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/Analysis/Complex/Basic.lean | Complex.norm_real | [] | [
152,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul_param | [] | [
116,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_restrict_iff_comap_subtype | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3617330\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.3617339\nδ : Type ?u.3617342\nR : Type ?u.3617345\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nf✝ g : α → β\nμ✝ ν : MeasureTheory.Measure ... | [
280,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
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Mathlib/Data/Seq/Computation.lean | Computation.eq_of_pure_mem | [] | [
376,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_iff_ringHom_rangeS | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\n⊢ p ∈ lifts f ↔ p ∈ RingHom.rangeS (mapRingHom f)",
"tactic": "simp only [coe_mapRingHom, lifts, Set.mem_range, RingHom.mem_rangeS]"
}
] | [
73,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Std/Data/List/Lemmas.lean | List.partition_eq_filter_filter | [
{
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"state_before": "α : Type u_1\np : α → Bool\nl : List α\n⊢ partition p l = (filter p l, filter (not ∘ p) l)",
"tactic": "simp [partition, aux]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl as✝ bs✝ : List α\n⊢ partition.loop p [] ... | [
1136,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1131,
9
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | inv_mul_cancel_left₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.20012\nM₀ : Type ?u.20015\nG₀ : Type u_1\nM₀' : Type ?u.20021\nG₀' : Type ?u.20024\nF : Type ?u.20027\nF' : Type ?u.20030\ninst✝ : GroupWithZero G₀\na b✝ c g h✝ x : G₀\nh : a ≠ 0\nb : G₀\n⊢ a⁻¹ * a * b = b",
"tactic": "simp [h]"
}
] | [
290,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_int | [] | [
380,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.restrictScalars_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_3\nM : Type u_2\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S M\ninst✝¹ : SMul S R\ninst✝ : IsScalarTower S R M\np✝ q p : Submodule R M\n⊢ restrictScalars S p = ⊤ ↔ p = ⊤",
... | [
171,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.coe_coePNatMonoidHom | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivWithinAt.csinh | [] | [
277,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_transfer | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nH : SimpleGraph V\nhp : ∀ (e : Sym2 V), e ∈ edges p → e ∈ edgeSet H\n⊢ ∀ (e : Sym2 V), e ∈ edges p → e ∈ edgeSet H",
"state_before": "V : Type u\nV' : Type v\nV'' ... | [
1763,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1758,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mem_support_toFun | [
{
"state_after": "case mk'\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ni : ι\nf : (i : ι) → β i\ns : Trunc { s // ∀ (i : ι), i ∈ s ∨ f i = 0 }\n⊢ i ∈ support { toFun := f, suppor... | [
1123,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.prod_map_snd | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.310080\nM₆ : Type ?u.310083\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\... | [
585,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_smul_const_iff | [] | [
1746,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1744,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.order_ω | [
{
"state_after": "case pp\np' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\n⊢ Nat.Prime 2\n\ncase h₁\np' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\n⊢ ¬orderOf (ωUnit (p' + 2)) ∣ 2 ^ (p' + 1)\n\ncase h₂\np' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\n⊢ orderOf (ωUnit (p' + 2)) ∣ 2 ^ (p' + 1 + 1)",
"state_before": "... | [
489,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_span | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.145468\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\ns t : Set E\n⊢ span 𝕜 s ⟂ span 𝕜 t ↔ ∀ ⦃u : E⦄, u ∈ s → ∀ ⦃v : E... | [
382,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Finset/Finsupp.lean | Finset.card_finsupp | [] | [
82,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/FieldTheory/ChevalleyWarning.lean | char_dvd_card_solutions_of_fintype_sum_lt | [
{
"state_after": "no goals",
"state_before": "K : Type u_3\nσ : Type u_2\nι : Type u_1\ninst✝⁶ : Fintype K\ninst✝⁵ : Field K\ninst✝⁴ : Fintype σ\ninst✝³ : DecidableEq σ\ninst✝² : DecidableEq K\np : ℕ\ninst✝¹ : CharP K p\ninst✝ : Fintype ι\nf : ι → MvPolynomial σ K\nh : ∑ i : ι, totalDegree (f i) < Fintype.c... | [
176,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ball_insert_iff | [] | [
1240,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_right_surjective | [] | [
530,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_eq_zero_iff | [] | [
429,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
11
] |
Mathlib/CategoryTheory/FullSubcategory.lean | CategoryTheory.fullSubcategoryInclusion.obj | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Inseparable.lean | Inducing.specializes_iff | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ?u.14588\nα : Type ?u.14591\nι : Type ?u.14594\nπ : ι → Type ?u.14599\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X\nf :... | [
198,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.ret_bind | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nf : α → Seq1 β\n⊢ join (f a, nil) = f a",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nf : α → Seq1 β\n⊢ bind (ret a) f = f a",
"tactic": "simp [ret, bind, map]"
},
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : ... | [
985,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.mem_gt | [] | [
975,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pureMulHom_apply | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.rpow_eq_nhds_of_pos | [
{
"state_after": "p : ℝ × ℝ\nhp_fst : 0 < p.fst\nthis : ∀ᶠ (x : ℝ × ℝ) in 𝓝 p, 0 < x.fst\n⊢ (fun x => x.fst ^ x.snd) =ᶠ[𝓝 p] fun x => exp (log x.fst * x.snd)\n\ncase this\np : ℝ × ℝ\nhp_fst : 0 < p.fst\n⊢ ∀ᶠ (x : ℝ × ℝ) in 𝓝 p, 0 < x.fst",
"state_before": "p : ℝ × ℝ\nhp_fst : 0 < p.fst\n⊢ (fun x => x.fst... | [
219,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/CategoryTheory/Category/Bipointed.lean | swap_comp_bipointedToPointedFst | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Order/Basic.lean | ge_of_tendsto | [] | [
198,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/CategoryTheory/Preadditive/Yoneda/Injective.lean | CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditiveYoneda_obj | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nJ : C\n⊢ Functor.PreservesEpimorphisms (yoneda.obj J) ↔ Functor.PreservesEpimorphisms (preadditiveYoneda.obj J)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nJ : C\n⊢ Injective J ↔ Functor.PreservesEpimorp... | [
43,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.bot_apply | [] | [
855,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measure_mul_lintegral_eq | [
{
"state_after": "G : Type u_1\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : Group G\ninst✝⁵ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝⁴ : SigmaFinite ν\ninst✝³ : SigmaFinite μ\ns : Set G\ninst✝² : MeasurableInv G\ninst✝¹ : IsMulLeftInvariant μ\ninst✝ : IsMulLeftInvariant ν\nsm : MeasurableSet s\nf : G → ℝ≥0∞\nhf : Mea... | [
262,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Nat/PSub.lean | Nat.ppred_zero | [] | [
39,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_pow | [
{
"state_after": "case zero\nα : Type u\nβ : Type v\np : α → Prop\nf✝ f : Perm α\nhf : ∀ (x : α), p x ↔ p (↑f x)\n⊢ subtypePerm f hf ^ Nat.zero = subtypePerm (f ^ Nat.zero) (_ : ∀ (x : α), p x ↔ p (↑(f ^ Nat.zero) x))\n\ncase succ\nα : Type u\nβ : Type v\np : α → Prop\nf✝ f : Perm α\nhf : ∀ (x : α), p x ↔ p (↑f... | [
410,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Sym/Card.lean | Sym2.card_image_offDiag | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.78623\ninst✝ : DecidableEq α\ns : Finset α\n⊢ Finset.card (image Quotient.mk' (offDiag s)) = Nat.choose (Finset.card s) 2",
"tactic": "rw [Nat.choose_two_right, mul_tsub, mul_one, ← offDiag_card,\n Nat.div_eq_of_eq_mul_right zero_l... | [
172,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.rel_eq_coe | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableOn.exp | [] | [
304,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Algebra/Parity.lean | Even.neg_zpow | [
{
"state_after": "case intro\nF : Type ?u.40950\nα : Type u_1\nβ : Type ?u.40956\nR : Type ?u.40959\ninst✝¹ : DivisionMonoid α\na✝ : α\ninst✝ : HasDistribNeg α\nc : ℤ\na : α\n⊢ (-a) ^ (c + c) = a ^ (c + c)",
"state_before": "F : Type ?u.40950\nα : Type u_1\nβ : Type ?u.40956\nR : Type ?u.40959\ninst✝¹ : Div... | [
191,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/Associated.lean | Prime.pow_dvd_of_dvd_mul_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.38286\nγ : Type ?u.38289\nδ : Type ?u.38292\ninst✝ : CancelCommMonoidWithZero α\np a b : α\nhp : Prime p\nn : ℕ\nh : ¬p ∣ b\nh' : p ^ n ∣ b * a\n⊢ p ^ n ∣ a",
"state_before": "α : Type u_1\nβ : Type ?u.38286\nγ : Type ?u.38289\nδ : Type ?u.38292\ninst✝ : CancelCom... | [
124,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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src/lean/Init/Core.lean | Bool.of_not_eq_false | [] | [
599,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
597,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_nonneg_of_three | [
{
"state_after": "α : Type u\nβ : Type ?u.180652\ninst✝ : LinearOrderedRing α\na✝ b✝ c✝ a b c : α\n⊢ (0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0) ∨ (0 ≤ b ∧ 0 ≤ c ∨ b ≤ 0 ∧ c ≤ 0) ∨ 0 ≤ c ∧ 0 ≤ a ∨ c ≤ 0 ∧ a ≤ 0",
"state_before": "α : Type u\nβ : Type ?u.180652\ninst✝ : LinearOrderedRing α\na✝ b✝ c✝ a b c : α\n⊢ 0 ≤ a *... | [
1089,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_closure | [] | [
1101,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.map_sum | [] | [
391,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_comm | [] | [
98,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_union_add_ncard_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.119105\ns✝ t✝ : Set α\na b x y : α\nf : α → β\ns t : Set α\nhs : autoParam (Set.Finite s) _auto✝\nht : autoParam (Set.Finite t) _auto✝\nhu : Set.Finite (s ∪ t)\n⊢ ncard (s ∪ t) + ncard (s ∩ t) = ncard s + ncard t",
"state_before": "α : Type u_1\nβ : Type ?u.119105... | [
465,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Topology/Connected.lean | connectedComponentIn_eq_empty | [] | [
593,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.I_ne_zero | [] | [
324,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Analysis/Complex/Conformal.lean | isConformalMap_iff_is_complex_or_conj_linear | [
{
"state_after": "case mp\nf : ℂ → ℂ\nz : ℂ\ng : ℂ →L[ℝ] ℂ\n⊢ IsConformalMap g → ((∃ map, restrictScalars ℝ map = g) ∨ ∃ map, restrictScalars ℝ map = comp g ↑conjCle) ∧ g ≠ 0\n\ncase mpr\nf : ℂ → ℂ\nz : ℂ\ng : ℂ →L[ℝ] ℂ\n⊢ ((∃ map, restrictScalars ℝ map = g) ∨ ∃ map, restrictScalars ℝ map = comp g ↑conjCle) ∧ g... | [
126,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Topology/ContinuousOn.lean | mem_nhdsWithin_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19402\nγ : Type ?u.19405\nδ : Type ?u.19408\ninst✝ : TopologicalSpace α\na : α\ns t : Set α\n⊢ t ∈ 𝓝[insert a s] a ↔ a ∈ t ∧ t ∈ 𝓝[s] a",
"tactic": "simp"
}
] | [
291,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Nat.comap_cast_atTop | [] | [
32,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.id_apply_self | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : Preadditive C\nR : Type u\ninst✝ : Semiring R\nM : Mat R\ni : ↑M\n⊢ 𝟙 M i i = 1",
"tactic": "simp [id_apply]"
}
] | [
597,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.mk_coe | [] | [
233,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.isZero_zero | [
{
"state_after": "case refine'_1\nι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasZeroObject V\nX : HomologicalComplex V c\nf : zero ⟶ X\n⊢ f = default\n\ncase refine'_2\nι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ ... | [
272,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Integrable.induction | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3384233\nι : Type ?u.3384236\nE : Type u_2\nF : Type ?u.3384242\n𝕜 : Type ?u.3384245\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf : α → E\np : ℝ≥0∞\nμ : Measure α\nP : (α → E) → Prop\nh_ind : ∀ (c : E) ⦃s : Set α⦄, MeasurableSet s → ↑↑μ s < ⊤ → P (ind... | [
1112,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
Mathlib/Logic/Equiv/Basic.lean | PLift.eq_up_iff_down_eq | [] | [
1723,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.empty_div | [] | [
577,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.insert | [
{
"state_after": "ι : Type u'\nι' : Type ?u.1209871\nR : Type ?u.1209874\nK : Type u_1\nM : Type ?u.1209880\nM' : Type ?u.1209883\nM'' : Type ?u.1209886\nV : Type u\nV' : Type ?u.1209891\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module K V\ninst✝ : Module K V'\nv : ι ... | [
1180,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_add_of_natDegree_lt_left | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nf p q : R[X]\npq : natDegree q < natDegree p\nn : ℕ\n⊢ coeff (eraseLead (p + q)) n = coeff (eraseLead p + q) n",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf p q : R[X]\npq : natDegree q < natDegree p\n⊢ eraseLead (p + q) = eraseLead p + q"... | [
169,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.injective | [] | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
11
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\nf✝ f : R[X]\n⊢ ↑(taylor 0) f = f",
"tactic": "rw [taylor_zero', LinearMap.id_apply]"
}
] | [
65,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Analysis/Calculus/Conformal/InnerProduct.lean | conformalAt_iff' | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : InnerProductSpace ℝ F\nf : E → F\nx : E\n⊢ ConformalAt f x ↔ ∃ c, 0 < c ∧ ∀ (u v : E), inner (↑(fderiv ℝ f x) u) (↑(fderiv ℝ f x) v)... | [
36,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | isBoundedBilinearMap_smulRight | [] | [
477,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_eq_mul_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f✝ : α → β\ninst✝¹ : CommMonoid β\nδ : Type u_1\ninst✝ : CommGroup δ\nf : ℕ → δ\nm n : ℕ\nh : m ≤ n\n⊢ (∏ k in Ico m n, f k) * ∏ k in range m, f k = ∏ k in range n, f k",
"tactic": "(rw [mul_co... | [
101,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_delete_edges_iff_exists_walk | [
{
"state_after": "case mp\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nv w : V\n⊢ Reachable (G \\ fromEdgeSet {Quotient.mk (Sym2.Rel.setoid V) (v, w)}) v w →\n ∃ p, ¬Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ Walk.edges p\n\ncase mpr\nV : Type u\nV' : T... | [
2462,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2450,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.mem_center_iff | [] | [
45,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Sigma/Lex.lean | PSigma.lex_iff | [
{
"state_after": "case mp\nι : Sort u_1\nα : ι → Sort u_2\nr r₁ r₂ : ι → ι → Prop\ns s₁ s₂ : (i : ι) → α i → α i → Prop\na b : (i : ι) ×' α i\n⊢ Lex r s a b → r a.fst b.fst ∨ ∃ h, s b.fst (h ▸ a.snd) b.snd\n\ncase mpr\nι : Sort u_1\nα : ι → Sort u_2\nr r₁ r₂ : ι → ι → Prop\ns s₁ s₂ : (i : ι) → α i → α i → Prop\... | [
166,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_mul | [] | [
89,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_iff_norm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.699389\nδ : Type ?u.699392\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\n⊢ HasFiniteIntegral f ↔ (∫⁻ (a : α), ENNReal.ofReal ‖f... | [
122,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | ofMul_zpow | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_iSup_left | [] | [
368,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.toLinearPMap_domain | [] | [
975,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | surjective_of_nonzero_of_finrank_eq_one | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁸ : DivisionRing K\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module K V\nW : Type u_1\nA : Type u_2\ninst✝⁵ : Semiring A\ninst✝⁴ : Module A V\ninst✝³ : AddCommGroup W\ninst✝² : Module K W\ninst✝¹ : Module A W\ninst✝ : LinearMap.CompatibleSMul V W K A\nh : finrank K W = 1\... | [
1329,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.rotateL | [
{
"state_after": "case nil\nα : Type u_1\nl : Ordnode α\nx : α\nhl : Sized l\nhr : Sized nil\n⊢ Sized (Ordnode.rotateL l x nil)\n\ncase node\nα : Type u_1\nl : Ordnode α\nx : α\nhl : Sized l\nsize✝ : ℕ\nl✝ : Ordnode α\nx✝ : α\nr✝ : Ordnode α\nhr : Sized (node size✝ l✝ x✝ r✝)\n⊢ Sized (Ordnode.rotateL l x (node ... | [
415,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.iInf_toSubalgebra | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.695010\nR : Type u_2\nA : Type u_3\nB : Type ?u.695019\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRin... | [
696,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Topology/Sheaves/LocalPredicate.lean | TopCat.stalkToFiber_injective | [
{
"state_after": "case refine_2\nX : TopCat\nT : ↑X → Type v\nP : LocalPredicate T\nx : ↑X\nw :\n ∀ (U V : OpenNhds x) (fU : (y : { x_1 // x_1 ∈ U.obj }) → T ↑y),\n PrelocalPredicate.pred P.toPrelocalPredicate fU →\n ∀ (fV : (y : { x_2 // x_2 ∈ V.obj }) → T ↑y),\n PrelocalPredicate.pred P.toPrel... | [
302,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.liftHom_comp | [] | [
339,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Topology/Order/Basic.lean | nhds_bot_basis_Iic | [] | [
1158,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | ContDiff.continuous_iteratedDeriv | [] | [
280,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.sub_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\nx✝ : a₂ ≡ b₂ [PMOD p]\nm : ℤ\nhm : b₂ - a₂ = m • p\n⊢ (∃ b, b₁ - b₂ - (a₁ - a₂) = ↑(Equiv.subRight m).symm.symm b • p) ↔ a₁ ≡ b₁ [PMOD p]",
"tactic": "simp [sub_sub_sub_comm, hm, su... | [
210,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.range_toLin' | [] | [
422,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Order/SuccPred/IntervalSucc.lean | Antitone.pairwise_disjoint_on_Ico_pred | [] | [
135,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_sub_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type ?u.30419\nN : Type u_2\nP : Type ?u.30425\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf f₁ f₂ g g₁ g₂ : α →₀ N\n⊢ neLocus (f₁ - g) (f₂ - g) = neLocus f₁ f₂",
"tactic": "simpa only [sub_eq_add_neg] using neLocus... | [
158,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.add | [] | [
981,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
11
] |
Mathlib/Data/Finset/Card.lean | Finset.card_insert_le | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.4838\ns✝ t : Finset α\na✝ b : α\ninst✝ : DecidableEq α\na : α\ns : Finset α\nh : a ∈ s\n⊢ card (insert a s) ≤ card s + 1\n\ncase neg\nα : Type u_1\nβ : Type ?u.4838\ns✝ t : Finset α\na✝ b : α\ninst✝ : DecidableEq α\na : α\ns : Finset α\nh : ¬a ∈ s\n⊢ card (i... | [
119,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.center_normal | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.40911\nA : Type ?u.40914\na a₁ a₂ b c : G\ninst✝ : Group G\n⊢ 1 ∈ center G",
"tactic": "simp [center]"
},
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.40911\nA : Type ?u.40914\na a₁ a₂ b c : G\... | [
291,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Topology/Order.lean | le_induced_generateFrom | [
{
"state_after": "α✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\nt : TopologicalSpace α\nb : Set (Set β)\nf : α → β\nh : ∀ (a : Set β), a ∈ b → IsOpen (f ⁻¹' a)\n⊢ t ≤ generateFrom (preimage f '' b)",
"state_before": "α✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\nt : TopologicalSpace α\nb : S... | [
575,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.star_rightMoves | [] | [
1844,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1843,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_addSubmonoid_closure | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring T\ns : Set R\nx : R\n⊢ x ∈ closure ↑(AddSubmonoid.closure s) ↔ x ∈ closure s",
"state_before": "R : Type u\nS : Type... | [
674,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_compl_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.45893\nι : Sort ?u.45896\nι' : Sort ?u.45899\nf✝ : α → β\ns✝ t : Set α\nf : α → β\ns : Set α\nH : Injective f\n⊢ Disjoint (f '' s) (f '' sᶜ)",
"tactic": "simp [disjoint_iff_inf_le, ←image_inter H]"
}
] | [
418,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.setOf_isOpen_injective | [] | [
233,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.bit0_mod_bit0 | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ bit0 n % bit0 m = bit0 (n % m)",
"tactic": "rw [bit0_eq_two_mul n, bit0_eq_two_mul m, bit0_eq_two_mul (n % m), Nat.mul_mod_mul_left]"
}
] | [
265,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.neg_comp | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/RingTheory/ClassGroup.lean | FractionalIdeal.coe_mk0 | [] | [
242,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrixₛₗ₂'_apply | [] | [
272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_preimage | [] | [
505,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Order/Monotone/Basic.lean | antitone_app | [] | [
336,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ne_zero | [] | [
379,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Complex.lean | QuadraticForm.complex_equivalent | [] | [
88,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nha : a ≠ 0\n⊢ trailingDegree (↑C a * X ^ n) = ↑n",
"tactic": "rw [C_mul_X_pow_eq_monomial, trailingDegree_monomial ha]"
}
] | [
254,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
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