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/Data/Int/Order/Basic.lean | Int.abs_eq_natAbs | [] | [
61,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/RingTheory/Polynomial/Vieta.lean | Multiset.prod_X_sub_C_coeff | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\ns : Multiset R\nk : ℕ\nh : k ≤ ↑card s\n⊢ coeff (prod (map (fun x => X + ↑C (-x)) s)) k = (-1) ^ (↑card s - k) * esymm s (↑card s - k)",
"state_before": "R : Type u_1\ninst✝ : CommRing R\ns : Multiset R\nk : ℕ\nh : k ≤ ↑card s\n⊢ coeff (prod (map (fun t =>... | [
136,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_pos_left | [
{
"state_after": "a b : Int\nh : 0 < b\nthis : 0 + a < b + a\n⊢ a < b + a",
"state_before": "a b : Int\nh : 0 < b\n⊢ a < b + a",
"tactic": "have : 0 + a < b + a := Int.add_lt_add_right h a"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : 0 < b\nthis : 0 + a < b + a\n⊢ a < b +... | [
817,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
815,
11
] |
Std/Logic.lean | or_congr_left | [] | [
257,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
257,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.map_comp | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nT T' T'' : D\nY Y' : C\nS : C ⥤ D\nf : T ⟶ T'\nf' : T' ⟶ T''\nh : CostructuredArrow S T\n⊢ (map (f ≫ f')).obj (mk h.hom) = (map f').obj ((map f).obj (mk h.hom))",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type ... | [
442,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.findGreatest_of_ne_zero | [] | [
677,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.dvd_of_mem_divisors | [
{
"state_after": "case zero\nn : ℕ\nh : n ∈ divisors zero\n⊢ n ∣ zero\n\ncase succ\nn n✝ : ℕ\nh : n ∈ divisors (succ n✝)\n⊢ n ∣ succ n✝",
"state_before": "n m : ℕ\nh : n ∈ divisors m\n⊢ n ∣ m",
"tactic": "cases m"
},
{
"state_after": "no goals",
"state_before": "case zero\nn : ℕ\nh : n ∈ div... | [
114,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.double_dual_bound | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type ?u.28709\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nx : E\n⊢ ‖↑(inclusionInDoubleDual 𝕜 E) x‖ ≤ ‖x‖",
"ta... | [
111,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | ball_prod_same | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.247136\nι : Type ?u.247139\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nx : α\ny : β\nr : ℝ\nz : α × β\n⊢ z ∈ ball x r ×ˢ ball y r ↔ z ∈ ball (x, y) r",
"tactic": "simp [Prod.dist_eq]"
}
] | [
1765,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1764,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.nnreal_tsum | [
{
"state_after": "α✝ : Type ?u.2984900\nβ : Type ?u.2984903\nγ : Type ?u.2984906\nγ₂ : Type ?u.2984909\nδ : Type ?u.2984912\nι✝ : Sort y\ns t u : Set α✝\ninst✝² : MeasurableSpace α✝\nα : Type u_1\ninst✝¹ : MeasurableSpace α\nι : Type u_2\ninst✝ : Countable ι\nf : ι → α → ℝ≥0\nμ : MeasureTheory.Measure α\nh : ∀ ... | [
1962,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1958,
1
] |
Mathlib/Order/Heyting/Basic.lean | Pi.hnot_apply | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.104333\nR : Type ?u.104336\nR' : Type ?u.104339\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\ns : Set α\n⊢ ↑(↑(restrict univ) m) s = ↑m s",
"tactic": "simp"
}
] | [
580,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_div2 | [] | [
846,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_lt_add_iff_lt_right | [] | [
84,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
83,
11
] |
Mathlib/Algebra/Field/Basic.lean | ofLex_rat_cast | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_id | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.46855\nα : Type u_1\nβ : Type ?u.46861\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ a⁻¹ ≤ b ↔ b⁻¹ ≤ a",
"tactic": "rw [← inv_le_inv hb (inv_pos.2 ha), inv_inv]"
}
] | [
265,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Order/LocallyFinite.lean | Set.finite_Ici | [] | [
679,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.induction | [
{
"state_after": "α✝ : Type ?u.922804\nβ : Type ?u.922807\nγ✝ : Type ?u.922810\nδ : Type ?u.922813\nα : Type u_1\nγ : Type u_2\ninst✝¹ : MeasurableSpace α\ninst✝ : AddMonoid γ\nP : (α →ₛ γ) → Prop\nh_ind : ∀ (c : γ) {s : Set α} (hs : MeasurableSet s), P (piecewise s hs (const α c) (const α 0))\nh_add : ∀ ⦃f g :... | [
1319,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
11
] |
Mathlib/Data/Real/Irrational.lean | Transcendental.irrational | [
{
"state_after": "case intro\na : ℚ\ntr : Transcendental ℚ ↑a\n⊢ False",
"state_before": "r : ℝ\ntr : Transcendental ℚ r\n⊢ Irrational r",
"tactic": "rintro ⟨a, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\na : ℚ\ntr : Transcendental ℚ ↑a\n⊢ False",
"tactic": "exact ... | [
43,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | cpow_eq_nhds | [
{
"state_after": "α : Type ?u.3016\na b : ℂ\nha : a ≠ 0\nthis : ∀ᶠ (x : ℂ) in 𝓝 a, x ≠ 0\n⊢ (fun x => x ^ b) =ᶠ[𝓝 a] fun x => Complex.exp (Complex.log x * b)\n\ncase this\nα : Type ?u.3016\na b : ℂ\nha : a ≠ 0\n⊢ ∀ᶠ (x : ℂ) in 𝓝 a, x ≠ 0",
"state_before": "α : Type ?u.3016\na b : ℂ\nha : a ≠ 0\n⊢ (fun x ... | [
56,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.exists_not_mem_of_length_lt | [
{
"state_after": "α✝ β : Type u\nα : Type u_1\nl : List α\nh : ∀ (z : α), z ∈ l\n⊢ (#α) ≤ ↑(List.length l)",
"state_before": "α✝ β : Type u\nα : Type u_1\nl : List α\nh : ↑(List.length l) < (#α)\n⊢ ∃ z, ¬z ∈ l",
"tactic": "contrapose! h"
},
{
"state_after": "no goals",
"state_before": "α✝ β ... | [
2263,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2256,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | one_div_pow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na✝ b a : α\nn : ℕ\n⊢ (1 / a) ^ n = 1 / a ^ n",
"tactic": "simp only [one_div, inv_pow]"
}
] | [
363,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.coe_rangeS | [] | [
603,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneDegree.le_add_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : Type v\ninst✝³ : Primcodable β\ninst✝² : Inhabited β\nγ : Type w\ninst✝¹ : Primcodable γ\ninst✝ : Inhabited γ\nd₁ d₂ : ManyOneDegree\n⊢ d₁ + ?m.115355 d₁ d₂ ≤ d₁ + d₂",
"tactic": "rfl"
}
] | [
500,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.empty_or_nonempty_of_hausdorffEdist_ne_top | [
{
"state_after": "case inl\nι : Sort ?u.55945\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\nfin : hausdorffEdist s t ≠ ⊤\nhs : s = ∅\n⊢ s = ∅ ∧ t = ∅ ∨ Set.Nonempty s ∧ Set.Nonempty t\n\ncase inr\nι : Sort ?u.55945\nα : Type u\nβ : Type ... | [
442,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.imp_head | [] | [
340,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.single_mul_single_of_ne | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nl : Type ?u.76298\nm : Type u_3\nn : Type u_1\nα : Type v\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq k\ninst✝¹ : DecidableEq m\ninst✝ : Semiring α\nb₁ b₂ : n\nhb : b₁ ≠ b₂\na : m\nc : k\n⊢ toMatrix (single a b₁) ⬝ toMatrix (s... | [
170,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_sub | [] | [
912,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.someVector_ray | [] | [
383,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousLinearMap.uncurryLeft_norm | [] | [
1443,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.isEulerian_iff | [
{
"state_after": "case mp\nV : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : Walk G u v\n⊢ IsEulerian p → IsTrail p ∧ ∀ (e : Sym2 V), e ∈ edgeSet G → e ∈ edges p\n\ncase mpr\nV : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : Walk G u v\n⊢ (IsTrail p ∧ ∀ (e : Sym2 V), e ∈ ed... | [
128,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_sub_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => a - x) ⁻¹' Ioo b c = Ioo (a - c) (a - b)",
"tactic": "simp [← Ioi_inter_Iio, inter_comm]"
}
] | [
257,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_of_is_closed' | [
{
"state_after": "case hf\nα : Type ?u.150229\nβ : Type ?u.150232\nγ : Type u_1\nγ₂ : Type ?u.150238\nδ : Type u_2\nι : Sort y\ns t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : OpensMeasurableSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : OpensMeasu... | [
355,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.844169\nβ : Type ?u.844172\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nι : Sort ?u.844189\nf g : ι → ℝ≥0∞\ns : Set ℝ≥0∞\nhf : ∀ (r : ℝ≥0∞), r ∈ s → r ≠ ⊤\n⊢ ENNReal.toReal (sSup s) = sSup (ENNReal.toReal '' s)",
"tactic": "simp only [ENNReal.toReal, toNNReal_s... | [
2395,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2393,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Ioi | [] | [
399,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.natAbs_le_iff_sq_le | [
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a ≤ natAbs b ↔ a * a ≤ b * b",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a ≤ natAbs b ↔ a ^ 2 ≤ b ^ 2",
"tactic": "rw [sq, sq]"
},
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a ≤ natAbs b ↔... | [
61,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.range_prod | [
{
"state_after": "𝕜 : Type u_5\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nE' : Type ?u.88570\ninst✝⁹ : NormedAddCommGroup E'\ninst✝⁸ : NormedSpace 𝕜 E'\nF : Type u_2\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type ?u.88... | [
471,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.bit1_re | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Minimal.lean | maximals_empty | [] | [
54,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_C_mul | [
{
"state_after": "case pos\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nr : R\np : R[X]\nh0 : r = 0\n⊢ content (↑C r * p) = ↑normalize r * content p\n\ncase neg\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nr : R\np : R[X]\nh0 ... | [
153,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Nat/Choose/Vandermonde.lean | Nat.add_choose_eq | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ choose (m + n) k = ∑ ij in antidiagonal k, choose m ij.fst * choose n ij.snd",
"tactic": "calc\n (m + n).choose k = ((X + 1) ^ (m + n)).coeff k := by rw [coeff_X_add_one_pow, Nat.cast_id]\n _ = ((X + 1) ^ m * (X + 1) ^ n).coeff k := by rw [pow... | [
39,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_updateColumn_single | [
{
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_card_le | [] | [
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Module.End.exists_ker_pow_eq_ker_pow_succ | [
{
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1492,
92
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1468,
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Mathlib/Data/Nat/Prime.lean | Nat.minFac_prime | [] | [
335,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.add_re | [] | [
215,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivAt.eventually_ne | [
{
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffAt.cos | [] | [
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41
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Mathlib/Algebra/Ring/Defs.lean | add_mul_self_eq | [
{
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] | [
269,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
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Mathlib/Data/Rat/Cast.lean | Rat.cast_nonpos | [
{
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] | [
338,
16
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337,
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Mathlib/Init/Data/Ordering/Lemmas.lean | Ordering.ite_eq_eq_distrib | [
{
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] | [
33,
26
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Mathlib/Analysis/Convex/Cone/Dual.lean | isClosed_innerDualCone | [
{
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136,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.uncurry | [
{
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269,
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262,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mul' | [] | [
412,
25
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410,
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Mathlib/Order/Filter/Basic.lean | Filter.map_inj | [] | [
2330,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2329,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | StronglyMeasurableAtFilter.filter_mono | [] | [
58,
18
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Hom.coe_comp | [] | [
1758,
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_interpolate_not_at_node' | [
{
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Mathlib/Order/BooleanAlgebra.lean | sup_sdiff_inf | [
{
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] | [
110,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero | [
{
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199,
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196,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.map_le_iff_le_comap | [] | [
618,
23
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Mathlib/Data/Set/Function.lean | Set.eq_restrict_iff | [] | [
69,
34
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Mathlib/Analysis/Convex/Basic.lean | convex_stdSimplex | [
{
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634,
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627,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_smul_left | [] | [
747,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
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Mathlib/Topology/Order.lean | continuous_coinduced_rng | [] | [
716,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
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Mathlib/Algebra/Lie/Matrix.lean | Matrix.lieConj_apply | [
{
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76,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Int/Lemmas.lean | Int.add_le_add_left | [
{
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] | [
751,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
750,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_int_mul_two_pi_add_pi | [
{
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}
] | [
1268,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_add_le_add | [
{
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129,
19
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121,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.pointwise_smul_subset_iff | [] | [
298,
22
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297,
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Mathlib/Order/CompleteLattice.lean | biSup_mono | [] | [
894,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
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Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal | [
{
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320,
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276,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.hasBinaryProducts_of_hasLimit_pair | [] | [
977,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.map | [] | [
1210,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
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Mathlib/Order/Basic.lean | le_of_strongLT | [] | [
829,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
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Mathlib/Data/Finsupp/Basic.lean | Nat.cast_finsupp_prod | [] | [
391,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toFun_eq_coe | [] | [
229,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/Algebra/Order/LatticeGroup.lean | mul_sup | [] | [
76,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
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Mathlib/NumberTheory/Liouville/Residual.lean | setOf_liouville_eq_irrational_inter_iInter_iUnion | [
{
"state_after": "case refine_1\n\n⊢ {x | Liouville x} ⊆ {x | Irrational x} ∩ ⋂ (n : ℕ), ⋃ (a : ℤ) (b : ℤ) (_ : 1 < b), ball (↑a / ↑b) (1 / ↑b ^ n)\n\ncase refine_2\n\n⊢ ({x | Irrational x} ∩ ⋂ (n : ℕ), ⋃ (a : ℤ) (b : ℤ) (_ : 1 < b), ball (↑a / ↑b) (1 / ↑b ^ n)) ⊆ {x | Liouville x}",
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55,
85
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44,
1
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Mathlib/Analysis/Convex/Segment.lean | Prod.image_mk_openSegment_right | [
{
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637,
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Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | affineSpan_eq_top_of_nonempty_interior | [] | [
140,
75
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137,
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.comp_zero | [] | [
72,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.root_X_sub_C | [
{
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}
] | [
1271,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
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Mathlib/Order/Filter/Basic.lean | Filter.comap_surjective_eq_bot | [
{
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2361,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2359,
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Mathlib/Data/List/Nodup.lean | List.Nodup.pairwise_of_forall_ne | [
{
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432,
34
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426,
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Mathlib/Analysis/Seminorm.lean | Seminorm.uniformContinuous_of_continuousAt_zero | [
{
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1140,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
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Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_one | [] | [
472,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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Mathlib/Topology/Order/Basic.lean | Icc_mem_nhdsWithin_Ioi' | [] | [
430,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.measurableSet_support | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.905162\nδ : Type ?u.905165\nm : MeasurableSpace α\ninst✝² : Zero β\ninst✝¹ : Zero γ\nμ : Measure α\nf✝ : α →ₛ β\ninst✝ : MeasurableSpace α\nf : α →ₛ β\n⊢ MeasurableSet (⋃ (y : β) (_ : y ∈ filter (fun y => y ≠ 0) (SimpleFunc.range f)), ↑f ⁻¹' {y})",
"... | [
1179,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
] |
Mathlib/Topology/DenseEmbedding.lean | isClosed_property | [] | [
318,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_apply_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ninst✝¹ : (i : ι) → Zero (β i)\np : ι → Prop\ninst✝ : DecidablePred p\nf : Π₀ (i : ι), β i\ni : ι\nh : ¬p i\n⊢ ↑(filter p f) i = 0",
"tactic": "simp only [filter_apply, if_neg h]"
}... | [
416,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.bind_map | [] | [
84,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | Additive.ofMul_symm_eq | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_iff_continuousAt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.331376\nδ : Type ?u.331379\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nx : α\nh : s ∈ 𝓝 x\n⊢ ContinuousWithinAt f s x ↔ Continu... | [
849,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ordConnected_setOf_closedBall_subset | [] | [
611,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.sum_dual_apply_smul_coord | [
{
"state_after": "case h\nR : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Fintype ι\nb : Basis ι R M\nf : Dual R M\nm : M\n⊢ ↑(∑ x : ι, ↑f (↑b x) • coord b x) m = ↑f m",
"state_before": "R : Type u\nM : Type v\nK :... | [
390,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.MeasurePreserving.zpow | [] | [
865,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.hasFDerivWithinAt | [] | [
270,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.inv_hom_id_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z✝ : C\nf : X ⟶ Y\nI : IsIso f\nZ : C\ng : Y ⟶ Z\n⊢ inv f ≫ f ≫ g = g",
"tactic": "simp [← Category.assoc]"
}
] | [
306,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
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