lean | inseparable_iff_mem_closure | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.31356\nZ : Type ?u.31359\nα : Type ?u.31362\nι : Type ?u.31365\nπ : ι → Type ?u.31370\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X... | [
303,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_succ_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.431878\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\nn : ℕ\n⊢ ∏ x in range (n + 1), f x = f n * ∏ x in range n, f x",
"tactic": "rw [range_succ, prod_insert not_mem_range_self]"
}... | [
1213,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_of_bisim | [] | [
317,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/List/Basic.lean | List.length_eq_three | [] | [
224,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_natAbs_eq_of_nonneg | [] | [
1329,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1327,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | pow_succ_padicValNat_not_dvd | [
{
"state_after": "p n : ℕ\nhp : Fact (Nat.Prime p)\nhn : n ≠ 0\n⊢ padicValNat p n < padicValNat p n + 1",
"state_before": "p n : ℕ\nhp : Fact (Nat.Prime p)\nhn : n ≠ 0\n⊢ ¬p ^ (padicValNat p n + 1) ∣ n",
"tactic": "rw [padicValNat_dvd_iff_le hn, not_le]"
},
{
"state_after": "no goals",
"stat... | [
478,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.comp_surjective | [] | [
379,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_disjoint_closedBall | [] | [
546,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_top | [] | [
503,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.set_induction | [] | [
374,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.toOuterMeasure_toMeasure | [] | [
693,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/List/Sigma.lean | List.sizeOf_kerase | [
{
"state_after": "α✝ : Type u\nβ✝ : α✝ → Type v\nl l₁ l₂ : List (Sigma β✝)\ninst✝² : DecidableEq α✝\nα : Type u_1\nβ : α → Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : SizeOf (Sigma β)\nx : α\nxs : List (Sigma β)\n⊢ rec 1 (fun head tail tail_ih => 1 + sizeOf head + tail_ih) (kerase x xs) ≤\n rec 1 (fun head tai... | [
558,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumDualDistrib_symm_inr | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.singleton_one | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/Constructions.lean | DenseRange.prod_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type u_3\nδ : Type ?u.64152\nε : Type ?u.64155\nζ : Type ?u.64158\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpa... | [
801,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Algebra/DirectSum/Algebra.lean | DirectSum.algHom_ext | [] | [
126,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_re | [] | [
1093,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
9
] |
Mathlib/Order/Filter/Curry.lean | Filter.Tendsto.curry | [] | [
77,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.measurePreserving_div_left | [
{
"state_after": "𝕜 : Type ?u.510422\nG : Type u_1\nH : Type ?u.510428\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : MeasurableSpace H\ninst✝⁴ : DivisionMonoid G\ninst✝³ : MeasurableMul G\ninst✝² : MeasurableInv G\nμ✝ μ : Measure G\ninst✝¹ : IsInvInvariant μ\ninst✝ : IsMulLeftInvariant μ\ng : G\n⊢ MeasurePreserving fu... | [
461,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.isBasis_iff_cover | [
{
"state_after": "case mp\nι : Type ?u.31277\nα : Type u_1\nβ : Type ?u.31283\nγ : Type ?u.31286\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nB : Set (Opens α)\n⊢ IsBasis B → ∀ (U : Opens α), ∃ Us, Us ⊆ B ∧ U = sSup Us\n\ncase mpr\nι : Type ?u.31277\nα : Type u_1\nβ : T... | [
325,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.mk_pow | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Computability/Language.lean | Language.le_iff | [] | [
200,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.invFun_neg | [] | [
442,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
src/lean/Init/Data/List/Basic.lean | List.concat_eq_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas : List α\na : α\n⊢ concat as a = as ++ a :: nil",
"tactic": "induction as <;> simp [concat, *]"
}
] | [
851,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
850,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | QuotientAddGroup.norm_mk | [
{
"state_after": "M : Type u_1\nN : Type ?u.27150\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nx : M\n⊢ infDist x (↑(IsometryEquiv.symm (IsometryEquiv.subLeft x)) ⁻¹' {m | ↑m = ↑x}) = infDist x ↑S",
"state_before": "M : Type u_1\nN : Type ?u.27150\ninst✝¹ : Semino... | [
127,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_ofFunction_le | [
{
"state_after": "α : Type u_2\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\nβ : Type u_1\nf : α → β\ns : Set β\n⊢ ↑(OuterMeasure.ofFunction m m_empty) (f ⁻¹' s) ≤ m (f ⁻¹' s)",
"state_before": "α : Type u_2\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\nβ : Type u_1\nf : α → β\ns : Set β\n⊢ ↑(↑(map f) (OuterMeasure.ofFunct... | [
796,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isRightRegular_of_mul_eq_one | [
{
"state_after": "R : Type u_1\ninst✝ : Monoid R\na b : R\nh : a * b = 1\n⊢ IsRightRegular 1",
"state_before": "R : Type u_1\ninst✝ : Monoid R\na b : R\nh : a * b = 1\n⊢ IsRightRegular (a * ?m.14188 h)",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ ... | [
316,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Set/Opposite.lean | Set.mem_unop | [] | [
48,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.id_comp | [
{
"state_after": "case mk\nL : Language\nL' : Language\nM : Type w\ninst✝ : Structure L M\nϕ : L →ᴸ L'\nL'' : Language\nonFunction✝ : ⦃n : ℕ⦄ → Functions L n → Functions L' n\nonRelation✝ : ⦃n : ℕ⦄ → Relations L n → Relations L' n\n⊢ LHom.id L' ∘' { onFunction := onFunction✝, onRelation := onRelation✝ } =\n ... | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_subset_uIcc_iff_le' | [] | [
949,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.mem_filterAt_iff | [
{
"state_after": "α : Type u_1\ninst✝ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nx : α\ns : Set (Set α)\n⊢ (s ∈ ⨅ (ε : ℝ) (_ : ε ∈ Ioi 0), 𝓟 {a | a ∈ setsAt v x ∧ a ⊆ closedBall x ε}) ↔\n ∃ ε, 0 < ε ∧ ∀ (a : Set α), a ∈ setsAt v x → a ⊆ closedBall x ε → a ∈ s",... | [
236,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_pos | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\na : Fin n\n⊢ 0 < succ a",
"tactic": "simp [lt_iff_val_lt_val]"
}
] | [
874,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.inl_le_inl_iff | [] | [
133,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.comp_inv | [
{
"state_after": "case h\nα : Type ?u.241739\nβ : Type ?u.241742\nM✝ : Type ?u.241745\nN : Type ?u.241748\nP : Type ?u.241751\nG : Type ?u.241754\nH : Type ?u.241757\nF : Type ?u.241760\ninst✝⁵ : Group G\ninst✝⁴ : CommGroup H\ninst✝³ : MulOneClass M✝\nM : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝² : MulOneCla... | [
1671,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1668,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_eq_sub_of_hasDeriv_right | [
{
"state_after": "case inl\nι : Type ?u.1842380\n𝕜 : Type ?u.1842383\nE : Type u_1\nF : Type ?u.1842389\nA : Type ?u.1842392\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝ : ℝ → E\ng' g φ : ℝ → ℝ\nf f' : ℝ → E\na b : ℝ\nhcont : ContinuousOn f [[a, b]]\nhderiv : ∀ (x : ℝ),... | [
1192,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.map_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.37158\nβ : Type ?u.37161\nn d✝ k N : ℕ\nx : Fin n → ℕ\nd : ℕ\na : Fin 0 → ℕ\n⊢ ↑(map d) a = 0",
"tactic": "simp [map]"
}
] | [
127,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_distrib | [] | [
2207,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2206,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | PosMulMonoRev.toPosMulStrictMono | [] | [
288,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.comap_bracket_eq | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ J₁ J₂ : LieIdeal R L'\nh : LieHom.IsIdealMorphism f\n⊢ Submodule.comap (↑f) (Submodule.span R {m | ∃ x n, ⁅↑... | [
325,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.kernelSubobject_arrow_eq_zero_of_exact_zero_left | [
{
"state_after": "V : Type u\ninst✝³ : Category V\ninst✝² : HasImages V\nA B C D : V\nf : A ⟶ B\ng : B ⟶ C\nh✝ : C ⟶ D\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasEqualizers V\nh : Exact 0 g\nthis : Epi (imageToKernel 0 g (_ : 0 ≫ g = 0))\n⊢ Subobject.arrow (kernelSubobject g) = 0",
"state_before": "V : Type u... | [
255,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.smul_apply | [] | [
598,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_mapRange_index | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nι : Type ?u.32313\nγ : Type ?u.32316\nA : Type ?u.32319\nB : Type ?u.32322\nC : Type ?u.32325\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : AddCommMonoid B\ninst✝³ : AddCommMonoid C\nt : ι → A → C\nh0✝ : ∀ (i : ι), t i 0 = 0\nh1 : ∀ (i : ι) (x y : A), t i (x... | [
89,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.coe_restrict_apply | [] | [
1153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.rightMoves_neg | [] | [
1246,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | smul_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type ?u.321762\ninst✝⁸ : CommSemiring R\ninst✝⁷ : CommSemiring S\ninst✝⁶ : Semiring A\ninst✝⁵ : Algebra R A\ninst✝⁴ : Semiring B\ninst✝³ : Algebra R B\nα : Type u_1\ninst✝² : Monoid α\ninst✝¹ : MulDistribMulAction α A\nins... | [
406,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.coe_comp | [] | [
240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_def | [] | [
148,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.restriction_of | [] | [
233,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.apply_of_ne | [
{
"state_after": "l : Type ?u.21103\nm : Type u_1\nn : Type u_2\nR : Type ?u.21112\nα : Type u_3\ninst✝³ : DecidableEq l\ninst✝² : DecidableEq m\ninst✝¹ : DecidableEq n\ninst✝ : Semiring α\ni : m\nj : n\nc : α\ni' : m\nj' : n\nh : ¬(i = i' ∧ j = j')\n⊢ i = i' → j = j' → c = 0",
"state_before": "l : Type ?u.... | [
132,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.mem_range_self | [] | [
799,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.le_def | [] | [
600,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.run_pure | [] | [
52,
97
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
52,
9
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.isConj_swap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nw x y✝ z✝ : α\nhwx : w ≠ x\nhyz✝ : y✝ ≠ z✝\ny z : α\nhyz : y ≠ z\nhwz : w ≠ z\n⊢ swap w y * swap x z * swap w x * (swap w y * swap x z)⁻¹ = swap y z",
"tactic": "rw [mul_inv_rev, swap_inv, swap_inv, mul_assoc (s... | [
300,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_le_of_sum_le | [] | [
56,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.mono_lie_left | [] | [
163,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeAddMonoid.countp_of | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nx : α\n⊢ ↑(countp p) (of x) = if p x = (true = true) then 1 else 0",
"tactic": "simp [countp, List.countp, List.countp.go]"
}
] | [
36,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_apply_of_squarefree | [] | [
956,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Data/Fintype/Basic.lean | exists_seq_of_forall_finset_exists' | [
{
"state_after": "case intro.intro\nα✝ : Type ?u.168313\nβ : Type ?u.168316\nγ : Type ?u.168319\nα : Type u_1\nP : α → Prop\nr : α → α → Prop\ninst✝ : IsSymm α r\nh : ∀ (s : Finset α), (∀ (x : α), x ∈ s → P x) → ∃ y, P y ∧ ∀ (x : α), x ∈ s → r x y\nf : ℕ → α\nhf : ∀ (n : ℕ), P (f n)\nhf' : ∀ (m n : ℕ), m < n → ... | [
1261,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | topologicalGroup_is_uniform_of_compactSpace | [
{
"state_after": "case h\nG : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : CompactSpace G\n⊢ Continuous fun p => p.fst / p.snd",
"state_before": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : CompactSpace G\... | [
589,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Topology/SubsetProperties.lean | noncompactSpace_of_neBot | [] | [
774,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.pow_eq_one_iff'' | [] | [
699,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/CategoryTheory/Limits/ConeCategory.lean | CategoryTheory.Limits.hasColimitsOfShape_iff_isRightAdjoint_const | [] | [
186,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.exists_null_pairwise_disjoint_diff | [
{
"state_after": "case refine'_1\nι : Type u_1\nα : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ns✝ t u v : Set α\ninst✝ : Countable ι\ns : ι → Set α\nhd : Pairwise (AEDisjoint μ on s)\ni : ι\n⊢ ↑↑μ ((fun i => toMeasurable μ (s i ∩ ⋃ (j : ι) (_ : j ∈ {i}ᶜ), s j)) i) = 0\n\ncase refine'_2\nι : Type u_1\nα : T... | [
48,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isVonNBounded_iff | [] | [
81,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | Seminorm.gaugeSeminorm_ball | [] | [
447,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.exists_lt_map_eq_of_mapsTo | [] | [
1433,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_eq_pi_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ 2 • θ = ↑π ↔ θ = ↑(π / 2) ∨ θ = ↑(-π / 2)",
"tactic": "rw [two_zsmul, ← two_nsmul, two_nsmul_eq_pi_iff]"
}
] | [
240,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.convex_gt | [] | [
397,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.refl | [] | [
1480,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
1
] |
Mathlib/Computability/Reduce.lean | ULower.down_computable | [] | [
289,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.reApplyInnerSelf_continuous | [] | [
2302,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2300,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.erase_add_right_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.97707\nγ : Type ?u.97710\ninst✝ : DecidableEq α\ns✝ t✝ : Multiset α\na✝ b a : α\ns t : Multiset α\nh : a ∈ t\n⊢ erase (s + t) a = s + erase t a",
"tactic": "rw [add_comm, erase_add_left_pos s h, add_comm]"
}
] | [
1056,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_one | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ xn a1 1 = a",
"tactic": "simp"
}
] | [
152,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_homothetyUnitsMulHom_apply_symm | [] | [
540,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Topology/Connected.lean | IsClopen.connectedComponent_subset | [] | [
991,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_id | [] | [
138,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCodetector_unop_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nG : Cᵒᵖ\n⊢ IsCodetector G.unop ↔ IsDetector G",
"tactic": "rw [IsDetector, IsCodetector, ← isCodetecting_unop_iff, Set.singleton_unop]"
}
] | [
431,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.length_le_sum_of_one_le | [
{
"state_after": "case nil\nι : Type ?u.8615\nα : Type ?u.8618\nM : Type ?u.8621\nN : Type ?u.8624\nP : Type ?u.8627\nM₀ : Type ?u.8630\nG : Type ?u.8633\nR : Type ?u.8636\nL : List ℕ\nh✝ : ∀ (i : ℕ), i ∈ L → 1 ≤ i\nh : ∀ (i : ℕ), i ∈ [] → 1 ≤ i\n⊢ length [] ≤ sum []\n\ncase cons\nι : Type ?u.8615\nα : Type ?u.... | [
81,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_mul | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI J : FractionalIdeal S P\n⊢ ↑{ val := ↑I * ↑J, property := (_ : IsFractional S (↑I * ↑J)) } = ↑I * ↑J",
"state_before": "R : Type u_1\ninst✝² : CommRing R\... | [
557,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | measurableSet_graph | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\n⊢ MeasurableSet {p | p.snd = f p.fst}",
"tactic": "simpa using measurableSet_region_between_cc hf hf MeasurableSet.univ"
}
] | [
531,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_sInf_eq_sInf_restrict | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.317389\nγ : Type ?u.317392\nδ : Type ?u.317395\nι : Type ?u.317398\nR : Type ?u.317401\nR' : Type ?u.317404\nm0✝ : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\nm0 : MeasurableSpac... | [
1877,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1870,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.max | [] | [
541,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
8
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_inj | [] | [
352,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.locallySmall_congr | [
{
"state_after": "case mp\nC✝ : Type u\ninst✝² : Category C✝\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\ne : C ≌ D\n⊢ LocallySmall C → LocallySmall D\n\ncase mpr\nC✝ : Type u\ninst✝² : Category C✝\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\ne : C ≌ D\n⊢ LocallySmall... | [
116,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_even | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\n⊢ tail (corec (fun s => head s) (fun s => tail (tail s)) s) =\n corec (fun s => head s) (fun s => tail (tail s)) (tail (tail s))",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\n⊢ tail (even s) = even (tail (tail s)... | [
472,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ico_succ_right_eq_insert | [] | [
508,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.Iio_eq_ssubsets | [] | [
73,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_sup | [] | [
370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
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