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/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.card_pos_of_affineSpan_eq_top | [
{
"state_after": "case intro.intro\nk : Type u_3\nV : Type u_4\nP : Type u_2\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\nι : Type u_1\ninst✝ : Fintype ι\np : ι → P\nh : affineSpan k (range p) = ⊤\ni : ι\n⊢ 0 < Fintype.card ι",
"state_before": "k : Type u_3... | [
815,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.pullback_top | [] | [
287,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_refl_refl | [] | [
67,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.inv_right | [] | [
101,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_of_le_one | [] | [
486,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Monotone.Ioc | [] | [
146,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/Data/Set/Prod.lean | Set.prod_subset_preimage_snd | [] | [
363,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ico_of_Ioo | [] | [
659,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.factorization_pos_of_dvd | [
{
"state_after": "no goals",
"state_before": "n p : ℕ\nhp : Prime p\nhn : n ≠ 0\nh : p ∣ n\n⊢ 0 < ↑(factorization n) p",
"tactic": "rwa [← factors_count_eq, count_pos, mem_factors_iff_dvd hn hp]"
}
] | [
191,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Int/Units.lean | Int.units_natAbs | [
{
"state_after": "u : ℤˣ\n⊢ natAbs 1 = 1",
"state_before": "u : ℤˣ\n⊢ natAbs ↑u * natAbs ↑u⁻¹ = 1",
"tactic": "rw [← natAbs_mul, Units.mul_inv]"
},
{
"state_after": "no goals",
"state_before": "u : ℤˣ\n⊢ natAbs 1 = 1",
"tactic": "rfl"
},
{
"state_after": "u : ℤˣ\n⊢ natAbs 1 = 1",... | [
29,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_of_mul_le_mul_left | [] | [
180,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_lt_of_forall_not_mulSalemSpencer | [
{
"state_after": "case intro.intro.intro\nF : Type ?u.142257\nα : Type u_1\nβ : Type ?u.142263\n𝕜 : Type ?u.142266\nE : Type ?u.142269\ninst✝³ : DecidableEq α\ninst✝² : Monoid α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid β\ns t✝ : Finset α\nn : ℕ\nh : ∀ (t : Finset α), t ∈ powersetLen n s → ¬MulSalemSpencer ↑t\nt... | [
414,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/List/AList.lean | AList.erase_erase | [] | [
255,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.compl_mem_nhds | [] | [
924,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.map_teichmuller | [] | [
131,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/Basic.lean | List.singleton_injective | [] | [
69,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_pow | [] | [
151,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_mk | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ext_coord_change_source | [] | [
1245,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/Topology/Order.lean | le_iff_nhds | [] | [
599,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_mul_pow_le | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nB C : Finset α\nn : ℕ\nhAB : ∀ (A' : Finset α), A' ⊆ ∅ → card (∅ * B) * card A' ≤ card (A' * B) * card ∅\n⊢ ↑(card (∅ * B ^ n)) ≤ (↑(card (∅ * B)) / ↑(card ∅)) ^ n * ↑(card ∅)\n\ncase inr\nα : Type u_1\ninst✝¹ : CommGroup α\n... | [
212,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_comap_setCoe_val | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.256913\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns✝ : Set α\nt : Set β\nf : Filter β\ns : Set β\n⊢ map Subtype.val (comap Subtype.val f) = f ⊓ 𝓟 s",
"tactic": "rw [map_comap,... | [
2257,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2255,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | cauchySeq_finset_of_norm_bounded | [] | [
75,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.le_cof_iff_blsub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.37432\nr : α → α → Prop\nb : Ordinal\na : Cardinal\nH : ∀ {ι : Type u} (f : ι → Ordinal), lsub f = b → a ≤ (#ι)\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nhf : blsub o f = b\n⊢ a ≤ card o",
"tactic": "simpa using H _ hf"
},
{
"sta... | [
429,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofLinear_apply | [] | [
2125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2124,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_iInf | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_3\nF : Type ?u.9687\nG : Type ?u.9690\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\nS T : ConvexCone 𝕜 E\nι : Sort u_1\nf : ι → ConvexCone 𝕜 E\n⊢ ↑(iInf f) = ⋂ (i : ι), ↑(f i)",
"tactic": "simp [iInf]"... | [
161,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/MinMax.lean | max_lt_max_left_iff | [] | [
194,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Filter.HasBasis.cauchySeq_iff' | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\ninst✝² : UniformSpace α\nγ : Sort u_1\ninst✝¹ : Nonempty β\ninst✝ : SemilatticeSup β\nu : β → α\np : γ → Prop\ns : γ → Set (α × α)\nH : HasBasis (𝓤 α) p s\nh : ∀ (i : γ), p i → ∃ N, ∀ (m : β), N ≤ m → ∀ (n : β), N ≤ n → (u m, u n) ∈ s i\ni : γ\nhi : p i... | [
302,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GeneralLinearGroup.coe_mul | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.εClosure_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ σ' : Type v\nM : εNFA α σ\nS : Set σ\nx : List α\ns✝ : σ\na : α\ns : σ\nhs : s ∈ εClosure M ∅\n⊢ False",
"tactic": "induction hs <;> assumption"
}
] | [
64,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Filter.Tendsto.inv | [] | [
235,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' v' : V\np : Walk G u' v'\n⊢ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) = edges p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG... | [
757,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.log_stirlingSeq_formula | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ Real.log (stirlingSeq (succ n)) =\n Real.log ↑(succ n)! - 1 / 2 * Real.log (2 * ↑(succ n)) - ↑(succ n) * Real.log (↑(succ n) / exp 1)",
"tactic": "rw [stirlingSeq, log_div, log_mul, sqrt_eq_rpow, log_rpow, Real.log_pow, tsub_tsub] <;> positivity"... | [
75,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.MeasurePreserving.set_lintegral_comp_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1687278\nδ : Type ?u.1687281\nm : MeasurableSpace α\nμ ν✝ : Measure α\nmb : MeasurableSpace β\nν : Measure β\ng : α → β\nhg : MeasurePreserving g\ns : Set β\nhs : MeasurableSet s\nf : β → ℝ≥0∞\nhf : Measurable f\n⊢ (∫⁻ (a ... | [
1345,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_iff_exists_right | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.274203\nP : Type u_3\nP' : Type ?u.274209\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y p₂ : P\n... | [
522,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_injective_iff | [] | [
587,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_cons_right | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.445806\nδ : Type ?u.445809\nr : α → β → Prop\np : γ → δ → Prop\nas : Multiset α\nb : β\nbs : Multiset β\n⊢ (∃ b_1 bs', flip r b b_1 ∧ Rel (flip r) bs bs' ∧ as = b_1 ::ₘ bs') ↔ ∃ a as', r a b ∧ Rel r as' bs ∧ as = a ::ₘ as'",
"state_before": "α : Type... | [
2742,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2738,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.space_bot | [] | [
259,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.inner_right_dfinsupp | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_4\nF : Type ?u.3612607\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\ndec_ι : DecidableEq ι\nG : ι → Type u_2\ninst✝¹ : (i : ι) → ... | [
2024,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2012,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.exp_of_re_eq_zero | [
{
"state_after": "q : ℍ\nhq : q.re = 0\n⊢ (fun x => ∑' (n : ℕ), (↑n !)⁻¹ • x ^ n) q = ↑(Real.cos ‖q‖) + (Real.sin ‖q‖ / ‖q‖) • q",
"state_before": "q : ℍ\nhq : q.re = 0\n⊢ exp ℝ q = ↑(Real.cos ‖q‖) + (Real.sin ‖q‖ / ‖q‖) • q",
"tactic": "rw [exp_eq_tsum]"
},
{
"state_after": "q : ℍ\nhq : q.re = ... | [
101,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_eq_of_lt_sub | [] | [
811,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.eq_zero_of_double_le | [] | [
106,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.smul_kroneckerTMul | [] | [
489,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongEpi.mk' | [] | [
66,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.right_mem_uIcc | [] | [
921,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.map_pure | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.one_le_rpow | [] | [
221,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Calculus/Series.lean | fderiv_tsum | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.60538\n𝕜 : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nf' : α → E → E →L[𝕜] F... | [
189,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioi | [] | [
155,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/List/Indexes.lean | List.mapIdxMAux'_eq_mapIdxMGo | [
{
"state_after": "α✝ : Type u\nβ : Type v\nm : Type u → Type v\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nα : Type u_1\nf : ℕ → α → m PUnit\nas : List α\n⊢ ∀ (arr : Array PUnit),\n mapIdxMAux' f (Array.size arr) as = SeqRight.seqRight (mapIdxM.go f as arr) fun x => pure PUnit.unit",
"state_before": "α✝ : ... | [
357,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.toBlock_inverse_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.151388\nm : Type u_2\nn : Type ?u.151394\no : Type ?u.151397\nm' : α → Type ?u.151402\nn' : α → Type ?u.151407\nR : Type v\ninst✝⁶ : CommRing R\nM N : Matrix m m R\nb : m → α\ninst✝⁵ : DecidableEq m\ninst✝⁴ : Fintype m\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\ninst... | [
306,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.sum_totient | [
{
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"state_before": "n : ℕ\n⊢ Finset.sum (divisors n) φ = n",
"tactic": "rcases n.eq_zero_or_pos with (rfl | hn)"
},
{
"state_after": "case inr\nn : ℕ\nhn : n > 0\n⊢ ∑ d in... | [
182,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_transpose_mul_self | [
{
"state_after": "l : Type ?u.270349\nm : Type u_1\nn : Type u_2\no : Type ?u.270358\nR : Type u_3\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : Fintype m\ninst✝ : LinearOrderedField R\nA : Matrix m n R\n⊢ finrank R { x // x ∈ LinearMap.range (mulVecLin (Aᵀ ⬝ A)) } = finrank R { x // x ∈ ... | [
254,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.congr_tmul | [] | [
874,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.zero_memℒp | [
{
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"state_before": "α : Type u_2\nE : Type u_1\nF : Type ?u.934... | [
220,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Order/Basic.lean | Pi.sdiff_apply | [] | [
915,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_mul_apply | [] | [
1662,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1660,
1
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Mathlib/Order/Filter/Basic.lean | Filter.congr_sets | [] | [
181,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_inf_comap_of_surjective | [] | [
478,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_eq_left_iff_dvd | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : m ∣ n\n⊢ gcd m n = m",
"tactic": "rw [gcd_rec, mod_eq_zero_of_dvd h, gcd_zero_left]"
}
] | [
65,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
63,
1
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Mathlib/Algebra/Regular/Basic.lean | isRegular_mul_and_mul_iff | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝ : Semigroup R\na b : R\n⊢ IsRegular (a * b) ∧ IsRegular (b * a) → IsRegular a ∧ IsRegular b\n\ncase refine'_2\nR : Type u_1\ninst✝ : Semigroup R\na b : R\n⊢ IsRegular a ∧ IsRegular b → IsRegular (a * b) ∧ IsRegular (b * a)",
"state_before": "R : Type u_1... | [
173,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Std/Data/Rat/Lemmas.lean | Rat.neg_divInt_neg | [
{
"state_after": "no goals",
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},
... | [
132,
85
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128,
1
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Mathlib/Data/Sum/Interval.lean | Finset.sumLift₂_mono | [] | [
108,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_subtype_support | [] | [
170,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Data/Nat/Count.lean | Nat.count_succ | [
{
"state_after": "no goals",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p (n + 1) = count p n + if p n then 1 else 0",
"tactic": "split_ifs with h <;> simp [count, List.range_succ, h]"
}
] | [
69,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | subset_spanPoints | [] | [
116,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_iSup_of_directed | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : Semiring B\ninst✝¹ : Algebra R B\nS✝ : Subalgebra R A\nι : Type u_1\ninst✝ : Nonempty ι\nS : ι → Subalgebra R A\ndir : Directed (fun x x_1 => x ≤ x_1) S\ni : ι := Nonempty.some (_ :... | [
1172,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
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Mathlib/Data/Set/Basic.lean | Set.ext_iff | [
{
"state_after": "no goals",
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}
] | [
243,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.sqrt_eq_rpow | [
{
"state_after": "x : ℝ≥0\n⊢ ↑(↑sqrt x) = ↑(x ^ (1 / 2))",
"state_before": "x : ℝ≥0\n⊢ ↑sqrt x = x ^ (1 / 2)",
"tactic": "refine' NNReal.eq _"
},
{
"state_after": "x : ℝ≥0\n⊢ Real.sqrt ↑x = ↑x ^ (1 / 2)",
"state_before": "x : ℝ≥0\n⊢ ↑(↑sqrt x) = ↑(x ^ (1 / 2))",
"tactic": "push_cast"
}... | [
126,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.withSeminorms_iff_nhds_eq_iInf | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.438464\n𝕝 : Type ?u.438467\n𝕝₂ : Type ?u.438470\nE : Type u_2\nF : Type ?u.438476\nG : Type ?u.438479\nι : Type u_3\nι' : Type ?u.438485\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\nt : TopologicalSpace E\ninst✝ : ... | [
439,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Analysis/Convex/Basic.lean | convex_iInter | [] | [
107,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_units_coe_left | [] | [
787,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iUnion_Iio_coe_nat | [
{
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"tactic": "ext x"
},
{
"state_after... | [
863,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.as_sum | [] | [
922,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.apply_symm_apply | [] | [
259,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_mul_of_div_lt | [] | [
643,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | AlgHom.coe_to_nonUnitalAlgHom | [] | [
441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Expr.of_cancel_lt | [] | [
554,
37
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
553,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.comp_holderWith | [] | [
135,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.Regular.exists_compact_not_null | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61981\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace α\nμ : Measure α\ninst✝ : Regular μ\n⊢ (∃ K, IsCompact K ∧ ↑↑μ K ≠ 0) ↔ μ ≠ 0",
"tactic": "simp_rw [Ne.def, ← measure_univ_eq_zero, isOpen_univ.measure_eq_iSup_isCompact,\... | [
488,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_bot | [] | [
1872,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1871,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_eq_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.502352\nγ : Type ?u.502355\nι : Type ?u.502358\nM : Type u_2\nM' : Type ?u.502364\nN : Type ?u.502367\nP : Type ?u.502370\nG : Type ?u.502373\nH : Type ?u.502376\nR : Type ?u.502379\nS : Type ?u.502382\ninst✝ : AddCommMonoid M\np✝ p : α... | [
1126,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.clm_apply | [
{
"state_after": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nG : Type u_1\ninst✝¹ :... | [
402,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isSymm | [] | [
347,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
11
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformly.tendsto_comp | [] | [
970,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_le_iff_of_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nE : Type ?u.74386\ninst✝⁴ : TopologicalSpace α\ninst✝³ : CompactSpace α\ninst✝² : MetricSpace β\ninst✝¹ : NormedAddCommGroup E\nf g : C(α, β)\nC : ℝ\ninst✝ : Nonempty α\n⊢ dist f g ≤ C ↔ ∀ (x : α), dist (↑f x) (↑g x) ≤ C",
"tactic... | [
144,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_le_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.270383\nβ : Type ?u.270386\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 1 ≤ a⁻¹ ↔ a ≤ 1",
"tactic": "rw [le_inv_iff_le_inv, inv_one]"
}
] | [
1512,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_fst | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX✝ Y✝ Z✝ : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf✝ : X✝ ⟶ T\ng✝ : Y✝ ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f✝ g✝\ninst✝¹ : HasPullback (f✝ ≫ i) (g✝ ≫ i)\ninst✝ :\n HasPullback (diagonal i)\n (map (f✝ ≫ i) (g✝ ≫ i) i i f✝ g✝ (𝟙 S)... | [
331,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x (-y) = 0\n⊢ angle x (x - y) ≤ π / 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ angle x (x - y) ≤ π / 2",
"t... | [
268,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_indicator_iff | [
{
"state_after": "case mp\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.339024\nι : Type ?u.339027\ninst✝³ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\nf g : α → β\ninst✝ : Zero β\ns : Set α\nhs : MeasurableSet s\n⊢ AEStronglyMeasurable (indicator s f... | [
1501,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1490,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_dist | [] | [
1560,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.toLocalHomeomorph_coe | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.of_h_eq_intFractPair_seq1_fst_b | [
{
"state_after": "case mk\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nfst✝ : IntFractPair K\nsnd✝ : Stream'.Seq (IntFractPair K)\naux_seq_eq : IntFractPair.seq1 v = (fst✝, snd✝)\n⊢ (of v).h = ↑(fst✝, snd✝).fst.b",
"state_before": "K : Type u_1\ninst✝¹ : LinearOrderedField K\nin... | [
168,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_add | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.449573\n𝕜 : Type ?u.449576\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : SMulCommClass ℝ 𝕜 E\ninst... | [
707,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Algebra/IsPrimePow.lean | Prime.isPrimePow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommMonoidWithZero R\nn p✝ : R\nk : ℕ\np : R\nhp : Prime p\n⊢ p ^ 1 = p",
"tactic": "simp"
}
] | [
61,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Algebra/Order/Group.lean | ContinuousOn.abs | [] | [
96,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
11
] |
Mathlib/Data/List/Sigma.lean | List.lookupAll_nil | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.eq_of_apply_eq | [] | [
341,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.lt_def | [] | [
231,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM_Except_eq | [
{
"state_after": "ε : Type u_1\nα✝ : Type u_2\np : α✝ → Prop\n⊢ ∀ {x : Except ε α✝}, SatisfiesM p x → ∀ (a : α✝), x = Except.ok a → p a",
"state_before": "ε : Type u_1\nα✝ : Type u_2\np : α✝ → Prop\nx : Except ε α✝\n⊢ SatisfiesM p x → ∀ (a : α✝), x = Except.ok a → p a",
"tactic": "revert x"
},
{
... | [
193,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
191,
9
] |
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