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/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_map | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\n⊢ length (Walk.map f p) = length p",
"tactic": "induction p <;> simp [*]"
}
] | [
1499,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1499,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_multilinearMap_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\ninst✝¹⁰ : Semiring R\nM : Type u_3\ninst✝⁹ : AddCommMonoid M\ninst✝⁸ : Module R M\nN : Type u_2\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module R N\nP : Type ?u.42102\ninst✝⁵ : AddCommMonoid P\ninst✝⁴ : Module R P\nM' : Type ?u.42132\ninst✝³ : AddCommGr... | [
179,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_self_eq_norm_mul_norm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.787535\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx : F\n⊢ ↑re (inner x x) = ‖x‖ * ‖x‖",
"tactic": "rw [norm_eq_sqrt_inner, ← sqrt_mul inner_self_nonneg (re ⟪x, x⟫), sqrt_mul_sel... | [
355,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.toMeasure_pure_apply | [] | [
91,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Ico_add_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ (⋃ (n : ℤ), Ico (a + ↑n) (a + ↑n + 1)) = univ",
"tactic": "simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using\n iUnion_Ico_add_zsmul zero_lt_one a"
}
] | [
1099,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.pi_apply | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/Separation.lean | Ne.nhdsWithin_compl_singleton | [] | [
395,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffWithinAt.univ_pi | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\ninst✝⁹ : NontriviallyNormedField 𝕜\nE✝ : Type ?u.136559\ninst✝⁸ : NormedAddCommGroup E✝\ninst✝⁷ : NormedSpace 𝕜 E✝\nF : Type ?u.136654\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.136744\ninst✝⁴ : NormedAddCommGroup G\n... | [
356,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.prodZeroIso_iso_inv_snd | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\n⊢ (limit.isoLimitCone { cone := BinaryFan.mk (𝟙 X) 0, isLimit := binaryFanZeroRightIsLimit X }).inv ≫ prod.fst = 𝟙 X",
"state_before": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasZeroObjec... | [
94,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_smul_inv | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.133858\nR₂ : Type ?u.133861\nR₃ : Type ?u.133864\nk : Type ?u.133867\nS : Type u_1\nS₃ : Type ?u.133873\nT : Type ?u.133876\nM : Type u_4\nM₁ : Type ?u.133882\nM₂ : Type ?u.133885\nM₃ : Type u_3\nN₁ : Type ?u.133891\nN₂ : Type ?u.13389... | [
346,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
11
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_pow_right_iff | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nhn : 0 < n\na b : ℕ\n⊢ coprime a (b ^ n) ↔ coprime a b",
"tactic": "rw [Nat.coprime_comm, coprime_pow_left_iff hn, Nat.coprime_comm]"
}
] | [
203,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.congr | [] | [
359,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_update_of_mem | [
{
"state_after": "ι : Type ?u.791147\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\ns : Finset α\ni : α\nh : i ∈ s\nf : α → β\nb : β\n⊢ (∏ x in s ∩ {i}, b) * ∏ x in s \\ {i}, f x = b * ∏ x in s \\ {i}, f x",
"state_before": "ι : T... | [
1623,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.exists_real_pos_lt_infEdist_of_not_mem_closure | [
{
"state_after": "ι : Sort ?u.18420\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx✝ y : α\ns t : Set α\nΦ : α → β\nx : α\nE : Set α\nh : ∃ r, 0 ≤ r ∧ 0 < ENNReal.ofReal r ∧ ENNReal.ofReal r < infEdist x E\n⊢ ∃ ε, 0 < ε ∧ ENNReal.ofReal ε < infEdist x E",
"state_befor... | [
181,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_neg_add_lt | [
{
"state_after": "a b c : Int\nh✝ : -b + a < c\nh : b + (-b + a) < b + c\n⊢ a < b + c",
"state_before": "a b c : Int\nh : -b + a < c\n⊢ a < b + c",
"tactic": "have h := Int.add_lt_add_left h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : -b + a < c\nh : b + (-b + a) < ... | [
1065,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1063,
11
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_Iic | [] | [
519,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Order/Lattice.lean | sup_right_idem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na b c d : α\n⊢ a ⊔ b ⊔ b = a ⊔ b",
"tactic": "simp"
}
] | [
270,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Set/Equitable.lean | Finset.equitableOn_iff_le_le_add_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8332\ns : Finset α\nf : α → ℕ\na : α\n⊢ (∃ b, ∀ (a : α), a ∈ ↑s → b ≤ f a ∧ f a ≤ b + 1) ↔\n ∀ (a : α), a ∈ s → (∑ i in s, f i) / card s ≤ f a ∧ f a ≤ (∑ i in s, f i) / card s + 1",
"state_before": "α : Type u_1\nβ : Type ?u.8332\ns : Finset α\nf : α → ℕ\na : α... | [
114,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_eq_zero | [] | [
639,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_one | [] | [
103,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_two_pi | [
{
"state_after": "no goals",
"state_before": "⊢ cos (2 * π) = 1",
"tactic": "simp [two_mul, cos_add]"
}
] | [
227,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_one | [] | [
146,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_sdiff | [] | [
2043,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2042,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.mul_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2141\nf fa : α → α\nfb : β → β\nx y : α\nm n✝ : ℕ\nhm : IsPeriodicPt f m x\nn : ℕ\n⊢ IsPeriodicPt f (m * n) x",
"tactic": "simp only [IsPeriodicPt, iterate_mul, hm.isFixedPt.iterate n]"
}
] | [
126,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
11
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.multiplicity_X_sub_C_finite | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\na : R\nh0 : p ≠ 0\nthis : Nontrivial R\n⊢ multiplicity.Finite (X - ↑C a) p",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\na ... | [
524,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_eq_sSup_image | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.92388\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.92397\nι : Type ?u.92400\nκ : Type ?u.92403\ninst✝ : CompleteLattice β\ns : Finset α\nf : α → β\n⊢ sup s f = sSup (f '' ↑s)",
"tactic": "classical rw [← Finset.coe_image, ← sup_id_eq_sSup, sup_image,... | [
305,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.add_closure_setOf_eq_single | [] | [
1125,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_restrict_of_forall_set_integral_eq_zero | [
{
"state_after": "case intro.intro\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : Measure α\ns t✝ : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → IntegrableOn f s\nhf_zero : ∀... | [
393,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Algebra/Order/SMul.lean | inv_smul_lt_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.109399\n𝕜 : Type u_1\nR : Type ?u.109405\nM : Type u_2\nN : Type ?u.109411\ninst✝⁵ : LinearOrderedSemifield 𝕜\ninst✝⁴ : OrderedAddCommMonoid M\ninst✝³ : OrderedAddCommMonoid N\ninst✝² : MulActionWithZero 𝕜 M\ninst✝¹ : MulActionWithZero 𝕜 N\ninst✝... | [
252,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.Functor.reprW_hom | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.139216\nγ : Type ?u.139219\nδ : Type ?u.139222\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\ns : Set α\nhs : IsOpen s\n⊢ IsOpen (id '' s)",
"tactic": "rwa [image_id]"
}
] | [
346,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
11
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.add_one_le_iff_lt | [
{
"state_after": "x y : PartENat\nhx : x ≠ ⊤\nh : x + 1 ≤ y\n⊢ x < y",
"state_before": "x y : PartENat\nhx : x ≠ ⊤\n⊢ x + 1 ≤ y ↔ x < y",
"tactic": "refine ⟨fun h => ?_, add_one_le_of_lt⟩"
},
{
"state_after": "case intro\ny : PartENat\nm : ℕ\nhx : ↑m ≠ ⊤\nh : ↑m + 1 ≤ y\n⊢ ↑m < y",
"state_be... | [
512,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_finsupp_sum | [] | [
2134,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2130,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.range_eq | [] | [
254,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleMap_ne_mem_ball | [] | [
140,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.injective_stableUnderComposition | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type ?u.89168\ninst✝¹ : Category D\ninst✝ : ConcreteCategory C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhf : MorphismProperty.injective C f\nhg : MorphismProperty.injective C g\n⊢ Injective ((forget C).map (f ≫ g))",
"state_before": "C : Type u\ninst✝² : Categ... | [
643,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.div_comp | [] | [
399,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyRel.eq_fst | [] | [
593,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_self_of_lt_one | [] | [
529,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isDetecting_empty_of_groupoid | [] | [
245,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/List/Lattice.lean | List.bagInter_nil_iff_inter_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₂ : List α\n⊢ List.bagInter [] l₂ = [] ↔ [] ∩ l₂ = []",
"tactic": "simp"
},
{
"state_after": "case neg\nα : Type u_1\nl l₁✝ l₂✝ : List α\np : α → Prop\na : α\ninst✝ : Decid... | [
280,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.pi_eq_bot_iff | [
{
"state_after": "G : Type ?u.330176\nG' : Type ?u.330179\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.330188\ninst✝³ : AddGroup A\nH✝ K : Subgroup G\nk : Set G\nN : Type ?u.330209\ninst✝² : Group N\nP : Type ?u.330215\ninst✝¹ : Group P\nη : Type u_2\nf : η → Type u_1\ninst✝ : (i : η) → Group (f i)\nH : (i... | [
1896,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1888,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_zero | [] | [
1037,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Order/Bounds/Basic.lean | Antitone.map_isLeast | [] | [
1342,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_range_eq_span_tmul | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.921730\ninst✝¹³ : Monoid R'\nR'' : Type ?u.921736\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_4\nP : Type u_3\nQ : Type u_5\nS : Type ?u.921754\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : A... | [
740,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | primitiveRoots_zero | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.1451860\nN : Type ?u.1451863\nG : Type ?u.1451866\nR : Type u_1\nS : Type ?u.1451872\nF : Type ?u.1451875\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ primitiveRoots 0... | [
325,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_set_mk | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ ¬coeff X 1 = coeff 0 1",
"tactic": "simp"
}
] | [
1206,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.prod_image_seq_comm | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.274965\nι : Sort ?u.274968\nι' : Sort ?u.274971\nι₂ : Sort ?u.274974\nκ : ι → Sort ?u.274979\nκ₁ : ι → Sort ?u.274984\nκ₂ : ι → Sort ?u.274989\nκ' : ι' → Sort ?u.274994\ns : Set α\nt : Set β\n⊢ seq ((fun x x_1 => x ∘ x_1) Prod.swap ∘ Prod.mk '' t) s = se... | [
2005,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2003,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_pair | [] | [
534,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.cos | [] | [
955,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_symm | [] | [
58,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sinh 0 = 0",
"tactic": "simp [sinh]"
}
] | [
1346,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | ModularGroup.coe_T_inv | [
{
"state_after": "no goals",
"state_before": "⊢ ↑T⁻¹ = ↑of ![![1, -1], ![0, 1]]",
"tactic": "simp [coe_inv, coe_T, adjugate_fin_two]"
}
] | [
364,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/List/Sigma.lean | List.kunion_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\nhead✝ : Sigma β\nl : List (Sigma β)\n⊢ kunion (head✝ :: l) [] = head✝ :: l",
"tactic": "rw [kunion, kerase_nil, kunion_nil]"
}
] | [
692,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.neg_sqrt_le_of_sq_le | [] | [
324,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.ext' | [
{
"state_after": "case mk.mk\nM : Type u_1\nN : Type ?u.6337\nP : Type ?u.6340\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nc d : Con M\nr✝ : M → M → Prop\niseqv✝ : Equivalence r✝\nmul'✝ : ∀ {w x y z : M}, r w x → r y z → r (w * y) (x * z)\nH : r = r\n⊢ { toSetoid := { r := r✝, iseqv := iseqv✝ }, mul' := mul... | [
188,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.comm | [] | [
65,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
11
] |
Mathlib/Data/List/Lattice.lean | List.mem_union | [
{
"state_after": "case nil\nα : Type u_1\nl l₁ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\n⊢ a ∈ [] ∪ l₂ ↔ a ∈ [] ∨ a ∈ l₂\n\ncase cons\nα : Type u_1\nl l₁ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : a ∈ tail✝ ∪ l₂ ↔ a ∈ tail✝ ∨ a ∈ l₂\n⊢ a ∈ head✝... | [
87,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.blt_eq | [] | [
98,
124
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
98,
9
] |
Mathlib/Data/Real/Irrational.lean | irrational_sub_rat_iff | [] | [
578,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.map_add | [] | [
620,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
11
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.monotone_comap | [] | [
312,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | AlternatingMap.measure_parallelepiped | [
{
"state_after": "E : Type ?u.2090966\ninst✝¹⁵ : NormedAddCommGroup E\ninst✝¹⁴ : NormedSpace ℝ E\ninst✝¹³ : MeasurableSpace E\ninst✝¹² : BorelSpace E\ninst✝¹¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝¹⁰ : IsAddHaarMeasure μ\nF : Type ?u.2091635\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace ℝ F\ninst✝... | [
573,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.sup_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\nβ : Type u_2\ninst✝³ : LinearOrderedField β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology β\ninst✝ : TopologicalRing β\nf g : C(α, β)\nx : α\n⊢ ↑(f ⊔ g) x = ↑(2⁻¹ • (f + g + Abs.abs (f - g))) x",
"tactic": "s... | [
942,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.iSup_insert | [
{
"state_after": "F : Type ?u.449532\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.449541\nι : Type ?u.449544\nκ : Type ?u.449547\ninst✝¹ : CompleteLattice β\ninst✝ : DecidableEq α\na : α\ns : Finset α\nt : α → β\n⊢ (⨆ (x : α) (_ : x ∈ {a} ∪ s), t x) = t a ⊔ ⨆ (x : α) (_ : x ∈ s), t x",
"state_before": "F : Type... | [
1960,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1957,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.mem_isPairSelfAdjointSubmodule | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1132945\nM : Type ?u.1132948\ninst✝²⁴ : Semiring R\ninst✝²³ : AddCommMonoid M\ninst✝²² : Module R M\nR₁ : Type ?u.1132984\nM₁ : Type ?u.1132987\ninst✝²¹ : Ring R₁\ninst✝²⁰ : AddCommGroup M₁\ninst✝¹⁹ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\ninst✝... | [
1104,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.decomposition_id | [
{
"state_after": "case h\nC : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : Preadditive C\nΔ : SimplexCategoryᵒᵖ\n⊢ ∀ (A : IndexSet Δ), ιSummand s A ≫ 𝟙 (X.obj Δ) = ιSummand s A ≫ ∑ A : IndexSet Δ, πSummand s A ≫ ιSummand s A",
"state_before... | [
75,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.length_subadditive_Icc_Ioo | [
{
"state_after": "f : StieltjesFunction\na b : ℝ\nc d : ℕ → ℝ\nss : Icc a b ⊆ ⋃ (i : ℕ), Ioo (c i) (d i)\n⊢ ∀ (s : Finset ℕ) (b : ℝ),\n (Icc a b ⊆ ⋃ (i : ℕ) (_ : i ∈ ↑s), Ioo (c i) (d i)) → ofReal (↑f b - ↑f a) ≤ ∑ i in s, ofReal (↑f (d i) - ↑f (c i))",
"state_before": "f : StieltjesFunction\na b : ℝ\nc ... | [
383,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.79454\nδ : Type ?u.79457\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\n⊢ s ×ˢ t = ∅ ↔ s = ∅ ∨ t = ∅",
"tactic": "simp only [not_nonempty_iff_eq_empty.symm, prod_nonempty_iff, not_and_or]"
}
] | [
325,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Logic/Denumerable.lean | Nat.Subtype.lt_succ_iff_le | [] | [
273,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_mul_cancel_assoc | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a⁻¹ * (b * a) = b",
"tactic": "rw [← mul_assoc, h.inv_mul_cancel]"
}
] | [
386,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.minpoly_eq | [
{
"state_after": "case pos\nK : Type u_2\nL : Type u_1\nL' : Type ?u.315453\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Field L'\ninst✝¹ : Algebra K L\ninst✝ : Algebra K L'\nS : IntermediateField K L\nx : { x // x ∈ S }\nhx : IsIntegral K x\n⊢ minpoly K x = minpoly K ↑x\n\ncase neg\nK : Type u_2\nL : Type u_1... | [
740,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.join_zero | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.think_mem | [] | [
384,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconcaveOn.convex_gt | [] | [
156,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.wellFounded_of_finite | [] | [
210,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MulEquiv.submonoidMap_symm_apply | [] | [
1456,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Algebra/CharP/Basic.lean | Commute.exists_add_pow_prime_eq | [] | [
61,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_countpAddMonoidHom | [] | [
2257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2256,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_coe | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.map_commutator | [
{
"state_after": "G : Type u_1\nG' : Type u_2\nF : Type ?u.88445\ninst✝² : Group G\ninst✝¹ : Group G'\ninst✝ : MonoidHomClass F G G'\nf✝ : F\ng₁ g₂ g₃ g : G\nH₁ H₂ H₃ K₁ K₂ : Subgroup G\nf : G →* G'\n⊢ (∀ (g₁ : G), g₁ ∈ H₁ → ∀ (g₂ : G), g₂ ∈ H₂ → ⁅↑f g₁, ↑f g₂⁆ ∈ ⁅map f H₁, map f H₂⁆) ∧\n ∀ (g₁ : G'), g₁ ∈ m... | [
181,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.two_power_aleph0 | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Order/RelIso/Set.lean | RelEmbedding.codRestrict_apply | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_induction | [] | [
499,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Basis.mem_ideal_iff' | [] | [
1982,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1980,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.snd_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.snd = (BinaryCofan.mk 0 (𝟙 Y)).ι.app j",
"state_befo... | [
407,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_le_inf | [] | [
655,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_neg_atBot_atTop | [] | [
852,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_smul_le | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.131813\nK : Type ?u.131816\nM : Type u_3\nM₂ : Type ?u.131822\nV : Type ?u.131825\nS✝ : Type ?u.131828\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝⁶ : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝⁵ : AddCommMonoid M₂\n... | [
438,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.multiplicative_factorization | [] | [
707,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalExtr.fderiv_eq_zero | [] | [
220,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.inf_le | [] | [
1035,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.add_apply | [] | [
678,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord.orderEmbedding_coe | [] | [
1477,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
] |
Mathlib/Algebra/Group/Opposite.lean | MulOpposite.op_intCast | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_snd_neBot | [] | [
2399,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2397,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.sum_le_foldr_max | [
{
"state_after": "case nil\nι : Type ?u.146362\nα : Type ?u.146365\nM : Type u_1\nN : Type u_2\nP : Type ?u.146374\nM₀ : Type ?u.146377\nG : Type ?u.146380\nR : Type ?u.146383\ninst✝² : AddMonoid M\ninst✝¹ : AddMonoid N\ninst✝ : LinearOrder N\nf : M → N\nh0 : f 0 ≤ 0\nhadd : ∀ (x y : M), f (x + y) ≤ max (f x) (... | [
548,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ico_of_lt | [] | [
724,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Definable.eq | [] | [
645,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.