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 |
|---|---|---|---|---|---|---|
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Certificate.of_combine_isUnsat | [] | [
693,
43
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691,
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_eq_univ | [
{
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"tactic": "rw [← coe_inj, coe_toFinset, coe_univ]"
}
] | [
753,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
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Mathlib/Data/Set/Function.lean | Set.InjOn.leftInvOn_invFunOn | [] | [
1248,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
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Mathlib/Topology/Order/Basic.lean | eventually_gt_nhds | [] | [
1200,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
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Mathlib/Algebra/GroupPower/Order.lean | le_max_of_sq_le_mul | [
{
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335,
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334,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.apply_lt_nfpBFamily | [
{
"state_after": "o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal → Ordinal\nH : ∀ (i : Ordinal) (hi : i < o), IsNormal (f i hi)\na b : Ordinal\nhb : b < nfpBFamily o f a\ni : Ordinal\nhi : i < o\n⊢ familyOfBFamily o f (enum (fun x x_1 => x < x_1) i (_ : i < type fun x x_1 => x < x_1)) b < nfpBFamily o f a",
... | [
299,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/Analysis/NormedSpace/RieszLemma.lean | riesz_lemma_of_norm_lt | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF✝ : Type ?u.15017\ninst✝¹ : SeminormedAddCommGroup F✝\ninst✝ : NormedSpace ℝ F✝\nc : 𝕜\nhc : 1 < ‖c‖\nR : ℝ\nhR : ‖c‖ < R\nF : Subspace 𝕜 E\nhFc : IsClosed ↑F\nhF : ∃ x, ¬x ∈ F\nR... | [
109,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_diagonal | [] | [
504,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | LinearIsometry.norm_compContinuousMultilinearMap | [
{
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1051,
60
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_refl | [] | [
317,
14
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316,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.nextCoeffUp_of_pos_natTrailingDegree | [
{
"state_after": "case hnc\nR : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np : R[X]\nhp : 0 < natTrailingDegree p\n⊢ ¬natTrailingDegree p = 0",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np : R[X]\nhp : 0 < natTrailingDegree p\n⊢ nextCoeffUp p = coeff p (nat... | [
498,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Topology/Basic.lean | Finset.closure_biUnion | [
{
"state_after": "no goals",
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"tactic": "classical\n ... | [
531,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/Logic/Basic.lean | or_of_or_of_imp_of_imp | [] | [
334,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Order/Bounded.lean | Set.unbounded_le_Ici | [] | [
288,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.id_app | [] | [
67,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Std/Data/Int/DivMod.lean | Int.div_eq_iff_eq_mul_right | [] | [
757,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
755,
11
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Mathlib/RingTheory/PrincipalIdealDomain.lean | isCoprime_of_dvd | [
{
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"state_before": "R : Type u\nM : Type v\ninst✝³ : CommRi... | [
397,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_zero | [
{
"state_after": "no goals",
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"tactic": "simp [Integrable, aestro... | [
649,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_pure | [] | [
647,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
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Mathlib/Data/Vector/Basic.lean | Vector.head_ofFn | [
{
"state_after": "no goals",
"state_before": "n✝ : ℕ\nα : Type u_1\nn : ℕ\nf : Fin (Nat.succ n) → α\n⊢ head (ofFn f) = f 0",
"tactic": "rw [← get_zero, get_ofFn]"
}
] | [
263,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
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Mathlib/Init/Data/Ordering/Lemmas.lean | cmpUsing_eq_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nlt : α → α → Prop\ninst✝ : DecidableRel lt\na b : α\n⊢ (cmpUsing lt a b = Ordering.eq) = (¬lt a b ∧ ¬lt b a)",
"tactic": "simp"
}
] | [
70,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/LinearAlgebra/Ray.lean | sameRay_smul_left_iff_of_ne | [] | [
554,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_self | [
{
"state_after": "no goals",
"state_before": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ c + c ≤ c",
"tactic": "convert mul_le_mul_right' ((nat_lt_aleph0 2).le.trans h) c using 1\n<;> simp [two_mul, mul_eq_self h]"
}
] | [
723,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.of_symm_image_eq | [] | [
548,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Data/Nat/Pairing.lean | iInf_unpair | [] | [
197,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Data/Rel.lean | Rel.image_comp | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nr : Rel α β\ns : Rel β γ\nt : Set α\nz : γ\n⊢ z ∈ image (r • s) t ↔ z ∈ image s (image r t)",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nr : Rel α β\ns : Rel β γ\nt : Set α\n⊢ image (r • s) t = image s (image r t)",
"tac... | [
166,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Topology/Basic.lean | ContinuousAt.preimage_mem_nhds | [] | [
1608,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
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] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.exists_length_eq_zero_iff | [
{
"state_after": "case mp\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\n⊢ (∃ p, length p = 0) → u = v\n\ncase mpr\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\n⊢ u = v → ∃ p, lengt... | [
435,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.natCast_get | [
{
"state_after": "no goals",
"state_before": "x : PartENat\nh : x.Dom\n⊢ ↑(Part.get x h) = x",
"tactic": "exact Part.ext' (iff_of_true trivial h) fun _ _ => rfl"
}
] | [
172,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_union_mul_inter | [] | [
380,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
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Mathlib/Order/Cover.lean | Wcovby.Icc_eq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.17119\ninst✝ : PartialOrder α\na b c✝ : α\nh : a ⩿ b\nc : α\n⊢ c ∈ Icc a b ↔ c ∈ {a, b}",
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"tactic": "ext c"
},
{
"state_after":... | [
177,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Order/RelIso/Basic.lean | RelHom.injective_of_increasing | [] | [
184,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_imI | [] | [
214,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
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Mathlib/Topology/UniformSpace/Separation.lean | idRel_sub_separationRel | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α✝\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\nα : Type u_1\ninst✝ : UniformSpace α\n⊢ idRel ⊆ ⋂₀ (𝓤 α).sets",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α✝\ninst✝² : UniformSpace β\ninst✝¹ ... | [
174,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.prod_mem_prod | [
{
"state_after": "case refine_1\nR : Type u\nι✝ : Type ?u.211911\ninst✝ : CommSemiring R\nI✝ J K L : Ideal R\nι : Type u_1\ns : Finset ι\nI : ι → Ideal R\nx : ι → R\n⊢ (∀ (i : ι), i ∈ ∅ → x i ∈ I i) → ∏ i in ∅, x i ∈ ∏ i in ∅, I i\n\ncase refine_2\nR : Type u\nι✝ : Type ?u.211911\ninst✝ : CommSemiring R\nI✝ J K... | [
470,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_of_le' | [] | [
544,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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Mathlib/Order/Bounds/Basic.lean | upperBounds_singleton | [] | [
642,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
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Mathlib/CategoryTheory/SingleObj.lean | CategoryTheory.SingleObj.id_as_one | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.subset_lieSpan | [
{
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"state_before": "R ... | [
688,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
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Mathlib/Data/Finset/Basic.lean | List.toFinset_replicate_of_ne_zero | [
{
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3314,
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Mathlib/Order/Monotone/Basic.lean | Antitone.comp_antitoneOn | [] | [
667,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.noSibling_tail? | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ Option.map (fun x => x.snd) (deleteMin le s) = some s' → NoSibling s'",
"state_before": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ tail? le s = some s' → NoSibling s'",
"tactic": "simp only [Heap.tail?]"
},
{
"state_afte... | [
112,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
108,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_closure | [] | [
309,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
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Mathlib/Topology/Separation.lean | biInter_basis_nhds | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\nι : Sort u_1\np : ι → Prop\ns : ι → Set α\nx : α\nh : HasBasis (𝓝 x) p s\n⊢ (∀ (i : ι), p i → x ∈ s i) ∧ ∀ (x_1 : α), (∀ (i : ι), p i → x_1 ∈ s i) → x_1 = x",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Topologi... | [
672,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
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Mathlib/Analysis/Convex/Body.lean | ConvexBody.bounded | [] | [
169,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Mathlib/Data/Stream/Init.lean | Stream'.head_map | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_sum_measure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.906802\nγ : Type ?u.906805\nδ : Type ?u.906808\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nm : MeasurableSpace α\nι : Type u_2\nf : α → ℝ≥0∞\nμ : ι → Measure α\n⊢ (⨆ (x : { i // ↑i ≤ fun a => f a }) (s : Finset ι), ∑ i in s, SimpleFunc.lintegral (↑x) (μ i)) =\n ⨆ (s... | [
622,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ Neg.neg '' [[a, b]] = [[-a, -b]]",
"tactic": "simp"
}
] | [
474,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Std/Logic.lean | false_ne_true | [] | [
761,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
761,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | aestronglyMeasurable_derivWithin_Ici | [] | [
801,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | dvd_sub_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11880\ninst✝ : NonUnitalRing α\na b c : α\n⊢ a ∣ b - c ↔ a ∣ c - b",
"tactic": "rw [← dvd_neg (α := α), neg_sub]"
}
] | [
123,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_le | [] | [
1944,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1943,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.natAdd_zero | [
{
"state_after": "case h.h\nn✝ m n : ℕ\nx✝ : Fin n\n⊢ ↑(↑(natAdd 0) x✝) = ↑(↑(RelIso.toRelEmbedding (cast (_ : n = 0 + n))) x✝)",
"state_before": "n✝ m n : ℕ\n⊢ natAdd 0 = RelIso.toRelEmbedding (cast (_ : n = 0 + n))",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h.h... | [
1412,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
1
] |
Mathlib/Logic/Relation.lean | WellFounded.transGen | [] | [
451,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_lt_gt | [] | [
2083,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2081,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Surjective.of_comp_iff' | [] | [
184,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | SubringClass.coeSubtype | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.map_smul | [] | [
232,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
11
] |
Std/Data/List/Lemmas.lean | List.filter_filter | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\np q : α✝ → Bool\na : α✝\nl : List α✝\n⊢ filter p (filter q (a :: l)) = filter (fun a => decide (p a = true ∧ q a = true)) (a :: l)",
"tactic": "by_cases hp : p a <;> by_cases hq : q a <;> simp [hp, hq, filter_filter _ l]"
}
] | [
1237,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1235,
9
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.counit_app | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_induction | [] | [
467,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_smul | [] | [
563,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactSpace.elim_nhds_subcover | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.75608\nπ : ι → Type ?u.75613\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns✝ t✝ : Set α\ninst✝ : CompactSpace α\nU : α → Set α\nhU : ∀ (x : α), U x ∈ 𝓝 x\nt : Finset α\ns : univ ⊆ ⋃ (x : α) (_ : x ∈ t), U x\n⊢ ∃ t, (⋃ (x : α)... | [
730,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coe_eta | [] | [
99,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Set.OrdConnected.measurableSet | [
{
"state_after": "α : Type u_1\nβ : Type ?u.603118\nγ : Type ?u.603121\nγ₂ : Type ?u.603124\nδ : Type ?u.603127\nι : Sort y\ns t u✝ : Set α\ninst✝¹⁶ : TopologicalSpace α\ninst✝¹⁵ : MeasurableSpace α\ninst✝¹⁴ : OpensMeasurableSpace α\ninst✝¹³ : TopologicalSpace β\ninst✝¹² : MeasurableSpace β\ninst✝¹¹ : OpensMeas... | [
561,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_div_of_right_invariant | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulRightInvariant μ\ny : G\n⊢ QuasiMeasurePreserving fun x => (x, y).fst / (x, y).snd",
"st... | [
472,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.emetric_closedBall_nnreal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.165907\nι : Type ?u.165910\ninst✝ : PseudoMetricSpace α\nx : α\nε : ℝ≥0\n⊢ EMetric.closedBall x ↑ε = closedBall x ↑ε",
"tactic": "rw [← Metric.emetric_closedBall ε.coe_nonneg, ENNReal.ofReal_coe_nnreal]"
}
] | [
1220,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.isUnit_resolvent | [] | [
177,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | imageToKernel_comp_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.13034\nV : Type u\ninst✝³ : Category V\ninst✝² : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ng : B ⟶ C\ninst✝¹ : HasKernels V\ninst✝ : HasImages V\nZ : V\nh : Z ⟶ A\nw : f ≫ g = 0\n⊢ (h ≫ f) ≫ g = 0",
"tactic": "simp [w]"
},
{
"state_after"... | [
113,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.coe_inj | [] | [
724,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasAntitoneBasis.map | [] | [
850,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | differentiable_circleMap | [] | [
184,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_inf | [] | [
230,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_mul_left_add_left | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ gcd (n * k + m) n = gcd m n",
"tactic": "rw [gcd_comm, gcd_mul_left_add_right, gcd_comm]"
}
] | [
71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | inv_mul_cancel_right₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.19210\nM₀ : Type ?u.19213\nG₀ : Type u_1\nM₀' : Type ?u.19219\nG₀' : Type ?u.19222\nF : Type ?u.19225\nF' : Type ?u.19228\ninst✝ : GroupWithZero G₀\na✝ b c g h✝ x : G₀\nh : b ≠ 0\na : G₀\n⊢ a * (b⁻¹ * b) = a",
"tactic": "simp [h]"
}
] | [
282,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | AddSubmonoid.iSup_eq_mrange_dfinsupp_sumAddHom | [
{
"state_after": "case a\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : AddCommMonoid γ\nS : ι → AddSubmonoid γ\n⊢ iSup S ≤ AddMonoidHom.mrange (sumAddHom fun i => AddSubmonoid.subtype (S i))\n\ncase a\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → T... | [
1956,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1948,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.getSection_isAmalgamation | [] | [
170,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofMul_mul | [] | [
160,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.ext | [] | [
1466,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithBot.succ_coe | [] | [
1216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.includeRight_apply | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.closure_range | [] | [
96,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Subsingleton.antivaryOn | [] | [
128,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.boxProd_adj_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9064\nG : SimpleGraph α\nH : SimpleGraph β\na₁ : α\nb : β\na₂ : α\n⊢ Adj (G □ H) (a₁, b) (a₂, b) ↔ Adj G a₁ a₂",
"tactic": "simp only [boxProd_adj, and_true, SimpleGraph.irrefl, false_and, or_false]"
}
] | [
63,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Algebra/MulAction.lean | Filter.Tendsto.smul_const | [] | [
96,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_comp | [] | [
1347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Function.Involutive.toPerm_symm | [] | [
1713,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1712,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.toSubmonoid_injective | [] | [
284,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isClassified_of_isPrimitiveClassified | [
{
"state_after": "case intro.intro\nx y z : ℤ\nh : PythagoreanTriple x y z\nm n : ℤ\nH :\n (x = m ^ 2 - n ^ 2 ∧ y = 2 * m * n ∨ x = 2 * m * n ∧ y = m ^ 2 - n ^ 2) ∧\n Int.gcd m n = 1 ∧ (m % 2 = 0 ∧ n % 2 = 1 ∨ m % 2 = 1 ∧ n % 2 = 0)\n⊢ IsClassified h",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x... | [
215,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_eq_finrank_span_row | [
{
"state_after": "case intro\nl : Type ?u.285266\nm : Type u_2\nn : Type u_3\no : Type ?u.285275\nR : Type u_1\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : LinearOrderedField R\ninst✝ : Finite m\nA : Matrix m n R\nval✝ : Fintype m\n⊢ rank A = finrank R { x // x ∈ Submodule.span R (Set.ra... | [
277,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_eq_iff_det_pos | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁴ : LinearOrderedCommRing R\nM : Type u_3\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ne₁ e₂ : Basis ι R M\n⊢ SameRay R (det e₁) (det e₂) ↔ SameRay R (↑(det e₁) ↑e₂ • det e₂) (det e₂)"... | [
225,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_quadratic | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1058825\nha : a ≠ 0\n⊢ ↑2 = 2",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1058825\nha : a ≠ 0\n⊢ degree (↑C a * X ^ 2 + ↑C b * X + ↑C c... | [
1192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1189,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_posPart | [] | [
904,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Ici_mem_atTop | [] | [
59,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Stream.toList_nil | [] | [
373,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
373,
9
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.mem_stepSet_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ σ' : Type v\nM : εNFA α σ\nS : Set σ\nx : List α\ns : σ\na : α\n⊢ s ∈ stepSet M S a ↔ ∃ t, t ∈ S ∧ s ∈ εClosure M (step M t (some a))",
"tactic": "simp_rw [stepSet, mem_iUnion₂, exists_prop]"
}
] | [
81,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.filter | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\np : α → Bool\nl₁ l₂ : List α\ns : l₁ ~ l₂\n⊢ List.filterMap (Option.guard fun x => p x = true) l₁ ~ List.filterMap (Option.guard fun x => p x = true) l₂",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\np : α → Bool\nl₁ l₂ : List α\n... | [
275,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.collectedBasis_coe | [
{
"state_after": "case h\nR : Type u\ninst✝² : Semiring R\nι : Type v\ndec_ι : DecidableEq ι\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nA : ι → Submodule R M\nh : IsInternal A\nα : ι → Type u_2\nv : (i : ι) → Basis (α i) R { x // x ∈ A i }\na : (i : ι) × α i\n⊢ ↑(collectedBasis h v) a = ↑(↑(v ... | [
371,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.dist_comm | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\n⊢ dist x y = dist y x",
"tactic": "simp [dist, @eq_comm _ x y, firstDiff_comm]"
}
] | [
284,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
11
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.exist_finset_disjoint_balls_large_measure | [
{
"state_after": "case inl\nα : Type u_1\ninst✝⁴ : MetricSpace α\nβ : Type u\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α ... | [
673,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
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