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/AlgebraicTopology/DoldKan/Compatibility.lean | AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.real_smul_eq_coe_smul | [
{
"state_after": "no goals",
"state_before": "K : Type u_2\nE : Type u_1\ninst✝⁴ : IsROrC K\ninst✝³ : AddCommGroup E\ninst✝² : Module K E\ninst✝¹ : Module ℝ E\ninst✝ : IsScalarTower ℝ K E\nr : ℝ\nx : E\n⊢ r • x = ↑r • x",
"tactic": "rw [IsROrC.ofReal_alg, smul_one_smul]"
}
] | [
104,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.mk_eq_mk_iff_sub_mem | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nI : Ideal R\na b : R\nS : Type v\nx✝ y✝ x y : R\n⊢ ↑(mk I) x = ↑(mk I) y ↔ x - y ∈ I",
"tactic": "rw [← eq_zero_iff_mem, map_sub, sub_eq_zero]"
}
] | [
142,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | Finset.nullMeasurableSet_biUnion | [] | [
382,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_fst' | [] | [
1086,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Topology/PathConnected.lean | locPathConnected_of_isOpen | [
{
"state_after": "case mk\nX : Type u_1\nY : Type ?u.705929\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx✝ y z : X\nι : Type ?u.705944\nF : Set X\ninst✝ : LocPathConnectedSpace X\nU : Set X\nh : IsOpen U\nx : X\nx_in : x ∈ U\n⊢ HasBasis (𝓝 { val := x, property := x_in }) (fun s => s ∈ 𝓝 { val :... | [
1259,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagram_fst | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.split | [
{
"state_after": "no goals",
"state_before": "𝒜 : Type u_1\ninst✝² : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝¹ : Preadditive 𝒜\ninst✝ : HasBinaryBiproducts 𝒜\nh : Splitting f g\n⊢ f ≫ g = 0",
"tactic": "rw [← h.inl_comp_iso_eq, Category.assoc, h.iso_co... | [
303,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_append_right | [
{
"state_after": "α✝ : Type u_1\nl l₁ l₂ : List α✝\n⊢ Disjoint l₁ l ∧ Disjoint l₂ l ↔ Disjoint l l₁ ∧ Disjoint l l₂",
"state_before": "α✝ : Type u_1\nl l₁ l₂ : List α✝\n⊢ Disjoint (l₁ ++ l₂) l ↔ Disjoint l l₁ ∧ Disjoint l l₂",
"tactic": "rw [disjoint_append_left]"
},
{
"state_after": "no goals",... | [
1387,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1386,
9
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.add_left | [] | [
114,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_lt_pow_of_lt_right | [] | [
35,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.congr_fun | [] | [
290,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.toPiFork_π_app_zero | [] | [
438,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domDomCongr_zero | [] | [
750,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsOpen.lowerSemicontinuousOn_indicator | [] | [
214,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.ofDual_inj | [] | [
89,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_lt_toNNReal | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.800710\nβ : Type ?u.800713\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ ⊤\nhb : b ≠ ⊤\nh : ENNReal.toNNReal a < ENNReal.toNNReal b\n⊢ a < b",
"tactic": "rwa [← coe_toNNReal ha, ← coe_toNNReal hb, coe_lt_coe]"
}
] | [
2043,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2042,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.finrank_eq_four | [] | [
1090,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_exists_compact | [
{
"state_after": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nU : Opens G\nhU : innerContent μ U ≠ ⊤\nε : ℝ≥0\nhε : ε ≠ 0\nh'ε : ↑ε ≠ 0\n⊢ ∃ K, ↑K ⊆ ↑U ∧ innerContent μ U ≤ (fun s => ↑(toFun μ s)) K + ↑ε",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nU : Opens G\nhU : i... | [
169,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.eq_ofRepr_eq_repr | [
{
"state_after": "case h.h\nι : Type u_1\nι' : Type ?u.247588\nR : Type u_2\nR₂ : Type ?u.247594\nK : Type ?u.247597\nM : Type u_3\nM' : Type ?u.247603\nM'' : Type ?u.247606\nV : Type u\nV' : Type ?u.247611\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\ninst✝⁶ : AddCommMonoid M'\ninst✝⁵ : ... | [
335,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Topology/Maps.lean | ClosedEmbedding.closed_iff_preimage_closed | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.271027\nδ : Type ?u.271030\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nhf : ClosedEmbedding f\ns : Set β\nhs : s ⊆ range f\n⊢ IsClosed s ↔ IsClosed (f ⁻¹' s)",
"tac... | [
672,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.card_fintype_Icc | [
{
"state_after": "no goals",
"state_before": "a b : ℕ+\n⊢ Fintype.card ↑(Set.Icc a b) = ↑b + 1 - ↑a",
"tactic": "rw [← card_Icc, Fintype.card_ofFinset]"
}
] | [
97,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.castRingHom_nat | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.app_injective_of_stalkFunctor_map_injective | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁶ : Category C\ninst✝⁵ : HasColimits C\nX Y Z : TopCat\ninst✝⁴ : ConcreteCategory C\ninst✝³ : PreservesFilteredColimits (forget C)\ninst✝² : HasLimits C\ninst✝¹ : PreservesLimits (forget C)\ninst✝ : ReflectsIsomorphisms (forget C)\nF : Sheaf C X... | [
481,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.exists_null_frontiers_thickening | [
{
"state_after": "case intro.intro.intro\nΩ : Type u_1\ninst✝³ : PseudoEMetricSpace Ω\ninst✝² : MeasurableSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : SigmaFinite μ\ns : Set Ω\nRs : ℕ → ℝ\nleft✝ : StrictAnti Rs\nRs_pos : ∀ (n : ℕ), 0 < Rs n\nRs_lim : Tendsto Rs atTop (𝓝 0)\n⊢ ∃ rs, Tendsto ... | [
465,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Std/Data/Int/Lemmas.lean | Int.not_le | [] | [
664,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
662,
11
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_inj | [] | [
143,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Set.Finite.measurableSet_sUnion | [] | [
158,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_insert_of_mem | [] | [
1117,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_neg | [] | [
209,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.factorThruImageSubobject_comp_self_assoc | [
{
"state_after": "case h\nC : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : HasImage f\nW W' : C\nk : W ⟶ W'\nk' : W' ⟶ X\nh : Factors (imageSubobject f) (k ≫ k' ≫ f)\n⊢ factorThru (imageSubobject f) (k ≫ k' ≫ f) h ≫ arrow (imageSubobject f) =\n (k ≫ k' ≫ factorThruImageSubobject f) ≫ arrow (ima... | [
356,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | cauchySeq_finset_of_geometric_bound | [] | [
395,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.RCond.mono | [] | [
437,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_pow_eq | [
{
"state_after": "case zero\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\n⊢ X s ^ Nat.zero = ↑(monomial R (single s Nat.zero)) 1\n\ncase succ\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nn : ℕ\nih : X s ^ n = ↑(monomial R (single s n)) 1\n⊢ X s ^ Nat.succ n = ↑(monomial R (single s (Nat.suc... | [
437,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Algebra/Group/Pi.lean | MonoidHom.single_apply | [] | [
459,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | Homeomorph.symm_toLocalHomeomorph | [] | [
1293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.toUniformSpace_eq | [] | [
718,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_toMonoidHom | [] | [
587,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Data/Real/Basic.lean | Real.iSup_of_not_bddAbove | [] | [
822,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Order/Cover.lean | wcovby_of_eq_or_eq | [] | [
80,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfDom_apply | [] | [
1515,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_mul | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b : Associates α\nh✝ : Subsingleton α\n⊢ factors (a * b) = factors a + factors b... | [
1526,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Topology/Order/Basic.lean | not_tendsto_nhds_of_tendsto_atTop | [] | [
1554,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic.dvd_X_pow_sub_one | [
{
"state_after": "n : ℕ\nR : Type u_1\ninst✝ : Ring R\n⊢ cyclotomic n ℤ ∣ X ^ n - 1",
"state_before": "n : ℕ\nR : Type u_1\ninst✝ : Ring R\n⊢ cyclotomic n R ∣ X ^ n - 1",
"tactic": "suffices cyclotomic n ℤ ∣ X ^ n - 1 by\n simpa only [map_cyclotomic_int, Polynomial.map_sub, Polynomial.map_one, Polynomi... | [
385,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftAlgHom_apply_ofFractionRing_mk | [] | [
965,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.IsSupFiniteCompact.isSupClosedCompact | [
{
"state_after": "ι : Sort ?u.26576\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : IsSupFiniteCompact α\ns : Set α\nhne : Set.Nonempty s\nhsc : ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a ⊔ b ∈ s\n⊢ sSup s ∈ s",
"state_before": "ι : Sort ?u.26576\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh ... | [
225,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_span | [
{
"state_after": "R : Type u_1\ninst✝³ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\nP : Type ?u.64270\ninst✝ : CommRing P\ns : Set R\n⊢ Submodule.span R (↑(Algebra.linearMap R S) '' s) = Submodule.span R (↑(algebraMap R S) '' s)",
"state_before": "R : Type u_1\nins... | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.CompatiblePreserving.apply_map | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA : Type u₃\ninst✝ : Category A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology A\nG : C ⥤ D\nhG : CompatiblePreserving K G\nℱ : SheafOfTypes K\nZ : C\nT : Presieve Z\nx : FamilyOfElements (Fu... | [
122,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | hasDerivAt_pow | [] | [
66,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | add_le_mul_of_right_le_left | [] | [
873,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.curry_symm_apply | [] | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.nonneg_prod_iff | [
{
"state_after": "ι : Type ?u.43590\nR✝ : Type ?u.43593\nM₁ : Type u_2\nM₂ : Type u_3\nN₁ : Type ?u.43602\nN₂ : Type ?u.43605\nMᵢ : ι → Type ?u.43610\nNᵢ : ι → Type ?u.43615\ninst✝¹⁵ : Semiring R✝\ninst✝¹⁴ : AddCommMonoid M₁\ninst✝¹³ : AddCommMonoid M₂\ninst✝¹² : AddCommMonoid N₁\ninst✝¹¹ : AddCommMonoid N₂\nin... | [
100,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.erase | [] | [
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_ker_comp | [
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Mathlib/Topology/Maps.lean | Embedding.comp | [] | [
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.deriv_apply | [] | [
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Mathlib/Data/Nat/Interval.lean | Nat.Ioc_eq_range' | [] | [
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Mathlib/MeasureTheory/Function/EssSup.lean | essSup_const | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.vanishingIdeal_anti_mono | [] | [
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_induction_on | [
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.eq_zero_or_one | [
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.not_mem_uIcc_of_lt | [
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.inv_apply_self | [] | [
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | Matrix.toEuclideanLin_conjTranspose_eq_adjoint | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_one | [] | [
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.lintegral_mono | [] | [
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.toContinuousMap_injective | [] | [
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.isLimit_lift | [] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_sum_elim | [
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Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotientInfEquivSupQuotient_injective | [
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.eventually_left_inverse | [] | [
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubgroup_strictMono | [] | [
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Mathlib/Order/Basic.lean | Decidable.eq_iff_le_not_lt | [] | [
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Mathlib/Order/Atoms.lean | Set.isAtom_iff | [
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_eq_ciSup | [
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_sec | [
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Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.add_mem_center | [
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Mathlib/Topology/Algebra/Order/Group.lean | tendsto_zero_iff_abs_tendsto_zero | [
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Mathlib/Data/Set/Image.lean | Subtype.coe_image_subset | [
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Mathlib/MeasureTheory/Function/EssSup.lean | essSup_map_measure | [
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Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_naturality | [
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Mathlib/Order/CompleteLattice.lean | Function.Surjective.iInf_comp | [] | [
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Mathlib/Data/Set/Basic.lean | Set.compl_subset_compl | [] | [
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.pre_pre | [
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.gen_univ | [] | [
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_eq_zero_of_ne | [
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Mathlib/FieldTheory/Fixed.lean | FixedPoints.finrank_le_card | [
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_arrow_factors_right | [
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Mathlib/Data/Set/Basic.lean | Set.subset_inter | [] | [
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Mathlib/Data/Part.lean | Part.sdiff_def | [] | [
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Mathlib/Algebra/Lie/UniversalEnveloping.lean | UniversalEnvelopingAlgebra.lift_unique | [
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_intOfNat | [] | [
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.exists_rep | [
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Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.compl | [] | [
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Mathlib/Data/List/AList.lean | AList.insert_entries_of_neg | [
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Mathlib/RingTheory/FreeRing.lean | FreeRing.induction_on | [
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.cutMap_add | [
{
"state_after": "case refine_1\nF : Type ?u.12016\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.12025\ninst✝² : LinearOrderedField α\ninst✝¹ : LinearOrderedField β\na✝ a₁ a₂ : α\nb✝ : β\nq✝ : ℚ\ninst✝ : Archimedean α\na b : α\nq : ℚ\nhq : q ∈ {t | ↑t < a + b}\n⊢ q ∈ Rat.cast ⁻¹' (cutMap β a + cutMap β b)\n\ncase re... | [
163,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.neg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[... | [
280,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
8
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.invOf_sym | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_and | [] | [
1320,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
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