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/Order/UpperLower/Basic.lean | lowerClosure_iUnion | [] | [
1449,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.inter_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21491\nγ : Type ?u.21494\ninst✝¹ : Fintype α\ns✝ t : Finset α\ninst✝ : DecidableEq α\ns : Finset α\n⊢ s ∩ univ = s",
"tactic": "rw [inter_comm, univ_inter]"
}
] | [
279,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | setOf_isPreconnected_subset_of_ordered | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁶ : ConditionallyCompleteLinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : ConditionallyCompleteLinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology β\ninst✝ : Nonempty γ\ns : Set α\nhs : s ∈ {s | IsPreconnecte... | [
331,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_div | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\nH1 : k ∣ m\nH2 : k ∣ n\nH0 : k = 0\n⊢ gcd (m / k) (n / k) = gcd m n / k",
"tactic": "simp [H0]"
},
{
"state_after": "m n k : Nat\nH1 : k ∣ m\nH2 : k ∣ n\nH3 : k > 0\n⊢ gcd (m / k) (n / k) * k = gcd m n / k * k",
"state_before": "m n ... | [
123,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
116,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.nonMemberSubfamily_memberSubfamily | [
{
"state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\na✝ : Finset α\n⊢ a✝ ∈ nonMemberSubfamily a (memberSubfamily a 𝒜) ↔ a✝ ∈ memberSubfamily a 𝒜",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\n⊢... | [
132,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | associated_normalize_iff | [] | [
123,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_c_eq_zero' | [] | [
354,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Topology/PathConnected.lean | Path.trans_range | [
{
"state_after": "X✝ : Type ?u.252930\nY : Type ?u.252933\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.252948\nγ : Path x y\nX : Type u_1\ninst✝ : TopologicalSpace X\na b c : X\nγ₁ : Path a b\nγ₂ : Path b c\n⊢ range\n ↑{\n toContinuousMap :=\n Cont... | [
413,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Order/SMul.lean | smul_lowerBounds_subset_lowerBounds_smul | [] | [
147,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_subtype_eq_filter | [] | [
351,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.hasBasis_nhds_units | [] | [
120,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.commute_cast | [] | [
111,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.coprime_of_mul_modEq_one | [
{
"state_after": "case intro\nm n✝ a✝ b✝ c d b a n : ℕ\nh : a * b ≡ 1 [MOD n]\ng : ℕ\nhh : n = gcd a n * g\n⊢ coprime a n",
"state_before": "m n✝ a✝ b✝ c d b a n : ℕ\nh : a * b ≡ 1 [MOD n]\n⊢ coprime a n",
"tactic": "obtain ⟨g, hh⟩ := Nat.gcd_dvd_right a n"
},
{
"state_after": "case intro\nm n✝ ... | [
397,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_cast | [
{
"state_after": "case mk.refl\nR : Type u_1\ninst✝ : AddMonoidWithOne R\nm : ℕ\n⊢ IsNat (↑↑m) m",
"state_before": "R : Type u_1\ninst✝ : AddMonoidWithOne R\nn m : ℕ\n⊢ IsNat n m → IsNat (↑n) m",
"tactic": "rintro ⟨⟨⟩⟩"
},
{
"state_after": "no goals",
"state_before": "case mk.refl\nR : Type ... | [
72,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | antilipschitzWith_iff_le_mul_nndist | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1159\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nK : ℝ≥0\nf : α → β\n⊢ (∀ (x y : α), ↑(nndist x y) ≤ ↑K * ↑(nndist (f x) (f y))) ↔ ∀ (x y : α), nndist x y ≤ K * nndist (f x) (f y)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Typ... | [
57,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbitRel.Quotient.mem_orbit | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\nb a✝ : β\n⊢ b ∈ orbit (Quotient.mk'' a✝) ↔ Quotient.mk'' b = Quotient.mk'' a✝",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\nb : β\nx : Quotient α β\n⊢ b ∈ ... | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Ico_real | [] | [
280,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_himp_himp | [] | [
459,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.reindex_reindex | [] | [
516,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.mem_source_at | [
{
"state_after": "R : Type u_3\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.424723\ninst✝⁸ : NontriviallyNormedField R\ninst✝⁷ : (x : B) → AddCommMonoid (E x)\ninst✝⁶ : (x : B) → Module R (E x)\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace R F\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace (Tota... | [
749,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.natPred_add_one | [] | [
44,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.coe_nat_num | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn : ℕ\n⊢ (↑n).num = ↑n",
"tactic": "rw [← Int.cast_ofNat, coe_int_num]"
}
] | [
534,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | eventually_singleton_add_smul_subset | [
{
"state_after": "case intro.intro\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\ns : Set E\nhs : Metric.Bounded s\nu : Set E\nhu : u ∈ 𝓝 x\nε : ℝ\nεpos : 0 < ε\nhε : closedBall x ε ⊆ u\n⊢ ∀ᶠ (r : 𝕜) in 𝓝 0, {x} + r • s ⊆ u",
"st... | [
144,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Homology/LocalCohomology.lean | Ideal.exists_pow_le_of_le_radical_of_fG | [
{
"state_after": "case intro\nR : Type u\ninst✝ : CommRing R\nI J : Ideal R\nhIJ : I ≤ radical J\nhJ : FG (radical J)\nk : ℕ\nhk : radical J ^ k ≤ J\n⊢ ∃ k, I ^ k ≤ J",
"state_before": "R : Type u\ninst✝ : CommRing R\nI J : Ideal R\nhIJ : I ≤ radical J\nhJ : FG (radical J)\n⊢ ∃ k, I ^ k ≤ J",
"tactic": ... | [
212,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Poly.mul_denote | [
{
"state_after": "ctx : Context\np₁ p₂ : Poly\n⊢ denote ctx [] + denote ctx p₁ * denote ctx p₂ = denote ctx p₁ * denote ctx p₂",
"state_before": "ctx : Context\np₁ p₂ : Poly\n⊢ denote ctx (mul p₁ p₂) = denote ctx p₁ * denote ctx p₂",
"tactic": "simp [mul, go]"
},
{
"state_after": "no goals",
... | [
169,
61
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
160,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.card_mul_index | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ relindex ⊥ H * index H = index ⊥",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ Nat.card { x // x ∈ H } * index H = Nat.card G",
"tactic": "rw [← relindex_bot_left, ← index_bot]"
},
{
"state_after": "... | [
294,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_lt_left_of_lt_add | [
{
"state_after": "n k m : Nat\nH : n ≤ k\nh : k < n + m\nthis : succ k - n ≤ n + m - n\n⊢ k - n < m",
"state_before": "n k m : Nat\nH : n ≤ k\nh : k < n + m\n⊢ k - n < m",
"tactic": "have := Nat.sub_le_sub_right (succ_le_of_lt h) n"
},
{
"state_after": "no goals",
"state_before": "n k m : Na... | [
459,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
457,
11
] |
Mathlib/Topology/Constructions.lean | isOpen_prod_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.47317\nδ : Type ?u.47320\nε : Type ?u.47323\nζ : Type ?u.47326\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
665,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.continuousAt_rpow_of_ne | [
{
"state_after": "p : ℝ × ℝ\nhp✝ : p.fst ≠ 0\nhp : p.fst < 0 ∨ p.fst > 0\n⊢ ContinuousAt (fun p => p.fst ^ p.snd) p",
"state_before": "p : ℝ × ℝ\nhp : p.fst ≠ 0\n⊢ ContinuousAt (fun p => p.fst ^ p.snd) p",
"tactic": "rw [ne_iff_lt_or_gt] at hp"
},
{
"state_after": "case inl\np : ℝ × ℝ\nhp✝ : p.f... | [
237,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_is_product' | [] | [
262,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_zero | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.appendList_data | [
{
"state_after": "α : Type u_1\narr : Array α\nl : List α\n⊢ (Array.appendList arr l).data = arr.data ++ l",
"state_before": "α : Type u_1\narr : Array α\nl : List α\n⊢ (arr ++ l).data = arr.data ++ l",
"tactic": "rw [← appendList_eq_append]"
},
{
"state_after": "α : Type u_1\narr : Array α\nl :... | [
204,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
201,
9
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pure_smul_pure | [] | [
1031,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comap_nhds_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.69386\nδ : Type ?u.69389\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\ny : β\n⊢ comap (↑h) (𝓝 y) = 𝓝 (↑(Homeomorph.symm h) y)",
"tacti... | [
389,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.one_le_div_iff | [
{
"state_after": "no goals",
"state_before": "m n k a b : ℕ\nhb : 0 < b\n⊢ 1 ≤ a / b ↔ b ≤ a",
"tactic": "rw [le_div_iff_mul_le hb, one_mul]"
}
] | [
616,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.boxProd_connected | [] | [
217,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.sign_of_cycleType | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\n⊢ prod (map (fun n => -(-1) ^ n) (cycleType f)) = (-1) ^ (sum (cycleType f) + ↑card (cycleType f))",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\n⊢ ↑sign f = (-1) ^ (sum (cycleType... | [
170,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_Icc | [] | [
256,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.right_inv | [] | [
163,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_le_sum | [] | [
701,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Topology/Basic.lean | frontier_inter_subset | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns t : Set α\n⊢ closure (s ∩ t) ∩ (closure (sᶜ) ∪ closure (tᶜ)) ⊆\n closure s ∩ closure (sᶜ) ∩ closure t ∪ closure s ∩ (closure t ∩ closure (tᶜ))",
"state_before": "α : Type u\... | [
748,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_add' | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np✝ q : R[X]\nS : Type u_1\ninst✝ : AddCommMonoid S\np : R[X]\nf g : ℕ → R → S\n⊢ sum p (f + g) = sum p f + sum p g",
"tactic": "simp [sum_def, Finset.sum_add_distrib]"
}
] | [
994,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.haveLebesgueDecomposition_of_finiteMeasure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.139824\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh :\n ∃ u,\n Monotone u ∧\n Filter.Tendsto u Filter.atTop (nhds (sSup (measurableLEEval ν μ))) ∧ ∀ (n : ℕ), u n ∈ measurableLEEval ν μ\n⊢ ∃ p, Measurable p.... | [
655,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.mono | [] | [
2471,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2469,
1
] |
Mathlib/Tactic/IntervalCases.lean | Int.le_sub_one_of_not_le | [] | [
239,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Topology/Connected.lean | IsIrreducible.isConnected | [] | [
81,
50
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80,
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Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.fpowerSeriesBilinear_radius | [] | [
97,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/Order/Basic.lean | le_of_eq_of_le | [] | [
179,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.curryLeft_compLinearMap | [
{
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1309,
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1301,
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src/lean/Init/Data/Nat/Div.lean | Nat.div_lt_self | [
{
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},
{
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"state_before": "n k : Nat\nhLtN : 0 < n\nhLtK : 1 < k\n⊢ ite... | [
65,
63
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.stream_succ_of_int | [
{
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112,
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108,
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Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.coe_inj | [] | [
97,
40
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Mathlib/Order/WellFoundedSet.lean | Set.IsWf.min_union | [
{
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662,
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655,
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.disjoint_span_image | [
{
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617,
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611,
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Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_map | [
{
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] | [
78,
38
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77,
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Mathlib/Data/Finset/Basic.lean | Finset.mem_of_mem_insert_of_ne | [] | [
1073,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
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Mathlib/Data/Finset/Lattice.lean | Finset.isLeast_min' | [] | [
1337,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_eq_empty_iff | [
{
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}
] | [
85,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Dynamics/PeriodicPts.lean | Function.mem_ptsOfPeriod | [] | [
201,
10
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200,
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_le_moveLeft | [] | [
486,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
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Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.polar_closure | [
{
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218,
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213,
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Mathlib/Analysis/Convex/Segment.lean | openSegment_subset_segment | [] | [
92,
65
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91,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_ne_zero_of_not_collinear | [] | [
459,
34
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457,
1
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Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_injective | [] | [
111,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.two_dvd_card_support | [
{
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203,
41
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197,
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Mathlib/Order/Antisymmetrization.lean | AntisymmRel.symm | [] | [
59,
11
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.sSup_le | [
{
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715,
61
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703,
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.norm_changeOriginSeriesTerm | [
{
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1116,
67
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1114,
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Mathlib/Computability/Primrec.lean | Nat.Primrec.casesOn1 | [
{
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}
] | [
112,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.tendsto_abv_eval₂_atTop | [
{
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117,
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102,
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.isClopen_fiber | [] | [
83,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.tan_sq_div_one_add_tan_sq | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℂ\nhx : cos x ≠ 0\n⊢ tan x ^ 2 / (1 + tan x ^ 2) = sin x ^ 2",
"tactic": "simp only [← tan_mul_cos hx, mul_pow, ← inv_one_add_tan_sq hx, div_eq_mul_inv, one_mul]"
}
] | [
1059,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
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Mathlib/MeasureTheory/Group/Arithmetic.lean | measurable_const_smul_iff₀ | [] | [
761,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nat_nadd | [
{
"state_after": "no goals",
"state_before": "a b c : Ordinal\nn : ℕ\n⊢ ↑n ♯ a = a + ↑n",
"tactic": "rw [nadd_comm, nadd_nat]"
}
] | [
323,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.isGreatest_u | [] | [
147,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_nonneg | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/RingTheory/Ideal/Cotangent.lean | AlgHom.ker_ker_sqare_lift | [
{
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194,
36
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190,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | ne_one_of_mem_sphere | [
{
"state_after": "no goals",
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714,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.sigmaCongrRight_trans | [] | [
739,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Option/Basic.lean | Option.pmap_eq_none_iff | [
{
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}
] | [
237,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.image.ι_zero' | [
{
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"state_before": "C : Type u\ninst✝⁵ : Category C\nD : Type u'... | [
627,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.isPreconnected_of_equivalent | [] | [
219,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumCompl_apply_inl | [] | [
322,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.map | [] | [
868,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.composePath_toPath | [] | [
175,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Dense.borel_eq_generateFrom_Ico_mem_aux | [
{
"state_after": "α✝ : Type ?u.609263\nβ : Type ?u.609266\nγ : Type ?u.609269\nγ₂ : Type ?u.609272\nδ : Type ?u.609275\nι : Sort y\ns✝ t u : Set α✝\ninst✝²⁰ : TopologicalSpace α✝\ninst✝¹⁹ : MeasurableSpace α✝\ninst✝¹⁸ : OpensMeasurableSpace α✝\ninst✝¹⁷ : TopologicalSpace β\ninst✝¹⁶ : MeasurableSpace β\ninst✝¹⁵ ... | [
612,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
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Mathlib/NumberTheory/Padics/PadicVal.lean | dvd_iff_padicValNat_ne_zero | [] | [
248,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.map | [] | [
87,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
11
] |
Mathlib/Algebra/Ring/Basic.lean | inv_neg' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Group α\ninst✝ : HasDistribNeg α\na : α\n⊢ (-a)⁻¹ = -a⁻¹",
"tactic": "rw [eq_comm, eq_inv_iff_mul_eq_one, neg_mul, mul_neg, neg_neg, mul_left_inv]"
}
] | [
116,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/GroupWithZero/Divisibility.lean | eq_of_forall_dvd | [] | [
136,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.pred_zero | [] | [
684,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
683,
19
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_prod_le_iff | [] | [
2389,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2388,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.toNNReal_coe_nat | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑(Real.toNNReal ↑n) = ↑↑n",
"tactic": "simp [Real.coe_toNNReal]"
}
] | [
405,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.isoColimitCocone_ι_hom | [
{
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"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Categ... | [
826,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioc.coe_eq_one | [
{
"state_after": "α : Type u_1\ninst✝¹ : StrictOrderedSemiring α\ninst✝ : Nontrivial α\nx : ↑(Ioc 0 1)\n⊢ x = 1 ↔ ↑x = 1",
"state_before": "α : Type u_1\ninst✝¹ : StrictOrderedSemiring α\ninst✝ : Nontrivial α\nx : ↑(Ioc 0 1)\n⊢ ↑x = 1 ↔ x = 1",
"tactic": "symm"
},
{
"state_after": "no goals",
... | [
269,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | zero_le_padicValRat_of_nat | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\n⊢ 0 ≤ padicValRat p ↑n",
"tactic": "simp"
}
] | [
214,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.algHom_ext' | [] | [
1950,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1945,
1
] |
Mathlib/Order/Basic.lean | Prod.mk_le_mk | [] | [
1198,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheory | [] | [
93,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_nsmul_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.99178\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ f (x - n • c) = f x",
"tactic": "simpa only [sub_eq_add_neg] using h.neg_nsmul n x"
}
] | [
218,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
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