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/Submonoid/Operations.lean | MonoidHom.map_mclosure | [] | [
1097,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.712523\nm : MeasurableSpace α\ns : SignedMeasure α\ni j : Set α\nhi : restrict s i ≤ restrict 0 i\nhi₁ : MeasurableSet i\nhj₁ : MeasurableSet j\n⊢ ↑{ val := ↑(-s) (i ∩ j), property := (_ : 0 ≤ ↑(-s) (i ∩ j)) } =\n ↑{ val := -↑s (i ∩ j), property := (_ : 0 ≤ -↑s (i ... | [
1381,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.903143\nγ : Type ?u.903146\nδ : Type ?u.903149\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhg : AEMeasurable g\n⊢ (∫⁻ (a : α), f a + g a ∂μ) = (∫⁻ (a : α), f a ∂μ) + ∫⁻ (a : α), g a ∂μ",
"tactic": "simpa only [add_comm]... | [
590,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.tendsto_Lp_iff_tendsto_ℒp' | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF : Type ?u.8121841\nG : Type ?u.8121844\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\nι : Type u_1\nfi : Filter ι\ninst✝ : Fact (1 ≤ p)\nf : ι → { x // x ∈ L... | [
1240,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_self_mul_right | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.636975\n𝕜 : Type ?u.636978\nα : Type ?u.636981\nι : Type ?u.636984\nκ : Type ?u.636987\nE : Type u_1\nF : Type ?u.636993\nG : Type ?u.636996\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na✝ a₁ a₂ b✝ b₁ b₂ : E\nr r₁ r₂ : ℝ\na b : E... | [
1403,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_congr_measure | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1651275\nG : Type ?u.1651278\n𝕜 : Type ?u.1651281\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ... | [
1649,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_const_iff | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.1273342\nG : Type ?u.1273345\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np : ℝ≥0∞\nc : E\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\n⊢ Memℒp (fun x ... | [
345,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.localInverse_unique | [] | [
659,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Algebra/Star/Pointwise.lean | Set.star_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns✝ t✝ : Set α\na : α\ninst✝ : InvolutiveStar α\ns t : Set α\n⊢ s⋆ ⊆ t ↔ s ⊆ t⋆",
"tactic": "rw [← star_subset_star, star_star]"
}
] | [
111,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10052\nγ : Type ?u.10055\nι : Type ?u.10058\nι' : Type ?u.10061\nr p q : α → α → Prop\nf g : ι → α\ns t u : Set α\na b : α\n⊢ Set.Pairwise (insert a s) r ↔ Set.Pairwise s r ∧ ∀ (b : α), b ∈ s → a ≠ b → r a b ∧ r b a",
"tactic": "sim... | [
157,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_lt_of_succ_bot | [
{
"state_after": "n m : ℕ\nhnm : n < m\nr : min m (n + 1) = n + 1\n⊢ filter (fun x => decide (x < n + 1)) (Ico n m) = [n]",
"state_before": "n m : ℕ\nhnm : n < m\n⊢ filter (fun x => decide (x < n + 1)) (Ico n m) = [n]",
"tactic": "have r : min m (n + 1) = n + 1 := (@inf_eq_right _ _ m (n + 1)).mpr hnm"
... | [
218,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.injective_comp | [] | [
183,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.lt_toDual | [] | [
117,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_ge_iff | [] | [
69,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseRange.equalizer | [] | [
364,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/Filter.lean | Filter.mem_nhds_iff | [] | [
108,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_nonpos_of_le | [
{
"state_after": "a b : Int\nh✝ : a ≤ b\nh : a + -b ≤ b + -b\n⊢ a - b ≤ 0",
"state_before": "a b : Int\nh : a ≤ b\n⊢ a - b ≤ 0",
"tactic": "have h := Int.add_le_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : a ≤ b\nh : a + -b ≤ b + -b\n⊢ a - b ≤ 0",
"t... | [
928,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
926,
11
] |
Mathlib/GroupTheory/Nilpotent.lean | upperCentralSeries_nilpotencyClass | [] | [
372,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_mul_deriv | [] | [
1502,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1499,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.pow_right | [
{
"state_after": "case zero\nM : Type u_1\ninst✝ : Monoid M\na x y : M\nh : SemiconjBy a x y\n⊢ SemiconjBy a (x ^ Nat.zero) (y ^ Nat.zero)\n\ncase succ\nM : Type u_1\ninst✝ : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : ℕ\nih : SemiconjBy a (x ^ n) (y ^ n)\n⊢ SemiconjBy a (x ^ Nat.succ n) (y ^ Nat.succ n)",
... | [
175,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/List/Basic.lean | List.insertNth_removeNth_of_le | [] | [
1638,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1632,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_nonneg | [
{
"state_after": "n : ℕ\n⊢ 0 ≤ if IsPrimePow n then Real.log ↑(minFac n) else 0",
"state_before": "n : ℕ\n⊢ 0 ≤ ↑Λ n",
"tactic": "rw [vonMangoldt_apply]"
},
{
"state_after": "case inl\nn : ℕ\nh✝ : IsPrimePow n\n⊢ 0 ≤ Real.log ↑(minFac n)\n\ncase inr\nn : ℕ\nh✝ : ¬IsPrimePow n\n⊢ 0 ≤ 0",
"sta... | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Computability/Language.lean | Language.iSup_mul | [] | [
219,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Order/Basic.lean | LT.lt.false | [] | [
308,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
11
] |
Mathlib/Algebra/Star/Free.lean | FreeMonoid.star_one | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.IsQuadratic.inv | [
{
"state_after": "case h\nR : Type u\ninst✝² : CommRing R\nR' : Type v\ninst✝¹ : CommRing R'\nR'' : Type w\ninst✝ : CommRing R''\nχ : MulChar R R'\nhχ : IsQuadratic χ\nx : Rˣ\n⊢ ↑χ⁻¹ ↑x = ↑χ ↑x",
"state_before": "R : Type u\ninst✝² : CommRing R\nR' : Type v\ninst✝¹ : CommRing R'\nR'' : Type w\ninst✝ : CommR... | [
500,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.is_glb_mem | [
{
"state_after": "F : Type ?u.408857\nα : Type u_1\nβ : Type ?u.408863\nγ : Type ?u.408866\nι : Type ?u.408869\nκ : Type ?u.408872\ninst✝ : LinearOrder α\ni : α\ns : Finset α\nhis : IsGLB (↑s) i\nhs : Finset.Nonempty s\n⊢ i ∈ ↑s",
"state_before": "F : Type ?u.408857\nα : Type u_1\nβ : Type ?u.408863\nγ : Ty... | [
1728,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_prod | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.mem_ball_self | [] | [
82,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEmbedding.restrict_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1222190\nδ : Type ?u.1222193\nι : Type ?u.1222196\nR : Type ?u.1222199\nR' : Type ?u.1222202\nm0 : MeasurableSpace α\nm1 : MeasurableSpace β\nf : α → β\nhf : MeasurableEmbedding f\nμ : MeasureTheory.Measure α\ns t : Set β\... | [
4215,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4213,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.lift_of_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semigroup β\nf : α → β\nx : α\ny : FreeSemigroup α\n⊢ ↑(↑lift f) (of x * y) = f x * ↑(↑lift f) y",
"tactic": "rw [map_mul, lift_of]"
}
] | [
554,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Logic/Basic.lean | congr_fun₂ | [] | [
593,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Std/Data/List/Lemmas.lean | List.map_filterMap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → Option β\ng : β → γ\nl : List α\n⊢ map g (filterMap f l) = filterMap (fun x => Option.map g (f x)) l",
"tactic": "simp only [← filterMap_eq_map, filterMap_filterMap, Option.map_eq_bind]"
}
] | [
1184,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1182,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.insert | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\na✝ b✝ : α\ninst✝ : LinearOrder γ\na b : γ\ns : Set γ\nhs : IsGreatest s b\n⊢ IsGreatest ({a} ∪ s) (max a b)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Pr... | [
961,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Data/List/MinMax.lean | List.max_le_of_forall_le | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.111970\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl✝ l : List α\na : α\nh✝ : ∀ (x : α), x ∈ l → x ≤ a\nh : ∀ (x : α), x ∈ [] → x ≤ a\n⊢ foldr max ⊥ [] ≤ a\n\ncase cons\nα : Type u_1\nβ : Type ?u.111970\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl✝¹ l✝ : ... | [
419,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_comap_of_surjective | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.258330\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : α → β\nhf : Surjective f\nl : Filter β\n⊢ range f ∈ l",
"tactic": "simp only [hf.range_eq, univ_mem]... | [
2275,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2273,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.IsProper.top_not_mem | [] | [
274,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_add | [] | [
209,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_diff_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.62385\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Iic b \\ Iic a = Ioc a b",
"tactic": "rw [diff_eq, compl_Iic, inter_comm, Ioi_inter_Iic]"
}
] | [
1097,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.contDiff | [] | [
156,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_eq_empty | [] | [
628,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mul_inv | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.417122\ninst✝ : CommMonoid P\nf : M →* N\nh : ∀ (y : { x // x ∈ S }), IsUnit (↑f ↑y)\nx₁ x₂ : M\ny₁ y₂ : { x // x ∈ S }\n⊢ ↑f x₁ * ↑(↑(IsUnit.liftRight (Monoid... | [
649,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Data/List/Sublists.lean | List.Pairwise.sublists' | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α → Prop\na : α\nl : List α\nH₁ : ∀ (a' : α), a' ∈ l → R a a'\nH₂ : Pairwise R l\n⊢ Pairwise (Lex (swap R)) (List.sublists' l) ∧\n Pairwise (fun a_1 b => Lex (swap R) (a :: a_1) (a :: b)) (List.sublists' l) ∧\n ∀ (a_1 : List α), a_1 <+ l → ∀ ... | [
363,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_const' | [
{
"state_after": "case inl\nι : Type ?u.3045534\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.3045543\nδ : Type ?u.3045546\nR : Type ?u.3045549\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nf g : α → β\nν : MeasureTheory.Measure α\nh : ∀ᵐ (x : α) (y : α) ... | [
249,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_addNat | [] | [
1464,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_union_distrib | [] | [
531,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformEmbedding_subtypeEmb | [] | [
266,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Order/Lattice.lean | le_of_inf_le_sup_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DistribLattice α\nx y z : α\nh₁ : x ⊓ z ≤ y ⊓ z\nh₂ : x ⊔ z ≤ y ⊔ z\n⊢ y ⊓ z ⊔ x = (y ⊔ x) ⊓ (x ⊔ z)",
"tactic": "rw [sup_inf_right, @sup_comm _ _ x]"
}
] | [
792,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_one_smul | [
{
"state_after": "no goals",
"state_before": "M✝ : Type ?u.26534\nN✝ : Type ?u.26537\nG : Type ?u.26540\nA : Type ?u.26543\nB : Type ?u.26546\nα : Type u_3\nβ : Type ?u.26552\nγ : Type ?u.26555\nδ : Type ?u.26558\nM : Type u_1\nN : Type u_2\ninst✝⁴ : Monoid N\ninst✝³ : SMul M N\ninst✝² : MulAction N α\ninst... | [
643,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_lt | [] | [
328,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.164124\nγ : Type ?u.164127\nι : Type ?u.164130\nM : Type u_2\nM' : Type ?u.164136\nN : Type ?u.164139\nP : Type ?u.164142\nG : Type ?u.164145\nH : Type ?u.164148\nR : Type ?u.164151\nS : Type ?u.164154\ninst✝ : Zero M\na a' : α\nf : α →... | [
649,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderEmbedding.monotone | [] | [
666,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.complex_ofReal_eval_T | [] | [
56,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Analysis/Filter.lean | CFilter.ofEquiv_val | [
{
"state_after": "case mk\nα : Type u_3\nβ : Type ?u.5122\nσ : Type u_1\nτ : Type u_2\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\na : τ\nf✝ : σ → α\npt✝ : σ\ninf✝ : σ → σ → σ\ninf_le_left✝ : ∀ (a b : σ), f✝ (inf✝ a b) ≤ f✝ a\ninf_le_right✝ : ∀ (a b : σ), f✝ (inf✝ a b) ≤ f✝ b\n⊢ f (ofEquiv E { f := f✝, ... | [
78,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inr_isoPushout_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nZ X Y P : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\nh : IsPushout f g inl inr\ninst✝ : HasPushout f g\n⊢ inr ≫ (isoPushout h).hom = pushout.inr",
"tactic": "simp [← Iso.eq_comp_inv]"
}
] | [
440,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | nhds_translation_mul_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : TopologicalSpace α\nf : α → G\ns : Set α\nx✝ : α\nx : G\n⊢ 𝓝 (1 * x⁻¹⁻¹) = 𝓝 x",
"tactic": "simp"
}
] | [
815,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/List/Basic.lean | List.foldr_eta | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.232631\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ ∀ (l : List α), foldr cons [] l = l",
"tactic": "simp only [foldr_self_append, append_nil, forall_const]"
}
] | [
2460,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2459,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_add | [] | [
194,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.pow_mk | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | sub_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.128156\nM : Type ?u.128159\ninst✝ : CommRing R\na b : R\n⊢ (a - b) ^ 2 = a ^ 2 - 2 * a * b + b ^ 2",
"tactic": "rw [sub_eq_add_neg, add_sq, neg_sq, mul_neg, ← sub_eq_add_neg]"
}
] | [
284,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.map_generalizedEigenrange_le | [
{
"state_after": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End K V\nμ : K\nn : ℕ\n⊢ Submodule.map f (LinearMap.range ((f - ↑(algebraMap K (End K V)) μ) ^ n)) =\n LinearMap.range (f * (f - ... | [
458,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.mapAlgEquiv_trans | [
{
"state_after": "case h.a\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_4\na a' a₁ a₂ : R\ne✝ : ℕ\ns : σ →₀ ℕ\ninst✝⁶ : CommSemiring R\nA₁ : Type u_1\nA₂ : Type u_2\nA₃ : Type u_3\ninst✝⁵ : CommSemiring A₁\ninst✝⁴ : CommSemiring A₂\ninst✝³ : CommSemiring A₃\ninst✝² : Algebra R A₁\ninst✝¹ : Alg... | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.liftpPreservation_iff_uniform | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\n⊢ LiftPPreservation ↔ IsUniform",
"tactic": "rw [← suppPreservation_iff_liftpPreservation, suppPreservation_iff_isUniform]"
}
] | [
286,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_def | [] | [
119,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Computability/DFA.lean | DFA.mem_accepts | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ : Type v\nM : DFA α σ\nx : List α\n⊢ x ∈ accepts M ↔ evalFrom M M.start x ∈ M.accept",
"tactic": "rfl"
}
] | [
101,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_Prop_eq | [] | [
1722,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1721,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.C_eq_algebraMap | [] | [
1086,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.le_iff_cmp | [
{
"state_after": "α : Type ?u.484320\nm n : Num\n⊢ Ordering.swap (cmp m n) = Ordering.lt ↔ cmp m n = Ordering.gt",
"state_before": "α : Type ?u.484320\nm n : Num\n⊢ cmp n m = Ordering.lt ↔ cmp m n = Ordering.gt",
"tactic": "rw [← cmp_swap]"
},
{
"state_after": "no goals",
"state_before": "α ... | [
885,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.fderiv_integral | [] | [
745,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableWithinAt_fst | [] | [
197,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_eq | [] | [
394,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11608\nγ : Type ?u.11611\nδ : Type ?u.11614\nδ' : Type ?u.11617\nι : Sort ?u.11620\ns t u : Set α\nMeasurableSet'✝¹ : Set α → Prop\nmeasurableSet_empty✝¹ : MeasurableSet'✝¹ ∅\nmeasurableSet_compl✝¹ : ∀ (s : Set α), MeasurableSet'✝¹ s → ... | [
257,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | IsPrecomplete.prec | [] | [
72,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.l_injective | [] | [
785,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | self_sub_toIcoDiv_zsmul | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Std/Data/List/Lemmas.lean | List.length_erase_of_mem | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ l\n⊢ length (eraseP (fun b => decide (a = b)) l) = pred (length l)",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ l\n⊢ length (List.erase l a) = pred (length l)",
"tactic": "rw [erase_eq... | [
1063,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1061,
9
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_eq_nhds | [] | [
221,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
9
] |
Mathlib/Data/Finset/Lattice.lean | Finset.lt_sup_iff | [
{
"state_after": "case mp\nF : Type ?u.212488\nα : Type u_1\nβ : Type ?u.212494\nγ : Type ?u.212497\nι : Type u_2\nκ : Type ?u.212503\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\na : α\n⊢ a < sup s f → ∃ b, b ∈ s ∧ a < f b\n\ncase mpr\nF : Type ?u.212488\nα : Type u_1\nβ : Type ?u.21249... | [
701,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
11
] |
Mathlib/Topology/OmegaCompletePartialOrder.lean | Scott.isωSup_iff_isLUB | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Preorder α\nc : Chain α\nx : α\n⊢ IsωSup c x ↔ IsLUB (range ↑c) x",
"tactic": "simp [IsωSup, IsLUB, IsLeast, upperBounds, lowerBounds]"
}
] | [
45,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_zero | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
966,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | exists_maximal_orthonormal | [
{
"state_after": "case refine_2\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.2163317\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type ?u.2163366\ndec_ι : DecidableEq ι\ns : Set E\nhs : ... | [
968,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.ext | [] | [
543,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Std/Data/List/Lemmas.lean | List.infix_refl | [] | [
1582,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1582,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_equivMapOfInjective_apply | [] | [
635,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.closedBall_subset_target | [] | [
522,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.adj_comm | [] | [
106,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Std/Data/List/Init/Lemmas.lean | List.take_concat_get | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\ni : Nat\nh : i < length l\n⊢ l = concat (take i l) l[i] ++ drop (i + 1) l",
"tactic": "rw [concat_eq_append, append_assoc, singleton_append, get_drop_eq_drop, take_append_drop]"
}
] | [
154,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
151,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_C_eq_bind₁ | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_fst_neBot | [] | [
2385,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2383,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.monoidHom_ext | [] | [
536,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.disjoint_of_mem_compression_of_not_mem | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a b : α\nh : a ∈ s ∧ compress u v a ∈ s ∨ ¬a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = a\nha : ¬a ∈ s\n⊢ Disjoint v a",
"state_before": "α : Type u_1\n... | [
244,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.modEq_zero_iff_dvd | [
{
"state_after": "no goals",
"state_before": "m n a b c d : ℕ\n⊢ a ≡ 0 [MOD n] ↔ n ∣ a",
"tactic": "rw [ModEq, zero_mod, dvd_iff_mod_eq_zero]"
}
] | [
79,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_unique | [
{
"state_after": "α : Type u_1\nβ : Type ?u.51338\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : card s = k\nf : Fin k → α\nhfs : ∀ (x : Fin k), f x ∈ s\nhmono : StrictMono f\n⊢ Set.range f = Set.range ↑(orderEmbOfFin s h)",
"state_before": "α : Type u_1\nβ : Type ?u.51338\ninst✝ : LinearOrder α\ns : Fins... | [
223,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/Vandermonde.lean | Matrix.vandermonde_transpose_mul_vandermonde | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nv : Fin n → R\ni j : Fin n\n⊢ ((vandermonde v)ᵀ ⬝ vandermonde v) i j = ∑ k : Fin n, v k ^ (↑i + ↑j)",
"tactic": "simp only [vandermonde_apply, Matrix.mul_apply, Matrix.transpose_apply, pow_add]"
}
] | [
75,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasStrictFDerivAt.prodMap | [] | [
342,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
11
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.mem_iff_index_eq | [] | [
383,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.coe_subtype | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_iff_image_closedBall_subset_compact | [] | [
181,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.one_imK | [] | [
202,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
9
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.