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/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.contDiffOn_extend_coord_change | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_4\nM : Type u_2\nH : Type u_1\nE' : Type ?u.174952\nM' : Type ?u.174955\nH' : Type ?u.174958\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\nf f' : LocalHomeomorp... | [
1000,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_C_ite | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\na : R\n⊢ degree (↑C a) = if a = 0 then ⊥ else 0",
"tactic": "split_ifs with h <;> simp only [h, map_zero, degree_zero, degree_C, Ne.def, not_false_iff]"
}
] | [
536,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_div_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.74483\nα : Type u_1\nβ : Type ?u.74489\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 ≤ a\nhb₀ : 0 < b\nhb₁ : b ≤ 1\n⊢ a ≤ a / b",
"tactic": "simpa only [div_one] using div_le_div_of_le_left ha hb₀ hb₁"
}
] | [
421,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.78498\nα : Type u_1\nβ : Type ?u.78504\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ 1 / a < b ↔ 1 / b < a",
"tactic": "simpa using inv_lt ha hb"
}
] | [
439,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_ne_top_of_nonneg | [] | [
423,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.closure_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nx : PrimeSpectrum R\n⊢ closure {x} = zeroLocus ↑x.asIdeal",
"tactic": "rw [← zeroLocus_vanishingIdeal_eq_closure, vanishingIdeal_singleton]"
}
] | [
479,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Int.cast_prod | [] | [
2256,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2254,
1
] |
Mathlib/Topology/SubsetProperties.lean | exists_compact_between | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.147975\nπ : ι → Type ?u.147980\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nhα : LocallyCompactSpace α\nK U : Set α\nhK : IsCompact K\nhU : IsOpen U\nh_KU : K ⊆ U\nV : ↑K → Set α\nhVc : ∀ (x : ↑K), IsCompact (V x)\nhxV : ∀ (x : ↑K),... | [
1176,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaUncurry_single | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.651005\nα : ι → Type ?u.651010\nδ : (i : ι) → α i → Type v\ninst✝² : (i : ι) → (j : α i) → Zero (δ i j)\ninst✝¹ : (i : ι) → DecidableEq (α i)\ninst✝ : (i... | [
1594,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
Mathlib/Algebra/Invertible.lean | invertible_unique | [
{
"state_after": "case hac\nα✝ α : Type u\ninst✝² : Monoid α\na b : α\ninst✝¹ : Invertible a\ninst✝ : Invertible b\nh : a = b\n⊢ a * ⅟b = 1",
"state_before": "α✝ α : Type u\ninst✝² : Monoid α\na b : α\ninst✝¹ : Invertible a\ninst✝ : Invertible b\nh : a = b\n⊢ ⅟a = ⅟b",
"tactic": "apply invOf_eq_right_in... | [
161,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq | [
{
"state_after": "case intro.intro\nι : Type u_1\nI J J₁✝ J₂✝ : Box ι\nπ π₁ π₂ : Prepartition I\nx✝ x : ι → ℝ\nJ₁ : Box ι\nh₁ : J₁ ∈ π\nhx₁ : x ∈ ↑Box.Icc J₁\nJ₂ : Box ι\nh₂ : J₂ ∈ π\nhx₂ : x ∈ ↑Box.Icc J₂\nH : {i | Box.lower J₁ i = x i} = {i | Box.lower J₂ i = x i}\n⊢ J₁ = J₂",
"state_before": "ι : Type u_... | [
197,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_inv_div_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33147\nG : Type ?u.33150\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ (a⁻¹ / b⁻¹)⁻¹ = a / b",
"tactic": "simp"
}
] | [
525,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.mono | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\ng : β → γ\nf : α → β\nhf : LeftOrdContinuous f\na₁ a₂ : α\nh : a₁ ≤ a₂\n⊢ a₂ ∈ upperBounds {a₁, a₂}",
"tactic": "simp [*]"
}
] | [
76,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.atBot_zsmul_const | [
{
"state_after": "α : Type u_2\nR : Type u_1\nl : Filter α\nf✝ : α → R\nr : R\ninst✝¹ : LinearOrderedAddCommGroup R\ninst✝ : Archimedean R\nf : α → ℤ\nhr : 0 < r\nhf : Tendsto (fun x => -f x) l atTop\n⊢ Tendsto (fun x => -f x • r) l atTop",
"state_before": "α : Type u_2\nR : Type u_1\nl : Filter α\nf✝ : α →... | [
246,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.lcm_dvd_iff | [] | [
297,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.convexOn | [
{
"state_after": "R : Type ?u.1285893\nR' : Type ?u.1285896\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1285902\n𝕜₃ : Type ?u.1285905\n𝕝 : Type ?u.1285908\nE : Type u_1\nE₂ : Type ?u.1285914\nE₃ : Type ?u.1285917\nF : Type ?u.1285920\nG : Type ?u.1285923\nι : Type ?u.1285926\ninst✝⁵ : NormedField 𝕜\ninst✝⁴ : AddCommGroup ... | [
1046,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.ediam_Ico | [] | [
1546,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csInf_empty | [
{
"state_after": "no goals",
"state_before": "⊢ ¬(Set.Nonempty ∅ ∧ BddBelow ∅)",
"tactic": "simp"
}
] | [
92,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.sum_over_range | [] | [
409,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.hasSum_integral_iUnion_ae | [
{
"state_after": "α : Type u_2\nβ : Type ?u.62254\nE : Type u_3\nF : Type ?u.62260\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\nf g : α → E\ns✝ t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\nι : Type u_1\ninst✝ : Countable ι\ns : ι → Set α\nhm : ∀... | [
243,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Order/Lattice.lean | sup_eq_sup_iff_right | [] | [
306,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_sup | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Degeneracies.lean | AlgebraicTopology.DoldKan.σ_comp_P_eq_zero | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn q : ℕ\n⊢ ∀ (i : Fin (n + 1)), n + 1 ≤ ↑i + q → SimplicialObject.σ X i ≫ HomologicalComplex.Hom.f (P q) (n + 1) = 0",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : Simplicial... | [
116,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_negSucc | [] | [
41,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
41,
15
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.add_mul_subset | [] | [
1079,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_iUnion₂_closure | [] | [
529,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add' | [
{
"state_after": "K : Type ?u.419164\nF : Type ?u.419167\nR : Type u_2\ninst✝⁴ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.419179\nΓ''₀ : Type ?u.419182\ninst✝³ : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\ninst✝ : LinearOrderedCommMonoidWithZero Γ'₀\nv... | [
180,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.rq_eq | [] | [
241,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.hext | [
{
"state_after": "case mk\nC : Type u_1\ninst✝ : Category C\nX Y : PresheafedSpace C\nβ : Hom X Y\nbase✝ : ↑X ⟶ ↑Y\nc✝ : Y.presheaf ⟶ base✝ _* X.presheaf\nw : { base := base✝, c := c✝ }.base = β.base\nh : HEq { base := base✝, c := c✝ }.c β.c\n⊢ { base := base✝, c := c✝ } = β",
"state_before": "C : Type u_1\... | [
132,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean | Complex.differentiableAt_tan | [] | [
66,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.86036\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.86048\ninst✝³ : HeytingAlgebra α\ninst✝² : HeytingAlgebra β\ninst✝¹ : HeytingAlgebra γ\ninst✝ : HeytingAlgebra δ\nf f₁ f₂ : HeytingHom α β\ng g₁ g₂ : HeytingHom β γ\nhg : Injective ↑g\nh : ... | [
363,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.val_image_orbit | [] | [
299,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Dense.borel_eq_generateFrom_Ico_mem | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.653000\nβ : Type ?u.653003\nγ : Type ?u.653006\nγ₂ : Type ?u.653009\nδ : Type ?u.653012\nι : Sort y\ns✝ t u : Set α✝\ninst✝²² : TopologicalSpace α✝\ninst✝²¹ : MeasurableSpace α✝\ninst✝²⁰ : OpensMeasurableSpace α✝\ninst✝¹⁹ : TopologicalSpace β\ninst✝... | [
620,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.contDiffAt | [] | [
238,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
11
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.bit0 | [] | [
354,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_inv_desc | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF✝ : J ⥤ C\nt✝ : Cocone F✝\nF G : J ⥤ C\ns : Cocone G\nr t : Cocone F\nP : IsColimit t\nQ : IsColimit s\nw : F ≅ G\n⊢ ∀ (j : J), s.ι.app j ≫ (coconePointsIsoOfNa... | [
851,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_injective | [] | [
62,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Vector/Mem.lean | Vector.mem_map_succ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nn : ℕ\na a' : α\nb : β\nv : Vector α (n + 1)\nf : α → β\n⊢ b ∈ toList (map f v) ↔ f (head v) = b ∨ ∃ a, a ∈ toList (tail v) ∧ f a = b",
"tactic": "rw [mem_succ_iff, head_map, tail_map, mem_map_iff, @eq_comm _ b]"
}
] | [
90,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_range_le | [] | [
180,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.leftInverse_symm | [] | [
917,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_lt_of_lt_sub_right | [
{
"state_after": "a b c : Int\nh✝ : a < c - b\nh : a + b < c - b + b\n⊢ a + b < c",
"state_before": "a b c : Int\nh : a < c - b\n⊢ a + b < c",
"tactic": "have h := Int.add_lt_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a < c - b\nh : a + b < c - b + b\n⊢... | [
1057,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1055,
11
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorizationEquiv_inv_apply | [] | [
340,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_list_sum | [] | [
100,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.coinduction | [] | [
353,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | lt_inv_mul_iff_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ 1 < b⁻¹ * a ↔ b < a",
"tactic": "rw [← mul_lt_mul_iff_left b, mul_one, mul_inv_cancel_left]"
}
] | [
200,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.liftRel_const_iff | [] | [
331,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_zero | [
{
"state_after": "no goals",
"state_before": "⊢ log 0 = 0",
"tactic": "simp [log]"
}
] | [
93,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | Units.smul_mk0 | [] | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | finrank_bot | [] | [
265,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.mem_ker_modByMonic | [] | [
452,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_surjective_of_injective | [] | [
394,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.swap | [
{
"state_after": "case single\nα : Type u_1\nβ : Type ?u.23725\nγ : Type ?u.23728\nδ : Type ?u.23731\nr : α → α → Prop\na b✝ c d b : α\nh : r b✝ b\n⊢ TransGen (Function.swap r) b b✝\n\ncase tail\nα : Type u_1\nβ : Type ?u.23725\nγ : Type ?u.23728\nδ : Type ?u.23731\nr : α → α → Prop\na b✝ c✝ d b c : α\na✝ : Tra... | [
500,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_iff_tendsto | [
{
"state_after": "case intro\nr : ℝ\nf : ℕ → ℝ\n⊢ IsSt (ofSeq f) r ↔ Germ.Tendsto (ofSeq f) (𝓝 r)",
"state_before": "x : ℝ*\nr : ℝ\n⊢ IsSt x r ↔ Germ.Tendsto x (𝓝 r)",
"tactic": "rcases ofSeq_surjective x with ⟨f, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nr : ℝ\nf ... | [
261,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/CompleteLattice.lean | Antitone.le_map_iInf₂ | [] | [
953,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.coe_toDual_self | [
{
"state_after": "case h\nR : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : DecidableEq ι\nb : Basis ι R M\ni : ι\nx✝ : M\n⊢ ↑(↑(toDual b) (↑b i)) x✝ = ↑(coord b i) x✝",
"state_before": "R : Type u\nM : Type v\nK : T... | [
333,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel.condition | [] | [
697,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv'_comp | [] | [
507,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Complex/Module.lean | imaginaryPart_apply_coe | [
{
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"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\nin... | [
464,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuous_finprod | [
{
"state_after": "ι : Type u_3\nα : Type ?u.452056\nX : Type u_1\nM : Type u_2\nN : Type ?u.452065\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : CommMonoid M\ninst✝ : ContinuousMul M\nf : ι → X → M\nhc : ∀ (i : ι), Continuous (f i)\nhf : LocallyFinite fun i => mulSupport (f i)\nx : X\n⊢ Co... | [
814,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Std/Data/Int/Lemmas.lean | Int.max_def | [] | [
687,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
687,
11
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_ne_zero | [
{
"state_after": "case zero\nα : Type u\nβ : Type ?u.249597\nx : α\ninst✝ : LinearOrderedRing α\nhx : x ≠ -1\nhn : Nat.zero ≠ 0\n⊢ ∑ i in range Nat.zero, x ^ i ≠ 0\n\ncase succ.zero\nα : Type u\nβ : Type ?u.249597\nx : α\ninst✝ : LinearOrderedRing α\nhx : x ≠ -1\nhn : Nat.succ Nat.zero ≠ 0\n⊢ ∑ i in range (Nat.... | [
555,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.vsub_le_vsub | [] | [
1144,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_map | [] | [
71,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.preimage_closedBall | [] | [
321,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean | MaximalSpectrum.toPrimeSpectrum_range | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\n⊢ range toPrimeSpectrum = {x | Ideal.IsMaximal x.asIdeal}",
"state_before": "R : Type u\ninst✝ : CommRing R\n⊢ range toPrimeSpectrum = {x | IsClosed {x}}",
"tactic": "simp only [isClosed_singleton_iff_isMaximal]"
},
{
"state_after": "case h.mk\nR... | [
72,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.sigma | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁ l₂✝ : List α\nr : α → α → Prop\na✝ b✝ : α\nσ : α → Type u_1\nl₂ : (a : α) → List (σ a)\nd₁ : Nodup l₁\nd₂ : ∀ (a : α), Nodup (l₂ a)\na : α\nx✝ : a ∈ l₁\nb b' : (fun a => σ a) a\nh : { fst := a, snd := b } = { fst := a, snd := b' }\n⊢... | [
363,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.IsCobounded.all | [] | [
347,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Logic/Basic.lean | Iff.not_left | [] | [
276,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | mem_posTangentConeAt_of_segment_subset' | [
{
"state_after": "no goals",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nx y : E\nh : segment ℝ x (x + y) ⊆ s\n⊢ y ∈ posTangentConeAt s x",
"tactic": "simpa only [add_sub_cancel'] using mem_posTangentConeAt_of_segment_... | [
107,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.ind | [
{
"state_after": "case mk\nn : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα✝ α : TypeVec n\np : Fix F α → Prop\nh : ∀ (x : F (α ::: Fix F α)), LiftP (PredLast α p) x → p (mk x)\n⊢ ∀ (a : MvPFunctor.W (P F) α), p (Quot.mk Setoid.r a)",
"state_before": "n : ℕ\nF : TypeVec (n + 1) → Typ... | [
326,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_eq_left | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b : R\nh : gcd a b = a\n⊢ gcd a b ∣ b",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b : R\nh : gcd a b = a\n⊢ a ∣ b",
"tactic": "rw [← h]"
},
{
"state_after": "no goals",
... | [
182,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.detAux_id | [] | [
163,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/List/Rotate.lean | List.get?_rotate | [
{
"state_after": "α : Type u\nl : List α\nn m : ℕ\nhml : m < length l\n⊢ get? (drop (n % length l) l ++ take (n % length l) l) m = get? l ((m + n) % length l)",
"state_before": "α : Type u\nl : List α\nn m : ℕ\nhml : m < length l\n⊢ get? (rotate l n) m = get? l ((m + n) % length l)",
"tactic": "rw [rota... | [
256,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Logic/Basic.lean | congr_arg_refl | [] | [
539,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_le_of_le_add_int | [] | [
828,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sub_int_mul_two_pi | [] | [
294,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.smul_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝³ : Semiring R\np✝ q✝ r : R[X]\ninst✝² : Monoid S\ninst✝¹ : DistribMulAction S R\ninst✝ : IsScalarTower S R R\ns : S\np q : R[X]\n⊢ comp (s • p) q = s • comp p q",
"tactic": "rw [← smul_o... | [
655,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | LocalHomeomorph.singletonChartedSpace_chartAt_eq | [] | [
995,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_dite | [] | [
1368,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_mul_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.122704\nι : Type ?u.122707\nM : Type u_2\nN : Type ?u.122713\ninst✝ : MulZeroClass M\ns✝ t : Set α\nf✝ g✝ : α → M\na : α\ns : Set α\nf g : α → M\n⊢ (if a ∈ s then f a * g a else 0) = f a * if a ∈ s then g a else 0",
"state_before": "α : Type u_1\nβ : Type ?u.12270... | [
700,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | mul_dvd_mul_left | [] | [
194,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.hasDerivAt_arsinh | [] | [
189,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.add_closure_iUnion_range_single | [
{
"state_after": "case h0\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → AddZeroClass (β i)\nx : Π₀ (i : ι), β i\nx✝ : x ∈ ⊤\n⊢ 0 ∈ AddSubmonoid.closure (⋃ (i : ι), Set.range (single i))\n\ncase ha\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ :... | [
1010,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | Set.PairwiseDisjoint.aedisjoint | [] | [
79,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
11
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.coe_sSup_eq | [] | [
585,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
11
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero | [
{
"state_after": "E : Type u_1\nF : Type ?u.699519\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
689,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Algebra/Group/Basic.lean | bit0_zero | [] | [
154,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Set.Infinite.exists_lt | [] | [
853,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Topology/Sequences.lean | UniformSpace.isCompact_iff_isSeqCompact | [] | [
395,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
11
] |
Mathlib/Data/List/Lattice.lean | List.cons_bagInter_of_pos | [
{
"state_after": "case nil\nα : Type u_1\nl l₁✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₁ : List α\nh : a ∈ []\n⊢ List.bagInter (a :: l₁) [] = a :: List.bagInter l₁ (List.erase [] a)\n\ncase cons\nα : Type u_1\nl l₁✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₁ : List α\nhead✝ : α\nta... | [
221,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/Group/Opposite.lean | MulOpposite.Commute.unop | [] | [
253,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.generalizedEigenspace_zero | [
{
"state_after": "no goals",
"state_before": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\nk : ℕ\n⊢ ↑(generalizedEigenspace f 0) k = LinearMap.ker (f ^ k)",
"tactic": "simp [Modu... | [
271,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.eventually_le_atBot | [] | [
236,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
11
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Structure.funMap_apply₂ | [] | [
437,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.of_pow | [] | [
126,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι✝ : Sort ?u.143260\nι : Sort u_1\nu : ι → UniformSpace α\na : α\n⊢ 𝓝 a = 𝓝 a",
"tactic": "simp only [@nhds_eq_comap_uniformity _ (iInf u), nhds_iInf,\niInf_uniformity, @nhds_eq_comap_uniformity _ (u _), ... | [
1355,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.domRestrict_apply | [
{
"state_after": "R : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.442039\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nS : Submodule R E\nx : { x // x ∈ S ⊓ f.domain }\ny : { x // x... | [
708,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mk_d_1_0 | [
{
"state_after": "ι : Type ?u.181945\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nX₀ X₁ X₂ : V\nd₀ : X₁ ⟶ X₀\nd₁ : X₂ ⟶ X₁\ns : d₁ ≫ d₀ = 0\nsucc :\n (t : (X₀ : V) ×' (X₁ : V) ×' (X₂ : V) ×' (d₀ : X₁ ⟶ X₀) ×' (d₁ : X₂ ⟶ X₁) ×' d₁ ≫ d₀ = 0) →\n (X₃ : V) ×' (d₂ : X₃ ⟶ t.snd.snd.fst) ×' d₂ ≫ t... | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryFinFinset_apply_const_aux | [
{
"state_after": "R : Type u\nι : Type u'\nn✝ : ℕ\nM : Fin (Nat.succ n✝) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : Fin (Nat.succ n✝)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : Fin (Nat.succ n✝)) →... | [
1609,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1604,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.normNoninc_of_isometry | [] | [
868,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
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