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/CompactOpen.lean | ContinuousMap.exists_tendsto_compactOpen_iff_forall | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.37922\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : TopologicalSpace γ\ninst✝³ : LocallyCompactSpace α\ninst✝² : T2Space α\ninst✝¹ : T2Space β\nι : Type u_3\nl : Filter ι\ninst✝ : Filter.NeBot l\nF : ι → C(α, β)\n⊢ (∃ f, Fi... | [
307,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Coalgebra.epi_of_epi | [] | [
389,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\na : α\nthis : tail (a :: const a) = const a\n⊢ tail (const a) = const a",
"tactic": "rwa [← const_eq] at this"
}
] | [
250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augment_X_zero | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.isPure_univ | [] | [
275,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_unit | [
{
"state_after": "l : Type ?u.51935\nm : Type ?u.51938\nn : Type u_2\no : Type ?u.51944\nR : Type u_1\nm_fin : Fintype m\ninst✝⁴ : Fintype n\ninst✝³ : Fintype o\ninst✝² : CommRing R\ninst✝¹ : StrongRankCondition R\ninst✝ : DecidableEq n\nA : (Matrix n n R)ˣ\n⊢ Fintype.card n ≤ rank ↑A",
"state_before": "l :... | [
98,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | Set.OrdConnected.smul | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : OrdConnected s\n⊢ OrdConnected (a • ↑(upperClosure s) ∩ a • ↑(lowerClosure s))",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : OrdConnected s\n⊢ OrdConnected (a • s)",
"tactic": "rw... | [
63,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_apply | [] | [
415,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_sep | [] | [
1407,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_subset_vsub_right | [] | [
673,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.tendstoUniformly_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.33140\ninst✝ : PseudoEMetricSpace α\nι : Type u_1\nF : ι → β → α\nf : β → α\np : Filter ι\n⊢ TendstoUniformly F f p ↔ ∀ (ε : ℝ≥0∞), ε > 0 → ∀ᶠ (n : ι) in p, ∀ (x : β), edist (f x) (F n x) < ε",
"tactic": "simp only [← tend... | [
372,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_biUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.508302\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\na : α\n⊢ Finset.biUnion {a} t = t a",
"tactic": "classical rw [← insert_emptyc_eq, biUnion_insert, biUnion_empty, union_empty]"
},
{
"s... | [
3577,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3576,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.subset_Icc_sInf_sSup_of_bounded | [] | [
194,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.center_eq_iInf | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.41553\ninst✝¹ : AddGroup A\nN : Type ?u.41559\ninst✝ : Group N\ns : Set G\ng : G\nS : Set G\nhS : closure S = ⊤\n⊢ center G = ⨅ (g : G) (_ : g ∈ S), centralizer (zpowers g)",
"tactic": "rw [← centralizer_top, ← hS,... | [
243,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/LinearAlgebra/FreeModule/PID.lean | Module.free_of_finite_type_torsion_free' | [
{
"state_after": "case mk\nι : Type ?u.216849\nR : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsPrincipalIdealRing R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nb✝ : ι → M\ninst✝¹ : Finite R M\ninst✝ : NoZeroSMulDivisors R M\nn : ℕ\nb : Basis (Fin n) R M\n⊢ Free R M",
"sta... | [
422,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Order/GaloisConnection.lean | OrderIso.bddAbove_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.32992\na a₁ a₂ : α\nb b₁ b₂ : β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\ns : Set β\n⊢ BddAbove (↑e ⁻¹' s) ↔ BddAbove s",
"tactic": "rw [← e.bddAbove_image, e.image_preimage]"
}
] | [
443,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_inj_of_lt_of_lt_pi_div_two | [] | [
999,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_carrier | [] | [
125,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domDomCongr_add | [] | [
756,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.exists_lt_apply_of_lt_op_nnnorm | [
{
"state_after": "case intro\n𝕜✝ : Type ?u.748535\n𝕜₂✝ : Type ?u.748538\n𝕜₃ : Type ?u.748541\nE✝ : Type ?u.748544\nEₗ : Type ?u.748547\nF✝ : Type ?u.748550\nFₗ : Type ?u.748553\nG : Type ?u.748556\nGₗ : Type ?u.748559\n𝓕 : Type ?u.748562\ninst✝²³ : SeminormedAddCommGroup E✝\ninst✝²² : SeminormedAddCommGroup... | [
533,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.lift_cone | [] | [
283,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.continuous_map₂ | [] | [
719,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.tendsto_mul_log_one_plus_div_atTop | [
{
"state_after": "t : ℝ\nh₁ : Tendsto (fun h => h⁻¹ * log (1 + t * h)) (𝓝[{0}ᶜ] 0) (𝓝 t)\n⊢ Tendsto (fun x => x * log (1 + t / x)) atTop (𝓝 t)",
"state_before": "t : ℝ\n⊢ Tendsto (fun x => x * log (1 + t / x)) atTop (𝓝 t)",
"tactic": "have h₁ : Tendsto (fun h => h⁻¹ * log (1 + t * h)) (𝓝[≠] 0) (𝓝 ... | [
219,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.IsConnected.of_any_functor_const_on_obj | [] | [
111,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.mk_eq | [
{
"state_after": "case mk\nT : Type u\ninst✝ : Category T\nleft✝ right✝ : T\nhom✝ : (𝟭 T).obj left✝ ⟶ (𝟭 T).obj right✝\n⊢ mk { left := left✝, right := right✝, hom := hom✝ }.hom = { left := left✝, right := right✝, hom := hom✝ }",
"state_before": "T : Type u\ninst✝ : Category T\nf : Arrow T\n⊢ mk f.hom = f"... | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.ae_eq_zero_of_lintegral_rpow_eq_zero | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nhp0 : 0 ≤ p\nf : α → ℝ≥0∞\nhf : AEMeasurable f\nhf_zero : (fun x => f x ^ p) =ᵐ[μ] 0\n⊢ f =ᵐ[μ] 0",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nhp0 : 0 ≤ p\nf : α ... | [
137,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.ext_fourfold' | [
{
"state_after": "case H.H.h.h.H.h.h\nR : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.731485\ninst✝¹³ : Monoid R'\nR'' : Type ?u.731491\ninst✝¹² : Semiring R''\nM : Type u_5\nN : Type u_4\nP : Type u_3\nQ : Type u_2\nS : Type u_6\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid... | [
611,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.end_mem_tail_support_of_ne | [
{
"state_after": "case intro.intro.intro\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nh : u ≠ v\nw✝² : V\nw✝¹ : Adj G u w✝²\nw✝ : Walk G w✝² v\n⊢ v ∈ List.tail (support (cons w✝¹ w✝))",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\... | [
603,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_lt_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ -y < x ↔ -x < y",
"tactic": "rw [← neg_neg x, neg_lt_neg_iff, neg_neg]"
}
] | [
1351,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1351,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_nat_lt_coe | [] | [
846,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Order/Basic.lean | associative_of_commutative_of_le | [
{
"state_after": "ι : Type ?u.10983\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.10994\nr : α → α → Prop\ninst✝ : PartialOrder α\nf : α → α → α\ncomm : Commutative f\nassoc : ∀ (a b c : α), f (f a b) c ≤ f a (f b c)\na b c : α\n⊢ f (f c b) a ≤ f c (f b a)",
"state_before": "ι : Type ?u.10983\nα : Ty... | [
592,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/CategoryTheory/Sites/Spaces.lean | Opens.pretopology_toGrothendieck | [
{
"state_after": "T : Type u\ninst✝ : TopologicalSpace T\n⊢ Pretopology.toGrothendieck (Opens T) (Pretopology.ofGrothendieck (Opens T) (grothendieckTopology T)) =\n grothendieckTopology T",
"state_before": "T : Type u\ninst✝ : TopologicalSpace T\n⊢ Pretopology.toGrothendieck (Opens T) (pretopology T) = g... | [
100,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.Iso.conj_eq_conj | [] | [
404,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_sub_zsmul | [
{
"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\nm : ℤ\n⊢ toIocDiv hp a (b - m • p) = toIocDiv hp a b - m",
"tactic": "rw [sub_eq_add_neg, ← neg_smul, toIocDiv_add_zsmul, sub_eq_add_neg]"
... | [
290,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_card_biUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns✝ t : Finset α\ninst✝ : DecidableEq (Finset α)\ns : Finset α\n⊢ powerset s = Finset.biUnion (range (card s + 1)) fun i => powersetLen i s",
"tactic": "simpa only [disjiUnion_eq_biUnion] using powerset_card_disjiUnion s"
}
] | [
301,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\nx : α × α\na : α\n⊢ Set.Nonempty (offDiag s) ↔ Set.Nontrivial s",
"tactic": "simp [offDiag, Set.Nonempty, Set.Nontrivial]"
}
] | [
550,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.map_id | [] | [
1680,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1679,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_toNonUnitalStarAlgHom | [] | [
487,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.exists_pos_measure_of_not_restrict_le_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.604160\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : TopologicalSpace M\ninst✝ : LinearOrderedAddCommMonoid M\nv w : VectorMeasure α M\ni j : Set α\nhi : ¬restrict v i ≤ restrict 0 i\nhi₁ : MeasurableSet i\n⊢ ∃ j, MeasurableSet j ∧ j ⊆ i ∧ 0 < ↑v j",
"state_befor... | [
1048,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.not_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9816\nγ : Type ?u.9819\ns t : Finset α\n⊢ ¬s ⊆ t ↔ ∃ x, x ∈ s ∧ ¬x ∈ t",
"tactic": "simp only [← coe_subset, Set.not_subset, mem_coe]"
}
] | [
392,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.finset_sup_apply | [
{
"state_after": "case h₁\nR : Type ?u.492548\nR' : Type ?u.492551\n𝕜 : Type u_1\n𝕜₂ : Type ?u.492557\n𝕜₃ : Type ?u.492560\n𝕝 : Type ?u.492563\nE : Type u_2\nE₂ : Type ?u.492569\nE₃ : Type ?u.492572\nF : Type ?u.492575\nG : Type ?u.492578\nι : Type u_3\ninst✝¹⁸ : SeminormedRing 𝕜\ninst✝¹⁷ : SeminormedRing ... | [
399,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGreatest_union_iff | [] | [
390,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/List/Func.lean | List.Func.get_eq_default_of_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na✝ : α\nas✝ as1 as2 as3 : List α\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\na : α\nas : List α\nh1 : length (a :: as) ≤ 0\n⊢ get 0 (a :: as) = default",
"tactic": "cases h1"
},
{
"state_after": "α : Type u\nβ : Ty... | [
128,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.valuation_nonneg | [
{
"state_after": "case pos\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : x = 0\n⊢ 0 ≤ valuation x\n\ncase neg\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : ¬x = 0\n⊢ 0 ≤ valuation x",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\n⊢ 0 ≤ valuation x",
"tactic": "by_cases hx : x = 0"
... | [
404,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | Finset.esymm_map_val | [
{
"state_after": "R : Type u_2\ninst✝ : CommSemiring R\nσ : Type u_1\nf : σ → R\ns : Finset σ\nn : ℕ\n⊢ sum (map ((fun x => prod x) ∘ (fun x => map f x) ∘ Finset.val) (Finset.powersetLen n s).val) =\n ∑ t in Finset.powersetLen n s, Finset.prod t f",
"state_before": "R : Type u_2\ninst✝ : CommSemiring R\n... | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_subtype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.123371\nγ : Type ?u.123374\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\na : α\nha : p a\n⊢ { val := a, property := ha } ∈ Finset.subtype p s ↔ ↑{ val := a, property := ha } ∈ s",
"tactic": "simp [Finset.subtype, ha]"
}
] | [
666,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.vadd | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.49343\nβ : Type ?u.49346\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nx : E\nhs : Convex 𝕜 s\nz : E\n⊢ Convex 𝕜 ({z} + s)",
"state_before": "𝕜 : Type u_1\n... | [
219,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | summable_prod_of_nonneg | [] | [
1341,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.support_esymm'' | [
{
"state_after": "σ : Type u_1\nR : Type u_2\nτ : Type ?u.175369\nS : Type ?u.175372\ninst✝⁵ : CommSemiring R\ninst✝⁴ : CommSemiring S\ninst✝³ : Fintype σ\ninst✝² : Fintype τ\nn : ℕ\ninst✝¹ : DecidableEq σ\ninst✝ : Nontrivial R\n⊢ support (∑ t in powersetLen n univ, ↑(monomial (∑ i in t, Finsupp.single i 1)) 1)... | [
242,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_eq_inv' | [] | [
305,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_csSup | [] | [
151,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.toWord_one | [] | [
1321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_eq_gcd_range_of_lt | [
{
"state_after": "case hab\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nn : ℕ\nh : natDegree p < n\n⊢ content p ∣ Finset.gcd (Finset.range n) (coeff p)\n\ncase hba\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X... | [
199,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_sub | [] | [
284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.Icc_eq_finset_subtype | [] | [
43,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Std/Data/Int/DivMod.lean | Int.fdiv_self | [
{
"state_after": "a : Int\nH : a ≠ 0\nthis : fdiv (1 * a) a = 1\n⊢ fdiv a a = 1",
"state_before": "a : Int\nH : a ≠ 0\n⊢ fdiv a a = 1",
"tactic": "have := Int.mul_fdiv_cancel 1 H"
},
{
"state_after": "no goals",
"state_before": "a : Int\nH : a ≠ 0\nthis : fdiv (1 * a) a = 1\n⊢ fdiv a a = 1",... | [
226,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
225,
19
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | expMapCircle_eq_expMapCircle | [
{
"state_after": "x y : ℝ\n⊢ (∃ n, ↑x * I = ↑y * I + ↑n * (2 * ↑π * I)) ↔ ∃ m, x = y + ↑m * (2 * π)",
"state_before": "x y : ℝ\n⊢ ↑expMapCircle x = ↑expMapCircle y ↔ ∃ m, x = y + ↑m * (2 * π)",
"tactic": "rw [Subtype.ext_iff, expMapCircle_apply, expMapCircle_apply, exp_eq_exp_iff_exists_int]"
},
{
... | [
93,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_iff_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.193145\nι : Sort x\ninst✝ : AddGroup β\nf g : α → β\nl : Filter α\nh : f - g =ᶠ[l] 0\n⊢ f =ᶠ[l] g",
"tactic": "simpa using h.add (EventuallyEq.refl l g)"
}
] | [
1616,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1614,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_cos_ofReal_re | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℂ\nx : ℝ\n⊢ ↑(starRingEnd ℂ) (cos ↑x) = cos ↑x",
"tactic": "rw [← cos_conj, conj_ofReal]"
}
] | [
956,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Data/Nat/Choose/Factorization.lean | Nat.prod_pow_factorization_choose | [
{
"state_after": "p n✝ k✝ n k : ℕ\nhkn : k ≤ n\n⊢ ∏ p in Finset.range (n + 1), p ^ ↑(factorization (choose n k)) p =\n Finsupp.prod (factorization (choose n k)) fun x x_1 => x ^ x_1",
"state_before": "p n✝ k✝ n k : ℕ\nhkn : k ≤ n\n⊢ ∏ p in Finset.range (n + 1), p ^ ↑(factorization (choose n k)) p = choos... | [
145,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_diag_uniformity | [] | [
502,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_sub_zsmul | [
{
"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\nm : ℤ\n⊢ toIcoDiv hp a (b - m • p) = toIcoDiv hp a b - m",
"tactic": "rw [sub_eq_add_neg, ← neg_smul, toIcoDiv_add_zsmul, sub_eq_add_neg]"
... | [
280,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_mul | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ b a₂ : R\n⊢ (a₁ + a₂) * b = a₁ * b + a₂ * b",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ b c₁ a₂ c₂ d : R\nx✝² : a₁ * ... | [
432,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_of_fintype | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.65546\nβ : Type ?u.65549\ninst✝³ : PseudoMetricSpace α\nx y z : α\ns t : Set α\ninst✝² : Decidable (Set.Nontrivial s)\ninst✝¹ : DecidableEq α\ninst✝ : Fintype ↑s\nhs : Set.Nontrivial s\n⊢ Finset.Nonempty (toFinset (offDiag s))",
"tactic": "simpa"... | [
476,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.preimage_add_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕝 : Type ?u.72862\nE : Type u_2\nF : Type ?u.72868\nβ : Type ?u.72871\ninst✝⁵ : OrderedSemiring 𝕜\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace F\ninst✝² : AddCancelCommMonoid E\ninst✝¹ : ContinuousAdd E\ninst✝ : Module 𝕜 E\ns : Set E... | [
234,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.comp_c | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.csinh | [] | [
531,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_drop | [
{
"state_after": "ι : Type ?u.212813\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L : List α\ni j : ℕ\nh : i + j < length L\nA : i < length L\n⊢ j < length (drop i L)",
"state_before": "ι : Type ?u.212813\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L : List α\ni j : ℕ\nh : i + j < lengt... | [
2222,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2217,
1
] |
Mathlib/Order/BoundedOrder.lean | eq_top_or_lt_top | [] | [
184,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/GroupRingAction/Invariant.lean | IsInvariantSubring.coe_subtypeHom' | [] | [
67,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_of_sub_eq_zero | [
{
"state_after": "a b : Int\nh : a - b = 0\nthis : 0 + b = b\n⊢ a = b",
"state_before": "a b : Int\nh : a - b = 0\n⊢ a = b",
"tactic": "have : 0 + b = b := by rw [Int.zero_add]"
},
{
"state_after": "a b : Int\nh : a - b = 0\nthis✝ : 0 + b = b\nthis : a - b + b = b\n⊢ a = b",
"state_before": ... | [
355,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
352,
11
] |
Mathlib/Algebra/GroupPower/Basic.lean | mul_zpow_neg_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na✝ b✝ a b : α\n⊢ (a * b) ^ (-1) = b ^ (-1) * a ^ (-1)",
"tactic": "simp only [zpow_neg, zpow_one, mul_inv_rev]"
}
] | [
346,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Set/Finite.lean | List.finite_toSet | [] | [
563,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Data/List/Basic.lean | List.get_reverse_aux₂ | [
{
"state_after": "ι : Type ?u.95388\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl r : List α\nh1 : length (a :: l) - 1 - 0 < length (reverseAux (a :: l) r)\nx✝ : 0 < length (a :: l)\naux :\n ∀ (h1 : 0 + length l < length (reverseAux l (a :: r))) (h2 : 0 < length (a :: r)),\n get ... | [
1453,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1438,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iff_ultrafilter_le_nhds | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Type ?u.10996\nπ : ι → Type ?u.11001\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\n⊢ Monotone fun f => ∃ a, a ∈ s ∧ ClusterPt a f\n\ncase refine'_2\nα : Type u\nβ : Type v\nι : Type ?u.10996\nπ : ι → Type ?u.11001\ninst✝¹ : T... | [
172,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Sym/Card.lean | Sym.card_sym_fin_eq_multichoose | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.6052\nβ : Type ?u.6055\nn✝ n : ℕ\n⊢ Fintype.card (Sym (Fin n) 0) = multichoose n 0",
"tactic": "simp"
},
{
"state_after": "α : Type ?u.6052\nβ : Type ?u.6055\nn k : ℕ\n⊢ Fintype.card (Sym (Fin 0) (k + 1)) = 0",
"state_before": "α : Ty... | [
109,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullback_map_openEmbedding_of_open_embeddings | [
{
"state_after": "case toEmbedding\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z✝ W X Y Z S T : TopCat\nf₁ : W ⟶ S\nf₂ : X ⟶ S\ng₁ : Y ⟶ T\ng₂ : Z ⟶ T\ni₁ : W ⟶ Y\ni₂ : X ⟶ Z\nH₁ : OpenEmbedding ((forget TopCat).map i₁)\nH₂ : OpenEmbedding ((forget TopCat).map i₂)\ni₃ : S ⟶ T\nH₃ : Mono i₃\neq₁ : f₁ ≫ i₃ = i₁ ≫... | [
287,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_def | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_mul | [] | [
384,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Algebra/Group/Units.lean | one_divp | [] | [
504,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_rightInverse | [] | [
403,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.not_eq_false' | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ ((!b) = false) = (b = true)",
"tactic": "cases b <;> simp"
}
] | [
129,
99
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
129,
9
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_map | [
{
"state_after": "case h\nF : Type u_2\ninst✝⁴ : Field F\nE : Type u_3\ninst✝³ : Field E\ninst✝² : Algebra F E\nS : Set E\nE' : Type u_1\ninst✝¹ : Field E'\ninst✝ : Algebra F E'\nf : E →ₐ[F] E'\nx : E'\n⊢ x ∈ map f (adjoin F S) ↔ x ∈ adjoin F (↑f '' S)",
"state_before": "F : Type u_2\ninst✝⁴ : Field F\nE : ... | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | fderivWithin.comp | [] | [
143,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_insert | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₂ : Type ?u.171174\nK : Type ?u.171177\nM : Type u_1\nM₂ : Type ?u.171183\nV : Type ?u.171186\nS : Type ?u.171189\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* ... | [
491,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wRec_eq | [
{
"state_after": "n : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\nC : Type u_1\ng : (a : P.A) → B (drop P) a ⟹ α → (PFunctor.B (last P) a → W P α) → (PFunctor.B (last P) a → C) → C\na : P.A\nf' : B (drop P) a ⟹ α\nf : PFunctor.B (last P) a → W P α\n⊢ (match\n let g := fun i => (f i).fst;\n let g' := wPa... | [
215,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.cons_nth_inits_core | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\na : α\nn : ℕ\n⊢ ∀ (l : List α) (s : Stream' α), a :: nth (initsCore l s) n = nth (initsCore (a :: l) s) n",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\n⊢ ∀ (a : α) (n : ℕ) (l : List α) (s : Stream' α), a :: nth (initsCore l s) n = nth (initsCore... | [
710,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_monomial | [] | [
651,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieIdeal.derivedSeries_map_le | [
{
"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⊢ map f (derivedSeries R L' Nat.zero) ≤ derivedSeries R L Nat.zero\n\ncase succ\nR : ... | [
188,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.MonoOver.bot_left | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_le_iff_le_map | [] | [
127,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_ball | [] | [
2730,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2729,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_map_of_involutive | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2322\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\nhf : Involutive f\na : α\nl : List α\n⊢ a ∈ map f l ↔ f a ∈ l",
"tactic": "rw [mem_map, hf.exists_mem_and_apply_eq_iff]"
}
] | [
141,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.ZeroAtFilter.add | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : TopologicalSpace β\ninst✝¹ : AddZeroClass β\ninst✝ : ContinuousAdd β\nl : Filter α\nf g : α → β\nhf : ZeroAtFilter l f\nhg : ZeroAtFilter l g\n⊢ ZeroAtFilter l (f + g)",
"tactic": "simpa using hf.add hg"
}
] | [
46,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
8
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.ext_iff | [] | [
902,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_or_le_of_add_eq_add_pred | [
{
"state_after": "case inl.h\nm n k l : ℕ\nh : k + l = m + n - 1\nh' : m ≤ k\n⊢ m ≤ k\n\ncase inr.h\nm n k l : ℕ\nh : k + l = m + n - 1\nh' : k < m\n⊢ n ≤ l",
"state_before": "m n k l : ℕ\nh : k + l = m + n - 1\n⊢ m ≤ k ∨ n ≤ l",
"tactic": "cases' le_or_lt m k with h' h' <;> [left; right]"
},
{
... | [
270,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.dist_map | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_5\nV : Type u_2\nV₁ : Type ?u.45178\nV₂ : Type u_3\nV₃ : Type ?u.45184\nV₄ : Type ?u.45187\nP₁ : Type ?u.45190\nP : Type u_4\nP₂ : Type u_1\nP₃ : Type ?u.45199\nP₄ : Type ?u.45202\ninst✝²⁰ : NormedField 𝕜\ninst✝¹⁹ : SeminormedAddCommGroup V\ninst✝¹⁸... | [
146,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.is_quotient_mk | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.inv_pow' | [
{
"state_after": "case zero\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\n⊢ A⁻¹ ^ Nat.zero = (A ^ Nat.zero)⁻¹\n\ncase succ\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℕ\nih : A⁻¹ ^ n = (A ^ n)... | [
48,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Ico | [] | [
136,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
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