file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.self_mem_ordConnectedComponent | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ x ∈ ordConnectedComponent s x ↔ x ∈ s",
"tactic": "rw [mem_ordConnectedComponent, uIcc_self, singleton_subset_iff]"
}
] | [
56,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.toSubgraph.isSpanning | [] | [
607,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
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Mathlib/Algebra/GroupPower/Order.lean | strictAnti_pow | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.230037\nA : Type ?u.230040\nG : Type ?u.230043\nM : Type ?u.230046\nR : Type u_1\ninst✝ : StrictOrderedSemiring R\na x y : R\nn✝ m : ℕ\nh₀ : 0 < a\nh₁ : a < 1\nn : ℕ\n⊢ a ^ (n + 1) < a ^ n",
"tactic": "simpa only [pow_succ, one_mul] using mul_lt_... | [
515,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
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Mathlib/Deprecated/Group.lean | MonoidHom.isMonoidHom_coe | [] | [
136,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | generateFrom_prod_eq | [
{
"state_after": "case a\nα✝ : Type ?u.538256\nα' : Type ?u.538259\nβ✝ : Type ?u.538262\nβ' : Type ?u.538265\nγ : Type ?u.538268\nE : Type ?u.538271\ninst✝⁵ : MeasurableSpace α✝\ninst✝⁴ : MeasurableSpace α'\ninst✝³ : MeasurableSpace β✝\ninst✝² : MeasurableSpace β'\ninst✝¹ : MeasurableSpace γ\nμ μ' : MeasureTheo... | [
133,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/Topology/Algebra/Ring/Ideal.lean | QuotientRing.isOpenMap_coe | [
{
"state_after": "R : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : CommRing R\nN : Ideal R\ninst✝ : TopologicalRing R\ns : Set R\ns_op : IsOpen s\n⊢ IsOpen (↑(mk N) '' s)",
"state_before": "R : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : CommRing R\nN : Ideal R\ninst✝ : TopologicalRing R\n⊢ IsOpenMap... | [
65,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/Analysis/SpecialFunctions/Sqrt.lean | HasFDerivAt.sqrt | [] | [
120,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Init/Propext.lean | Iff.to_eq | [] | [
32,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
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Mathlib/GroupTheory/OrderOfElement.lean | pow_gcd_card_eq_one_iff | [
{
"state_after": "G : Type u\nA : Type v\nx y : G\na b : A\nn m✝ : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Fintype G\nh : x ^ gcd n (Fintype.card G) = 1\nm : ℕ\nhm : n = gcd n (Fintype.card G) * m\n⊢ x ^ n = 1",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝² : Group G\n... | [
1024,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
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Mathlib/Data/List/Pairwise.lean | List.Pairwise.imp_of_mem | [
{
"state_after": "no goals",
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"tactic": "constructor"
},
{
"state_after": "case cons.a\nα : Type ... | [
74,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Data/Finset/Basic.lean | Finset.inter_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.183003\nγ : Type ?u.183006\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t t₁ t₂ u v : Finset α\na b : α\ns : Finset α\nx✝ : α\n⊢ x✝ ∈ s ∧ x✝ ∈ ∅ ↔ x✝ ∈ ∅",
"tactic": "simp"
}
] | [
1635,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1634,
1
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.uniformContinuous_toFun | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44602\nι : Type ?u.44605\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n⊢ ∀ (i : α), UniformContinuous fun x => ↑toFun x i",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44602\nι : Type ?u.44605\ns s' : Set α\nx : ... | [
493,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_finset_preimage_atTop_atTop | [] | [
1395,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
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Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.isSheaf_yoneda' | [
{
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67,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
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Mathlib/Algebra/Order/Group/Abs.lean | sub_le_of_abs_sub_le_left | [] | [
293,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_epsilon | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_apply_apply_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2369326\nα : Type u_1\nβ : Type ?u.2369332\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y : α\nf : Perm α\nx : α\n⊢ ↑(cycleOf f x) (↑f x) = ↑f (↑f x)",
"tactic": "convert cycleOf_apply_apply_pow_self f x 1 using 1"
}
] | [
1032,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/Topology/Separation.lean | Embedding.t1Space | [] | [
596,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
11
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv' | [] | [
464,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.coe_comp_orderHom | [] | [
189,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/Order/Zorn.lean | zorn_nonempty_preorder₀ | [
{
"state_after": "case refine_2\nα : Type u_1\nβ : Type ?u.5559\nr : α → α → Prop\nc : Set α\ninst✝ : Preorder α\ns : Set α\nih :\n ∀ (c : Set α), c ⊆ s → IsChain (fun x x_1 => x ≤ x_1) c → ∀ (y : α), y ∈ c → ∃ ub, ub ∈ s ∧ ∀ (z : α), z ∈ c → z ≤ ub\nx : α\nhxs : x ∈ s\nH : ∃ m, m ∈ {y | y ∈ s ∧ x ≤ y} ∧ ∀ (z ... | [
145,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Set.algebraMap_mem_centralizer | [] | [
1387,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
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Mathlib/Data/Finsupp/AList.lean | Finsupp.toAList_keys_toFinset | [
{
"state_after": "case a\nα : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nf : α →₀ M\na✝ : α\n⊢ a✝ ∈ List.toFinset (AList.keys (toAList f)) ↔ a✝ ∈ f.support",
"state_before": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nf : α →₀ M\n⊢ List.toFinset (AList.keys (toA... | [
47,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/Order/Filter/Basic.lean | Filter.eventually_of_forall | [] | [
1102,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\nhf : Function.Surjective ↑(Quotient.mk I)\n⊢ jacobson I = I ↔ jacobson ⊥ = ⊥",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\n⊢ jacobson I = I ↔ jacobson ⊥ = ⊥",
... | [
286,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.length_think | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nh : Terminates s\n⊢ length (think s) ≤ length s + 1\n\ncase a\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nh : Terminates s\n⊢ length s + 1 ≤ length (think s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns ... | [
570,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.I_mul_im | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (I * z).im = z.re",
"tactic": "simp"
}
] | [
350,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_one_div_le_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0\nz : ℝ\nhz : 0 < z\n⊢ x ^ (1 / z) ≤ y ↔ x ≤ y ^ z",
"tactic": "rw [← rpow_le_rpow_iff hz, rpow_self_rpow_inv hz.ne']"
}
] | [
165,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/MinMax.lean | MonotoneOn.map_max | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\nhf : MonotoneOn f s\nha : a ∈ s\nhb : b ∈ s\n⊢ f (max a b) = max (f a) (f b)",
"tactic": "cases' le_total a b with h h <;>\n simp only [max_eq_right, m... | [
241,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.const_smul | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝³ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type u_3\ninst✝² : NormedRing 𝕜\ninst✝¹ : (i : α) → Module 𝕜 (E i)\ninst✝ : ∀ (i : α), BoundedSMul 𝕜 (E i)\nf : (i : α) → E i\nc : 𝕜\nhf : Memℓp f 0\n⊢ Memℓp (c • f) 0\n\ncase inr.inl\nα :... | [
284,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.add | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nE' : Type ?u.45775\nF : Type ?u.45778\nG : Type ?u.45781\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : NormedAddCommGroup G\ninst✝² : InnerProductSpace �... | [
99,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_disjointed_spanningSetsIndex | [] | [
3512,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3510,
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] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.max | [] | [
622,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.zero_apply | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | comp_tendsto_lim | [] | [
59,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
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] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Kernels.lean | CategoryTheory.Limits.preserves_cokernel_iso_comp_cokernel_map | [
{
"state_after": "no goals",
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230,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.mk_eq_of_comm | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝¹ : Category D\nB A : C\nX : Subobject B\nf : A ⟶ B\ninst✝ : Mono f\ni : A ≅ underlying.obj X\nw : i.hom ≫ arrow X = f\n⊢ i.symm.hom ≫ f = arrow X",
"tactic": "rw [Iso.symm_hom, Iso.inv_comp_eq,... | [
304,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.elim_comp_inl | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_union_distrib_right | [] | [
1761,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1760,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.aux_inj_roots_of_min_poly | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subset.antisymm_iff | [] | [
376,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.lt_power_cof | [
{
"state_after": "case intro.intro\nα✝ : Type ?u.171374\nr✝ : α✝ → α✝ → Prop\nc : Cardinal\nα : Type u\nh : ℵ₀ ≤ Quotient.mk isEquivalent α\nr : α → α → Prop\nwo : IsWellOrder α r\nre : ord (#α) = type r\n⊢ Quotient.mk isEquivalent α < Quotient.mk isEquivalent α ^ Ordinal.cof (ord (Quotient.mk isEquivalent α))"... | [
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33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.dual_id | [] | [
882,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_id | [
{
"state_after": "case a.h\nR : Type u_1\ninst✝⁷ : CommSemiring R\nl : Type ?u.1742508\nm : Type ?u.1742511\nn : Type u_2\ninst✝⁶ : Fintype n\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq n\nM₁ : Type u_3\nM₂ : Type ?u.1742535\ninst✝³ : AddCommMonoid M₁\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₁\ninst✝ : Modu... | [
624,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.lt_inducedMap_iff | [
{
"state_after": "no goals",
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229,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
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Mathlib/Logic/Basic.lean | forall_prop_congr' | [] | [
922,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.annihilator_smul | [] | [
174,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxOn.comp_mapsTo | [] | [
436,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_subtype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.16758\ns✝ t : Finset α\nf : α → β\nn : ℕ\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\n⊢ card (Finset.subtype p s) = card (filter p s)",
"tactic": "simp [Finset.subtype]"
}
] | [
258,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactConvNhd_mem_comp | [] | [
116,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/RingTheory/Noetherian.lean | IsNoetherian.bijective_of_surjective_endomorphism | [] | [
443,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.add | [] | [
148,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.inverseAssociator_map_inr_inl | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.comap_le_comap_iff | [
{
"state_after": "case intro.refl\nR : Type u_3\nR₁ : Type ?u.1263750\nR₂ : Type u_2\nR₃ : Type ?u.1263756\nR₄ : Type ?u.1263759\nS : Type ?u.1263762\nK : Type ?u.1263765\nK₂ : Type ?u.1263768\nM : Type u_4\nM' : Type ?u.1263774\nM₁ : Type ?u.1263777\nM₂ : Type u_1\nM₃ : Type ?u.1263783\nM₄ : Type ?u.1263786\nN... | [
1430,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.map_mul_left_eq_self | [] | [
87,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | midpoint_le_midpoint | [] | [
115,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_diff_le_iff_le_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25758\nγ : Type ?u.25761\nδ : Type ?u.25764\nι : Type ?u.25767\nR : Type ?u.25770\nR' : Type ?u.25773\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nhs : MeasurableSet s\nhst : s ⊆ t\nhs' : ↑↑μ s ≠ ⊤\nε : ℝ≥0∞\n⊢ ↑↑μ (t... | [
260,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_eventually_congr_set' | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ ... | [
924,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.closure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44868\nδ : Type ?u.44871\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set α\nt : Set β\nx✝ : α\n... | [
590,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_of_subsingleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.51067\nE : Type ?u.51070\nF : Type ?u.51073\nG : Type ?u.51076\nE' : Type u_1\nF' : Type u_3\nG' : Type ?u.51085\nE'' : Type ?u.51088\nF'' : Type ?u.51091\nG'' : Type ?u.51094\nR : Type ?u.51097\nR' : Type ?u.51100\n𝕜 : Type ?u.51103\n... | [
278,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_comp | [
{
"state_after": "case h\nR : Type ?u.950251\nR' : Type ?u.950254\n𝕜 : Type u_3\n𝕜₂ : Type u_1\n𝕜₃ : Type ?u.950263\n𝕝 : Type ?u.950266\nE : Type u_4\nE₂ : Type u_2\nE₃ : Type ?u.950275\nF : Type ?u.950278\nG : Type ?u.950281\nι : Type ?u.950284\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ :... | [
802,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_zero | [] | [
783,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_add | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : AddMonoid R\nΓ' : Type u_2\ninst✝ : PartialOrder Γ'\nf : Γ ↪o Γ'\nx y : HahnSeries Γ R\ng : Γ'\n⊢ coeff (embDomain f (x + y)) g = coeff (embDomain f x + embDomain f y) g",
"state_before": "Γ : Type u_1\nR : Type u_... | [
424,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Order/RelClasses.lean | right_iff_left_not_left | [] | [
583,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | AntilipschitzWith.mul_div_lipschitzWith | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1212646\n𝕜 : Type ?u.1212649\nα : Type u_1\nι : Type ?u.1212655\nκ : Type ?u.1212658\nE : Type u_2\nF : Type ?u.1212664\nG : Type ?u.1212667\ninst✝² : SeminormedCommGroup E\ninst✝¹ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ninst✝ : ... | [
1905,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1903,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.exists_lt_of_tendsto_atTop | [
{
"state_after": "case intro\nι : Type ?u.68133\nι' : Type ?u.68136\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.68145\ninst✝² : SemilatticeSup α\ninst✝¹ : Preorder β\ninst✝ : NoMaxOrder β\nu : α → β\nh : Tendsto u atTop atTop\na : α\nb b' : β\nhb' : b < b'\n⊢ ∃ a', a' ≥ a ∧ b < u a'",
"state_before": "ι : Type... | [
530,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Init/Algebra/Order.lean | ne_iff_lt_or_gt | [] | [
364,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.scalar.commute | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.487731\nm : Type ?u.487734\nn : Type u_1\no : Type ?u.487740\nm' : o → Type ?u.487745\nn' : o → Type ?u.487750\nR : Type ?u.487753\nS : Type ?u.487756\nα : Type v\nβ : Type w\nγ : Type ?u.487763\ninst✝² : CommSemiring α\ninst✝¹ : Fintype n\ninst✝ : D... | [
1294,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_coe_ennreal | [] | [
453,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.eq_of_card_le_one_of_prod_eq | [
{
"state_after": "ι : Type ?u.793618\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nhc : card s ≤ 1\nf : α → β\nb : β\nh : ∏ x in s, f x = b\nx : α\nhx : x ∈ s\n⊢ f x = b",
"state_before": "ι : Type ?u.793618\nβ : Type u\nα : Type v\nγ : Ty... | [
1643,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1631,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.traverse_pure | [] | [
645,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.CoverPreserving.comp | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA : Type u₃\ninst✝ : Category A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology A\nF : C ⥤ D\nhF : CoverPreserving J K F\nG : D ⥤ A\nhG : CoverPreserving K L G\nU✝ : C\nS✝ : Sieve U✝\nhS : S✝ ... | [
81,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.divInt_mul_divInt | [
{
"state_after": "no goals",
"state_before": "n₁ n₂ d₁ d₂ : Int\nz₁ : d₁ ≠ 0\nz₂ : d₂ ≠ 0\n⊢ n₁ /. d₁ * (n₂ /. d₂) = n₁ * n₂ /. (d₁ * d₂)",
"tactic": "rcases Int.eq_nat_or_neg d₁ with ⟨_, rfl | rfl⟩ <;>\nrcases Int.eq_nat_or_neg d₂ with ⟨_, rfl | rfl⟩ <;>\nsimp_all [divInt_neg', Int.mul_neg, Int.ofNat_m... | [
283,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
279,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.succ_dvd_centralBinom | [
{
"state_after": "n : ℕ\nh_s : coprime (n + 1) (2 * n + 1)\n⊢ n + 1 ∣ centralBinom n",
"state_before": "n : ℕ\n⊢ n + 1 ∣ centralBinom n",
"tactic": "have h_s : (n + 1).coprime (2 * n + 1) := by\n rw [two_mul, add_assoc, coprime_add_self_right, coprime_self_add_left]\n exact coprime_one_left n"
},
... | [
140,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Sbtw.angle₁₃₂_eq_zero | [] | [
382,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sigmaToiUnion_surjective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.299540\nι : Sort ?u.299543\nι' : Sort ?u.299546\nι₂ : Sort ?u.299549\nκ : ι → Sort ?u.299554\nκ₁ : ι → Sort ?u.299559\nκ₂ : ι → Sort ?u.299564\nκ' : ι' → Sort ?u.299569\nt : α → Set β\nb : β\nhb : b ∈ ⋃ (i : α), t i\n⊢ ∃ a... | [
2172,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2168,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.Prime.properDivisors | [
{
"state_after": "no goals",
"state_before": "n p : ℕ\npp : Prime p\n⊢ Nat.properDivisors p = {1}",
"tactic": "rw [← erase_insert properDivisors.not_self_mem, insert_self_properDivisors pp.ne_zero,\n pp.divisors, pair_comm, erase_insert fun con => pp.ne_one (mem_singleton.1 con)]"
}
] | [
323,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.fixedPoints_eq_center | [
{
"state_after": "case h\nα : Type ?u.77795\nM : Type ?u.77798\nG : Type u_1\nG₀ : Type ?u.77804\nR : Type ?u.77807\nK : Type ?u.77810\ninst✝ : Group G\nx : G\n⊢ x ∈ fixedPoints (ConjAct G) G ↔ x ∈ ↑(center G)",
"state_before": "α : Type ?u.77795\nM : Type ?u.77798\nG : Type u_1\nG₀ : Type ?u.77804\nR : Typ... | [
307,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_perm | [] | [
117,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.restrict_mass | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝⁴ : MeasurableSpace Ω\nR : Type ?u.39681\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nμ : FiniteMeasure Ω\nA : Set Ω\n⊢ mass (restrict μ A) = (fun s => ENNReal.toNNReal (↑↑↑μ... | [
297,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_le_add_iff_le_left | [] | [
68,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
67,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_map_restrict_ae_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.579235\nγ : Type ?u.579238\nδ : Type ?u.579241\nι : Type ?u.579244\nR : Type ?u.579247\nR' : Type ?u.579250\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β✝\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : ... | [
2863,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2861,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | mul_finprod_cond_ne | [
{
"state_after": "α : Type u_1\nβ : Type ?u.370818\nι : Type ?u.370821\nG : Type ?u.370824\nM : Type u_2\nN : Type ?u.370830\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na✝ b : α\ns t : Set α\na : α\nhf : Set.Finite (mulSupport f)\n⊢ (f a * ∏ᶠ (i : α) (_ : i ≠ a), f i) = ∏ i in Finite.toFinset hf,... | [
1112,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_iInf | [
{
"state_after": "α β : Type u\nι : Sort u_1\nf : ι → Cardinal\n⊢ lift (sInf (range f)) = sInf (range fun i => lift (f i))",
"state_before": "α β : Type u\nι : Sort u_1\nf : ι → Cardinal\n⊢ lift (iInf f) = ⨅ (i : ι), lift (f i)",
"tactic": "unfold iInf"
},
{
"state_after": "case h.e'_3.h.e'_3\nα... | [
1108,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_source | [] | [
822,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Memℒp.integrable_norm_rpow' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.835159\nδ : Type ?u.835162\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝³ : MeasurableSpace δ\ninst✝² : NormedAddCommGroup β\ninst✝¹ : NormedAddCommGroup γ\ninst✝ : IsFiniteMeasure μ\nf : α → β\np : ℝ≥0∞\nhf : Memℒp f p\nh_zero : p = 0\n⊢ Inte... | [
514,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast_append' | [
{
"state_after": "case nil\nι : Type ?u.30314\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nh : l₂ ≠ []\n⊢ getLast ([] ++ l₂) (_ : [] ++ l₂ ≠ []) = getLast l₂ h\n\ncase cons\nι : Type ?u.30314\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nh : l₂ ≠ []\nhead✝ : α\ntai... | [
717,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.head_nil | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Topology/LocallyFinite.lean | Equiv.locallyFinite_comp_iff | [] | [
207,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.invOn | [] | [
185,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
11
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_const_vadd_iff | [] | [
189,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.subset_pointwise_smul_iff | [] | [
131,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_eq_iff_re | [
{
"state_after": "case intro\nr : ℝ\n⊢ ↑(↑r).re = ↑r",
"state_before": "z : ℂ\n⊢ (∃ r, z = ↑r) → ↑z.re = z",
"tactic": "rintro ⟨r, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nr : ℝ\n⊢ ↑(↑r).re = ↑r",
"tactic": "simp [ofReal']"
}
] | [
552,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Data/Bundle.lean | Bundle.sigma_mk_eq_totalSpaceMk | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | mul_bit1 | [
{
"state_after": "α : Type ?u.271140\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : NonAssocRing R\nn r : R\n⊢ r * (bit0 n + 1) = 2 • (r * n) + r",
"state_before": "α : Type ?u.271140\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB :... | [
577,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Set/Basic.lean | Set.singleton_ne_empty | [] | [
1304,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.div_neBot_iff | [] | [
471,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tmul_zero | [] | [
150,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1651966\nE : Type u_2\nF : Type ?u.1651972\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nhf : IntegrableOn f s\nh't : ∀ᵐ (x : α) ∂μ, ¬x ∈ s → f x = 0\n⊢ IntegrableOn f univ",
"state_before": "α : Type u_1\nβ ... | [
348,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Std/Data/List/Lemmas.lean | List.get_append | [
{
"state_after": "α : Type u_1\na : α\nl x✝ : List α\nn : Nat\nh : n + 1 < length (a :: l)\n⊢ get (List.append l x✝) { val := Nat.add n 0, isLt := (_ : succ (Nat.add n 0) ≤ length (List.append l x✝)) } =\n get l { val := Nat.add n 0, isLt := (_ : succ (Nat.add n 0) ≤ length l) }",
"state_before": "α : Ty... | [
593,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
590,
1
] |
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