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/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_iUnion_measurableSet | [] | [
522,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.ord_card_unbounded | [
{
"state_after": "a : Ordinal\n⊢ ord (card (ord (succ (card a)))) = ord (succ (card a))",
"state_before": "a : Ordinal\n⊢ ord (succ (card a)) ∈ {b | ord (card b) = b}",
"tactic": "dsimp"
},
{
"state_after": "no goals",
"state_before": "a : Ordinal\n⊢ ord (card (ord (succ (card a)))) = ord (s... | [
361,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_append | [
{
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"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu✝ v✝ u' v' : V\np✝ : Walk G u✝ v✝\nu v w : V\np : Walk G u v\nq : Walk G v w\n⊢ Walk.map f (append p q) = append (Walk.map f p) (W... | [
1503,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_le | [] | [
227,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.congr_fun | [] | [
161,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Analysis/Calculus/Taylor.lean | taylor_within_zero_eval | [
{
"state_after": "𝕜 : Type ?u.139420\nE : Type u_1\nF : Type ?u.139426\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\ns : Set ℝ\nx₀ x : ℝ\n⊢ ↑(PolynomialModule.eval x) (taylorWithin f 0 s x₀) = f x₀",
"state_before": "𝕜 : Type ?u.139420\nE : Type u_1\nF : Type ?u.139426\ninst✝¹ : Norm... | [
105,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.coeFn_smul | [
{
"state_after": "case h\nΩ : Type u_2\ninst✝⁵ : MeasurableSpace Ω\nR : Type u_1\ninst✝⁴ : SMul R ℝ≥0\ninst✝³ : SMul R ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0 ℝ≥0\nc : R\nμ : FiniteMeasure Ω\nx✝ : Set Ω\n⊢ ENNReal.toNNReal (↑↑↑(c • μ) x✝) = (c • f... | [
250,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurableSet_of_differentiableWithinAt_Ici_of_isComplete | [
{
"state_after": "F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK✝ K : Set F\nhK : IsComplete K\n⊢ MeasurableSet\n (⋂ (e : ℕ), ⋃ (n : ℕ), ⋂ (p : ℕ) (_ : p ≥ n) (q : ℕ) (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e))",
"state_before": "F : Type u_1\ninst✝¹ ... | [
759,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | completeSpace_iff_ultrafilter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\n⊢ CompleteSpace α ↔ ∀ (l : Ultrafilter α), Cauchy ↑l → ∃ x, ↑l ≤ 𝓝 x",
"tactic": "simp [completeSpace_iff_isComplete_univ, isComplete_iff_ultrafilter]"
}
] | [
410,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_sin_inj | [
{
"state_after": "case inl\nθ ψ : ℝ\nHcos : cos θ = cos ψ\nHsin : sin θ = sin ψ\nhc : ↑θ = ↑ψ\n⊢ ↑θ = ↑ψ\n\ncase inr\nθ ψ : ℝ\nHcos : cos θ = cos ψ\nHsin : sin θ = sin ψ\nhc : ↑θ = -↑ψ\n⊢ ↑θ = ↑ψ",
"state_before": "θ ψ : ℝ\nHcos : cos θ = cos ψ\nHsin : sin θ = sin ψ\n⊢ ↑θ = ↑ψ",
"tactic": "cases' cos_eq... | [
302,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.cobounded_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.10138\nα : Type u_1\nβ : Type ?u.10144\ninst✝ : Bornology α\n⊢ cobounded α = ⊥ ↔ BoundedSpace α",
"tactic": "rw [← isBounded_univ, isBounded_def, compl_univ, empty_mem_iff_bot]"
}
] | [
337,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/List/Count.lean | List.count_eq_zero | [] | [
264,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_op_distrib | [
{
"state_after": "no goals",
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84,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/Order/Basic.lean | ge_antisymm | [] | [
97,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.independent_iff_dfinsupp_sumAddHom_injective | [] | [
538,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_le_coe | [] | [
369,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
11
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.vanishingIdeal_union | [
{
"state_after": "case h\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nt t' : Set (ProjectiveSpectrum 𝒜)\n⊢ HomogeneousIdeal.toIdeal (vanishingIdeal (t ∪ t')) = HomogeneousIdeal.toIdeal (vanishingIdeal t ⊓ vani... | [
250,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/Order/Basic.lean | Ico_mem_nhds | [] | [
353,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_add | [] | [
115,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
11
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_subset_uIcc_union_uIcc | [
{
"state_after": "ι : Type ?u.208607\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Set.uIcc a c ⊆ Set.uIcc a b ∪ Set.uIcc b c",
"state_before": "ι : Type ?u.208607\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n... | [
1031,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.quotientToQuotientRangePowQuotSucc_injective | [
{
"state_after": "R : Type u\ninst✝⁴ : CommRing R\nS : Type v\ninst✝³ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhfp : NeZero e\ninst✝² : IsDomain S\ninst✝¹ : IsDedekindDomain S\ninst✝ : IsPrime P\ni : ℕ\nhi : i < e\na : S\na_mem : a ∈ P ^ i\na_not_mem : ¬a ∈ P ^ (i + 1)\nx✝ : S ⧸ P\nx : S\ny✝ : S ⧸ P... | [
571,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.inverseAssociator_obj_inr_inl | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_nonpos_iff | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ logb b x ≤ 0 ↔ x ≤ 1",
"tactic": "rw [← not_lt, logb_pos_iff hb hx, not_lt]"
}
] | [
207,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S₁\np q : MvPolynomial σ R\ninst✝¹ : Algebra R S₁\ninst✝ : CommSemiring S₂\nf✝ : σ → S₁\nf : R →+* S₂\n⊢ e... | [
1481,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.dvd_iff | [
{
"state_after": "case mp\nk m : ℕ+\nh : k ∣ m\n⊢ ↑k ∣ ↑m\n\ncase mpr\nk m : ℕ+\nh : ↑k ∣ ↑m\n⊢ k ∣ m",
"state_before": "k m : ℕ+\n⊢ k ∣ m ↔ ↑k ∣ ↑m",
"tactic": "constructor <;> intro h"
},
{
"state_after": "case mp.intro\nk w✝ : ℕ+\n⊢ ↑k ∣ ↑(k * w✝)",
"state_before": "case mp\nk m : ℕ+\nh :... | [
408,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Multiset.aemeasurable_prod | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nι : Type ?u.4511300\nα : Type u_2\ninst✝² : CommMonoid M\ninst✝¹ : MeasurableSpace M\ninst✝ : MeasurableMul₂ M\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf : ι → α → M\ns : Multiset (α → M)\nhs : ∀ (f : α → M), f ∈ s → AEMeasurable f\n⊢ A... | [
927,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_iInf_of_map_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.43806\nι : Sort u_3\nf✝ f₁ f₂ : Filter α\nh h₁ h₂ : Set α → Set β\nf : ι → Filter α\ng : Set α → Set β\nhg : ∀ {s t : Set α}, g (s ∩ t) = g s ∩ g t\nhg' : g univ = univ\ns t : Set α\n⊢ (𝓟 ∘ g) (s ∩ t) = (𝓟 ∘ g) s ⊓ (𝓟 ∘... | [
398,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_iff_mul_left_eq | [
{
"state_after": "case refine'_1\no : Ordinal\nh : Principal (fun x x_1 => x * x_1) o\na : Ordinal\nha₀ : 0 < a\nhao : a < o\n⊢ a * o = o\n\ncase refine'_2\no : Ordinal\nh : ∀ (a : Ordinal), 0 < a → a < o → a * o = o\na b : Ordinal\nhao : a < o\nhbo : b < o\n⊢ (fun x x_1 => x * x_1) a b < o",
"state_before"... | [
337,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.not_nonempty_iff_eq_bot | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.28024\nα : Type u_1\nβ : Type ?u.28030\nγ : Type ?u.28033\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nU : Opens α\n⊢ ¬Set.Nonempty ↑U ↔ U = ⊥",
"tactic": "rw [← coe_inj, coe_bot, ← Set.not_nonempty_iff_e... | [
271,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Topology/ContinuousOn.lean | Continuous.continuousWithinAt | [] | [
913,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Analysis/Calculus/LagrangeMultipliers.lean | IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt | [
{
"state_after": "E : Type u_2\nF : Type ?u.106682\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nf✝ : E → F\nφ : E → ℝ\nx₀ : E\nf'✝ : E →L[ℝ] F\nφ' : E →L[ℝ] ℝ\nι : Type u_1\ninst✝ : Fintype ... | [
123,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_le_mul_left | [] | [
591,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.coe_toEmbedding | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Dynamics/Minimal.lean | IsOpen.exists_smul_mem | [] | [
75,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Order/CompactlyGenerated.lean | le_iff_compact_le_imp | [
{
"state_after": "ι : Sort ?u.88112\nα : Type u_1\ninst✝² : CompleteLattice α\nf : ι → α\ninst✝¹ : CompleteLattice α\ninst✝ : IsCompactlyGenerated α\na✝ b✝ : α\ns : Set α\na b : α\nh : ∀ (c : α), CompleteLattice.IsCompactElement c → c ≤ a → c ≤ b\n⊢ sSup {c | CompleteLattice.IsCompactElement c ∧ c ≤ a} ≤ sSup {... | [
359,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_eq_one_of_finrank_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.957050\ninst✝¹² : CommRing R\nM✝ : Type ?u.957056\ninst✝¹¹ : AddCommGroup M✝\ninst✝¹⁰ : Module R M✝\nM' : Type ?u.957641\ninst✝⁹ : AddCommGroup M'\ninst✝⁸ : Module R M'\nι : Type ?u.958183\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : Fintype ι\ne : Basis ι R M✝... | [
308,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.get?_congr | [] | [
1197,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.rel_get_of_lt | [] | [
115,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Set/Semiring.lean | SetSemiring.down_ssubset_down | [] | [
93,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_left_comm | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\n⊢ n + (m + k) = m + (n + k)",
"tactic": "rw [← Nat.add_assoc, Nat.add_comm n m, Nat.add_assoc]"
}
] | [
143,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
142,
11
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_X_right | [] | [
155,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.update_mem_cylinder | [
{
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"tactic": "simp [hi.ne]"
}
] | [
192,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.drop_map | [] | [
148,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.snd_comp_quotientInfEquivQuotientProd | [
{
"state_after": "case h\nR : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nI J : Ideal R\ncoprime : I ⊔ J = ⊤\n⊢ RingHom.comp (RingHom.comp (RingHom.snd (R ⧸ I) (R ⧸ J)) ↑(quotientInfEquivQuotientProd I J coprime))\n (Quotient.mk (I ⊓ J)) =\n RingHom.comp (Quotient.factor (I ⊓ J) J (_ ... | [
542,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk_add | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.le_set' | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.112020\nγ : Type ?u.112023\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\no : Ordinal\nH : IsNormal f\np : Set α\np0 : Set.Nonempty p\ng : α → Ordinal\nb : Ordinal\nH₂ : ∀ (o : Ordinal), b ≤ o ↔ ∀ (a : α),... | [
468,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | Real.pow_arith_mean_le_arith_mean_pow | [] | [
66,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.Adhesive.mono_of_isPushout_of_mono_left | [] | [
251,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | derivWithin_exp | [] | [
240,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_eq_find | [] | [
80,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Basic.lean | compare_of_injective_eq_compareOfLessAndEq | [
{
"state_after": "ι : Type ?u.93186\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.93197\nr : α → α → Prop\na b : α\ninst✝² : LinearOrder β\ninst✝¹ : DecidableEq α\nf : α → β\ninj : Injective f\ninst✝ : Decidable (a < b)\nh : compare (f a) (f b) = compareOfLessAndEq (f a) (f b)\n⊢ compare (f a) (f b) = co... | [
1023,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | Even.strictConvexOn_pow | [
{
"state_after": "n : ℕ\nhn : Even n\nh : n ≠ 0\n⊢ StrictMono (deriv fun a => a ^ n)",
"state_before": "n : ℕ\nhn : Even n\nh : n ≠ 0\n⊢ StrictConvexOn ℝ univ fun x => x ^ n",
"tactic": "apply StrictMono.strictConvexOn_univ_of_deriv (continuous_pow n)"
},
{
"state_after": "n : ℕ\nhn : Even n\nh ... | [
58,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_one | [] | [
53,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.generateHas_def | [] | [
650,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
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Mathlib/Data/Finset/Prod.lean | Finset.diag_inter | [
{
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"tactic": "simpa only [mem_diag, mem_inter] using and_and_right"
}
] | [
383,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_multiset_of_nonempty | [] | [
1073,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
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Mathlib/Analysis/Convex/Segment.lean | Pi.image_update_segment | [
{
"state_after": "case h\n𝕜 : Type u_3\nE : Type ?u.385768\nF : Type ?u.385771\nG : Type ?u.385774\nι : Type u_1\nπ : ι → Type u_2\ninst✝³ : OrderedSemiring 𝕜\ninst✝² : (i : ι) → AddCommMonoid (π i)\ninst✝¹ : (i : ι) → Module 𝕜 (π i)\ns : Set ι\ninst✝ : DecidableEq ι\ni : ι\nx₁ x₂ : π i\ny z : (a : ι) → π a\... | [
665,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Data/List/OfFn.lean | List.forall_mem_ofFn_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\nf : Fin n → α\nP : α → Prop\n⊢ (∀ (i : α), i ∈ ofFn f → P i) ↔ ∀ (j : Fin n), P (f j)",
"tactic": "simp only [mem_ofFn, Set.forall_range_iff]"
}
] | [
210,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_toPartENat | [] | [
117,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.bind_ret | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : WSeq α\n⊢ join (map (ret ∘ f) s) ~ʷ map f s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : WSeq α\n⊢ bind s (ret ∘ f) ~ʷ map f s",
"tactic": "dsimp [bind]"
},
{
"state_after": "α : Type u\nβ : Type v\nγ :... | [
1739,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.isTorsion'_powers_iff | [
{
"state_after": "case mp\nR : Type u_2\nM : Type u_1\ninst✝² : Monoid R\ninst✝¹ : AddCommMonoid M\ninst✝ : DistribMulAction R M\np : R\n⊢ IsTorsion' M { x // x ∈ Submonoid.powers p } → ∀ (x : M), ∃ n, p ^ n • x = 0\n\ncase mpr\nR : Type u_2\nM : Type u_1\ninst✝² : Monoid R\ninst✝¹ : AddCommMonoid M\ninst✝ : Di... | [
768,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_trichotomy | [
{
"state_after": "a b c : ℕ\nh : a ≠ lxor' b c\nv : ℕ := lxor' a (lxor' b c)\nhv : v = lxor' a (lxor' b c)\n⊢ lxor' b c < a ∨ lxor' a c < b ∨ lxor' a b < c",
"state_before": "a b c : ℕ\nh : a ≠ lxor' b c\n⊢ lxor' b c < a ∨ lxor' a c < b ∨ lxor' a b < c",
"tactic": "set v := lxor' a (lxor' b c) with hv"
... | [
316,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Set/Finite.lean | Set.exists_min_image | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : LinearOrder β\ns : Set α\nf : α → β\nh1 : Set.Finite s\nx : α\nhx : x ∈ s\n⊢ ∃ a, a ∈ s ∧ ∀ (b : α), b ∈ s → f a ≤ f b",
"tactic": "simpa only [exists_prop, Finite.mem_toFinset] using\n h1.toFinset.exi... | [
1447,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootSet_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\np q : R[X]\ninst✝³ : CommRing T\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra T S\na : T\n⊢ rootSet (↑C a) S = ∅",
"tactic": "rw [rootSet_def, map_C, ... | [
899,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.quotientPi_aux.map_smul | [] | [
122,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.map_surjective | [] | [
289,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.coe_sup | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_zero_equiv | [] | [
1460,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_le | [] | [
846,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.universally_stableUnderBaseChange | [] | [
584,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.exists_finset_adjoin_eq_top | [
{
"state_after": "case mk.intro\nR : Type u_2\nM : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommMonoid M\nS : Finset (MonoidAlgebra R M)\nhS : adjoin R ↑S = ⊤\n⊢ ∃ G, adjoin R (↑(of R M) '' ↑G) = ⊤",
"state_before": "R : Type u_2\nM : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommMonoid M\nh : FiniteType R (Mono... | [
549,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.82158\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.82167\nι : Type ?u.82170\nκ : Type ?u.82173\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns s₁ s₂ : Finset β\nf✝ g : β → α\na : α\nf : β → α\nS : Finset β\n⊢ sup S f = ⊥ ↔ ∀ (s : β), s ∈ S → f s = ⊥",
... | [
279,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
11
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.324567\nι : Type ?u.324570\nG : Type ?u.324573\nM : Type u_1\nN : Type ?u.324579\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\n⊢ (∏ᶠ (i : α) (_ : i ∈ ∅), f i) = 1",
"tactic": "simp"
}
] | [
749,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.units_inv_apply_apply | [
{
"state_after": "no goals",
"state_before": "f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\nx : ℝ\n⊢ ↑↑f⁻¹ (↑↑f x) = x",
"tactic": "simp only [← mul_apply, f.inv_mul, coe_one, id]"
}
] | [
214,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/SetTheory/Lists.lean | Lists.equiv_atom | [
{
"state_after": "case refl\nα : Type u_1\na : α\n⊢ atom a = atom a",
"state_before": "α : Type u_1\na : α\nl : Lists α\nh : atom a ~ l\n⊢ atom a = l",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "case refl\nα : Type u_1\na : α\n⊢ atom a = atom a",
"tactic": "rfl"... | [
310,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_eq_arg_iff | [
{
"state_after": "x y : ℂ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ arg x = arg y ↔ arg (↑(↑abs y) / ↑(↑abs x) * x) = arg y",
"state_before": "x y : ℂ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ arg x = arg y ↔ ↑(↑abs y) / ↑(↑abs x) * x = y",
"tactic": "simp only [ext_abs_arg_iff, map_mul, map_div₀, abs_ofReal, abs_abs,\n div_mul_can... | [
193,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_add | [] | [
159,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Sign.lean | SignType.neg_one_lt_one | [] | [
234,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Std/Logic.lean | not_not_of_not_imp | [] | [
26,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
26,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_le_eq | [] | [
29,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.funMap_sum_inr | [] | [
924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.coe_nnreal_ennreal | [] | [
1787,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.tendsto_units | [] | [
128,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iio_bot | [] | [
1221,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
8
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderComposition.op | [] | [
114,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Part.lean | Part.mem_some_iff | [] | [
173,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.apply_lt_top | [] | [
145,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_id | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_mono | [] | [
123,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparator_def | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y : C\nf g : X ⟶ Y\nH : C\nh : Y ⟶ H\nhG : IsCoseparator H\nhfg : ∀ (h : Y ⟶ H), f ≫ h = g ≫ h\nhH : H ∈ {H}\n⊢ f ≫ h = g ≫ h",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nG : C\nhG... | [
476,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Analysis/PSeries.lean | Real.summable_one_div_int_pow | [
{
"state_after": "p : ℕ\nh : 1 < p\nn : ℕ\n⊢ 1 / (-1) ^ ↑p * (1 / ↑n ^ ↑p) = 1 / ↑(-↑n) ^ ↑p",
"state_before": "p : ℕ\n⊢ (Summable fun n => 1 / ↑n ^ ↑p) ↔ 1 < p",
"tactic": "refine'\n ⟨fun h => Real.summable_one_div_nat_pow.mp (h.comp_injective Nat.cast_injective), fun h =>\n summable_int_of_summabl... | [
232,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_zero | [] | [
251,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.shadow_image_compl | [
{
"state_after": "case a\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns✝ t : Finset α\na : α\nk r : ℕ\ns : Finset α\n⊢ s ∈ image compl ((∂ ) 𝒜) ↔ s ∈ (∂⁺ ) (image compl 𝒜)",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α... | [
291,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.rename_esymm | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_3\nτ : Type u_2\nS : Type ?u.127979\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : Fintype σ\ninst✝ : Fintype τ\nn : ℕ\ne : σ ≃ τ\n⊢ ↑(rename ↑e) (esymm σ R n) = ∑ x in powersetLen n univ, ∏ i in x, X (↑e i)",
"tactic": ... | [
211,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.smul_snd | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ioc_left | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ioc a (f i) = Ioc (update f i a) f",
"tactic": "simpa using image_update_Ioc f i a (f i)"
}
] | [
172,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.add_eq_lift_id_desc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nX Y : C\nf g : X ⟶ Y\ninst✝ : HasBinaryBiproduct X X\n⊢ f + g = lift (𝟙 X) (𝟙 X) ≫ desc f g",
"tactic": "simp"
}
] | [
631,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.zero_left | [] | [
76,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.cantor_surjective | [] | [
279,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_eq_iff | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ (c ∈ Set.Ico a (a + p) ∧ ∃ z, b = c + z • p) → toIcoMod hp a b = c",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b ... | [
181,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
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