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/Data/Set/Pointwise/SMul.lean | Set.preimage_smul_inv₀ | [] | [
1030,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
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Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.coe_to_linearEquiv | [] | [
1023,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Complex.ofReal_cpow_of_nonpos | [
{
"state_after": "case inl\ny : ℂ\nhx : 0 ≤ 0\n⊢ ↑0 ^ y = (-↑0) ^ y * exp (↑π * I * y)\n\ncase inr\nx : ℝ\nhx : x ≤ 0\ny : ℂ\nhlt : x < 0\n⊢ ↑x ^ y = (-↑x) ^ y * exp (↑π * I * y)",
"state_before": "x : ℝ\nhx : x ≤ 0\ny : ℂ\n⊢ ↑x ^ y = (-↑x) ^ y * exp (↑π * I * y)",
"tactic": "rcases hx.eq_or_lt with (rf... | [
258,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_succ | [] | [
894,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.tendsto_div_nhds_zero | [
{
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1821,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1815,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae | [
{
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842,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | closure_one_eq | [] | [
1135,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.card_Ico_eq_card_Icc_sub_one | [] | [
227,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.PosDef.add | [] | [
954,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
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Mathlib/GroupTheory/Sylow.lean | Sylow.characteristic_of_normal | [
{
"state_after": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Finite (Sylow p G)\nP : Sylow p G\nh : Normal ↑P\nthis : Subsingleton (Sylow p G)\n⊢ Characteristic ↑P",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : ... | [
720,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_le_add_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.75944\nβ : Type ?u.75947\nγ : Type ?u.75950\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\n⊢ a + ↑0 ≤ b + ↑0 ↔ a ≤ b",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.75944\nβ : Typ... | [
141,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Data/Option/Basic.lean | Option.mem_pmem | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.7041\nδ : Type ?u.7044\np : α → Prop\nf : (a : α) → p a → β\nx : Option α\na : α\nh : ∀ (a : α), a ∈ x → p a\nha✝ : a ∈ x\nha : x = some a\n⊢ pmap f x h = some (f a (_ : p a))",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.7041\nδ : Type ... | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.exists_eq_spanSingleton_mul | [
{
"state_after": "case intro.intro\nR : Type ?u.1535657\ninst✝⁷ : CommRing R\nS : Submonoid R\nP : Type ?u.1535864\ninst✝⁶ : CommRing P\ninst✝⁵ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝⁴ : CommRing R₁\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R₁ K\ninst✝¹ : IsFractionRing R₁ K\ninst✝... | [
1509,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.continuous_sin | [] | [
93,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.coe_coe | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_iUnion_apply_ae | [
{
"state_after": "α : Type u_2\nβ : Type ?u.302552\nγ : Type ?u.302555\nδ : Type ?u.302558\nι : Type u_1\nR : Type ?u.302564\nR' : Type ?u.302567\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\ninst✝ : Countable ι\ns : ι → Set... | [
1761,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1755,
1
] |
Mathlib/Order/CompleteLattice.lean | toDual_sInf | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.neg_posPart | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.refl | [] | [
68,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Std/Data/List/Basic.lean | List.takeD_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : Nat\nl : List α\na : α\n⊢ takeD (n + 1) l a = Option.getD (head? l) a :: takeD n (tail l) a",
"tactic": "simp [takeD]"
}
] | [
590,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
589,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Ico | [] | [
3348,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3347,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Expr.toPoly_denote | [
{
"state_after": "no goals",
"state_before": "ctx : Context\ne : Expr\n⊢ Poly.denote ctx (toPoly e) = denote ctx e",
"tactic": "induction e with\n| num k =>\n simp!; by_cases h : k == 0 <;> simp! [*]\n simp [eq_of_beq h]\n| var v => simp!\n| add a b => simp! [Poly.add_denote, *]\n| mul a b => simp! [P... | [
178,
42
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
171,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t",
"tactic": "simp only [subset_def, mem_insert_iff, or_imp, forall_and, forall_eq]"
}
] | [
1156,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.map_mk' | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nL R : ListBlank Γ\n⊢ map f (mk' L R) = mk' (ListBlank.map f L) (ListBlank.map f R)",
"tactic": "simp only [Tape.mk', Tape.map, ListBlank.head_map, eq_self_iff_true,... | [
724,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.dual_id | [] | [
727,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.const_mul_atBot | [] | [
1208,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.not_dvd_of_degree_lt | [] | [
208,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | LocalHomeomorph.contDiffAt_symm | [
{
"state_after": "case h0\n𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁰ : NormedAddCommGroup D\ninst✝⁹ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type uG\ninst✝... | [
1827,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1783,
1
] |
Mathlib/Topology/Maps.lean | Inducing.isClosed_preimage | [] | [
171,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Ico | [] | [
494,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_op_mul | [
{
"state_after": "case a\nι : 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\n⊢ map (↑(opLinearEquiv R)) (M * N) ≤ map (↑(opLinearEquiv R)) N * map (↑(opLinearEquiv R)) M\n\ncase a\nι : Sort uι\nR : Type u\ninst✝²... | [
293,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableWithinAt.prod | [] | [
100,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : cos x = 1\nn : ℤ\nhn : ↑n * π = x\nhn0 : n % 2 = 0\n⊢ ↑(n / 2) * (2 * π) = x",
"tactic": "rwa [← mul_assoc, ← @Int.cast_two ℝ, ← Int.cast_mul,\n Int.ediv_mul_cancel ((Int.dvd_iff_emod_eq_zero _ _).2 hn0)]"
},
{
"state_after": "x : ℝ\nh : ... | [
542,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Std/Data/Int/Lemmas.lean | Int.min_eq_right | [
{
"state_after": "a b : Int\nh : b ≤ a\n⊢ min b a = b",
"state_before": "a b : Int\nh : b ≤ a\n⊢ min a b = b",
"tactic": "rw [Int.min_comm a b]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : b ≤ a\n⊢ min b a = b",
"tactic": "exact Int.min_eq_left h"
}
] | [
706,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
705,
11
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_toHomeomorph_symm | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul | [
{
"state_after": "E : Type u_2\nF : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : FiniteDimensional ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ns : Set E\nf✝ : E → E\nf' : E → E →L[ℝ] E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\nμ : Measure E\ninst✝¹ : Is... | [
1266,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.Functor.rightDerived_map_eq | [
{
"state_after": "C : Type u\ninst✝⁵ : Category C\nD : Type u_2\ninst✝⁴ : Category D\ninst✝³ : Abelian C\ninst✝² : HasInjectiveResolutions C\ninst✝¹ : Abelian D\nF : C ⥤ D\ninst✝ : Additive F\nn : ℕ\nX Y : C\nf : Y ⟶ X\nP : InjectiveResolution X\nQ : InjectiveResolution Y\ng : Q.cocomplex ⟶ P.cocomplex\nw : Q.ι... | [
127,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit_lt_bit | [] | [
716,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.one_right | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : MulOneClass M\na : M\n⊢ SemiconjBy a 1 1",
"tactic": "rw [SemiconjBy, mul_one, one_mul]"
}
] | [
93,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.center_toSubring | [] | [
1360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Init/Logic.lean | ExistsUnique.exists | [] | [
245,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.symm_trans_apply | [] | [
924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mem_mker | [] | [
1166,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.comapEq_symm | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nβ γ : Type w\nf g : β → γ\nh : f = g\n⊢ comapEq C (_ : g = f) = (comapEq C h).symm",
"tactic": "aesop_cat"
}
] | [
108,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | norm_algebraMap_nNReal | [] | [
526,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_mk | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Fintype/Powerset.lean | Fintype.card_finset_len | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Fintype α\nk : ℕ\n⊢ card { s // Finset.card s = k } = Nat.choose (card α) k",
"tactic": "simp [Fintype.subtype_card, Finset.card_univ]"
}
] | [
57,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.exists_pow_neg_lt_rat | [
{
"state_after": "case intro\np : ℕ\nhp : Fact (Nat.Prime p)\nε : ℚ\nhε : 0 < ε\nk : ℕ\nhk : ↑p ^ (-↑k) < ↑ε\n⊢ ∃ k, ↑p ^ (-↑k) < ε",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nε : ℚ\nhε : 0 < ε\n⊢ ∃ k, ↑p ^ (-↑k) < ε",
"tactic": "obtain ⟨k, hk⟩ := @exists_pow_neg_lt p _ ε (by exact_mod_cast hε)"
... | [
355,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | sq_eq_sq_iff_eq_or_eq_neg | [] | [
297,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.eq | [] | [
387,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.le_sup_of_le_right | [] | [
1792,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1790,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.liftOfRightInverse_comp_apply | [] | [
3359,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3356,
1
] |
Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.annIdealGenerator_aeval_eq_zero | [] | [
140,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_extend_extend | [
{
"state_after": "case refine'_1\nF : Type ?u.548018\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : PseudoMetricSpace β\ninst✝² : PseudoMetricSpace γ\nf✝ g : α →ᵇ β\nx✝ : α\nC : ℝ\nδ : Type u_1\ninst✝¹ : TopologicalSpace δ\ninst✝ : DiscreteTopology δ\nf : α ↪ δ\ng₁ g₂ : α →ᵇ β\nh₁ h₂... | [
504,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/MeasureTheory/Integral/RieszMarkovKakutani.lean | rieszContentAux_mono | [] | [
68,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.bind_congr | [] | [
1035,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.ext | [] | [
126,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.zero_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp 0 p = 0",
"tactic": "rw [← C_0, C_comp]"
}
] | [
568,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_gc | [] | [
87,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.imClm_coe | [] | [
922,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.stronglyMeasurable_in_set | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.228351\nι : Type ?u.228354\ninst✝² : Countable ι\nf✝ g : α → β\nm : MeasurableSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : Zero β\ns : Set α\nf : α → β\nhs : MeasurableSet s\nhf : StronglyMeasurable f\nhf_zero : ∀ (x : α), ¬x ∈ s → f x = 0\ng_seq_s : ℕ ... | [
904,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.coe_toLp | [] | [
1738,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.mul_apply | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.zero_of_nonpos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ≤ 0\n⊢ expNegInvGlue x = 0",
"tactic": "simp [expNegInvGlue, hx]"
}
] | [
67,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.uniformEmbedding | [] | [
203,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_comm | [] | [
1148,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.nsmul_modEq_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\ninst✝ : NoZeroSMulDivisors ℕ α\nhn : n ≠ 0\nm : ℤ\n⊢ n • b - n • a = m • n • p ↔ b - a = m • p",
"tactic": "rw [← smul_sub, smul_comm, smul_right_inj hn]"
}
] | [
178,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_sdiff_add_card_eq_card | [] | [
437,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_nonempty | [] | [
61,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/LinearAlgebra/Matrix/Diagonal.lean | Matrix.diagonal_comp_stdBasis | [] | [
45,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.comp_assoc | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.inl_eq_prod | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/Group/UniqueProds.lean | UniqueMul.iff_existsUnique | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.2277\ninst✝¹ : Mul G\ninst✝ : Mul H\nA B : Finset G\na0 b0 : G\naA : a0 ∈ A\nbB : b0 ∈ B\nx✝ : UniqueMul A B a0 b0\n⊢ ∀ (y : (a0, b0) ∈ A ×ˢ B), (fun x => (a0, b0).fst * (a0, b0).snd = a0 * b0) y → y = (_ : (a0, b0) ∈ A ×ˢ B)",
"tac... | [
93,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.interior_eq_empty_of_null | [] | [
88,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Balanced.del | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\nc : RBColor\nn : Nat\ncut : α → Ordering\nt : RBNode α\n⊢ DelProp (isBlack nil) (del cut nil) 0",
"tactic": "exact ⟨_, .nil⟩"
},
{
"state_after": "case black\nα : Type u_1\nc : RBColor\nn✝ : Nat\ncut : α → Ordering\nt a : RBNo... | [
454,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
432,
11
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_lift_assoc | [] | [
358,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.zigzag_obj_of_zigzag | [] | [
290,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | dslope_sub_smul_of_ne | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf✝ : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nf : 𝕜 → E\nh : b ≠ a\n⊢ dslope (fun x => (x - a) • f x) a b = f b",
"tactic": "rw [dslope_of_ne _ h... | [
77,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.smul_mem_iff | [] | [
391,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.mem_nthRootsFinset | [] | [
640,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
8
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.Nodup.disjSum | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ns : Multiset α\nt : Multiset β\ns₁ s₂ : Multiset α\nt₁ t₂ : Multiset β\na : α\nb : β\nx✝ : α ⊕ β\nhs✝ : Nodup s\nht✝ : Nodup t\nx : α ⊕ β\nhs : x ∈ Multiset.map inl s\nht : x ∈ Multiset.map inr t\n⊢ False",
"state_before": "α : Type u_1\nβ : Type u_2\ns : Multis... | [
112,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.image_mem_nhds | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.309590\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedSpace 𝕜... | [
342,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.lim_im | [
{
"state_after": "f : CauSeq ℂ ↑abs\n⊢ CauSeq.lim (cauSeqIm f) = (↑(CauSeq.lim (cauSeqRe f)) + ↑(CauSeq.lim (cauSeqIm f)) * I).im",
"state_before": "f : CauSeq ℂ ↑abs\n⊢ CauSeq.lim (cauSeqIm f) = (CauSeq.lim f).im",
"tactic": "rw [lim_eq_lim_im_add_lim_re]"
},
{
"state_after": "no goals",
"s... | [
1303,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.functor_map_eq_iff | [
{
"state_after": "case mp\nC : Type u_1\ninst✝ : Category C\nr : HomRel C\nh : Congruence r\nX Y : C\nf f' : X ⟶ Y\n⊢ (functor r).map f = (functor r).map f' → r f f'\n\ncase mpr\nC : Type u_1\ninst✝ : Category C\nr : HomRel C\nh : Congruence r\nX Y : C\nf f' : X ⟶ Y\n⊢ r f f' → (functor r).map f = (functor r).m... | [
160,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_nonsing_inv_det_iff | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.252005\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA✝ B A : Matrix n n α\n⊢ IsUnit (det A⁻¹) ↔ IsUnit (det A)",
"tactic": "rw [Matrix.det_nonsing_inv, isUnit_ring_inverse]"
}
] | [
422,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Involutive.rightInverse | [] | [
893,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_zero_iff_of_nonneg | [
{
"state_after": "case refine'_1\nι : Type u_2\nκ : Type ?u.35269\nα : Type u_1\ninst✝² : OrderedAddCommMonoid α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nf g : ι → α\na a₁ a₂ : α\nhf : ∀ (i : ι), 0 ≤ f i\nhf' : HasSum f 0\n⊢ f = 0\n\ncase refine'_2\nι : Type u_2\nκ : Type ?u.35269\nα : Type ... | [
154,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.trans | [] | [
67,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.isPell_star | [
{
"state_after": "no goals",
"state_before": "d x y : ℤ\n⊢ IsPell { re := x, im := y } ↔ IsPell (star { re := x, im := y })",
"tactic": "simp [IsPell, Zsqrtd.star_mk]"
}
] | [
86,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.ker_isPGroup_of_injective | [] | [
302,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Order/Basic.lean | lt_update_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type u_2\nr : α → α → Prop\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → Preorder (π i)\nx y : (i : ι) → π i\ni : ι\na b : π i\n⊢ x < update x i a ↔ x i < a",
"tactic": "simp [lt_iff_le_not_le]"
}
] | [
894,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.nonempty_of_isAlgClosed_of_finiteDimensional | [
{
"state_after": "case intro.intro\n𝕜 : Type u\nA : Type v\ninst✝⁴ : Field 𝕜\ninst✝³ : Ring A\ninst✝² : Algebra 𝕜 A\ninst✝¹ : IsAlgClosed 𝕜\ninst✝ : Nontrivial A\nI : FiniteDimensional 𝕜 A\na : A\np : 𝕜[X]\nh_mon : Monic p\nh_eval_p : eval₂ ↑ₐ a p = 0\n⊢ Set.Nonempty (σ a)",
"state_before": "𝕜 : Type... | [
166,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isRightRegular_of_rightCancelSemigroup | [] | [
349,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isClosed_infty | [
{
"state_after": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ IsOpen (range some)",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ IsClosed {∞}",
"tactic": "rw [← compl_range_coe, isClosed_compl_iff]"
},
{
"state_aft... | [
284,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_antisymm | [
{
"state_after": "a b : Int\nh₁ : a ≤ b\nh₂ : b ≤ a\nn : Nat\nhn : a + ↑n = b\n⊢ a = b",
"state_before": "a b : Int\nh₁ : a ≤ b\nh₂ : b ≤ a\n⊢ a = b",
"tactic": "let ⟨n, hn⟩ := le.dest h₁"
},
{
"state_after": "a b : Int\nh₁ : a ≤ b\nh₂ : b ≤ a\nn : Nat\nhn : a + ↑n = b\nm : Nat\nhm : b + ↑m = a\... | [
619,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
615,
11
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_top | [] | [
1353,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.not_facet_iff_subface | [
{
"state_after": "case refine'_1\n𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.69803\ninst✝² : OrderedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nK : SimplicialComplex 𝕜 E\ns t : Finset E\nx : E\nhs : s ∈ K.faces\nhs' : ¬(s ∈ K.faces ∧ ∀ ⦃t : Finset E⦄, t ∈ K.faces → s ⊆ t → s = t)\n⊢ ∃ t, t ∈ K.faces ∧... | [
211,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toLinearIsometry_inj | [] | [
619,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | list_prod_mem | [
{
"state_after": "case intro\nM : Type u_1\nA : Type ?u.11708\nB : Type u_2\ninst✝² : Monoid M\ninst✝¹ : SetLike B M\ninst✝ : SubmonoidClass B M\nS : B\nl : List { x // x ∈ S }\n⊢ List.prod (List.map Subtype.val l) ∈ S",
"state_before": "M : Type u_1\nA : Type ?u.11708\nB : Type u_2\ninst✝² : Monoid M\ninst... | [
79,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1256704\nG : Type ?u.1256707\n𝕜 : Type ?u.1256710\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ℝ F'\nins... | [
1222,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
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