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/Lattice.lean | Set.iUnion_inter_subset | [] | [
586,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Algebra/ContinuedFractions/ContinuantsRecurrence.lean | GeneralizedContinuedFraction.continuantsAux_recurrence | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝ : DivisionRing K\ngp ppred pred : Pair K\nnth_s_eq : Stream'.Seq.get? g.s n = some gp\nnth_conts_aux_eq : continuantsAux g n = ppred\nsucc_nth_conts_aux_eq : continuantsAux g (n + 1) = pred\n⊢ contin... | [
33,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_map | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G →* G'\n⊢ index (map f H) = index (H ⊔ MonoidHom.ker f) * index (MonoidHom.range f)",
"tactic": "rw [← comap_map_eq, index_comap, relindex_mul_index (H.map_le_range f)]... | [
330,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.37259\na : α\ns t : Multiset α\nf✝ g : α → Multiset β\nm : Multiset α\nn : Multiset β\nf : α → β → Multiset γ\n⊢ (bind 0 fun a => bind n fun b => f a b) = bind n fun b => bind 0 fun a => f a b",
"tactic":... | [
179,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_def | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.238\nβ✝ : Type ?u.241\nγ✝ : Type ?u.244\nf✝ : α✝ → β✝ → γ✝\na✝ : Option α✝\nb✝ : Option β✝\nc : Option γ✝\nα β γ : Type u_1\nf : α → β → γ\na : Option α\nb : Option β\n⊢ map₂ f a b = Seq.seq (f <$> a) fun x => b",
"tactic": "cases a <;> rfl"
}... | [
50,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.pure_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.43728\nδ : Type ?u.43731\nι : Sort ?u.43734\ns : Set α\nt : Set β\nf✝ : Filter α\ng : Filter β\na : α\nf : Filter β\n⊢ pure a ×ˢ f = map (Prod.mk a) f",
"tactic": "rw [prod_eq, map_pure, pure_seq_eq_map]"
}
] | [
407,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/CharP/Basic.lean | frobenius_add | [] | [
402,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.mul_refl | [] | [
142,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | HomotopyCategory.quotient_map_out | [] | [
84,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_C | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\ninst✝ : StrictOrderedSemiring Γ\nr : R\nn : Γ\n⊢ coeff (↑(ofPowerSeries Γ R) (↑(PowerSeries.C R) r)) n = coeff (↑C r) n",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\ninst✝ : StrictOrderedSemiring Γ\nr : R\... | [
1205,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_one | [] | [
410,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.top_coe_lieSubalgebra | [] | [
779,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.hasSum_cos | [
{
"state_after": "case h.e'_5\nz : ℂ\n⊢ (fun n => (-1) ^ n * z ^ (2 * n) / ↑(2 * n)!) = fun n => (z * I) ^ (2 * n) / ↑(2 * n)!",
"state_before": "z : ℂ\n⊢ HasSum (fun n => (-1) ^ n * z ^ (2 * n) / ↑(2 * n)!) (cos z)",
"tactic": "convert Complex.hasSum_cos' z using 1"
},
{
"state_after": "no goal... | [
73,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_zero | [] | [
212,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.X_mem_lifts | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf✝ f : R →+* S\n⊢ ↑(mapRingHom f) X = X",
"tactic": "simp only [coe_mapRingHom, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true, map_X,\n and_self_iff]"
}
] | [
102,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.to_subtype_range | [
{
"state_after": "ι✝ : Type u'\nι' : Type ?u.240558\nR : Type u_2\nK : Type ?u.240564\nM : Type u_3\nM' : Type ?u.240570\nM'' : Type ?u.240573\nV : Type u\nV' : Type ?u.240578\nv : ι✝ → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹ ... | [
500,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | Filter.EventuallyEq.support | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nM : Type ?u.6683\nE : Type ?u.6686\ninst✝ : Zero β\nf g : α → β\nl : Filter α\nh : f =ᶠ[l] g\nx : α\nhx : f x = g x\n⊢ Function.support f x = Function.support g x",
"state_before": "α : Type u_2\nβ : Type u_1\nM : Type ?u.6683\nE : Type ?u.6686\ninst✝ : ... | [
105,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/CategoryTheory/Category/TwoP.lean | TwoP.coe_toBipointed | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_nil | [
{
"state_after": "case h\nM : Type u_1\ninst✝² : Zero M\nl : List M\ninst✝¹ : DecidablePred fun x => getD l x 0 ≠ 0\nn : ℕ\ninst✝ : DecidablePred fun i => getD [] i 0 ≠ 0\na✝ : ℕ\n⊢ ↑(toFinsupp []) a✝ = ↑0 a✝",
"state_before": "M : Type u_1\ninst✝² : Zero M\nl : List M\ninst✝¹ : DecidablePred fun x => getD ... | [
92,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mk_X_2 | [] | [
1003,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.casesOn_mk | [] | [
453,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_pow | [] | [
215,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.binaryCoproductIso_inl_comp_hom | [] | [
236,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.incidenceSet_inter_incidenceSet_of_adj | [
{
"state_after": "ι : Sort ?u.100917\n𝕜 : Type ?u.100920\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nh : Adj G a b\n⊢ {Quotient.mk (Sym2.Rel.setoid V) (a, b)} ⊆ incidenceSet G a ∩ incidenceSet G b",
"state_before": "ι : Sort ?u.100917\n𝕜 : Type ... | [
859,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.orelse_pure | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nc₁ : Computation α\na : α\n⊢ destruct ({ hOrElse := fun a b => OrElse.orElse a b }.1 (think c₁) fun x => pure a) = Sum.inl a",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc₁ : Computation α\na : α\n⊢ destruct (HOrElse.hOrElse (think c₁) fun x =>... | [
949,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.affinity | [] | [
291,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.infsep_of_nontrivial | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.72020\nβ : Type ?u.72023\ninst✝ : PseudoMetricSpace α\nx y z : α\ns t : Set α\nhsf : Set.Finite s\nhs : Set.Nontrivial s\n⊢ Finset.Nonempty (Finite.toFinset (_ : Set.Finite (offDiag s)))",
"tactic": "simpa"
},
{
"state_after": "no goals",... | [
497,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t✝ : Set α\na✝ b✝ : α\ninst✝ : LinearOrder γ\na b : γ\ns t : Set γ\nha : IsGreatest s a\nhb : IsGreatest t b\n⊢ max a b ∈ s ∪ t",
"tactic": "cases' le_total a b with... | [
468,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioc_of_Ico | [] | [
224,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.modMonomial_add_divMonomial | [] | [
147,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup'_cons | [
{
"state_after": "F : Type ?u.231366\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.231375\nι : Type ?u.231378\nκ : Type ?u.231381\ninst✝ : SemilatticeSup α\ns : Finset β\nH : Finset.Nonempty s\nf : β → α\nb : β\nhb : ¬b ∈ s\nh : Finset.Nonempty (cons b s hb)\n⊢ ↑(sup' (cons b s hb) h f) = ↑(f b ⊔ sup' s H f)",
"... | [
790,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_eq_arg_add_pi_of_im_neg | [
{
"state_after": "x : ℂ\nhi : x.im < 0\n⊢ arccos ((-x).re / ↑abs (-x)) = -arccos (x.re / ↑abs x) + π",
"state_before": "x : ℂ\nhi : x.im < 0\n⊢ arg (-x) = arg x + π",
"tactic": "rw [arg_of_im_neg hi, arg_of_im_pos (show 0 < (-x).im from Left.neg_pos_iff.2 hi)]"
},
{
"state_after": "no goals",
... | [
382,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.continuous_of_isClosed_ker | [
{
"state_after": "case pos\n𝕜 : Type u\nhnorm : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module 𝕜 E\ninst✝¹² : TopologicalSpace E\ninst✝¹¹ : TopologicalAddGroup E\ninst✝¹⁰ : ContinuousSMul 𝕜 E\nF : Type w\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜 F\ninst✝⁷ : TopologicalS... | [
176,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.isoProduct_hom | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nf : J → C\ninst✝ : HasBiproduct f\nj : Discrete J\n⊢ (isoProduct f).hom ≫ limit.π (Discrete.functor f) j = Pi.lift (π f) ≫ limit.π (Discrete.functor f) j",
"tactic": "simp [biproduct.i... | [
483,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ciSup_const_zero | [
{
"state_after": "case inl\nx y : ℝ\nα : Sort u_1\nh✝ : IsEmpty α\n⊢ (⨆ (x : α), 0) = 0\n\ncase inr\nx y : ℝ\nα : Sort u_1\nh✝ : Nonempty α\n⊢ (⨆ (x : α), 0) = 0",
"state_before": "x y : ℝ\nα : Sort u_1\n⊢ (⨆ (x : α), 0) = 0",
"tactic": "cases isEmpty_or_nonempty α"
},
{
"state_after": "no goals... | [
813,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.inv_comp_eq_id | [] | [
251,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_iff_exists_edge | [
{
"state_after": "ι : Sort ?u.71588\n𝕜 : Type ?u.71591\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\nv w : V\n⊢ (v ≠ w ∧ ∃ e, e ∈ edgeSet G ∧ v ∈ e ∧ w ∈ e) → Adj G v w",
"state_before": "ι : Sort ?u.71588\n𝕜 : Type ?u.715... | [
561,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.clog | [] | [
216,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_option | [] | [
615,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.spanSingleton_mul_inv | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.52548\nA : Type ?u.52551\nK : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing A\ninst✝⁸ : Field K\ninst✝⁷ : IsDomain A\nR₁ : Type u_2\ninst✝⁶ : CommRing R₁\ninst✝⁵ : IsDomain R₁\ninst✝⁴ : Algebra R₁ K\ninst✝³ : IsFractionRing R₁ K\nI J : Fractional... | [
176,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semiring α\nm n : PosNum\n⊢ ↑(m * n) = ↑m * ↑n",
"tactic": "rw [← cast_to_nat, mul_to_nat, Nat.cast_mul, cast_to_nat, cast_to_nat]"
}
] | [
689,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.support_pow_eq_iff | [
{
"state_after": "ι : Type ?u.1128878\nα : Type u_1\nβ : Type ?u.1128884\nf g : Perm α\nx y : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : IsCycle f\nn : ℕ\n⊢ support (f ^ n) = support f ↔ ¬f ^ n = 1",
"state_before": "ι : Type ?u.1128878\nα : Type u_1\nβ : Type ?u.1128884\nf g : Perm α\nx y : α\ninst... | [
638,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.exists_eq_add_translationNumber | [
{
"state_after": "case intro\nf g : CircleDeg1Lift\nhf : Continuous ↑f\na : ℝ\nha : ↑f a ≤ a + τ f\n⊢ ∃ x, ↑f x = x + τ f",
"state_before": "f g : CircleDeg1Lift\nhf : Continuous ↑f\n⊢ ∃ x, ↑f x = x + τ f",
"tactic": "obtain ⟨a, ha⟩ : ∃ x, f x ≤ x + τ f := by\n by_contra' H\n exact lt_irrefl _ (f.lt_t... | [
938,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.sheafHom_restrict_eq | [
{
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Mathlib/FieldTheory/Separable.lean | IsSeparable.of_algHom | [
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Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_iff_exists_mem | [] | [
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Mathlib/Order/Cover.lean | covby_iff_wcovby_and_lt | [] | [
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Mathlib/LinearAlgebra/Projection.lean | Submodule.prodComm_trans_prodEquivOfIsCompl | [] | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.inv_eq_zero | [] | [
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Mathlib/Order/Max.lean | IsMin.fst | [] | [
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Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_one_le_of_lt_of_nonneg | [] | [
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Std/Data/List/Init/Lemmas.lean | List.append_left_inj | [] | [
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Mathlib/Computability/Partrec.lean | Partrec.none | [
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Mathlib/Data/List/Sigma.lean | List.kreplace_nodupKeys | [
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Mathlib/Algebra/Parity.lean | Odd.neg_pow | [
{
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Mathlib/FieldTheory/Normal.lean | AlgEquiv.restrict_liftNormal | [] | [
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Mathlib/Algebra/Hom/Aut.lean | MulAut.coe_mul | [] | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_eq_const | [
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_updateRow_add_self | [
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Mathlib/Data/Set/Sups.lean | Set.sups_left_comm | [] | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_tsub_iff_right | [
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Mathlib/Algebra/Group/Pi.lean | Set.piecewise_mul | [] | [
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Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.Isometry.coe_toLinearEquiv | [] | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.map_updateRow | [
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Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.list_prod_mem | [
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_mul_right_add_right | [
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Mathlib/Data/Complex/Basic.lean | Complex.neg_re | [] | [
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Mathlib/Order/Filter/AtTopBot.lean | OrderIso.map_atBot | [] | [
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Mathlib/Data/Complex/Basic.lean | Complex.sq_abs_sub_sq_re | [
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_eq_support_biUnion_support | [
{
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.exists_of_lt_bmex | [
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Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.isSheaf_yoneda_obj | [] | [
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Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.map_exp | [
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Mathlib/Topology/Paracompact.lean | precise_refinement | [
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Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean | AlgebraicTopology.DoldKan.identity_N₂ | [
{
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Mathlib/Order/RelIso/Basic.lean | RelIso.ext | [] | [
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Mathlib/Algebra/Group/Units.lean | IsUnit.mul | [
{
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... | [
665,
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Mathlib/Order/WellFoundedSet.lean | Finset.partiallyWellOrderedOn_bUnion | [
{
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂'_comp | [
{
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Set.Finite.measurableSet_sInter | [] | [
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_floor_atTop | [
{
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Mathlib/Logic/Basic.lean | and_symm_left | [
{
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Mathlib/Data/Bool/Basic.lean | Bool.beq_eq_decide_eq | [] | [
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.not_wOppSide | [
{
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_bot | [
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_pellZd | [
{
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... | [
344,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Prod.lean | Prod.swap_mul | [] | [
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Mathlib/Data/Stream/Init.lean | Stream'.all_def | [] | [
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6
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112,
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Mathlib/Topology/Algebra/ConstMulAction.lean | isClosedMap_smul₀ | [
{
"state_after": "case inl\nM✝ : Type ?u.106576\nα : Type ?u.106579\nβ : Type ?u.106582\nG₀ : Type ?u.106585\ninst✝¹⁰ : TopologicalSpace α\ninst✝⁹ : GroupWithZero G₀\ninst✝⁸ : MulAction G₀ α\ninst✝⁷ : ContinuousConstSMul G₀ α\ninst✝⁶ : TopologicalSpace β\nf : β → α\nb : β\nc : G₀\ns : Set β\n𝕜 : Type u_1\nM : ... | [
374,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_three | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\n⊢ ↑↑3 = ↑3",
"tactic": "rw [cast_ofNat, Nat.cast_ofNat]"
}
] | [
159,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_zero | [] | [
48,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.ite_eq_true_distrib | [
{
"state_after": "no goals",
"state_before": "c : Prop\ninst✝ : Decidable c\na b : Bool\n⊢ ((if c then a else b) = true) = if c then a = true else b = true",
"tactic": "by_cases c <;> simp [*]"
}
] | [
175,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_bind_set | [] | [
71,
164
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
71,
9
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.eq_bot_of_equiv | [
{
"state_after": "R : Type u_3\nR₁ : Type ?u.1967014\nR₂ : Type u_1\nR₃ : Type ?u.1967020\nR₄ : Type ?u.1967023\nS : Type ?u.1967026\nK : Type ?u.1967029\nK₂ : Type ?u.1967032\nM : Type u_4\nM' : Type ?u.1967038\nM₁ : Type ?u.1967041\nM₂ : Type u_2\nM₃ : Type ?u.1967047\nM₄ : Type ?u.1967050\nN : Type ?u.196705... | [
2147,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2144,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1806740\nγ : Type ?u.1806743\nδ : Type ?u.1806746\nm m0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nf_meas : Measurable f\nhf : ∀ᵐ (x : α) ∂μ, f x < ⊤\ng : α → ℝ≥0∞\n⊢ (∫⁻ (a : α), (f * g) a ∂μ) ≤ ∫⁻ (a : α), g a ∂Measure.withDensity μ f",
"state_before": "α... | [
1858,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1835,
1
] |
Mathlib/Analysis/Convex/Function.lean | concaveOn_iff_forall_pos | [] | [
334,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Order/Basic.lean | PUnit.not_lt | [] | [
1381,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.hom_lt_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : DecidableEq β\ninst✝ : Preorder β\nf : α → β\nh₁ : StrictMono f\nA B : Finset α\n⊢ (∃ k,\n (∀ {x : β}, k < x → ((∃ a, a ∈ A ∧ f a = x) ↔ ∃ a, a ∈ B ∧ f a = x)) ∧\n (∀ (x : α), x ∈ A → ¬f x = k) ∧ ∃ a, a ∈ B ∧ f a = k) ↔\n... | [
135,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_mono_right | [] | [
85,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Count.lean | List.countp_nil | [] | [
33,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
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