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/Fin/Basic.lean | Fin.orderEmbedding_eq | [] | [
611,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_mem_compression_of_mem_compression | [
{
"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\nha : a ∈ s ∧ compress u v a ∈ s ∨ ¬a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = a\n⊢ compress u v a ∈ s ∧ compress u v (compress u v a) ∈ s ∨\n ... | [
190,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Vector/Mem.lean | Vector.mem_cons_self | [] | [
61,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_subset_smul_right | [] | [
183,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isBounded_iff_eventually | [] | [
701,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_empty_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u s t : Set α\n⊢ s ∪ t ⊆ ∅ ↔ s ⊆ ∅ ∧ t ⊆ ∅",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u s t : Set α\n⊢ s ∪ t = ∅ ↔ s = ∅ ∧ t = ∅",
"tactic": "simp only [← subse... | [
873,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.out_eq' | [] | [
138,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.norm_inv_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\nx : FreeGroup α\n⊢ norm x⁻¹ = norm x",
"tactic": "simp only [norm, toWord_inv, invRev_length]"
}
] | [
1411,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsFractionRing.ideal_span_singleton_map_subset | [
{
"state_after": "R : Type u_2\ninst✝¹⁷ : CommRing R\nM : Submonoid R\nS : Type u_3\ninst✝¹⁶ : CommRing S\ninst✝¹⁵ : Algebra R S\nP : Type ?u.667790\ninst✝¹⁴ : CommRing P\nA : Type ?u.667796\nK : Type u_4\ninst✝¹³ : CommRing A\ninst✝¹² : IsDomain A\nL : Type u_1\ninst✝¹¹ : IsDomain R\ninst✝¹⁰ : IsDomain S\ninst... | [
464,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Order/Directed.lean | directed_of_sup | [] | [
113,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | adjoin_le_integralClosure | [
{
"state_after": "R : Type u_1\nA : Type u_2\nB : Type ?u.694032\nS : Type ?u.694035\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nx : A\nhx : IsIntegral R x\n⊢ {x} ⊆ ↑(integralClosure R A)",
"state_before": "R : ... | [
571,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_comm | [] | [
1881,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_atBot | [
{
"state_after": "case h.e'_3\nα : Type u_2\nβ : Type u_1\ninst✝¹ : NormedLinearOrderedField β\nu v : α → β\nl : Filter α\ninst✝ : OrderTopology β\nhuv : u ~[l] v\nhu : Tendsto u l atBot\n⊢ v = Neg.neg ∘ fun x => -v x",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : NormedLinearOrderedField β\nu v : ... | [
325,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Polynomial/DenomsClearable.lean | DenomsClearable.add | [
{
"state_after": "R : Type u_1\nK : Type u_2\ninst✝¹ : Semiring R\ninst✝ : CommSemiring K\ni : R →+* K\na b : R\nbi : K\nN : ℕ\nf g : R[X]\nx✝¹ : DenomsClearable a b N f i\nx✝ : DenomsClearable a b N g i\nDf : R\nbf : K\nbfu : bf * ↑i b = 1\nHf : ↑i Df = ↑i b ^ N * eval (↑i a * bf) (Polynomial.map i f)\nDg : R\... | [
68,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Real/Basic.lean | Real.add_lt_add_iff_left | [
{
"state_after": "case h\nx y b c : ℝ\ny✝ : CauSeq ℚ abs\n⊢ c + mk y✝ < c + b ↔ mk y✝ < b",
"state_before": "x y a b c : ℝ\n⊢ c + a < c + b ↔ a < b",
"tactic": "induction a using Real.ind_mk"
},
{
"state_after": "case h.h\nx y c : ℝ\ny✝¹ y✝ : CauSeq ℚ abs\n⊢ c + mk y✝¹ < c + mk y✝ ↔ mk y✝¹ < mk ... | [
374,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_op_norm | [
{
"state_after": "case intro.intro\n𝕜 : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type ?u.300329\nE : Type u_2\nEₗ : Type ?u.300335\nF : Type u_1\nFₗ : Type ?u.300341\nG : Type ?u.300344\nGₗ : Type ?u.300347\n𝓕 : Type ?u.300350\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : Seminorm... | [
207,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | Submodule.exists_lieSubalgebra_coe_eq_iff | [
{
"state_after": "case mp\nR : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\np : Submodule R L\n⊢ (∃ K, K.toSubmodule = p) → ∀ (x y : L), x ∈ p → y ∈ p → ⁅x, y⁆ ∈ p\n\ncase mpr\nR : Type u\nL : Typ... | [
367,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_natCast | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.251851\nα : Type u_1\nβ : Type ?u.251857\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nn : ℕ\n⊢ round ↑n = ↑n",
"tactic": "simp [round]"
}
] | [
1347,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1347,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.map_subtype_span_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₂ : Type ?u.205557\nK : Type ?u.205560\nM : Type u_2\nM₂ : Type ?u.205566\nV : Type ?u.205569\nS : Type ?u.205572\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 →+*... | [
588,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.BicartesianSq.of_has_biproduct₂ | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasBinaryBiproduct X Y\n⊢ BicartesianSq 0 0 biprod.inl biprod.inr",
"tactic": "convert of_is_biproduct₂ ... | [
987,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_nonempty | [] | [
595,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieModuleHom.coe_restrictLie | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.char_ne_zero_of_finite | [
{
"state_after": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : Finite R\ninst✝ : CharP R 0\n⊢ False",
"state_before": "R : Type u_1\ninst✝² : NonAssocRing R\np : ℕ\ninst✝¹ : CharP R p\ninst✝ : Finite R\n⊢ p ≠ 0",
"tactic": "rintro rfl"
},
{
"state_after": "R : Type u_1\ninst✝² : NonAssocRing ... | [
483,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.mkRat_def | [] | [
89,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
89,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_dvd_of_dvd | [
{
"state_after": "case inl\nb : ℕ\nh : 0 ∣ b\n⊢ φ 0 ∣ φ b\n\ncase inr\na b : ℕ\nh : a ∣ b\nha0 : a ≠ 0\n⊢ φ a ∣ φ b",
"state_before": "a b : ℕ\nh : a ∣ b\n⊢ φ a ∣ φ b",
"tactic": "rcases eq_or_ne a 0 with (rfl | ha0)"
},
{
"state_after": "case inr.inl\na : ℕ\nha0 : a ≠ 0\nh : a ∣ 0\n⊢ φ a ∣ φ 0\... | [
373,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.add_apply | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_mul_eq_opow_omega | [
{
"state_after": "case inl\na b : Ordinal\nhb : 0 < b\nhba : b ≤ a ^ ω\nha : a = 0\n⊢ nfp (fun x => a * x) b = a ^ ω\n\ncase inr\na b : Ordinal\nhb : 0 < b\nhba : b ≤ a ^ ω\nha : 0 < a\n⊢ nfp (fun x => a * x) b = a ^ ω",
"state_before": "a b : Ordinal\nhb : 0 < b\nhba : b ≤ a ^ ω\n⊢ nfp (fun x => a * x) b =... | [
663,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Data/List/Indexes.lean | List.length_mapIdx | [
{
"state_after": "case nil\nα✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\nf✝ f : ℕ → α → β\n⊢ length (mapIdx f []) = length []\n\ncase cons\nα✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\nf✝ : ℕ → α → β\nhd : α\ntl : List α\nIH : ∀ (f : ℕ → α → β), length (mapIdx f tl) = length tl\nf : ℕ → α → β\... | [
194,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_apply_combination_of_not_mem | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.106545\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni j : ι\ne : ι ≃ ι'\nhi : ¬i ∈ s\nw : ι → k\nhw : Finset.sum... | [
202,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_mul_left | [] | [
613,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
613,
11
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_comp_linearIsometryEquiv | [
{
"state_after": "case zero\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\nφ : E ≃ₗᵢ[ℝ] E\nhφ : 0 < ↑LinearMap.det ↑φ.toLinearEquiv\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\nx : Fin Nat.zero → E\n⊢ ↑(volumeForm o) (↑φ ∘ x) = ↑(volumeForm o) x\n\ncase ... | [
349,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_pos_iff_of_neg | [
{
"state_after": "k : Type u_1\nM : Type u_2\nN : Type ?u.36780\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhc : c < 0\n⊢ -c • a < 0 ↔ a < 0",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.36780\ninst✝³ : OrderedRing k\nin... | [
88,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/GroupTheory/Sylow.lean | IsPGroup.exists_le_sylow | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nP : Subgroup G\nhP : IsPGroup p { x // x ∈ P }\nc : Set (Subgroup G)\nhc1 : c ⊆ {Q | IsPGroup p { x // x ∈ Q }}\nhc2 : IsChain (fun x x_1 => x ≤ x_1) c\nQ : Subgroup G\nhQ : Q ∈ c\nx✝ :\n { x //\n x ∈\n {\n toSubmonoid :=\n {\n ... | [
164,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.dist_eq_of_L2 | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.289391\n𝕜' : Type ?u.289394\nι : Type u_2\nα : ι → Type ?u.289402\nβ✝ : ι → Type ?u.289407\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp 2 β\n⊢ Real.sqrt (∑ i : ι, ‖(x - y) i‖ ^ 2) = Real.sqrt (∑... | [
606,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_dvd_of_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : Group α\ns t : Subgroup α\nH : Type u_2\ninst✝² : Group H\ninst✝¹ : Fintype α\ninst✝ : Fintype H\nf : α →* H\nhf : Injective ↑f\n⊢ card α ∣ card H",
"tactic": "classical calc\n card α = card (f.range : Subgroup H) := card_congr (Equ... | [
814,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_neg_of_neg_of_pos | [
{
"state_after": "a b : Int\nha : a < 0\nhb : 0 < b\nh : a * b < 0 * b\n⊢ a * b < 0",
"state_before": "a b : Int\nha : a < 0\nhb : 0 < b\n⊢ a * b < 0",
"tactic": "have h : a * b < 0 * b := Int.mul_lt_mul_of_pos_right ha hb"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nha : a <... | [
1202,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1200,
11
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_comap | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.restrictNonposSeq_subset | [
{
"state_after": "case succ\nα : Type u_1\nβ : Type ?u.19730\ninst✝³ : MeasurableSpace α\nM : Type ?u.19736\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns : SignedMeasure α\ni j : Set α\nn✝ : ℕ\n⊢ MeasureTheory.SignedMeasure.someExistsOneDivLT s\n (i \\\n ⋃... | [
180,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
9
] |
Mathlib/Algebra/Order/Ring/Defs.lean | bit1_pos | [] | [
303,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Order/CompleteLatticeIntervals.lean | subset_sSup_of_within | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Set α\ninst✝¹ : SupSet α\ninst✝ : Inhabited ↑s\nt : Set ↑s\nh : sSup (Subtype.val '' t) ∈ s\n⊢ sSup (Subtype.val '' t) = ↑(sSup t)",
"tactic": "simp [dif_pos h]"
}
] | [
60,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_closure_range_iff_nat | [
{
"state_after": "no goals",
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1910,
68
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1907,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix'_apply | [
{
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348,
30
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_restrict | [
{
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1381,
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.compl_infty | [] | [
140,
45
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139,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.germ_stalkSpecializes | [] | [
331,
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329,
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Mathlib/Data/Fin/VecNotation.lean | Matrix.head_cons | [] | [
149,
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148,
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src/lean/Init/Control/Lawful.lean | ReaderT.run_seqRight | [] | [
207,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | volume_preimage_coe | [
{
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54
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Mathlib/Order/Lattice.lean | Antitone.map_inf | [] | [
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1205,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_sup_eq | [] | [
3159,
61
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Mathlib/Data/Stream/Init.lean | Stream'.nth_succ_cons | [] | [
87,
6
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Mathlib/Algebra/Order/Group/Defs.lean | div_le_self_iff | [
{
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365,
76
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Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.eventually_measure_lt_top | [
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Mathlib/Analysis/Convex/Basic.lean | Convex.add_smul_sub_mem | [
{
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486,
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483,
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Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_mul_aleph0 | [] | [
162,
69
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161,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curry0_norm | [] | [
1666,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1664,
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Mathlib/Algebra/Star/Unitary.lean | unitary.coe_div | [
{
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] | [
175,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/Analysis/Seminorm.lean | absorbent_ball | [
{
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Mathlib/Data/Pi/Algebra.lean | Pi.pow_def | [] | [
128,
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127,
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Mathlib/Topology/Basic.lean | diff_subset_closure_iff | [
{
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] | [
468,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_eq | [
{
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199,
83
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194,
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Mathlib/Analysis/Convex/Quasiconvex.lean | AntitoneOn.quasiconvexOn | [] | [
197,
18
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196,
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Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_zero | [
{
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] | [
68,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
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Mathlib/Data/TypeVec.lean | TypeVec.append1_cases_append1 | [] | [
143,
6
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141,
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Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_eq_zero | [
{
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] | [
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84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.subsingleton_of_finrank_adjoin_le_one | [] | [
782,
69
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Mathlib/Data/List/Basic.lean | List.takeI_eq_take | [] | [
2337,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.add_comp | [
{
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.mapsTo_extend | [
{
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Mathlib/Algebra/GroupPower/Lemmas.lean | smul_pow' | [
{
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_le_aleph0 | [
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] | [
1261,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
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Mathlib/Data/Set/Function.lean | Set.piecewise_insert_of_ne | [
{
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Mathlib/Analysis/Fourier/FourierTransform.lean | Fourier.fourierIntegral_comp_add_right | [] | [
225,
57
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222,
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Mathlib/Logic/Function/Basic.lean | Function.update_eq_iff | [] | [
596,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
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Mathlib/Data/Set/Basic.lean | Set.sep_eq_self_iff_mem_true | [
{
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"tactic": "simp_rw [ext_iff, mem_sep_iff, and_iff_left_iff_imp]"
}
] | [
1434,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1433,
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Mathlib/LinearAlgebra/Finrank.lean | finrank_span_eq_card | [
{
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337,
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Mathlib/Data/Rat/Defs.lean | Rat.divInt_ne_zero | [] | [
92,
26
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Mathlib/Analysis/Convex/Gauge.lean | gauge_def' | [
{
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivWithinAt.const_mul | [
{
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252,
26
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Mathlib/Data/Set/Pairwise/Lattice.lean | Set.PairwiseDisjoint.biUnion | [
{
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89,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.neg_mul_atTop | [
{
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90,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_one | [
{
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"state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝... | [
342,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/Topology/Algebra/Monoid.lean | continuous_list_prod | [] | [
542,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.extend_apply' | [] | [
476,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
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] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.mem_basicOpen | [] | [
772,
10
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771,
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Mathlib/Data/Nat/Size.lean | Nat.size_one | [
{
"state_after": "no goals",
"state_before": "⊢ size (bit1 0) = 1",
"tactic": "rw [size_bit1, size_zero]"
}
] | [
103,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.of_zero | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.is3Clique_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nG H : SimpleGraph α\nn : ℕ\ns : Finset α\ninst✝ : DecidableEq α\na b c : α\nh : IsNClique G 3 s\n⊢ ∃ a b c, Adj G a b ∧ Adj G a c ∧ Adj G b c ∧ s = {a, b, c}\n\ncase refine'_2\nα : Type u_1\nG H : SimpleGraph α\nn : ℕ\ns : Finset α\ninst✝ : DecidableEq α\na b c : ... | [
147,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.lift.range_eq_closure | [
{
"state_after": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\ninst✝ : Group β\nf : α → β\nx y : FreeGroup α\n⊢ Subgroup.closure (Set.range f) ≤ MonoidHom.range (↑lift f)",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\ninst✝ : Group β\nf : α → β\nx y : FreeGroup α\n⊢ ... | [
778,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.rel_bind | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na : α\ns✝ t✝ : Multiset α\nf✝ g✝ : α → Multiset β\nr : α → β → Prop\np : γ → δ → Prop\ns : Multiset α\nt : Multiset β\nf : α → Multiset γ\ng : β → Multiset δ\nh : (r ⇒ Rel p) f g\nhst : Rel r s t\n⊢ Rel (Rel p) (map f s) (map g t)... | [
199,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nz w : ℂ\ns : Set ℂ\nhs : Set.Countable s\nHc : ContinuousOn f ([[z.re, w.re]] ×ℂ [[z.im, w.im]])\nHd :\n ∀ (x : ℂ), x ∈ Ioo (min z.re w.re) (max z.re w.re) ×ℂ Ioo (min z.im w.im) (max z.im... | [
265,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₂ : Type ?u.274344\nK : Type ?u.274347\nM : Type u_1\nM₂ : Type ?u.274353\nV : Type ?u.274356\nS : Type ?u.274359\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ns : Set M\n⊢ span R (-s) = span R (↑(-LinearMap.id) '' s)",
"tacti... | [
825,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Data/Set/Function.lean | Set.RightInvOn.eqOn | [] | [
1105,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Logic/Basic.lean | not_ball | [] | [
1093,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.toMultilinearMap_zero | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_relabel | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.238835\nP : Type ?u.238838\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nφ✝ ψ : Formula L α\nv✝ : α → M\nφ : Formula L α\ng : α → β\nv : β → M\n⊢ BoundedFormula.Realize φ (Sum.elim v... | [
677,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.IsVonNBounded.of_topologicalSpace_le | [] | [
113,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factors_comp_arrow | [] | [
97,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.map_comap_le | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.249498\n𝕜 : Type ?u.249501\nV : Type u\nW : Type v\nX : Type w\nG✝ : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nf : V ↪ W\nG : SimpleGraph W\n⊢ SimpleGraph.map f (SimpleGraph.comap (↑f) G) ≤ G",
"tactic": "rw [map_le_iff_le_... | [
1296,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.add_descFactorial_eq_ascFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ descFactorial (n + 0) 0 = ascFactorial n 0",
"tactic": "rw [ascFactorial_zero, descFactorial_zero]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ descFactorial (n + succ k) (succ k) = ascFactorial n (succ k)",
"tactic":... | [
413,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
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