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 |
|---|---|---|---|---|---|---|
Std/Data/RBMap/WF.lean | Std.RBNode.All.del | [
{
"state_after": "α : Type u_1\np : α → Prop\ncut : α → Ordering\nc✝ : RBColor\na✝² : RBNode α\na✝¹ : α\na✝ : RBNode α\nhy : p a✝¹\nha : All p a✝²\nhb : All p a✝\n⊢ All p\n (match cut a✝¹ with\n | Ordering.lt =>\n match isBlack a✝² with\n | black => balLeft (del cut a✝²) a✝¹ a✝\n | red => n... | [
416,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
406,
11
] |
Mathlib/Analysis/Convex/Slope.lean | concaveOn_of_slope_anti_adjacent | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhs : Convex 𝕜 s\nhf : ∀ {x y z : 𝕜}, x ∈ s → z ∈ s → x < y → y < z → (f z - f y) / (z - y) ≤ (f y - f x) / (y - x)\n⊢ ConvexOn 𝕜 s (-f)",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf :... | [
146,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.length_pos_of_bot_eq_bot_of_top_eq_top_of_length_pos | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nhb : bot s₁ = bot s₂\nht : top s₁ = top s₂\n⊢ s₂.length = 0 → s₁.length = 0",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nhb : bot s₁... | [
731,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/Prod/Lex.lean | Prod.Lex.toLex_mono | [
{
"state_after": "case mk.mk.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.18624\ninst✝¹ : PartialOrder α\ninst✝ : Preorder β\na₁ : α\nb₁ : β\na₂ : α\nb₂ : β\nha : (a₁, b₁).fst ≤ (a₂, b₂).fst\nhb : (a₁, b₁).snd ≤ (a₂, b₂).snd\n⊢ ↑toLex (a₁, b₁) ≤ ↑toLex (a₂, b₂)",
"state_before": "α : Type u_1\nβ : Type u_... | [
122,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.zero_mem | [] | [
313,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.toEquiv_pointReflection | [] | [
573,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Std/Data/Array/Lemmas.lean | Array.data_pop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\n⊢ (pop a).data = List.dropLast a.data",
"tactic": "simp [pop]"
}
] | [
133,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
9
] |
Mathlib/Analysis/NormedSpace/Ray.lean | SameRay.norm_smul_eq | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro\nE : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.9880\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nu : E\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nh : SameRay ℝ (a • u) (b • u)\n⊢ ‖a • u‖ • b • u = ‖b • u... | [
56,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_mul' | [] | [
211,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_toPath_subset | [] | [
1437,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_map | [
{
"state_after": "case a.h\nl : Type ?u.129660\nm : Type u_1\nn : Type u_2\no : Type u_5\np : Type ?u.129672\nq : Type ?u.129675\nm' : o → Type ?u.129680\nn' : o → Type ?u.129685\np' : o → Type ?u.129690\nR : Type ?u.129693\nS : Type ?u.129696\nα : Type u_3\nβ : Type u_4\ninst✝² : DecidableEq o\ninst✝¹ : Zero α... | [
378,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_nsmul | [] | [
472,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Part.lean | Part.mem_assert | [] | [
464,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_prod' | [] | [
1430,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_rat_add | [] | [
213,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.not_or_self | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x : Bool), (!x || x) = true",
"tactic": "decide"
}
] | [
260,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.radius_eq_top_of_eventually_eq_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.93541\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSp... | [
176,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_lt_mul_of_nonneg_left | [] | [
258,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | MonotoneOn.convexOn_of_deriv | [
{
"state_after": "E : Type ?u.423301\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.423397\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_mono : MonotoneOn (deriv f) (inter... | [
995,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
src/lean/Init/Core.lean | dif_eq_if | [] | [
821,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
818,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_of_ae_le | [] | [
401,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.indep_generateFrom_of_disjoint | [
{
"state_after": "Ω : Type u_1\nι : Type u_2\nm0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasure μ\ns : ι → Set Ω\nhsm : ∀ (n : ι), MeasurableSet (s n)\nhs : iIndepSet s\nS T : Set ι\nhST : Disjoint S T\n⊢ Indep (generateFrom (piiUnionInter (fun k => {s k}) S)) (generateFrom (piiU... | [
440,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.rank_le | [] | [
399,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.inl_inj | [] | [
134,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.induction_on_max | [
{
"state_after": "case a\nF : Type ?u.398044\nα : Type u_1\nβ : Type ?u.398050\nγ : Type ?u.398053\nι : Type ?u.398056\nκ : Type ?u.398059\ninst✝¹ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ninst✝ : DecidableEq α\np : Finset α → Prop\nh0 : p ∅\nstep : ∀ (a : α) (s : Finset α), (∀ (x : α), x ∈... | [
1633,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1626,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Ioc ↑a ↑b = Ioc a b",
"tactic": "simp [← Ioi_inter_Iic]"
}
] | [
176,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.exists_pow_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1885361\nα : Type u_1\nβ : Type ?u.1885367\nf g : Perm α\ns✝ t : Set α\na b x y : α\ns : Finset α\nhf : IsCycleOn f ↑s\nha : a ∈ s\nhb : b ∈ s\n⊢ ∃ n, n < card s ∧ ↑(f ^ n) a = b",
"tactic": "classical\n obtain ⟨n, rfl⟩ := hf.2 ha hb\n obtain ⟨... | [
907,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | xInTermsOfW_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : DecidableEq R\ninst✝ : Invertible ↑p\n⊢ xInTermsOfW p R 0 = X 0",
"tactic": "rw [xInTermsOfW_eq, range_zero, sum_empty, pow_zero, C_1, mul_one, sub_zero]"
}
] | [
249,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Ring/Units.lean | Units.neg_divp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝¹ : Monoid α\ninst✝ : HasDistribNeg α\na✝ b a : α\nu : αˣ\n⊢ -(a /ₚ u) = -a /ₚ u",
"tactic": "simp only [divp, neg_mul]"
}
] | [
52,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivWithinAt.mul | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type ?u.197200\n... | [
172,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.ext | [] | [
282,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.Augmented.w₀ | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ : SimplicialObject C\nX Y : Augmented C\nf : X ⟶ Y\n⊢ (drop.map f).app [0].op ≫ Y.hom.app [0].op = X.hom.app [0].op ≫ point.map f",
"tactic": "convert congr_app f.w (op (SimplexCategory.mk 0))"
}
] | [
343,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingHom.prod_unique | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.36124\nβ : Type ?u.36127\nR : Type u_1\nR' : Type ?u.36133\nS : Type u_3\nS' : Type ?u.36139\nT : Type u_2\nT' : Type ?u.36145\ninst✝² : NonAssocSemiring R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\nf✝ : R →+* S\ng : R →+* T\nf : R →+*... | [
241,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/MonoidAlgebra/Support.lean | MonoidAlgebra.support_single_mul_subset | [
{
"state_after": "k : Type u₁\nG : Type u₂\ninst✝² : Semiring k\ninst✝¹ : DecidableEq G\ninst✝ : Mul G\nf : MonoidAlgebra k G\nr : k\na x : G\nhx : x ∈ (single a r * f).support\n⊢ x ∈ image ((fun x x_1 => x * x_1) a) f.support",
"state_before": "k : Type u₁\nG : Type u₂\ninst✝² : Semiring k\ninst✝¹ : Decida... | [
39,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.extendDomain_one | [] | [
310,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | isOfFinOrder_iff_pow_eq_one | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nx : G\n⊢ IsOfFinOrder x ↔ ∃ n, 0 < n ∧ x ^ n = 1",
"tactic": "simp [IsOfFinOrder, mem_periodicPts, isPeriodicPt_mul_iff_pow_eq_one]"
}
] | [
78,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/FieldTheory/Adjoin.lean | PowerBasis.equivAdjoinSimple_symm_gen | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\npb : PowerBasis K L\n⊢ ↑(AlgEquiv.symm (equivAdjoinSimple pb)) pb.gen = AdjoinSimple.gen K pb.gen",
"tactic": "rw [equivAdjoinSimple, equivOfMinpoly_symm, equivOfMinpoly_gen... | [
1306,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_injective | [
{
"state_after": "α : Type u\nβ : Type v\nf : α → β\nh : Injective (preimage f)\ny : β\n⊢ ∃ a, f a = y",
"state_before": "α : Type u\nβ : Type v\nf : α → β\n⊢ Injective (preimage f) ↔ Surjective f",
"tactic": "refine' ⟨fun h y => _, Surjective.preimage_injective⟩"
},
{
"state_after": "case intro... | [
1537,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_left_inj | [] | [
603,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_subset_coe | [] | [
660,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasStrictDerivAt_right | [] | [
654,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_image | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.67433\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nhΦ : Isometry Φ\n⊢ infDist (Φ x) (Φ '' t) = infDist x t",
"tactic": "simp [infDist, infEdist_image hΦ]"
}
] | [
618,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.norm_vComp_le | [] | [
238,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Std/Data/Option/Lemmas.lean | Option.bind_eq_some | [
{
"state_after": "no goals",
"state_before": "α✝¹ : Type u_1\nb : α✝¹\nα✝ : Type u_2\nx : Option α✝\nf : α✝ → Option α✝¹\n⊢ Option.bind x f = some b ↔ ∃ a, x = some a ∧ f a = some b",
"tactic": "cases x <;> simp"
}
] | [
94,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
93,
9
] |
Std/Data/Int/DivMod.lean | Int.ofNat_fdiv | [
{
"state_after": "no goals",
"state_before": "x✝ : Nat\n⊢ ↑(0 / x✝) = fdiv ↑0 ↑x✝",
"tactic": "simp [fdiv]"
}
] | [
23,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
21,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.blocksFun_mem_blocks | [] | [
175,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_ne_zero | [] | [
82,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.exists_const | [] | [
341,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Order/Cover.lean | Prod.fst_eq_or_snd_eq_of_wcovby | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α × β\nh : x ⩿ y\nhab : ¬(x.fst = y.fst ∨ x.snd = y.snd)\n⊢ False",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b... | [
506,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_def | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.coe_smul | [] | [
1498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1497,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_le_mk | [] | [
490,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_map_mul_right | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.113460\nγ : Type ?u.113463\ninst✝ : NonUnitalNonAssocSemiring α\na : α\ns : Multiset ι\nf : ι → α\n⊢ sum (map (fun i => f i * a) 0) = sum (map f 0) * a",
"tactic": "simp"
},
{
"state_after": "no goals",
"st... | [
343,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.fst' | [] | [
753,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nm n : ℕ\na : R\n⊢ (if single () m = single () n then a else 0) = if m = n then a else 0",
"tactic": "simp only [Finsupp.unique_single_eq_iff]"
}
] | [
1349,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g σ : Perm α\n⊢ support σ⁻¹ = support σ",
"tactic": "simp_rw [Finset.ext_iff, mem_support, not_iff_not, inv_eq_iff_eq.trans eq_comm, imp_true_iff]"
}
] | [
355,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Logic/Relation.lean | Equivalence.eqvGen_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.30661\nγ : Type ?u.30664\nδ : Type ?u.30667\nr : α → α → Prop\na b : α\nh✝ : Equivalence r\nh : EqvGen r a b\n⊢ r a b",
"state_before": "α : Type u_1\nβ : Type ?u.30661\nγ : Type ?u.30664\nδ : Type ?u.30667\nr : α → α → Prop\na b : α\nh : Equivalence r\n⊢ EqvGen r... | [
684,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.univ_nonempty | [] | [
109,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_inv_lt_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.38209\nα : Type u_1\nβ : Type ?u.38215\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : 0 < b\n⊢ a * b⁻¹ < c ↔ a < c * b",
"tactic": "rw [mul_comm, inv_mul_lt_iff' h]"
}
] | [
207,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Pi/Interval.lean | Pi.card_Iic | [] | [
76,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_const_smul_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.87779\nι : Type ?u.87782\ninst✝¹⁰ : Countable ι\nf g : α → β\nM : Type ?u.87796\nG : Type u_3\nG₀ : Type ?u.87802\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : Monoid M\ninst✝⁷ : MulAction M β\ninst✝⁶ : ContinuousConstSMul M β\ni... | [
494,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na✝ b a : α\n⊢ ∂ ∂ a = ∂ a",
"tactic": "rw [boundary, hnot_boundary, inf_top_eq]"
}
] | [
135,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/Order/Basic.lean | Filter.Eventually.exists_lt | [] | [
2426,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2424,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.continuous_mul | [] | [
140,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.continuous_of_dominated | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF✝ : Type ?u.1031647\n𝕜 : Type ?u.1031650\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F✝\ninst✝³ : No... | [
1080,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Order/Monotone/Basic.lean | Antitone.antitoneOn | [] | [
384,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
11
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.one_leftUnitor | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM : Mon_ C\n⊢ (λ_ (𝟙_ C)).inv ≫ (λ_ (𝟙_ C)).hom ≫ M.one = M.one",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM : Mon_ C\n⊢ ((λ_ (𝟙_ C)).inv ≫ (𝟙 (𝟙_ C) ⊗ M.one)) ≫ (λ_ M.X).hom = M.one",
... | [
399,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_zero | [] | [
315,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_lintegral_nnnorm_tendsto' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nι : Type u_1\nE : Type u_3\ninst✝³ : MeasurableSpace α\nμ : Measure α\nl : Filter ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NeBot l\ninst✝ : IsCountablyGenerated l\nφ : ι → Set α\nhφ : AECover μ l φ\nf : α → E\nI : ℝ≥0\nhfm : AEStronglyMeasurable ... | [
436,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | finEquivZpowers_symm_apply | [
{
"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✝ : Finite G\nx : G\nn : ℕ\nhn : ∃ m, x ^ m = x ^ n\n⊢ ↑(finEquivPowers x).symm\n (↑(Equiv.Set.ofEq (_ : ↑(Submonoid.powers x) = ↑(zpowers x))).symm { val := x ^ n, property := hn }) =\n { v... | [
862,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Order/MinMax.lean | Max.left_comm | [] | [
231,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_inr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.80560\nι : Sort ?u.80563\nι' : Sort ?u.80566\nf : ι → α\ns t : Set α\n⊢ range Sum.inr = {x | Sum.isRight x = true}",
"tactic": "ext (_|_) <;> simp"
}
] | [
886,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_norm_tendsto_zero | [] | [
400,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
9
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_add_right | [
{
"state_after": "case inr\nι : Type ?u.7319192\n𝕜 : Type ?u.7319195\nE : Type u_1\nF : Type ?u.7319201\nA : Type ?u.7319204\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedRing A\nf g : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhf : IntervalIntegrable f volume a b\nc : ℝ\nthis :\n ∀ {a b : ℝ}, IntervalInteg... | [
328,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_add | [] | [
827,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
11
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_fin_repeat | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm : ℕ\na : Fin m → α\nn : ℕ\n⊢ ofFn (Fin.repeat n a) = join (replicate n (ofFn a))",
"tactic": "simp_rw [ofFn_mul, ← ofFn_const, Fin.repeat, Fin.modNat, add_comm,\n Nat.add_mul_mod_self_right, Nat.mod_eq_of_lt (Fin.is_lt _)]"
}
] | [
223,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | self_subset_gauge_le_one | [] | [
203,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.IntegrableOn.continuousOn_mul | [] | [
419,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.congr_right | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx✝ : α\np : Filter ι\np' : Filter α\ng✝ : ι → α\ninst✝ : TopologicalSpace α\ng : α → β\nhf : TendstoLocallyUniformlyOn F f p s\nhg : EqOn f g s\nu : Set (β × β)\nhu : u ∈ 𝓤 β\nx : ... | [
798,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | RingHom.ext_int | [] | [
330,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_one_of_lt' | [] | [
812,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_map | [] | [
146,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
144,
9
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.self_trans_symm | [] | [
828,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_eq_iff_mk'_eq | [] | [
807,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.inv_mul | [] | [
263,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_fin_two | [
{
"state_after": "m : Type ?u.2609749\nn : Type ?u.2609752\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix (Fin 2) (Fin 2) R\n⊢ A 0 0 * A 1 1 + -(A 0 1 * A 1 0) = A 0 0 * A 1 1 - A 0 1 * A 1 0",
"state_before": "m : Type ?u.... | [
802,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.le_ker_iff_map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1229974\nR₂ : Type u_2\nR₃ : Type ?u.1229980\nR₄ : Type ?u.1229983\nS : Type ?u.1229986\nK : Type ?u.1229989\nK₂ : Type ?u.1229992\nM : Type u_3\nM' : Type ?u.1229998\nM₁ : Type ?u.1230001\nM₂ : Type u_4\nM₃ : Type ?u.1230007\nM₄ : Typ... | [
1368,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_zero_measure | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.1303582\n𝕜 : Type ?u.1303585\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : Norm... | [
1425,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.exists_antitone_seq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.104073\nγ : Type ?u.104076\nι : Type ?u.104079\nι' : Sort ?u.104082\nf : Filter α\ninst✝ : IsCountablyGenerated f\nx : ℕ → Set α\nhx : HasAntitoneBasis f x\n⊢ ∀ {s : Set α}, s ∈ f ↔ ∃ i, x i ⊆ s",
"tactic": "simp [hx.1.mem_iff]"
}... | [
1106,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
Mathlib/Algebra/Hom/Embedding.lean | mul_left_embedding_eq_mul_right_embedding | [
{
"state_after": "case h\nR : Type ?u.1165\nG : Type u_1\ninst✝ : CancelCommMonoid G\ng x✝ : G\n⊢ ↑(mulLeftEmbedding g) x✝ = ↑(mulRightEmbedding g) x✝",
"state_before": "R : Type ?u.1165\nG : Type u_1\ninst✝ : CancelCommMonoid G\ng : G\n⊢ mulLeftEmbedding g = mulRightEmbedding g",
"tactic": "ext"
},
... | [
55,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
src/lean/Init/Data/String/Basic.lean | String.prev_lt_of_pos | [
{
"state_after": "s : String\ni : Pos\nh : i ≠ 0\n⊢ (utf8PrevAux s.data 0 i).byteIdx < i.byteIdx",
"state_before": "s : String\ni : Pos\nh : i ≠ 0\n⊢ (prev s i).byteIdx < i.byteIdx",
"tactic": "simp [prev, h]"
},
{
"state_after": "no goals",
"state_before": "s : String\ni : Pos\nh : i ≠ 0\n⊢... | [
153,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
151,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderivWithin_mul' | [] | [
367,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_im | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1187584\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ I * (↑(starRingEnd 𝕜) (inner x x) - inner x x) / 2 = ↑0",
"st... | [
457,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_nonpos_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ arsinh x ≤ 0 ↔ x ≤ 0",
"tactic": "rw [← sinh_le_sinh, sinh_zero, sinh_arsinh]"
}
] | [
169,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Std/Data/Int/DivMod.lean | Int.neg_div | [
{
"state_after": "no goals",
"state_before": "n : Int\n⊢ div (-0) n = -div 0 n",
"tactic": "simp [Int.neg_zero]"
}
] | [
87,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
84,
19
] |
Mathlib/GroupTheory/Finiteness.lean | Group.rank_spec | [] | [
392,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
src/lean/Init/Core.lean | true_ne_false | [] | [
589,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
588,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.pow_induction_on_right' | [
{
"state_after": "case zero\nι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n✝ : A\nC : (n : ℕ) → (x : A) → x ∈ M ^ n → Prop\nhr : ∀ (r : R), C 0 (↑(algebraMap R A) r) (_ : ↑(algebraMap R A) r ∈ 1)\nhadd : ∀ (x y : ... | [
475,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
11
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.det_fintype | [
{
"state_after": "α : Type u_1\nβ : Type ?u.117449\nm : Type u_2\nn : Type ?u.117455\no : Type ?u.117458\nm' : α → Type ?u.117463\nn' : α → Type ?u.117468\nR : Type v\ninst✝⁷ : CommRing R\nM N : Matrix m m R\nb : m → α\ninst✝⁶ : DecidableEq m\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst... | [
236,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.le_map_sSup_subset_fixedPoints | [] | [
257,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.