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/Set/Pointwise/Basic.lean | Set.image2_mul | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.mem_sInf | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\ninst✝¹ : SemilatticeSup P\ninst✝ : OrderBot P\nx : P\nI J K : Ideal P\nS : Set (Ideal P)\n⊢ x ∈ sInf S ↔ ∀ (s : Ideal P), s ∈ S → x ∈ s",
"tactic": "simp_rw [← SetLike.mem_coe, coe_sInf, mem_iInter₂]"
}
] | [
458,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Order/CompleteLattice.lean | biInf_prod | [] | [
1564,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1562,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snormEssSup_indicator_eq_snormEssSup_restrict | [
{
"state_after": "α : Type u_1\nE : Type ?u.655000\nF : Type u_2\nG : Type ?u.655006\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs✝ : MeasurableSet s\nc : E\nf✝ : α → E\nhf : AEStronglyMeasur... | [
648,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.add_div_le_add_div | [
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhc0 : c = 0\n⊢ a / c + b / c ≤ (a + b) / c",
"tactic": "simp [hc0]"
},
{
"state_after": "m n a✝ b✝ c✝ d a b c : ℕ\nhc0 : ¬c = 0\n⊢ a / c + b / c ≤ a / c + b / c + if c ≤ a % c + b % c then 1 else 0",
"state_before": "m n... | [
486,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_limRatioMeas | [
{
"state_after": "case h\nα : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.3482095\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\n... | [
442,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumCongr_refl | [
{
"state_after": "case H\nα : Type u_1\nβ : Type u_2\ni : α ⊕ β\n⊢ ↑(sumCongr (Equiv.refl α) (Equiv.refl β)) i = ↑(Equiv.refl (α ⊕ β)) i",
"state_before": "α : Type u_1\nβ : Type u_2\n⊢ sumCongr (Equiv.refl α) (Equiv.refl β) = Equiv.refl (α ⊕ β)",
"tactic": "ext i"
},
{
"state_after": "no goals"... | [
294,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.omega_ne_zero | [] | [
2417,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2416,
1
] |
Mathlib/Algebra/Parity.lean | even_iff_exists_two_mul | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.60474\nα : Type u_1\nβ : Type ?u.60480\nR : Type ?u.60483\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm✝ n m : α\n⊢ Even m ↔ ∃ c, m = 2 * c",
"tactic": "simp [even_iff_exists_two_nsmul]"
}
] | [
247,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Finsupp/AList.lean | AList.empty_lookupFinsupp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u_2\ninst✝ : Zero M\n⊢ lookupFinsupp ∅ = 0",
"tactic": "classical\n ext\n simp"
},
{
"state_after": "case h\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\na✝ : α\n⊢ ↑(lookupFinsupp ∅) a✝ = ↑0 a✝",
"state_before": "α : Type ... | [
111,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.mul | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhq : q = 0\n⊢ padicNorm p (q * r) = padicNorm p q * padicNorm p r",
"tactic": "simp [hq]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhq : ¬q = 0\nhr : r = 0\n... | [
160,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
11
] |
Mathlib/Data/Finset/Image.lean | Finset.map_toFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.15667\nf : α ↪ β\ns✝ : Finset α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Multiset α\nx✝ : β\n⊢ x✝ ∈ map f (toFinset s) ↔ x✝ ∈ toFinset (Multiset.map (↑f) s)",
"tactic": "simp only [mem_map, Multiset.mem_map,... | [
122,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_prod | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_moveLeft_inl | [
{
"state_after": "case mk\ny : PGame\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\ni : LeftMoves (mk α✝ β✝ a✝¹ a✝)\n⊢ moveLeft (mk α✝ β✝ a✝¹ a✝ + y) (↑toLeftMovesAdd (Sum.inl i)) = moveLeft (mk α✝ β✝ a✝¹ a✝) i + y",
"state_before": "x y : PGame\ni : LeftMoves x\n⊢ moveLeft (x + y) (↑toLeftMovesAdd (... | [
1511,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Mathlib/Data/List/Sigma.lean | List.kextract_eq_dlookup_kerase | [
{
"state_after": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nb : β a'\nl : List (Sigma β)\n⊢ (if h : a' = a then (some ((_ : { fst := a', snd := b }.fst = a) ▸ b), l)\n else ((kextract a l).fst, { fst := a', snd := b } :: (kextract a l).snd)) =\n (dlookup a ({ ... | [
619,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_union_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.265412\nγ : Type ?u.265415\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na b : α\nha : a ∈ t\ns : Finset α\n⊢ erase s a ∪ t = s ∪ t",
"tactic": "rw [← insert_erase (mem_union_right s ha), erase_union_distrib, ← union_insert, insert_e... | [
2278,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2277,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.index_exists | [
{
"state_after": "n : ℕ\nc : Composition n\nj : ℕ\nh : j < n\nn_pos : 0 < n\n⊢ ∃ i, j < sizeUpTo c (Nat.succ i) ∧ i < length c",
"state_before": "n : ℕ\nc : Composition n\nj : ℕ\nh : j < n\n⊢ ∃ i, j < sizeUpTo c (Nat.succ i) ∧ i < length c",
"tactic": "have n_pos : 0 < n := lt_of_le_of_lt (zero_le j) h"... | [
331,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ico_coe_coe | [] | [
1168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_edist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.19776\nι : Type ?u.19779\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ nndist x y = ENNReal.toNNReal (edist x y)",
"tactic": "simp [edist_nndist]"
}
] | [
323,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.algHomOfLinearMapTensorProduct_apply | [] | [
695,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.one_lt_rOut_div_rIn | [
{
"state_after": "E : Type u_1\nX : Type ?u.67116\nc : E\nf : ContDiffBump c\n⊢ f.rIn < f.rOut",
"state_before": "E : Type u_1\nX : Type ?u.67116\nc : E\nf : ContDiffBump c\n⊢ 1 < f.rOut / f.rIn",
"tactic": "rw [one_lt_div f.rIn_pos]"
},
{
"state_after": "no goals",
"state_before": "E : Type... | [
351,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.comp_comp | [] | [
344,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderEmbedding.le_iff_le | [] | [
652,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.smul_def | [] | [
727,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
11
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.replaceEquiv_eq_self | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.22794\nδ : Type ?u.22797\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne'✝ : LocalHomeomorph β γ\ne' toLocalEquiv✝ : LocalEquiv α β\nopen_source✝ : Is... | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.ne_top_of_tsum_ne_top | [] | [
897,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
11
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_sSup_of_directed | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.91322\nK : Type ?u.91325\nM : Type u_1\nM₂ : Type ?u.91331\nV : Type ?u.91334\nS : Type ?u.91337\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ :... | [
321,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Analysis/Convex/Segment.lean | mem_openSegment_of_ne_left_right | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.46146\nG : Type ?u.46149\nι : Type ?u.46152\nπ : ι → Type ?u.46157\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns : Set E\nx y z : E\nhx : x ≠ z\nhy : y ≠ z\nhz : z ∈ insert x (insert y (openSegment 𝕜 x y))\n⊢ z ∈ openSe... | [
158,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Covby.pred_eq | [] | [
785,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/Sigma/Basic.lean | Function.Injective.of_sigma_map | [] | [
125,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_rangeRestrict | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1598122\nR₂ : Type ?u.1598125\nR₃ : Type ?u.1598128\nR₄ : Type ?u.1598131\nS : Type ?u.1598134\nK : Type ?u.1598137\nK₂ : Type ?u.1598140\nM : Type u_2\nM' : Type ?u.1598146\nM₁ : Type ?u.1598149\nM₂ : Type u_3\nM₃ : Type ?u.1598155\nM... | [
1769,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_sub_left_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonUnitalNonAssocRing α\na b c : α\n⊢ a * (b - c) = a * b - a * c",
"tactic": "simpa only [sub_eq_add_neg, neg_mul_eq_mul_neg] using mul_add a b (-c)"
}
] | [
365,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.nat_cast | [
{
"state_after": "case zero\nK : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx : ℕ\n⊢ ↑x = mk K p (Nat.zero, ↑x)\n\ncase succ\nK : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx n : ℕ\nih : ↑x = mk K p (n, ↑x)\n⊢ ↑x = mk K p (Nat.suc... | [
429,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.divByMonic_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Ring R\np✝ q p : R[X]\nh : Monic 0\nthis : Subsingleton R\n⊢ p /ₘ 0 = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Ring R\np✝ q p : R[X]\nh : Monic 0\n⊢ p /ₘ 0 = 0",
... | [
203,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/List/Rotate.lean | List.nil_eq_rotate_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ [] = rotate l n ↔ [] = l",
"tactic": "rw [eq_comm, rotate_eq_nil_iff, eq_comm]"
}
] | [
212,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.add | [] | [
541,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Logic/Relation.lean | Transitive.comap | [] | [
113,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.char_ne_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : NonAssocSemiring R\ninst✝ : Nontrivial R\np : ℕ\nhc : CharP R p\nhp : p = 1\n⊢ 1 = 0",
"tactic": "simpa using (cast_eq_zero_iff R p 1).mpr (hp ▸ dvd_refl p)"
}
] | [
517,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_pos | [] | [
618,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_power | [] | [
560,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.div | [] | [
1319,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
11
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime_pow_mul_X_pow_sub_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\np k : ℕ\nhn : Fact (Nat.Prime p)\n⊢ cyclotomic (p ^ (k + 1)) R * (X ^ p ^ k - 1) = X ^ p ^ (k + 1) - 1",
"tactic": "rw [cyclotomic_prime_pow_eq_geom_sum hn.out, geom_sum_mul, ← pow_mul, pow_succ, mul_comm]"
}
] | [
582,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Topology/SubsetProperties.lean | exists_mem_compactCovering | [] | [
1319,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
Mathlib/Order/SymmDiff.lean | Pi.symmDiff_apply | [] | [
865,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.sum_partition_boxes | [] | [
86,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/BoundedOrder.lean | eq_top_of_bot_eq_top | [] | [
674,
24
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673,
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Mathlib/Data/List/Perm.lean | List.Perm.erase | [
{
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771,
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Mathlib/Data/Int/Order/Units.lean | Int.sq_eq_one_of_sq_le_three | [] | [
64,
70
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Mathlib/Data/Fintype/Basic.lean | Finset.eq_univ_iff_forall | [
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72
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Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.tmulEquiv_symm_apply | [] | [
656,
19
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653,
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere' | [
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144,
44
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_eq_iInf' | [
{
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167,
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Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.prod_map | [
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239,
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Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.boundaries_eq_imageSubobject | [] | [
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24
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsNormal.isFundamentalSequence | [
{
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.ext_iff | [] | [
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785,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_iSup | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernelIsoOfEq_refl | [
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Mathlib/Order/Ideal.lean | Order.Ideal.directed | [] | [
137,
14
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136,
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Mathlib/Algebra/Order/Field/Basic.lean | one_div_nonpos | [] | [
88,
32
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Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_sub | [] | [
97,
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_sin | [] | [
44,
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Mathlib/GroupTheory/Finiteness.lean | Group.rank_le_of_surjective | [
{
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413,
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406,
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Mathlib/Data/Multiset/Basic.lean | Multiset.ext' | [] | [
2513,
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2512,
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Mathlib/Data/Set/Lattice.lean | Set.Nonempty.of_sUnion_eq_univ | [] | [
1127,
47
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1126,
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Mathlib/Algebra/BigOperators/Fin.lean | finFunctionFinEquiv_apply | [] | [
351,
6
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349,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.degree_le_maxDegree | [
{
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1562,
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsAdjointPair.smul | [
{
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Mathlib/Topology/Instances/NNReal.lean | HasSum.toNNReal | [
{
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158,
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Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_map_inl_inl | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | GaloisConnection.u_csInf | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.comp_assoc | [] | [
439,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
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Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.realSize_merge | [
{
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211,
38
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194,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.sin_angle_sub_of_inner_eq_zero | [
{
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294,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.algebraMap_aevalEquiv | [] | [
395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.comap_mono | [] | [
372,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.imClm_apply | [] | [
927,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
926,
1
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Mathlib/NumberTheory/Padics/PadicVal.lean | one_le_padicValNat_of_dvd | [
{
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"tactic": "rwa [← PartENat.coe_le_coe, padicValNat_def' hp.out.ne_one hn, ← pow_dvd_iff_le_multiplicity,\n pow_one]"
}
] | [
242,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasDerivWithinAt | [] | [
40,
85
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40,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_nnreal_sub | [] | [
455,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_of_not_le | [
{
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"tactic": "simp"
},
{
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119,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.conj | [] | [
125,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Comonad.Coalgebra.comp_f | [] | [
416,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/Algebra/Lie/Basic.lean | LieHom.coe_comp | [] | [
424,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.smul_mono | [
{
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276,
43
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264,
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Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes | [] | [
247,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.map_prod_map | [
{
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610,
38
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603,
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src/lean/Init/Prelude.lean | congr | [] | [
360,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
359,
1
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_le_log | [
{
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"tactic": "rw [← exp_le_exp, exp_log h, exp_log h₁]"
}
] | [
146,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conjAut_zpow | [] | [
168,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
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Mathlib/Data/Matrix/Basic.lean | Matrix.ext_iff | [
{
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75,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.norm_fst_eq_snd | [
{
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634,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_pos | [] | [
130,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Set/NAry.lean | Set.Nonempty.image2 | [] | [
158,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.smul_apply | [] | [
275,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_eval | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np : R[X]\nx : R\n⊢ eval x (↑derivative p) = sum p fun n a => a * ↑n * x ^ (n - 1)",
"tactic": "simp_rw [derivative_apply, eval_sum, eval_mul_X_pow, eval_C]"
}
] | [
332,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min_mem_image_coe | [] | [
1530,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1528,
1
] |
Std/Data/String/Lemmas.lean | String.utf8SetAux_of_valid | [
{
"state_after": "no goals",
"state_before": "c' : Char\ncs cs' : List Char\ni p : Nat\nhp : i + utf8Len [] = p\n⊢ utf8SetAux c' ([] ++ []) { byteIdx := i } { byteIdx := p } = [] ++ List.modifyHead (fun x => c') []",
"tactic": "rfl"
},
{
"state_after": "no goals",
"state_before": "c' : Char\... | [
243,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
234,
1
] |
Mathlib/Order/CompleteLattice.lean | inf_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.102664\nβ₂ : Type ?u.102667\nγ : Type ?u.102670\nι : Sort u_1\nι' : Sort ?u.102676\nκ : ι → Sort ?u.102681\nκ' : ι' → Sort ?u.102686\ninst✝¹ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b : α\ninst✝ : Nonempty ι\nf : ι → α\na : α\n⊢ (a ⊓ ⨅... | [
1262,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.find_eq_some_iff | [] | [
942,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
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