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/Algebra/Ring/BooleanRing.lean | add_self | [
{
"state_after": "α : Type u_1\nβ : Type ?u.543\nγ : Type ?u.546\ninst✝ : BooleanRing α\na b : α\nthis : a + a = a + a + (a + a)\n⊢ a + a = 0",
"state_before": "α : Type u_1\nβ : Type ?u.543\nγ : Type ?u.546\ninst✝ : BooleanRing α\na b : α\n⊢ a + a = 0",
"tactic": "have : a + a = a + a + (a + a) :=\n c... | [
76,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_abs | [
{
"state_after": "case pos\nx✝ y x : ℝ\nh : x = 0\n⊢ log (abs x) = log x\n\ncase neg\nx✝ y x : ℝ\nh : ¬x = 0\n⊢ log (abs x) = log x",
"state_before": "x✝ y x : ℝ\n⊢ log (abs x) = log x",
"tactic": "by_cases h : x = 0"
},
{
"state_after": "no goals",
"state_before": "case pos\nx✝ y x : ℝ\nh :... | [
110,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.corec_eq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : β → Option (α × β)\nb : β\n⊢ Option.map\n (fun a' =>\n (a',\n tail\n { val := corec' (Corec.f f) (some b),\n property :=\n (_ : ∀ {n : ℕ}, corec' (Corec.f f) (some b) n = none → corec' (Corec.f ... | [
359,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.map₂_coe_coe | [] | [
724,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.frequently_lt_rpow_neg | [
{
"state_after": "case intro.intro\np q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nhlt : q < p\nC : ℝ\n_hC₀ : 0 < C\nhC : ∃ᶠ (n : ℕ) in atTop, 1 ≤ n ∧ ∃ m, x ≠ ↑m / ↑n ∧ abs (x - ↑m / ↑n) < C / ↑n ^ p\n⊢ ∃ᶠ (n : ℕ) in atTop, ∃ m, x ≠ ↑m / ↑n ∧ abs (x - ↑m / ↑n) < ↑n ^ (-q)",
"state_before": "p q x... | [
111,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Set/Finite.lean | Set.exists_finite_iff_finset | [] | [
993,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.pair_lt_pair_right | [
{
"state_after": "case pos\na b₁ b₂ : ℕ\nh : b₁ < b₂\nh₁ : a < b₁\n⊢ b₁ * b₁ + a < if a < b₂ then b₂ * b₂ + a else a * a + (a + b₂)\n\ncase neg\na b₁ b₂ : ℕ\nh : b₁ < b₂\nh₁ : ¬a < b₁\n⊢ a * a + (a + b₁) < if a < b₂ then b₂ * b₂ + a else a * a + (a + b₂)",
"state_before": "a b₁ b₂ : ℕ\nh : b₁ < b₂\n⊢ pair a... | [
152,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/List/Basic.lean | List.modifyNth_eq_take_cons_drop | [
{
"state_after": "ι : Type ?u.220838\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\nn : ℕ\nl : List α\nh : n < length l\n⊢ take n l ++ modifyHead f (get l { val := n, isLt := h } :: drop (n + 1) l) =\n take n l ++ f (get l { val := n, isLt := h }) :: drop (n + 1) l",
"state_b... | [
2288,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2286,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | IsFractional.pow | [] | [
526,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_le_one' | [] | [
63,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.neg_apply | [] | [
901,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | norm_smul | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\ninst✝³ : NormedDivisionRing α\ninst✝² : SeminormedAddGroup β\ninst✝¹ : MulActionWithZero α β\ninst✝ : BoundedSMul α β\nr : α\nx : β\nh : r = 0\n⊢ ‖r • x‖ = ‖r‖ * ‖x‖\n\ncase neg\nα : Type u_2\nβ : Type u_1\ninst✝³ : NormedDivisionRing α\ninst✝² : Seminorme... | [
99,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_iff_integrable_of_support_subset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1654027\nE : Type u_2\nF : Type ?u.1654033\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nh1s : support f ⊆ s\nh : IntegrableOn f s\n⊢ Integrable f",
"state_before": "α : Type u_1\nβ : Type ?u.1654027\nE : Typ... | [
363,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\n⊢ Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂",
"state_before": "V : Type u_1\nP : Type u_2... | [
468,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.zero_testBit | [
{
"state_after": "no goals",
"state_before": "i : ℕ\n⊢ testBit 0 i = false",
"tactic": "simp only [testBit, shiftr_zero, bodd_zero]"
}
] | [
73,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.mul_coe | [] | [
278,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_self | [] | [
410,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_inf | [] | [
661,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_bot | [] | [
559,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.forall | [
{
"state_after": "case H\nα : Type u_1\nβ : Type ?u.6230\nR S T : α → α → Prop\na : α\nl : List α\nhR : Symmetric R\nhl : Pairwise R l\n⊢ Symmetric fun x y => x ≠ y → R x y\n\ncase H₁\nα : Type u_1\nβ : Type ?u.6230\nR S T : α → α → Prop\na : α\nl : List α\nhR : Symmetric R\nhl : Pairwise R l\n⊢ ∀ (x : α), x ∈ ... | [
148,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_sum | [] | [
658,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.substructureEquivMap_apply | [] | [
967,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | uniformCauchySeqOnFilter_of_fderiv | [
{
"state_after": "ι : Type u_3\nl : Filter ι\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx : E\nhf' : Uni... | [
166,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Convex/Between.lean | affineSegment_vadd_const_image | [] | [
101,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.mono | [] | [
239,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.aemeasurable | [] | [
65,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
11
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.comp_injective | [] | [
371,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_inter | [] | [
1848,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1847,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.card_support_conj | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3040728\nα : Type u_1\nβ : Type ?u.3040734\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ τ : Perm α\n⊢ card (support (σ * τ * σ⁻¹)) = card (support τ)",
"tactic": "simp"
}
] | [
1766,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.prod_topology | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nX Y : TopCat\nhomeo : ↑(X ⨯ Y) ≃ₜ ↑(of (↑X × ↑Y)) := homeoOfIso (prodIsoProd X Y)\n⊢ (X ⨯ Y).str = induced ((forget TopCat).map prod.fst) X.str ⊓ induced ((forget TopCat).map prod.snd) Y.str",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nX Y : ... | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/List/Basic.lean | List.get_succ_scanl | [] | [
2670,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2666,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.sup_mul_inf | [
{
"state_after": "R : Type ?u.886660\nA : Type u_1\nK : Type ?u.886666\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : IsDedekindDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nI J : Ideal A\nthis : DecidableEq (Ideal A) := Classical.decEq (Ideal A)\n⊢ (I ⊔... | [
853,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.compl_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.144485\nγ : Type ?u.144488\nι : Sort ?u.144491\nι' : Sort ?u.144494\nι₂ : Sort ?u.144497\nκ : ι → Sort ?u.144502\nκ₁ : ι → Sort ?u.144507\nκ₂ : ι → Sort ?u.144512\nκ' : ι' → Sort ?u.144517\nS : Set (Set α)\nx : α\n⊢ x ∈ (⋃₀ S)ᶜ ↔ x ∈ ⋂₀... | [
1239,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_span | [
{
"state_after": "case refine_1\nR : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nrc : RingHomClass F R S\nf✝ : F\nI J : Ideal R\nK L : Ideal S\nG : Type ?u.756873\nrcg : RingHomClass G S R\nf : F\ns : Set R\n⊢ ↑f '' s ⊆ ↑(map f (span s))\n\ncase refine_2\nR : Type u\nS : Type v\nF... | [
1417,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1413,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.ext | [] | [
602,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_ne_zero' | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sqrt x ≠ 0 ↔ 0 < x",
"tactic": "rw [← not_le, not_iff_not, sqrt_eq_zero']"
}
] | [
347,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_apply_eq_of_ne_zero | [] | [
63,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | supsSupHom_apply | [] | [
994,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.smul_def | [] | [
296,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | equiv_lpPiLp_norm | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : Fintype α\nf : { x // x ∈ lp E 0 }\n⊢ ‖↑Equiv.lpPiLp f‖ = ‖f‖\n\ncase inr.inl\nα : Type u_1\nE : α → Type u_2\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : Fintype α\nf : { x // x ∈ lp E ⊤ }\... | [
82,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | generateFrom_generatePiSystem_eq | [
{
"state_after": "case a.h\nα : Type u_1\ng : Set (Set α)\n⊢ ∀ (t : Set α), t ∈ generatePiSystem g → MeasurableSet t\n\ncase a.h\nα : Type u_1\ng : Set (Set α)\n⊢ ∀ (t : Set α), t ∈ g → MeasurableSet t",
"state_before": "α : Type u_1\ng : Set (Set α)\n⊢ generateFrom (generatePiSystem g) = generateFrom g",
... | [
275,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_emod_right | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a * b % a = 0",
"tactic": "rw [Int.mul_comm, mul_emod_left]"
}
] | [
471,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
9
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.inf_le' | [] | [
1072,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_top_le_iff | [] | [
895,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Std/Logic.lean | forall_congr' | [] | [
374,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
373,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.Stable.exists_pow_smul_eq | [
{
"state_after": "case intro\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nn₀ : ℕ\nhn : ∀ (n : ℕ), n ≥ n₀ → I • N F n = N F (n + 1)\n⊢ ∃ n₀, ∀ (k : ℕ), N F (n₀ + k) = I ^ k • N F n₀",
"state_before": "R M : Type u\ninst✝² : CommRing R\ni... | [
223,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | achart_def | [] | [
563,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Order/RelIso/Basic.lean | Surjective.wellFounded_iff | [
{
"state_after": "case refine_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.15958\nδ : Type ?u.15961\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nu : δ → δ → Prop\nf : α → β\nhf : Surjective f\no : ∀ {a b : α}, r a b ↔ s (f a) (f b)\n⊢ β → α\n\ncase refine_2\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.15958... | [
199,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/Separation.lean | totallySeparatedSpace_of_t1_of_basis_clopen | [
{
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1926,
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Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_convexHull_of_balanced | [
{
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414,
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407,
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Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.toInvSubmonoid_mul | [] | [
74,
69
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73,
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Mathlib/Data/Set/NAry.lean | Set.image_image2 | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.trans | [] | [
2392,
92
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2392,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.pred_zero | [] | [
200,
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199,
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Mathlib/Deprecated/Subgroup.lean | Subgroup.isSubgroup | [] | [
765,
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762,
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Mathlib/Data/Set/Basic.lean | Set.Subset.refl | [] | [
355,
55
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_nsmul | [] | [
102,
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101,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Ico_eq_integral_Ioo' | [] | [
627,
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Mathlib/Data/Int/Sqrt.lean | Int.sqrt_nonneg | [] | [
40,
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Mathlib/Data/Finset/Powerset.lean | Finset.mem_powersetLen | [
{
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207,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.bijective | [] | [
639,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioc | [
{
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] | [
627,
80
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Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_eq_biInter_inter | [] | [
211,
97
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Mathlib/Algebra/Group/Prod.lean | MulHom.coe_prod | [] | [
348,
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff_of_eventuallyEq | [] | [
416,
63
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413,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto | [
{
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... | [
765,
40
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_comp_comm | [
{
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261,
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253,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.le_op_norm_mul_pow_card_of_le | [
{
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mul_inv_left | [
{
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.one_im | [
{
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}
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164,
67
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164,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.coe_inj | [] | [
150,
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149,
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Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.setSeq_mono | [] | [
661,
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660,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.lt_def | [] | [
542,
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Mathlib/Control/Traversable/Lemmas.lean | Traversable.traverse_comp | [
{
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124,
28
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120,
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.one_mem_boundary | [] | [
76,
70
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76,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.set_walk_self_length_zero_eq | [
{
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Std/Data/List/Lemmas.lean | List.exists_of_eraseP | [
{
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{
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953,
57
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_eq_bot_iff | [
{
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2844,
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Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augment_d_zero_one | [] | [
277,
6
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275,
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Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integrableOn_Ioi_cpow_of_lt | [
{
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100,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_le_toIcoMod_add | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp a b ≤ toIocDiv hp a b + 1",
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712,
49
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709,
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Mathlib/Data/Fintype/Card.lean | not_surjective_finite_infinite | [] | [
1180,
57
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1179,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableOn_const | [] | [
1109,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
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Mathlib/LinearAlgebra/AffineSpace/MidpointZero.lean | lineMap_one_half | [
{
"state_after": "no goals",
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}
] | [
34,
32
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32,
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Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.C | [] | [
109,
45
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108,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Mem.ext | [] | [
288,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
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Mathlib/Data/Finset/Sym.lean | Finset.sym_univ | [] | [
209,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.face_points' | [] | [
847,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/NAry.lean | Filter.le_map₂_iff | [] | [
102,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.adjoin_X | [
{
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180,
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Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.curry_id_eq_coev | [
{
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"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nA B X X' Y Y... | [
244,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Algebraic.lean | Algebra.isAlgebraic_iff | [
{
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.card_eq_or_dvd | [
{
"state_after": "case inl\np : ℕ\nG : Type u_1\ninst✝ : Group G\nhG : IsPGroup p G\nhp : Fact (Nat.Prime p)\nval✝ : Fintype G\n⊢ Nat.card G = 1 ∨ p ∣ Nat.card G\n\ncase inr\np : ℕ\nG : Type u_1\ninst✝ : Group G\nhG : IsPGroup p G\nhp : Fact (Nat.Prime p)\nval✝ : Infinite G\n⊢ Nat.card G = 1 ∨ p ∣ Nat.card G",
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156,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
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Mathlib/Topology/Algebra/Monoid.lean | ContinuousOn.pow | [] | [
619,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.card_image_polynomial_eval | [
{
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75,
37
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.of_forall_diff_eq_zero | [] | [
339,
72
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337,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.isoSourceOfSelf_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf g : X ⟶ Y\n⊢ 𝟙 X ≫ f = 𝟙 X ≫ f",
"tactic": "simp"
},
{
"state_after": "case h\nC : Type u\ninst✝ : Category C\nX Y : C\nf g : X ⟶ Y\n⊢ (isoSourceOfSelf f).inv ≫ ι f f = lift (𝟙 X) (_ : 𝟙 X ≫ f = 𝟙 X ≫ f... | [
917,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | AffineEquiv.map_midpoint | [] | [
62,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | lebesgue_number_lemma_of_metric_sUnion | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.453997\nι : Type ?u.454000\ninst✝ : PseudoMetricSpace α\ns : Set α\nc : Set (Set α)\nhs : IsCompact s\nhc₁ : ∀ (t : Set α), t ∈ c → IsOpen t\nhc₂ : s ⊆ ⋃ (i : ↑c), ↑i\n⊢ ∃ δ, δ > 0 ∧ ∀ (x : α), x ∈ s → ∃ t, t ∈ c ∧ ball x δ ⊆ t",
"state_before": "α : Typ... | [
2283,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2281,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_ofFn | [
{
"state_after": "no goals",
"state_before": "n✝ : ℕ\nα : Type u_1\nn : ℕ\nf : Fin (n + 1) → α\n⊢ toList (ofFn f) = List.ofFn f",
"tactic": "rw [ofFn, List.ofFn_succ, toList_cons, toList_ofFn]"
}
] | [
81,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
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