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/Int/Lemmas.lean | Int.negSucc_not_pos | [
{
"state_after": "n : Nat\n⊢ -[n+1] ≤ 0",
"state_before": "n : Nat\n⊢ 0 < -[n+1] ↔ False",
"tactic": "simp only [Int.not_lt, iff_false]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ -[n+1] ≤ 0",
"tactic": "constructor"
}
] | [
744,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
743,
9
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.coe_mulRight₀ | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/Order/Basic.lean | Filter.Eventually.exists_gt | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : DenselyOrdered α\na✝ b : α\ns : Set α\ninst✝ : NoMaxOrder α\na : α\np : α → Prop\nh : ∀ᶠ (x : α) in 𝓝 a, p x\n⊢ ∃ b, b > a ∧ p b",
"t... | [
2403,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2400,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.mul | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.916695\nγ : Type ?u.916698\nδ : Type ?u.916701\nm : MeasurableSpace α\ninst✝² : Zero β✝\ninst✝¹ : Zero γ\nμ : Measure α\nf✝ : α →ₛ β✝\nβ : Type u_1\ninst✝ : MonoidWithZero β\nf g : α →ₛ β\nhf : SimpleFunc.FinMeasSupp f μ\nhg : SimpleFunc.FinMeasSupp g μ\n⊢ SimpleFunc... | [
1245,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
11
] |
Mathlib/Algebra/Support.lean | Pi.mulSupport_mulSingle_of_ne | [
{
"state_after": "no goals",
"state_before": "A : Type u_2\nB : Type u_1\ninst✝¹ : DecidableEq A\ninst✝ : One B\na : A\nb : B\nh : b ≠ 1\nx : A\nhx : x = a\n⊢ x ∈ mulSupport (mulSingle a b)",
"tactic": "rwa [mem_mulSupport, hx, mulSingle_eq_same]"
}
] | [
479,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.nonempty_iInter_of_nonempty_biInter | [] | [
2763,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2760,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_mono | [] | [
212,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.attach_insert | [] | [
599,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.ext | [] | [
146,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.zero_map | [] | [
363,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.strictMonoOn_log | [] | [
208,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Algebra/Homology/Additive.lean | CategoryTheory.NatTrans.mapHomologicalComplex_id | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : Preadditive V\nc✝ : ComplexShape ι\nC D E : HomologicalComplex V c✝\nf g : C ⟶ D\nh k : D ⟶ E\ni : ι\nW : Type u_3\ninst✝² : Category W\ninst✝¹ : Preadditive W\nc : ComplexShape ι\nF : V ⥤ W\ninst✝ : Functo... | [
211,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_abs_log_rpow_rpow_nhds_zero | [
{
"state_after": "no goals",
"state_before": "s r : ℝ\nhs : s < 0\nx : ℝ\nhx : x ∈ Set.Icc 0 1\n⊢ x ∈ {x | (fun x => ((fun x => log x ^ r) ∘ fun x => x⁻¹) x = (fun x => abs (log x) ^ r) x) x}",
"tactic": "simp [abs_of_nonpos, log_nonpos hx.1 hx.2]"
},
{
"state_after": "no goals",
"state_befo... | [
318,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.tendsto_log_atTop | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ Tendsto (fun x => log (exp x)) atTop atTop",
"tactic": "simpa only [log_exp] using tendsto_id"
}
] | [
295,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_pos_of_pos | [
{
"state_after": "F : Type ?u.54964\nι : Type ?u.54967\nα : Type ?u.54970\nβ : Type ?u.54973\nK : Type u_1\ninst✝ : LinearOrderedField K\nr : ℚ\nhr : 0 < r\n⊢ 0 < ↑r.num / ↑r.den",
"state_before": "F : Type ?u.54964\nι : Type ?u.54967\nα : Type ?u.54970\nβ : Type ?u.54973\nK : Type u_1\ninst✝ : LinearOrdere... | [
301,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_abs_left | [] | [
777,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Subset.antisymm | [] | [
371,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | summable_iff_not_tendsto_nat_atTop_of_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.345613\nβ : Type ?u.345616\nγ : Type ?u.345619\nf : ℕ → ℝ\nhf : ∀ (n : ℕ), 0 ≤ f n\n⊢ Summable f ↔ ¬Tendsto (fun n => ∑ i in Finset.range n, f i) atTop atTop",
"tactic": "rw [← not_iff_not, Classical.not_not, not_summable_iff_tendsto_nat_atTop_of... | [
1330,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.mem_sup | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\nx : M\n⊢ (∃ y, y ∈ ↑N ∧ ∃ z, z ∈ ↑N' ∧ y + z =... | [
498,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_map_iff | [] | [
2709,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2707,
1
] |
Mathlib/Data/Num/Prime.lean | Num.minFac_to_nat | [] | [
124,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Max.lean | IsMax.mono | [] | [
310,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mk_X_0 | [] | [
991,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_X_add_C | [] | [
1369,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.stable_iff_exists_pow_smul_eq_of_ge | [
{
"state_after": "R M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nh✝ : Stable F\nh : ∃ n₀, ∀ (n : ℕ), n ≥ n₀ → N F n = I ^ (n - n₀) • N F n₀\nn : ℕ\nhn : n ≥ Exists.choose h\n⊢ I • N F n = N F (n + 1)",
"state_before": "R M : Type u\ninst✝²... | [
238,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Finset/Card.lean | Multiset.card_toFinset | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_inf_distrib_left | [] | [
995,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
11
] |
Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.symmₗ_linearMapAt | [
{
"state_after": "R : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁷ : Semiring R\ninst✝⁶ : TopologicalSpace F\ninst✝⁵ : TopologicalSpace B\ne✝ : Pretrivialization F TotalSpace.proj\nx : TotalSpace E\nb✝ : B\ny✝ : E b✝\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module R F\ninst✝² : (x : B) → AddCommMon... | [
157,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_pow | [
{
"state_after": "case zero\nα : Type u_2\nβ : Type ?u.21041\nA : Type ?u.21044\nB : Type ?u.21047\nM : Type u_1\nN : Type ?u.21053\nP : Type ?u.21056\nR : Type ?u.21059\nS : Type ?u.21062\nG : Type ?u.21065\nM₀ : Type ?u.21068\nG₀ : Type ?u.21071\nι : Sort ?u.21074\ninst✝ : Monoid M\nf : α → M\n⊢ (mulSupport f... | [
270,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_inter | [
{
"state_after": "α✝ : Type ?u.102784\nβ : Type ?u.102787\nγ : Type ?u.102790\nι✝ : Sort ?u.102793\nι' : Sort ?u.102796\nι₂ : Sort ?u.102799\nκ : ι✝ → Sort ?u.102804\nκ₁ : ι✝ → Sort ?u.102809\nκ₂ : ι✝ → Sort ?u.102814\nκ' : ι' → Sort ?u.102819\nι : Type u_1\nα : Type u_2\ns : Set ι\nhs : Set.Nonempty s\nf : ι →... | [
954,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.exists_inv_mem_iff_exists_mem | [] | [
609,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
11
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.zero_le_restrict_not_measurable | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.589378\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\nv w : VectorMeasure α M\ni j : Set α\nhi : ¬MeasurableSet i\n⊢ restrict 0 i ≤ restrict v i",
"tactic": "rw [restrict_zero, res... | [
1010,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsIntegralClosure.isFractionRing_of_finite_extension | [] | [
355,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.mem_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na y : Lists α\nl : Lists' α true\n⊢ a ∈ cons y l ↔ a ~ y ∨ a ∈ l",
"tactic": "simp [mem_def, or_and_right, exists_or]"
}
] | [
165,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.inv_eq_val_inv | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_max | [] | [
173,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_id | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.add_div_eq_of_le_mod_add_mod | [
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nhc : c ≤ a % c + b % c\nhc0 : 0 < c\n⊢ (a + b) / c = a / c + b / c + 1",
"tactic": "rw [add_div hc0, if_pos hc]"
}
] | [
481,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Data/Set/Image.lean | Set.surjective_onto_range | [] | [
1062,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.max | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.710602\nγ : Type ?u.710605\nγ₂ : Type ?u.710608\nδ : Type u_1\nι : Sort y\ns t u : Set α\ninst✝¹⁷ : TopologicalSpace α\ninst✝¹⁶ : MeasurableSpace α\ninst✝¹⁵ : OpensMeasurableSpace α\ninst✝¹⁴ : TopologicalSpace β\ninst✝¹³ : MeasurableSpa... | [
791,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | volume_regionBetween_eq_lintegral' | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\nhg : Measurable g\nhs : MeasurableSet s\n⊢ (∫⁻ (x : α), ↑↑volume (Prod.mk x ⁻¹' regionBetween f g s) ∂μ) = ∫⁻ (y : α) in s, ofReal ((g - f) y) ∂μ\n\nα : Type u_1\ninst✝ : Measurable... | [
551,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le | [
{
"state_after": "𝕜 : 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✝¹⁶ : Fintype ι\ninst✝¹⁵ : Fintype ι'\ninst✝¹⁴ : NontriviallyNormedField 𝕜\ninst✝¹³ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
849,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorph.isLocallyHomeomorphOn | [] | [
100,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.bex | [] | [
507,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_eq_inter_iff_left | [] | [
993,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | HasCompactMulSupport.exists_pos_le_norm | [
{
"state_after": "case intro.intro\n𝓕 : Type ?u.1239473\n𝕜 : Type ?u.1239476\nα : Type u_2\nι : Type ?u.1239482\nκ : Type ?u.1239485\nE : Type u_1\nF : Type ?u.1239491\nG : Type ?u.1239494\ninst✝¹ : NormedAddGroup α\nf : α → E\ninst✝ : One E\nhf : HasCompactMulSupport f\nK : Set α\nhK1 : IsCompact K\nhK2 : ∀ ... | [
2087,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2079,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_uIcc | [] | [
905,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
src/lean/Init/Prelude.lean | Eq.subst | [] | [
300,
17
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
299,
1
] |
Mathlib/Init/Logic.lean | rec_subsingleton | [] | [
351,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.apply_mem_iff | [
{
"state_after": "case h.e'_4\nι : Type ?u.1652962\nα : Type u_1\nβ : Type ?u.1652968\nf g : Perm α\ns t : Set α\na b x y : α\nhf : IsCycleOn f s\nhx : ↑f x ∈ s\n⊢ x = ↑f⁻¹ (↑f x)",
"state_before": "ι : Type ?u.1652962\nα : Type u_1\nβ : Type ?u.1652968\nf g : Perm α\ns t : Set α\na b x y : α\nhf : IsCycleO... | [
831,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_nonUnitalRingHom_inj_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.82658\nα : Type ?u.82661\nβ : Type ?u.82664\nR✝ : Type ?u.82667\nS✝ : Type ?u.82670\nS' : Type ?u.82673\ninst✝⁴ : NonUnitalNonAssocSemiring R✝\ninst✝³ : NonUnitalNonAssocSemiring S✝\ninst✝² : NonUnitalNonAssocSemiring S'\nR : Type u_1\nS : Type u_2\n... | [
624,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.unop_map_list_prod | [] | [
36,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
11
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.exists_forall_le | [] | [
139,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Convex/Segment.lean | mem_segment_translate | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.127506\nG : Type ?u.127509\nι : Type ?u.127512\nπ : ι → Type ?u.127517\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\na x b ... | [
264,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.uniformInducing | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.411266\nδ : Type ?u.411269\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : UniformSpace δ\nh : α ≃ᵤ β\n⊢ UniformInducing (↑(UniformEquiv.symm h) ∘ ↑h)",
"tactic": "simp only [symm_comp... | [
243,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.zero_le | [] | [
411,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Equalizer.Sieve.equalizer_sheaf_condition | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP : Cᵒᵖ ⥤ Type (max v₁ u₁)\nX : C\nR : Presieve X\nS : Sieve X\n⊢ Presieve.IsSheafFor P S.arrows ↔\n ∀ (x : Presieve.FamilyOfElements P S.arrows),\n firstMap P S (↑(firstObjEqFamily P S.arrows).symm x) = secondMap P S (↑(firstObjEqFamily P S.arrows).sym... | [
929,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_diff_singleton_add_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.13732\ns t : Set α\na b x y : α\nf : α → β\nh : a ∈ s\nhs : autoParam (Set.Finite s) _auto✝\nh' : ¬a ∈ s \\ {a}\n⊢ ncard (s \\ {a}) + 1 = ncard s",
"state_before": "α : Type u_1\nβ : Type ?u.13732\ns t : Set α\na b x y : α\nf : α → β\nh : a ∈ s\nhs : autoParam (Se... | [
189,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
9
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.mapRange_apply | [] | [
621,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.le_toLex_update_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nβ : ι → Type u_2\nr : ι → ι → Prop\ns : {i : ι} → β i → β i → Prop\ninst✝² : LinearOrder ι\ninst✝¹ : IsWellOrder ι fun x x_1 => x < x_1\ninst✝ : (i : ι) → PartialOrder (β i)\nx y : (i : ι) → β i\ni : ι\na : β i\n⊢ ↑toLex x ≤ ↑toLex (update x i a) ↔... | [
169,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.fst_of_isColimit | [
{
"state_after": "case x\nC : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nt : BinaryBicone X Y\nht : IsColimit (BinaryBicone.toCocone t)\n⊢ ∀ (j : Discrete WalkingPair), (BinaryBicone.toCocone t).ι.app j ≫ t.fst = (BinaryCofan.mk (𝟙 X) 0).ι.app j",
"state_befo... | [
401,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.comp_apply | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_le_zpow' | [] | [
391,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Filter.Tendsto.const_div' | [] | [
1094,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_iff | [] | [
379,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Control/Basic.lean | joinM_map_map | [] | [
162,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Logic/Basic.lean | imp_or | [] | [
416,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Lattice.lean | toDual_min | [] | [
987,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIxxMod_total' | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c✝ : α\nn : ℤ\na b c : α\nthis : toIcoMod hp 0 (a - b) + toIcoMod hp 0 (c - b) + (toIocMod hp 0 (b - a) + toIocMod hp 0 (b - c)) = p + p\n⊢ toIcoMod hp b a ≤ toIocMod hp b c ∨ toIcoMod hp b c ≤ toIo... | [
902,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
9
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_dvd_index_of_normal | [] | [
168,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_le_mul_of_nonneg_right | [
{
"state_after": "a b c : Int\nh₁ : a ≤ b\nh₂ : 0 ≤ c\n⊢ c * a ≤ c * b",
"state_before": "a b c : Int\nh₁ : a ≤ b\nh₂ : 0 ≤ c\n⊢ a * c ≤ b * c",
"tactic": "rw [Int.mul_comm, Int.mul_comm b]"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh₁ : a ≤ b\nh₂ : 0 ≤ c\n⊢ c * a ≤ c * b... | [
1172,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1170,
11
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essSup_const' | [] | [
67,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.mem_target | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.6519\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.6530\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne : Pretrivialization F proj\nx✝ : Z\nx : B × F\n⊢ x ∈ e.target ↔ x.fst ∈ e.baseSet",
"tactic": "rw [e.ta... | [
145,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudo_injective_of_mono | [
{
"state_after": "C : Type u\ninst✝² : Category C\ninst✝¹ : Abelian C\nP Q : C\nf : P ⟶ Q\ninst✝ : Mono f\nabar abar' : Pseudoelement P\n⊢ pseudoApply f abar = pseudoApply f abar' → abar = abar'",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : Abelian C\nP Q : C\nf : P ⟶ Q\ninst✝ : Mono f\n⊢ Fun... | [
312,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_mk | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.smul_sup | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR' : Type ?u.213053\n𝕜 : Type u_2\n𝕜₂ : Type ?u.213059\n𝕜₃ : Type ?u.213062\n𝕝 : Type ?u.213065\nE : Type u_3\nE₂ : Type ?u.213071\nE₃ : Type ?u.213074\nF : Type ?u.213077\nG : Type ?u.213080\nι : Type ?u.213083\ninst✝⁵ : SeminormedRing 𝕜\nins... | [
256,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_neg | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Ring R\np : R[X]\n⊢ Finset.max (support (-p)) = Finset.max (support p)",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Ring R\np : R[X]\n⊢ degree (-p) = degree p",
"tactic": "unfold degree"
},
{
"sta... | [
537,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/FieldTheory/Separable.lean | Irreducible.separable | [
{
"state_after": "F : Type u\ninst✝² : Field F\nK : Type v\ninst✝¹ : Field K\ninst✝ : CharZero F\nf : F[X]\nhf : Irreducible f\n⊢ ¬↑(natDegree f - 1) = ⊥\n\ncase hp\nF : Type u\ninst✝² : Field F\nK : Type v\ninst✝¹ : Field K\ninst✝ : CharZero F\nf : F[X]\nhf : Irreducible f\n⊢ 0 < natDegree f",
"state_befor... | [
474,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.ne_left | [] | [
243,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | derivWithin_sqrt | [] | [
102,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/Compare.lean | le_iff_le_of_cmp_eq_cmp | [
{
"state_after": "α : Type u_1\nβ✝ : Type ?u.20401\ninst✝¹ : LinearOrder α\nx y : α\nβ : Type u_2\ninst✝ : LinearOrder β\nx' y' : β\nh : cmp x y = cmp x' y'\n⊢ ¬y < x ↔ ¬y' < x'",
"state_before": "α : Type u_1\nβ✝ : Type ?u.20401\ninst✝¹ : LinearOrder α\nx y : α\nβ : Type u_2\ninst✝ : LinearOrder β\nx' y' :... | [
262,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfMulEquiv_mk' | [] | [
1587,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edgeSet_toSubgraph | [] | [
2249,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2248,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.eq_one_of_roots_le | [
{
"state_after": "α : Type ?u.181042\nR : Type ?u.181045\ninst✝³ : NormedRing R\ninst✝² : IsAbsoluteValue norm\nF : Type u_1\nK : Type u_2\ninst✝¹ : CommRing F\ninst✝ : NormedField K\np : F[X]\nf : F →+* K\nB : ℝ\nh1 : Monic p\nh2 : Splits f p\nh3 : ∀ (z : K), z ∈ roots (map f p) → ‖z‖ ≤ B\nhB : natDegree p ≠ 0... | [
162,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measurePreserving_mul_right | [] | [
146,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Finset/PImage.lean | Part.coe_toFinset | [] | [
53,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.one_comp | [] | [
1509,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.SatelliteConfig.exists_normalized_aux3 | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : c a (last N) = 0\nlastr : r a (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\ni j : Fin (Nat.succ N)\ninej : i ≠ j\nhi : 2 < ‖c a i‖\nhij : ‖c a i‖ ≤ ‖c a j‖\nah :\n ∀ ... | [
500,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.comp_apply | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_blockDiagonal | [] | [
384,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_succ | [] | [
958,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.familyOfBFamily_enum | [
{
"state_after": "case h.e'_4\nα : Type ?u.272202\nβ : Type ?u.272205\nγ : Type ?u.272208\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → α\ni : Ordinal\nhi : i < o\n⊢ (type fun x x_1 => x < x_1) = o",
"state_before": "α : Type ?u.272202\nβ : Type ?u.272205\nγ... | [
1168,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.prod_div_divisors | [
{
"state_after": "case pos\nn✝ : ℕ\nα : Type u_1\ninst✝ : CommMonoid α\nn : ℕ\nf : ℕ → α\nhn : n = 0\n⊢ ∏ d in divisors n, f (n / d) = Finset.prod (divisors n) f\n\ncase neg\nn✝ : ℕ\nα : Type u_1\ninst✝ : CommMonoid α\nn : ℕ\nf : ℕ → α\nhn : ¬n = 0\n⊢ ∏ d in divisors n, f (n / d) = Finset.prod (divisors n) f",
... | [
522,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.apply_symm_apply | [] | [
428,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_sInf | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Set (Subalgebra R A)\nx : A\n⊢ x ∈ sInf S ↔ ∀ (p : Subalgebra R A), p ∈ S → x ∈ p",
"tactic": "simp only [← ... | [
860,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinite_real | [
{
"state_after": "r : ℝ\n⊢ ∃ r_1 s, ↑r_1 < ↑r ∧ ↑r < ↑s",
"state_before": "r : ℝ\n⊢ ¬Infinite ↑r",
"tactic": "rw [not_infinite_iff_exist_lt_gt]"
},
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ ∃ r_1 s, ↑r_1 < ↑r ∧ ↑r < ↑s",
"tactic": "exact ⟨r - 1, r + 1, coe_lt_coe.2 <| sub_on... | [
620,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.ι_desc | [] | [
761,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.prev_nat_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.8519\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\n⊢ ComplexShape.prev (ComplexShape.up ℕ) 0 = 0",
"tactic": "classical\n refine' dif_neg _\n push_neg\n intro\n apply Nat.noConfusion"
},
{
"state_after": "ι : Type ?u.8... | [
162,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Order/Basic.lean | commutative_of_le | [] | [
583,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.polynomial_comp_attachBound | [
{
"state_after": "case h\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf : { x // x ∈ A }\ng : ℝ[X]\na✝ : X\n⊢ ↑(comp (Polynomial.toContinuousMapOn g (Set.Icc (-‖f‖) ‖f‖)) (attachBound ↑f)) a✝ = ↑↑(↑(Polynomial.aeval f) g) a✝",
"state_before": "X : Type u_1\ni... | [
75,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.