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/Topology/Instances/Rat.lean | Rat.uniformContinuous_abs | [
{
"state_after": "no goals",
"state_before": "ε : ℝ\nε0 : ε > 0\na✝ b✝ : ℚ\nh : dist a✝ b✝ < ε\n⊢ dist (abs a✝) (abs b✝) ≤ dist a✝ b✝",
"tactic": "simpa [Rat.dist_eq] using abs_abs_sub_abs_le_abs_sub _ _"
}
] | [
113,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Order/Heyting/Basic.lean | sdiff_triangle | [
{
"state_after": "ι : Type ?u.141596\nα : Type u_1\nβ : Type ?u.141602\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ a \\ (a \\ b) ≤ c ⊔ b \\ c",
"state_before": "ι : Type ?u.141596\nα : Type u_1\nβ : Type ?u.141602\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ a \\ c ≤ a... | [
720,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Data/List/Basic.lean | List.zipRight'_nil_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.464373\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nas : List α\nb : β\nbs : List β\n⊢ zipRight' [] bs = (map (fun b => (none, b)) bs, [])",
"tactic": "cases bs <;> rfl"
}
] | [
4073,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4072,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | monotone_mul_left_of_nonneg | [] | [
270,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_iInf | [] | [
246,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_right_cancel_iff' | [] | [
199,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
11
] |
Std/Data/String/Lemmas.lean | Substring.Valid_default | [] | [
780,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
780,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableOrder.lean | MeasureTheory.aemeasurable_of_exist_almost_disjoint_supersets | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nβ : Type u_2\ninst✝⁶ : CompleteLinearOrder β\ninst✝⁵ : DenselyOrdered β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : OrderTopology β\ninst✝² : SecondCountableTopology β\ninst✝¹ : MeasurableSpace β\ninst✝ : BorelSpace β\ns : Set β\ns_count : Set.Cou... | [
110,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.curry_natural_left | [] | [
180,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/GroupTheory/Abelianization.lean | card_commutator_closureCommutatorRepresentatives | [
{
"state_after": "G : Type u\ninst✝ : Group G\n⊢ Nat.card { x // x ∈ _root_.commutator { x // x ∈ closureCommutatorRepresentatives G } } =\n Nat.card\n { x //\n x ∈\n map (Subgroup.subtype (closureCommutatorRepresentatives G))\n (_root_.commutator { x // x ∈ closureCommutatorR... | [
317,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/FieldTheory/Normal.lean | AlgHom.liftNormal_commutes | [] | [
425,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Order/Grade.lean | grade_toDual | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_inv_atTop_zero | [] | [
140,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.sub_one_lt_iff | [] | [
115,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y : PresheafedSpace C\nα : X ⟶ Y\nx x' : ↑↑X\nh : x = x'\n⊢ stalk X x = stalk X x'",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nin... | [
184,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDeriv_mul_le | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹¹ : NormedAddCommGroup D\ninst✝¹⁰ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁵ : Norm... | [
2522,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2516,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_mono | [] | [
390,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_zero | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleFactorsFinset_mul_inv_mem_eq_sdiff | [
{
"state_after": "ι : Type ?u.2782985\nα : Type u_1\nβ : Type ?u.2782991\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ng : Perm α\n⊢ ∀ {f : Perm α}, f ∈ cycleFactorsFinset g → cycleFactorsFinset (g * f⁻¹) = cycleFactorsFinset g \\ {f}",
"state_before": "ι : Type ?u.2782985\nα : Type u_1\nβ : Type ?u.2782991\n... | [
1600,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | Finset.prod_nonneg_of_card_nonpos_even | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommRing β\nf : α → β\ninst✝ : DecidablePred fun x => f x ≤ 0\ns : Finset α\nh0 : Even (card (filter (fun x => f x ≤ 0) s))\nx : α\nx✝ : x ∈ s\nhx : f x ≤ 0\n⊢ 0 ≤ -1 * f x\n\ncase inr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder... | [
73,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Icc_of_Icc | [] | [
259,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/Algebra/Free.lean | FreeMagma.lift_comp_of' | [] | [
135,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.Ioi_eq_finset_subtype | [
{
"state_after": "case a\nn : ℕ\na b a✝ : Fin n\n⊢ a✝ ∈ Ioi a ↔ a✝ ∈ Finset.fin n (Ioc (↑a) n)",
"state_before": "n : ℕ\na b : Fin n\n⊢ Ioi a = Finset.fin n (Ioc (↑a) n)",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nn : ℕ\na b a✝ : Fin n\n⊢ a✝ ∈ Ioi a ↔ a✝ ∈ Fins... | [
129,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_unop_mul | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM✝ N✝ P Q : Submodule R A\nm n : A\nM N : Submodule R Aᵐᵒᵖ\nthis : Function.Injective ↑↑(opLinearEquiv R)\n⊢ map (↑(opLinearEquiv R)) (map (↑(Lin... | [
311,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
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] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_inv | [] | [
99,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_ne_bit0 | [] | [
155,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
11
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | Prod.ωSup_zip | [
{
"state_after": "case H\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.22086\ninst✝² : OmegaCompletePartialOrder α\ninst✝¹ : OmegaCompletePartialOrder β\ninst✝ : OmegaCompletePartialOrder γ\nc₀ : Chain α\nc₁ : Chain β\n⊢ ∀ (c : α × β), ωSup (Chain.zip c₀ c₁) ≤ c ↔ (ωSup c₀, ωSup c₁) ≤ c",
"state_before": "α : Ty... | [
456,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Int/GCD.lean | Int.exists_gcd_one | [] | [
376,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.contDiff_normed | [] | [
497,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_cons_nil | [] | [
274,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.fst_eq_snd_of_mono_eq | [] | [
1933,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1931,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimate | [
{
"state_after": "Ω : Type u_1\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.76875\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nμ : FiniteMeasure Ω\nf g : Ω →ᵇ ℝ≥0\n⊢ (∫⁻ (ω : Ω), ↑(↑f ω... | [
417,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.snd_mul | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoMod hp (p + a) b = p + toIcoMod hp a b",
"tactic": "rw [add_comm, toIcoMod_add_right', add_comm]"
}
] | [
499,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | mem_innerDualCone | [] | [
58,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.hlup | [] | [
941,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
9
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_sup | [] | [
778,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_neg | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Algebra/Star/Module.lean | star_rat_smul | [] | [
73,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.MonoidalFunctor.prod'_toLaxMonoidalFunctor | [] | [
480,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheaf_of_le | [] | [
745,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousOn.inner | [] | [
2278,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2277,
1
] |
Mathlib/Deprecated/Subfield.lean | IsSubfield.iInter | [] | [
170,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prime_of_mem_factorization | [] | [
141,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_left | [] | [
151,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
21
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhds_nhds_eq_uniformity_uniformity_prod | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.78279\ninst✝ : UniformSpace α\na b : α\n⊢ (Filter.lift (𝓤 α) fun s => Filter.lift' (𝓤 α) fun t => {y | (y, a) ∈ s} ×ˢ ball b t) =\n Filter.lift (𝓤 α) fun s => Filter.lift' (𝓤 α) fun t => {y | (y, a) ∈ s} ×ˢ {y | (b, y) ∈ t}... | [
883,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_lt_add | [] | [
408,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
407,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.mem_lp_const_smul | [] | [
626,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_lt_self_iff | [] | [
782,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_iff_le | [] | [
253,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableWithinAt.comp' | [] | [
127,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inclusion_injective | [] | [
822,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
src/lean/Init/Classical.lean | Classical.epsilon_singleton | [] | [
104,
44
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
103,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.invFun_as_coe | [] | [
197,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
9
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subset_clopen | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.31419\nπ : ι → Type ?u.31424\ninst✝ : TopologicalSpace α\ns✝ t✝ u v s t : Set α\nhs : IsPreconnected s\nht : IsClopen t\nhne : Set.Nonempty (s ∩ t)\n⊢ s ⊆ t ∪ tᶜ",
"tactic": "simp"
}
] | [
449,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_neg_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ -π < -π / 2 ∧ -π / 2 ≤ π",
"tactic": "constructor <;> linarith [pi_pos]"
}
] | [
624,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_le_left | [
{
"state_after": "case a\nι : Type ?u.109806\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na✝ b✝ c a b : α\ninst✝ : DecidablePred fun x => x ≤ a\nhab : a < b\nx : α\n⊢ x ∈ filter (fun x => x ≤ a) (Ico a b) ↔ x ∈ {a}",
"state_before": "ι : Type ?u.109806\nα : Type u_1\ninst✝² : Parti... | [
637,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_sub_div | [
{
"state_after": "x n p : Nat\nh₁ : x < n * p\nnpos : 0 < n\n⊢ (n * p - succ x) / n = p - succ (x / n)",
"state_before": "x n p : Nat\nh₁ : x < n * p\n⊢ (n * p - succ x) / n = p - succ (x / n)",
"tactic": "have npos : 0 < n := (eq_zero_or_pos _).resolve_left fun n0 => by\n rw [n0, Nat.zero_mul] at h₁; ... | [
619,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
608,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.degrees_esymm | [
{
"state_after": "σ : Type u_2\nR : Type u_1\nτ : Type ?u.196415\nS : Type ?u.196418\ninst✝⁴ : CommSemiring R\ninst✝³ : CommSemiring S\ninst✝² : Fintype σ\ninst✝¹ : Fintype τ\ninst✝ : Nontrivial R\nn : ℕ\nhpos : 0 < n\nhn : n ≤ Fintype.card σ\nthis : (↑Finsupp.toMultiset ∘ fun t => ∑ i in t, Finsupp.single i 1)... | [
278,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_mem | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.409694\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 t : Finset α\nf : α → β\n⊢ (∏ i in s, if i ∈ t then f i else 1) = ∏ i in s ∩ t, f i",
"tactic": "rw [← Finset.pr... | [
1044,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Iso.map_mem_edgeSet_iff | [] | [
1925,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
] |
Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.ext | [] | [
75,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.eq_of_mem_classes | [] | [
133,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Std/Data/List/Init/Lemmas.lean | List.map_cons | [] | [
88,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
88,
1
] |
Mathlib/Data/List/Basic.lean | List.reverse_bijective | [] | [
624,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_mk_coeff | [] | [
295,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDerivWithin_add_apply' | [] | [
1240,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/Order/WithBot.lean | WithTop.not_none_lt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.89059\nγ : Type ?u.89062\nδ : Type ?u.89065\ninst✝ : LT α\na✝ b : α\na : WithTop α\n⊢ ¬↑WithTop.toDual a < ↑WithTop.toDual none",
"state_before": "α : Type u_1\nβ : Type ?u.89059\nγ : Type ?u.89062\nδ : Type ?u.89065\ninst✝ : LT α\na✝ b : α\na : WithTop α\n⊢ ¬none... | [
1076,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_zero_right | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_iInter | [] | [
1602,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieIdeal.derivedSeries_eq_derivedSeriesOfIdeal_comap | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\n⊢ derivedSeries R { x // x ∈ ↑I } Nat.zero = comap (incl I) (derivedSeriesOfIdeal R L... | [
160,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexAlgEquiv_mul | [] | [
152,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAt_snd | [] | [
259,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.isometry_comp | [] | [
864,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.smul_sup | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.177768\nR : Type u_2\nR' : Type ?u.177774\nE : Type u_1\nF : Type ?u.177780\nG : Type ?u.177783\ninst✝³ : Group E\ninst✝² : SMul R ℝ\ninst✝¹ : SMul R ℝ≥0\ninst✝ : IsScalarTower R ℝ≥0 ℝ\nr : R\np q : GroupSeminorm E\nx y : ℝ\n⊢ r • max x y = max (r • ... | [
674,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_prod | [] | [
198,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Rel.lean | Set.preimage_eq_core | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.42890\nf : α → β\ns : Set β\n⊢ f ⁻¹' s = Rel.core (Function.graph f) s",
"tactic": "simp [Set.preimage, Function.graph, Rel.core]"
}
] | [
283,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Order/SupIndep.lean | Finset.supIndep_univ_fin_two | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14885\nι : Type ?u.14888\nι' : Type ?u.14891\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\ns t : Finset ι\nf✝ : ι → α\ni : ι\nf : Fin 2 → α\n⊢ 0 ≠ 1",
"tactic": "simp"
}
] | [
131,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Std/Data/List/Lemmas.lean | List.append_eq_append | [] | [
108,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
108,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.Integrable.prod_left_ae | [] | [
295,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.repr_symm_single | [] | [
432,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
11
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_iff_one_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝⁴ : MulOneClass α\ninst✝³ : Zero α\ninst✝² : Preorder α\ninst✝¹ : PosMulMono α\ninst✝ : PosMulMonoRev α\na0 : 0 < a\n⊢ a ≤ a * b ↔ a * 1 ≤ a * b",
"tactic": "rw [mul_one]"
}
] | [
617,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.dual_comp | [] | [
1574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isFractional_span_singleton | [] | [
1288,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.map_bot' | [
{
"state_after": "F : Type ?u.106047\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.106056\nδ : Type ?u.106059\ninst✝¹ : LE α\ninst✝ : PartialOrder β\nf : α ≃o β\nx : α\ny : β\nhx : ∀ (x' : α), x ≤ x'\nhy : ∀ (y' : β), y ≤ y'\n⊢ ↑f x ≤ y",
"state_before": "F : Type ?u.106047\nα : Type u_1\nβ : Type u_2\nγ : Type ... | [
1170,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasurableEmbedding.integrableOn_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nE : Type u_3\nF : Type ?u.1519544\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\nf✝ g : α → E\ns✝ t : Set α\nμ✝ ν : Measure α\ninst✝ : MeasurableSpace β\ne : α → β\nhe : MeasurableEmbedding e\nf : β → E\nμ : Measure α\ns ... | [
240,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.gc_map_comap | [] | [
276,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.icc_eq | [] | [
106,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Monad/Coequalizer.lean | CategoryTheory.Monad.beckCofork_π | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_mul_le_Lp_mul_Lq | [
{
"state_after": "case pos\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ✝ μ : MeasureTheory.Measure α\np q : ℝ\nhpq : Real.IsConjugateExponent p q\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\nhg : AEMeasurable g\nhf_zero : (∫⁻ (a : α), f a ^ p ∂μ) = 0\n⊢ (∫⁻ (a : α), (f * g) a ∂μ) ≤ (∫⁻ (a : α), f a ^ p ∂μ) ^ (1 / p) * ... | [
178,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Rat.cast_finsupp_prod | [] | [
429,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.subsingleton_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nx y : R\nI : Ideal R\n⊢ Subsingleton (R ⧸ I) ↔ I = ⊤",
"tactic": "rw [eq_top_iff_one, ← subsingleton_iff_zero_eq_one, eq_comm, ← (mk I).map_one,\n Quotient.eq_zero_iff_mem]"
}
] | [
158,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Fintype.range_total | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nM : Type u_1\nR : Type u_2\ninst✝⁶ : Fintype α\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_4\ninst✝² : Semiring S\ninst✝¹ : Module S M\ninst✝ : SMulCommClass R S M\nv : α → M\n⊢ LinearMap.range (↑(Fintype.total R... | [
1092,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.conjugatesOfSet_subset' | [] | [
694,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.20964\nβ : Type ?u.20967\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ ENNReal.ofReal 0 = 0",
"tactic": "simp [ENNReal.ofReal]"
}
] | [
242,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
9
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.abs_sub_right_of_mem_uIcc | [] | [
496,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_toList | [] | [
3355,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3354,
1
] |
Mathlib/Data/List/Infix.lean | List.tails_reverse | [
{
"state_after": "α : Type u_1\nβ : Type ?u.47240\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ tails (reverse l) = reverse (map reverse (reverse (map reverse (tails (reverse l)))))",
"state_before": "α : Type u_1\nβ : Type ?u.47240\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ tails (reve... | [
412,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.mem_smul_pointwise_iff_exists | [] | [
476,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isLeftRegular_zero_iff_subsingleton | [] | [
209,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
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