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/GroupTheory/GroupAction/ConjAct.lean | ConjAct.toConjAct_inv | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Order/Monotone/Union.lean | StrictMonoOn.union | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\na : α\nf : α → β\ns t : Set α\nc : α\nh₁ : StrictMonoOn f s\nh₂ : StrictMonoOn f t\nhs : IsGreatest s c\nht : IsLeast t c\nA : ∀ (x : α), x ∈ s ∪ t → x ≤ c → x ∈ s\nB : ∀ (x : α), x ∈ s ∪ t → c ≤ x → x ∈ t\nx : α\nhx : x ∈... | [
54,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
11
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Sentence.realize_not | [] | [
730,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Finset.Nat.antidiagonalTuple_one | [] | [
257,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isClosed_iff_zeroLocus_radical_ideal | [] | [
435,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/ShrinkingLemma.lean | ShrinkingLemma.PartialRefinement.le_chainSup | [] | [
172,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | antitone_Ici | [] | [
28,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_pred | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : 0 < n + 1\nhi : { val := 0, isLt := h } ≠ 0\n⊢ succ (pred { val := 0, isLt := h } hi) = { val := 0, isLt := h }",
"tactic": "simp only [mk_zero, ne_eq, not_true] at hi"
}
] | [
1506,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsClosed.smul₀ | [] | [
380,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Algebra/GroupWithZero/Divisibility.lean | dvdNotUnit_of_dvd_of_not_dvd | [
{
"state_after": "case left\nα : Type u_1\ninst✝ : CommMonoidWithZero α\na b : α\nhd : a ∣ b\nhnd : ¬b ∣ a\n⊢ a ≠ 0\n\ncase right\nα : Type u_1\ninst✝ : CommMonoidWithZero α\na b : α\nhd : a ∣ b\nhnd : ¬b ∣ a\n⊢ ∃ x, ¬IsUnit x ∧ b = a * x",
"state_before": "α : Type u_1\ninst✝ : CommMonoidWithZero α\na b : ... | [
80,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sq_pi_over_two_pow | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nn : ℕ\n⊢ sin (π / 2 ^ (n + 1)) ^ 2 = 1 - (sqrtTwoAddSeries 0 n / 2) ^ 2",
"tactic": "rw [sin_sq, cos_pi_over_two_pow]"
}
] | [
752,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
src/lean/Init/SimpLemmas.lean | decide_False | [] | [
157,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
157,
9
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.zero_ndunion | [] | [
154,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_eq_iff | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni : Fin (n + 1)\nx : α i\np : (j : Fin n) → α (↑(succAbove i) j)\nq : (j : Fin (n + 1)) → α j\n⊢ insertNth i x p = q ↔ q i = x ∧ p = fun j => q (↑(succAbove i) j)",
"tactic": "simp [funext_iff, forall_iff_succAb... | [
698,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Topology/Connected.lean | ConnectedComponents.range_coe | [] | [
1479,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1478,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_interpolate_not_at_node | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhx : ∀ (i : ι), i ∈ s → x ≠ v i\n⊢ ∑ x_1 in s, r x_1 * eval x (Lagrange.basis s v x_1) =\n ∑ x_1 in s, eval x (nodal s v) * (nodalWeight s v x_1 * (x - v x_1)⁻¹ * r x_1)",
... | [
605,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.del | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nc✝ : RBColor\nparent : Path α\nx : α\nb a : RBNode α\nha : RBNode.Ordered cmp a\nhp : Ordered cmp parent\nxb : All (fun x_1 => cmpLT cmp x x_1) b\nxp : RootOrdered cmp parent x\nbp : All (RootOrdered cmp parent) b\nhb : RBNode.Ordered cmp b\nH : All (RootO... | [
331,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
319,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ioo' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.104239\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\nx : α\n⊢ x ∈ Iio b ∪ Ioo c d ↔ x ∈ Iio (max b d)",
"state_before": "α : Type u_1\nβ : Type ?u.104239\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\n⊢ Iio b ∪ Ioo c d = Iio (m... | [
1440,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/Data/List/Perm.lean | List.concat_perm | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ l : List α\na : α\n⊢ concat l a ~ a :: l",
"tactic": "simp"
}
] | [
148,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_lt_one_mul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nz1 z2 : ℤ_[p]\nhz2 : ‖z2‖ < 1\n⊢ ‖z1 * z2‖ = ‖z1‖ * ‖z2‖",
"tactic": "simp"
}
] | [
462,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasDerivWithinAt_left | [] | [
957,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_lattice_hom | [] | [
1311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.congr_fun | [] | [
691,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_lt_one_iff_abs_lt_one | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.269074\nA : Type ?u.269077\nG : Type ?u.269080\nM : Type ?u.269083\nR : Type u_1\ninst✝ : LinearOrderedRing R\nx✝ y x : R\n⊢ x ^ 2 < 1 ↔ abs x < 1",
"tactic": "simpa only [one_pow, abs_one] using @sq_lt_sq _ _ x 1"
}
] | [
736,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Std/Data/AssocList.lean | Std.AssocList.findEntryP?_eq | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\np : α → β → Bool\nkey✝ : α\nvalue✝ : β\ntail✝ : AssocList α β\ntail_ih✝ :\n findEntryP? p tail✝ =\n List.find?\n (fun x =>\n match x with\n | (a, b) => p a b)\n (toList tail✝)\n⊢ (bif p key✝ value✝ then some (key✝, value✝) else... | [
105,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
103,
9
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | measurableEmbedding_const_smul₀ | [] | [
90,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_homothetyUnitsMulHom_apply | [] | [
534,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Complex.continuousAt_cpow_of_re_pos | [
{
"state_after": "case mk\nz w : ℂ\nh₁ : 0 ≤ (z, w).fst.re ∨ (z, w).fst.im ≠ 0\nh₂ : 0 < (z, w).snd.re\n⊢ ContinuousAt (fun x => x.fst ^ x.snd) (z, w)",
"state_before": "p : ℂ × ℂ\nh₁ : 0 ≤ p.fst.re ∨ p.fst.im ≠ 0\nh₂ : 0 < p.snd.re\n⊢ ContinuousAt (fun x => x.fst ^ x.snd) p",
"tactic": "cases' p with z... | [
377,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.continuousAt_infty | [
{
"state_after": "no goals",
"state_before": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nY : Type u_1\ninst✝ : TopologicalSpace Y\nf : OnePoint X → Y\n⊢ Tendsto (f ∘ some) (coclosedCompact X) (𝓝 (f ∞)) ↔\n ∀ (s : Set Y), s ∈ 𝓝 (f ∞) → ∃ t, IsClosed t ∧ IsCompact t ∧ Map... | [
381,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.dual | [] | [
87,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.CG.sup | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\ninst✝ : Structure L M\nN₁ N₂ : Substructure L M\nhN₁ : CG N₁\nhN₂ : CG N₂\nt₁ : Set M\nht₁ : Set.Countable t₁ ∧ LowerAdjoint.toFun (closure L) t₁ = N₁\nt₂ : Set M\nht₂ : Set.Countable t₂ ∧ LowerAdjoint.toFun (closure L) t₂ = N₂\n⊢ Low... | [
156,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.mul_def | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.natDegree_scaleRoots | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.35822\nK : Type ?u.35825\nR : Type u_1\nS : Type ?u.35831\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\ns : R\n⊢ natDegree (scaleRoots p s) = natDegree p",
"tactic... | [
90,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_top_mul | [
{
"state_after": "α : Type ?u.827518\nβ : Type ?u.827521\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ ENNReal.toReal (a * ⊤) = 0",
"state_before": "α : Type ?u.827518\nβ : Type ?u.827521\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ ENNReal.toReal (⊤ * a) = 0",
"tactic": "rw [mul_comm]"
},
{
"state_a... | [
2264,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2262,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.rotateL_node | [] | [
262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/Connected.lean | Continuous.image_connectedComponent_eq_singleton | [] | [
1329,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.congr_fun | [] | [
814,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Algebra/Module/Hom.lean | AddMonoidHom.coe_smul | [] | [
46,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
9
] |
Mathlib/Topology/Basic.lean | interior_Inter₂_subset | [] | [
395,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_sub | [] | [
797,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxOn.on_preimage | [] | [
421,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_bind | [
{
"state_after": "α : Type u\nβ : Type v\nl l₁✝ l₂ : List α\nr : α → α → Prop\na b : α\nl₁ : List α\nf : α → List β\n⊢ (Pairwise (fun a b => Disjoint (f a) (f b)) l₁ ∧ ∀ (l : List β) (x : α), f x = l → x ∈ l₁ → Nodup l) ↔\n Pairwise (fun a b => Disjoint (f a) (f b)) l₁ ∧ ∀ (x : α), x ∈ l₁ → Nodup (f x)",
... | [
343,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Topology/Separation.lean | compact_exists_clopen_in_open | [] | [
1991,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1989,
1
] |
Mathlib/Order/Heyting/Hom.lean | BiheytingHom.comp_apply | [] | [
586,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Finsupp/Indicator.lean | Finsupp.indicator_injective | [
{
"state_after": "ι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : (i : ι) → i ∈ s → α\ni : ι\na b : (i : ι) → i ∈ s → α\nh : (fun f => indicator s f) a = (fun f => indicator s f) b\n⊢ a = b",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : (i : ι) → i ∈ s → α\ni ... | [
67,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.HasLines.exists_bijective_of_card_eq | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\nL : Type u_2\ninst✝³ : Membership P L\ninst✝² : HasLines P L\ninst✝¹ : Fintype P\ninst✝ : Fintype L\nh : Fintype.card P = Fintype.card L\n⊢ ∃ f, Function.Bijective f ∧ ∀ (l : L), pointCount P l = lineCount L (f l)",
"tactic": "classical\n obta... | [
282,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Finite/Defs.lean | not_infinite_iff_finite | [] | [
110,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv | [] | [
331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.map_obj_arrow | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_eq_image' | [
{
"state_after": "case h.e'_3.h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.73157\nG : Type ?u.73160\nι : Type ?u.73163\nπ : ι → Type ?u.73168\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\na✝¹ : 𝕜\na✝ : a✝¹... | [
214,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Coloring.to_colorable | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC✝ : Coloring G α\ninst✝ : Fintype α\nC : Coloring G α\n⊢ Fintype.card α ≤ Fintype.card (Fin (Fintype.card α))",
"tactic": "simp"
}
] | [
207,
34
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Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_apply | [
{
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Hom.cast_eq_iff_heq | [
{
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Mathlib/Data/BinaryHeap.lean | BinaryHeap.size_heapifyUp | [] | [
74,
61
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Mathlib/Logic/Basic.lean | forall₂_imp | [] | [
629,
39
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627,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | IsUnit.mul_left_eq_zero | [] | [
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_left_strictMono | [] | [
572,
63
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Mathlib/Data/Matrix/Reflection.lean | Matrix.transposeᵣ_eq | [
{
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116,
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Mathlib/Algebra/Order/SMul.lean | OrderedSMul.mk' | [
{
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215,
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_induction_on' | [
{
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196,
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Mathlib/Topology/Order/LowerTopology.lean | WithLowerTopology.to_withLowerTopology_symm_eq | [] | [
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Mathlib/Analysis/Convex/Star.lean | StarConvex.linear_image | [
{
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210,
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_le_add_right | [
{
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{
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393,
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Mathlib/Data/Polynomial/Monomial.lean | Polynomial.monomial_one_eq_iff | [
{
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Mathlib/Data/Nat/Order/Lemmas.lean | Nat.div_eq_zero_iff | [
{
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27
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Mathlib/Algebra/Group/Prod.lean | Prod.snd_one | [] | [
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Mathlib/Analysis/Convex/Basic.lean | Convex.add | [
{
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.merge_nil_left | [
{
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640,
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Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow_iff | [] | [
506,
37
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | deriv_csin | [] | [
230,
27
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Mathlib/RingTheory/Ideal/Over.lean | Ideal.IsIntegralClosure.comap_ne_bot | [] | [
329,
84
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326,
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Mathlib/Computability/TuringMachine.lean | Turing.TM1.stmts₁_trans | [
{
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Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.tendsto_filterAt_iff | [
{
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.mem_maximalGeneralizedEigenspace | [
{
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312,
101
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Mathlib/LinearAlgebra/Span.lean | LinearMap.map_eq_top_iff | [
{
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902,
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Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.Ok.zero | [
{
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613,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
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Mathlib/Algebra/Quandle.lean | Quandle.conj_swap | [
{
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... | [
461,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.app_left_eq_ι | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.image.ι_zero | [
{
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616,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
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Mathlib/Computability/Halting.lean | Partrec.merge' | [
{
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101,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableAt.fderivWithin | [] | [
605,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_mono | [] | [
373,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.inv_def | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.const_pos | [] | [
606,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.neg_right | [] | [
366,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_le_iff_le_rpow_of_base_lt_one | [
{
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}
] | [
273,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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Std/Data/List/Init/Lemmas.lean | List.mapM_nil | [] | [
218,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
218,
9
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_zero_of_lt | [] | [
173,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.ker_incl | [
{
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... | [
1241,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Join.lean | convexJoin_iUnion_left | [
{
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99,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictDerivAt_exp_smul_const_of_mem_ball' | [
{
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352,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
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Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | ModuleCat.Free.left_unitality | [
{
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131,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/Topology/Filter.lean | Filter.closure_singleton | [
{
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"state_before": "ι : Sort ?u.16896\nα : Type u_1\nβ : Type ?u.16902\nX : Type ?u.16905\nY : Type ?u.16908\nl : Filter α\n⊢ closure {l} = Ici ... | [
176,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
11
] |
Mathlib/NumberTheory/Divisors.lean | Nat.one_mem_properDivisors_iff_one_lt | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 1 ∈ properDivisors n ↔ 1 < n",
"tactic": "rw [mem_properDivisors, and_iff_right (one_dvd _)]"
}
] | [
198,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | AffineSubspace.map_pointwise_vadd | [
{
"state_after": "k : Type u_1\ninst✝⁹ : Ring k\nV : Type ?u.30849\nP : Type ?u.30852\nV₁ : Type u_2\nP₁ : Type u_3\nV₂ : Type u_4\nP₂ : Type u_5\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AffineSpace V P\ninst✝⁵ : AddCommGroup V₁\ninst✝⁴ : Module k V₁\ninst✝³ : AffineSpace V₁ P₁\ninst✝² : AddCommG... | [
86,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | Fintype.prod_dvd_of_coprime | [] | [
102,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_apply | [] | [
975,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_le_nnnorm_add_nnnorm_div' | [] | [
959,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_min' | [
{
"state_after": "F : Type ?u.350869\nα : Type u_1\nβ : Type ?u.350875\nγ : Type ?u.350878\nι : Type ?u.350881\nκ : Type ?u.350884\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset αᵒᵈ\nhs : Finset.Nonempty s\n⊢ ↑(↑ofDual (min' s hs)) = ↑(max' (image (↑ofDual) s) (_ : Finset.Nonem... | [
1436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
] |
Mathlib/Data/Sum/Interval.lean | Sum.Icc_inr_inr | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
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