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/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivBFamily_fp | [
{
"state_after": "o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal → Ordinal\ni : Ordinal\nhi : i < o\nH : IsNormal (f i hi)\na : Ordinal\n⊢ familyOfBFamily o f (enum (fun x x_1 => x < x_1) i (_ : i < type fun x x_1 => x < x_1)) (derivBFamily o f a) =\n derivBFamily o f a",
"state_before": "o : Ordinal\n... | [
374,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_mul_le | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\nι : Type ?u.567630\np q : R[X]\n⊢ degree (∑ x in support p, sum q fun j a => ↑(monomial (x + j)) (coeff p x * a)) ≤\n sup (support p) fun i => degree (sum q fun j a => ↑(monomial (i + j)) (coeff p i * a))",
... | [
782,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasFDerivWithinAt_iff_hasDerivWithinAt | [] | [
174,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.pred_eq_succ_iff | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k n m : ℕ\n⊢ pred n = succ m ↔ n = m + 2",
"tactic": "cases n <;> constructor <;> rintro ⟨⟩ <;> rfl"
}
] | [
316,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.comp_contDiffAt_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜... | [
338,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_orbit | [] | [
64,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLeast_univ_iff | [] | [
826,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
9
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.bound_of_shell | [
{
"state_after": "case inl.intro\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddComm... | [
118,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryFin1_apply | [] | [
1735,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1733,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.coe_coeMonoidHom | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | MulOpposite.comap_op_nhds | [] | [
79,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairOp_left | [] | [
151,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.322097\nδ : Type ?u.322100\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns t : Set α\nx : α\n⊢ ContinuousWithinAt f (s ∪ t) x ↔ ContinuousWit... | [
718,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.mem_closure | [] | [
1985,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1984,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | exists_deriv_eq_zero' | [
{
"state_after": "f f' : ℝ → ℝ\na b l : ℝ\nhab : a < b\nhfa : Tendsto f (𝓝[Ioi a] a) (𝓝 l)\nhfb : Tendsto f (𝓝[Iio b] b) (𝓝 l)\nh : ∃ x, x ∈ Ioo a b ∧ ¬DifferentiableAt ℝ f x\n⊢ ∃ x, x ∈ Ioo a b ∧ ¬DifferentiableAt ℝ f x",
"state_before": "f f' : ℝ → ℝ\na b l : ℝ\nhab : a < b\nhfa : Tendsto f (𝓝[Ioi a]... | [
345,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.continuousLinearMap_comp | [] | [
228,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Algebra/Group/Units.lean | divp_mul_divp | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : CommMonoid α\nx y : α\nux uy : αˣ\n⊢ x /ₚ ux * (y /ₚ uy) = x * y /ₚ (ux * uy)",
"tactic": "rw [divp_mul_eq_mul_divp, divp_assoc', divp_divp_eq_divp_mul]"
}
] | [
549,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.toSubgraph_rotate | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\ninst✝ : DecidableEq V\nc : Walk G v v\nh : u ∈ support c\n⊢ Walk.toSubgraph (rotate c h) = Walk.toSubgraph c",
"tactic": "rw [rotate, toSubgraph_... | [
2271,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2269,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isSuccLimit_succ | [] | [
93,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_finset_iUnion | [] | [
214,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/List/Zip.lean | List.get?_zip_eq_some | [
{
"state_after": "case mk\nα : Type u\nβ : Type u_1\nγ : Type ?u.155522\nδ : Type ?u.155525\nε : Type ?u.155528\nl₁ : List α\nl₂ : List β\ni : ℕ\nfst✝ : α\nsnd✝ : β\n⊢ get? (zip l₁ l₂) i = some (fst✝, snd✝) ↔ get? l₁ i = some (fst✝, snd✝).fst ∧ get? l₂ i = some (fst✝, snd✝).snd",
"state_before": "α : Type u... | [
396,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_eq | [] | [
86,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
86,
9
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_mem_Ioc_zpow | [
{
"state_after": "case intro\nα : Type ?u.560921\nβ : Type ?u.560924\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ny : ℝ≥0∞\nhy : 1 < y\nh'y : y ≠ ⊤\nx : ℝ≥0\nhx : ↑x ≠ 0\n⊢ ∃ n, ↑x ∈ Ioc (y ^ n) (y ^ (n + 1))",
"state_before": "α : Type ?u.560921\nβ : Type ?u.560924\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y : ℝ≥0∞\nhx : x ≠ 0\nh'... | [
1897,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1887,
1
] |
Mathlib/Order/Heyting/Hom.lean | BiheytingHom.coe_id | [] | [
553,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_bit0 | [
{
"state_after": "α : Type u_1\ninst✝ : Semiring α\nn : Num\n⊢ ↑n + ↑n = _root_.bit0 ↑n",
"state_before": "α : Type u_1\ninst✝ : Semiring α\nn : Num\n⊢ ↑(Num.bit0 n) = _root_.bit0 ↑n",
"tactic": "rw [← bit0_of_bit0, _root_.bit0, cast_add]"
},
{
"state_after": "no goals",
"state_before": "α :... | [
736,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_one | [] | [
154,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_le_of_le' | [] | [
228,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.measure_apply | [] | [
387,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_eq_norm_integral_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.11586972\n𝕜 : Type ?u.11586975\nE : Type u_1\nF : Type ?u.11586981\nA : Type ?u.11586984\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\n⊢ ‖∫ (x : ℝ) i... | [
535,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ioc_right | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : Preorder α\na✝ b c a : α\n⊢ (⋃ (b : α), Ioc a b) = Ioi a",
"tactic": "simp only [← Ioi_inter_Iic, ← inter_iUnion, iUnion_Iic, inter_univ]"
}
] | [
83,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_mul | [
{
"state_after": "n m : ℕ+\nu : PrimeMultiset := factorMultiset n\n⊢ factorMultiset (n * m) = factorMultiset n + factorMultiset m",
"state_before": "n m : ℕ+\n⊢ factorMultiset (n * m) = factorMultiset n + factorMultiset m",
"tactic": "let u := factorMultiset n"
},
{
"state_after": "n m : ℕ+\nu :... | [
306,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Type ?u.15886\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : MetricSpace E\nf : ℕ → α → E\ng : α → E\nhfg : TendstoInMeasure μ f atTop g\nn : ℕ\n⊢ seqTendstoAeSeq hfg (n + 1) = max (seqTendstoAeSeqAux hfg (n + 1)) (seqTendstoAeSeq... | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.prod_span | [
{
"state_after": "ι✝ : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nM✝ N : Submodule R A\nm n : A\nι : Type u_1\ns : Finset ι\nM : ι → Set A\nthis : DecidableEq ι := Classical.decEq ι\n⊢ ∏ i in s, span R (M i) = span R (∏ i in s, M i)",
"state_befor... | [
614,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | MonoidHom.ker_eq_bot_of_cancel | [
{
"state_after": "no goals",
"state_before": "A : Type u\nB : Type v\ninst✝¹ : Group A\ninst✝ : Group B\nf : A →* B\nh : ∀ (u v : { x // x ∈ ker f } →* A), comp f u = comp f v → u = v\n⊢ ker f = ⊥",
"tactic": "simpa using _root_.congr_arg range (h f.ker.subtype 1 (by aesop_cat))"
},
{
"state_aft... | [
37,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_mono_left | [] | [
85,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_f_idem | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f PInfty n ≫ HomologicalComplex.Hom.f PInfty n = HomologicalComplex.Hom.f PInfty n",
"tactic": "simp only [PInfty_f, P_f_idem]"
}
] | [
107,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toAdd_inv | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.smul_contLinear | [] | [
153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.neg | [] | [
487,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.cancel_natIso_inv_right_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G : C ⥤ D\nα : F ≅ G\nW X X' : D\nY : C\nf : W ⟶ X\ng : X ⟶ G.obj Y\nf' : W ⟶ X'\ng' : X' ⟶ G.obj Y\n⊢ f ≫ g ≫ α.inv.app Y = f' ≫ g' ≫ α.inv.app Y ↔ f ≫ g = f'... | [
161,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | totallyBounded_iff_filter | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\n⊢ TotallyBounded s → ∀ (f : Filter α), NeBot f → f ≤ 𝓟 s → ∃ c, c ≤ f ∧ Cauchy c\n\ncase mpr\nα : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\n⊢ (∀ (f : Filter α), NeBot f → f ≤ 𝓟 s → ∃ c, c ≤ f ∧ Cauchy c) → Total... | [
565,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_Ioc_of_ae_eq | [] | [
159,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.zero_imK | [] | [
858,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
9
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.map_zsmul | [] | [
98,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_univ_of_one_mem | [] | [
984,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_iff_eq_of_div_eq_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.62821\nβ : Type ?u.62824\nG : Type u_1\ninst✝ : Group G\na b c d : G\nH : a / b = c / d\n⊢ a = b ↔ c = d",
"tactic": "rw [← div_eq_one, H, div_eq_one]"
}
] | [
849,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.eq_zero_iff_forall_dual_eq_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nhx : x = 0\n⊢ ∀ (g : Dual 𝕜 E), ↑g x = 0",
"tactic": "simp [hx]"
}
] | [
155,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | Equiv.pointReflection_midpoint_left | [
{
"state_after": "no goals",
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75,
41
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72,
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Mathlib/Data/Set/Function.lean | Set.eqOn_union | [] | [
226,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_of_lt | [] | [
361,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Ioo_right | [] | [
207,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
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Mathlib/CategoryTheory/Abelian/LeftDerived.lean | CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi | [
{
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Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.Initial.left_inv' | [
{
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}
] | [
238,
37
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237,
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src/lean/Init/Control/StateCps.lean | StateCpsT.runK_pure | [] | [
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135
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOn.uniformCauchySeqOnFilter | [
{
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418,
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417,
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Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.subset_right_C | [] | [
131,
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130,
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Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.le_card_nonuniformWitness | [
{
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179,
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174,
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Mathlib/Data/Part.lean | Part.some_toOption | [] | [
254,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.iInf_ker_lapply_le_bot | [
{
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148,
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146,
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Mathlib/Order/CompleteLattice.lean | sInf_union | [] | [
472,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_update | [
{
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1088,
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1084,
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_mono_right | [] | [
1718,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1718,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.coe_rpow_def | [] | [
369,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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Mathlib/Data/Finset/Basic.lean | Finset.erase_empty | [] | [
1870,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1869,
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Std/Data/String/Lemmas.lean | String.takeWhile_eq | [] | [
1102,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1101,
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Mathlib/FieldTheory/Normal.lean | AlgHom.fieldRange_of_normal | [
{
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351,
86
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344,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.linearMap_ext | [] | [
326,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x + a) ⁻¹' Icc b c = Icc (b - a) (c - a)",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
109,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.hasFDerivAt | [] | [
274,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
11
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Std/Data/List/Basic.lean | List.fillNones_eq_fillNonesTR | [
{
"state_after": "case h.h.h\nα : Type u_1\nas : List (Option α)\nas' : List α\n⊢ fillNones as as' = fillNonesTR as as'",
"state_before": "⊢ @fillNones = @fillNonesTR",
"tactic": "funext α as as'"
},
{
"state_after": "case h.h.h\nα : Type u_1\nas : List (Option α)\nas' : List α\n⊢ fillNones as a... | [
1453,
25
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1446,
10
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Std/Data/List/Basic.lean | List.erase_eq_eraseTR | [
{
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},
{
"state_after": "case h.h.h.h\nα : Type u_1\nx✝ : BEq α\nl : List α\na : α\n⊢ List.erase l a = eraseTR.go l a l... | [
50,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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10
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_sInf | [
{
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"state_before": "α β : Type u\ns : Set Cardinal\n⊢ lift (sInf s) = sInf (lift '' s)",
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1100,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
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Mathlib/Topology/Basic.lean | interior_compl | [
{
"state_after": "no goals",
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"tactic": "simp [closure_eq_compl_interior_compl]"
}
] | [
552,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Std/Data/List/Init/Lemmas.lean | List.foldlM_append | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nβ : Type u_1\nα : Type u_3\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : β → α → m β\nb : β\nl l' : List α\n⊢ List.foldlM f b (l ++ l') = do\n let init ← List.foldlM f b l\n List.foldlM f init l'",
"tactic": "induction l genera... | [
164,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
162,
9
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_nonsing_inv | [
{
"state_after": "case pos\nl : Type ?u.242378\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nh : IsUnit (det A)\n⊢ det A⁻¹ = Ring.inverse (det A)\n\ncase neg\nl : Type ?u.242378\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\n... | [
404,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.monotone_principal | [] | [
658,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Data/Multiset/Functor.lean | Multiset.pure_def | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.aemeasurable | [] | [
1866,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1863,
11
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.trans_right | [] | [
964,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.896628\na a' a₁ a₂ : R\ne : ℕ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\np : MvPolynomial (Fin (n + 1)) R\n⊢ ↑(finSuccEquiv R n) p =\n ↑(eval₂Hom (RingHom.comp Polynomial.C C) fun i => Fin.cases ... | [
339,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_sub | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Odd (m - n) ↔ (Odd m ↔ Even n)",
"tactic": "rw [odd_iff_not_even, even_sub, not_iff, odd_iff_not_even]"
}
] | [
189,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.comp_map | [] | [
72,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_insert | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.1235297\nR : Type ?u.1235300\nK : Type u_1\nM : Type ?u.1235306\nM' : Type ?u.1235309\nM'' : Type ?u.1235312\nV : Type u\nV' : Type ?u.1235317\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module ... | [
1221,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.nsmul_f_apply | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk''_eq_mk | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.isQuadratic_χ₄ | [
{
"state_after": "a : ZMod 4\n⊢ ↑χ₄ a = 0 ∨ ↑χ₄ a = 1 ∨ ↑χ₄ a = -1",
"state_before": "⊢ MulChar.IsQuadratic χ₄",
"tactic": "intro a"
},
{
"state_after": "case head\n\n⊢ ↑χ₄ { val := 0, isLt := (_ : 0 < 3 + 1) } = 0 ∨\n ↑χ₄ { val := 0, isLt := (_ : 0 < 3 + 1) } = 1 ∨ ↑χ₄ { val := 0, isLt := (_... | [
55,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.Disjoint.cycleType | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ τ : Perm α\nh : Disjoint σ τ\n⊢ Multiset.Disjoint (cycleFactorsFinset σ).val (cycleFactorsFinset τ).val",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ τ : Perm α\nh : Disjoint σ τ\n⊢ Perm.cycleType (σ... | [
128,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_add_pi | [] | [
1145,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAt.unique | [] | [
399,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.subset_infs | [] | [
355,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_neg | [] | [
468,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
9
] |
Mathlib/Analysis/Calculus/ContDiff.lean | HasFTaylorSeriesUpToOn.hasStrictFDerivAt | [] | [
1943,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1939,
1
] |
src/lean/Init/Prelude.lean | Or.elim | [] | [
536,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
533,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_mul_unit_right_right | [] | [
269,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lcs_succ | [] | [
71,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/RelIso/Basic.lean | preimage_equivalence | [] | [
221,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.wideCospan_map_term | [] | [
586,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Topology/Separation.lean | Dense.diff_finite | [
{
"state_after": "case h.e'_3.h.e'_4\nα : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : T1Space α\ninst✝ : ∀ (x : α), NeBot (𝓝[{x}ᶜ] x)\ns : Set α\nhs : Dense s\nt : Set α\nht : Set.Finite t\n⊢ t = ↑(Finite.toFinset ht)",
"state_before": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\nins... | [
731,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_univ | [] | [
159,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | ContinuousAt.arsinh | [] | [
220,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
8
] |
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