file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Geometry/Manifold/ChartedSpace.lean | LocalHomeomorph.singletonChartedSpace_chartAt_source | [] | [
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4
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998,
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Mathlib/Data/Finset/Card.lean | Finset.card_eq_one | [
{
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Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffWithinAt.pi | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_add_index | [
{
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Mathlib/Algebra/Group/TypeTags.lean | ofMul_inv | [] | [
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Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerRight_comp | [] | [
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Mathlib/Topology/Algebra/InfiniteSum/Real.lean | dist_le_tsum_of_dist_le_of_tendsto₀ | [
{
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87,
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Mathlib/Order/Filter/Basic.lean | Filter.eventually_of_mem | [] | [
1090,
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1088,
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Std/Data/Nat/Lemmas.lean | Nat.min_eq_left | [
{
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187,
96
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Mathlib/Algebra/Associated.lean | Prime.not_dvd_one | [] | [
44,
39
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_eq_one | [
{
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] | [
271,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.revzip_powersetAux | [
{
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131,
45
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Mathlib/Dynamics/OmegaLimit.lean | mem_omegaLimit_iff_frequently | [
{
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144,
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Mathlib/Data/Fin/Basic.lean | Fin.range_castLE | [] | [
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_le_add_iff_left | [] | [
696,
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Mathlib/RingTheory/ClassGroup.lean | coe_toPrincipalIdeal | [
{
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Mathlib/Topology/Algebra/Ring/Basic.lean | Subsemiring.le_topologicalClosure | [] | [
118,
24
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Mathlib/Topology/LocalExtr.lean | IsLocalMax.bicomp_mono | [] | [
285,
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Mathlib/Topology/LocalHomeomorph.lean | TopologicalSpace.Opens.localHomeomorphSubtypeCoe_target | [
{
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Mathlib/Order/Hom/Basic.lean | OrderHom.comp_mono | [] | [
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Mathlib/Algebra/Ring/Divisibility.lean | dvd_add_right | [
{
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_sub_eq_add_norm_iff_angle_eq_pi | [
{
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297,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfLeftIso_inr | [] | [
1790,
83
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_cons_of_mem | [] | [
964,
34
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963,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_single_add | [
{
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_surjective_of_surjective | [] | [
459,
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Mathlib/Data/Multiset/Basic.lean | Multiset.union_le | [
{
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_iff_one_le_left' | [
{
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410,
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407,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_inj | [
{
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] | [
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_add | [
{
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Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.cancel_left | [
{
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357,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAsLocalEquiv_source | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
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Mathlib/RingTheory/Subring/Pointwise.lean | Subring.mem_inv_pointwise_smul_iff₀ | [] | [
163,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.iso_of_restrict_iso | [
{
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_eq_neg_inv | [
{
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}
] | [
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Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.imp | [] | [
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Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.liftAux_tprodCoeff | [] | [
380,
50
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379,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isCircuit_def | [] | [
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54
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894,
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Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.Q_succ | [
{
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Mathlib/Order/Iterate.lean | StrictMono.strictAnti_iterate_of_map_lt | [] | [
266,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.comp_mul_comm | [
{
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402,
68
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.sup | [
{
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Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_taylor | [
{
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"tactic": "simp only [taylor_apply, comp_assoc, map_add, add_comp, X_comp, C_comp, ... | [
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92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.closedBall_prod_same | [
{
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715,
39
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713,
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Mathlib/Analysis/Convex/Segment.lean | mem_segment_sub_add | [
{
"state_after": "case h.e'_4\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.162050\nG : Type ?u.162053\nι : Type ?u.162056\nπ : ι → Type ?u.162061\ninst✝³ : LinearOrderedRing 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\nx✝ y✝ : E\ninst✝ : Invertible 2\nx y : E\n⊢ x = midpoint 𝕜 (x - y) (x + y)",
"state_b... | [
313,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Control/Traversable/Instances.lean | Option.traverse_eq_map_id | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα β : Type u_1\nf : α → β\nx : Option α\n⊢ Option.traverse (pure ∘ f) x = pure (f <$> x)",
"tactic": "cases x <;> rfl"
}
] | [
47,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/List/Range.lean | List.range'_one | [] | [
34,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
9
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.transpose_mem | [
{
"state_after": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\nhA : A ⬝ J l R ⬝ Aᵀ = J l R\n⊢ Aᵀ ⬝ J l R ⬝ Aᵀᵀ = J l R",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA... | [
173,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.bind_pure' | [
{
"state_after": "case bisim\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\n⊢ IsBisimulation fun c₁ c₂ => c₁ = c₂ ∨ ∃ s, c₁ = bind s pure ∧ c₂ = s\n\ncase r\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\n⊢ bind s pure = s ∨ ∃ s_1, bind s pure = bind s_1 pure ∧ s = s_1",
"state_before": "α ... | [
770,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Resp.eval_val | [] | [
619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Topology/Algebra/Order/ProjIcc.lean | continuous_projIcc | [] | [
43,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_union_elim | [
{
"state_after": "no goals",
"state_before": "case refine'_1\nα : Type u_1\nβ : Type ?u.400981\nγ : Type ?u.400984\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns : Finset α\nt₁ t₂ : Set α\nh : ↑s ⊆ t₁ ∪ t₂\n⊢ filter (fun x => x ∈ t₁) s ∪ filter (fun x => ¬x ∈ t... | [
2882,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2872,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_eq_top_iff | [] | [
1424,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.unitsSMul_apply | [] | [
1249,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_neg | [] | [
269,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.FineSubfamilyOn.measure_diff_biUnion | [] | [
155,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.min | [] | [
516,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
8
] |
Std/Data/Int/Lemmas.lean | Int.toNat_lt | [
{
"state_after": "no goals",
"state_before": "n : Nat\nz : Int\nh : 0 ≤ z\n⊢ toNat z < n ↔ z < ↑n",
"tactic": "rw [← Int.not_le, ← Nat.not_le, Int.le_toNat h]"
}
] | [
1384,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1383,
9
] |
Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | Subalgebra.restrictScalars_toSubmodule | [] | [
112,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.add | [] | [
124,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_reindex_self | [] | [
268,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.zmodEquivZpowers_symm_apply_pow | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.3141531\nN : Type ?u.3141534\nG : Type ?u.3141537\nR : Type u_1\nS : Type ?u.3141543\nF : Type ?u.3141546\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ninst✝¹ : DivisionCommMonoid G\nk l : ℕ\ninst✝ : CommRing R\nζ : Rˣ\nh : IsPrimitiveRoot ζ k\ni : ... | [
732,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | innerSL_apply_norm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3288929\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ ‖x‖ ≤ ‖↑(innerSL 𝕜) x‖",
"state_before": "𝕜 : Type u_1\nE : ... | [
1798,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.zero_mem_smul_iff | [
{
"state_after": "case mp\nF : Type ?u.93331\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.93340\ninst✝³ : Zero α\ninst✝² : Zero β\ninst✝¹ : SMulWithZero α β\ns : Set α\nt : Set β\ninst✝ : NoZeroSMulDivisors α β\na : α\n⊢ 0 ∈ s • t → 0 ∈ s ∧ Set.Nonempty t ∨ 0 ∈ t ∧ Set.Nonempty s\n\ncase mpr\nF : Type ?u.93331\nα :... | [
837,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.absorbent_ball_zero | [] | [
986,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
11
] |
Std/Logic.lean | imp_true_iff | [] | [
116,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
116,
1
] |
Mathlib/Control/Basic.lean | map_seq | [
{
"state_after": "α β γ : Type u\nF : Type u → Type v\ninst✝¹ : Applicative F\ninst✝ : LawfulApplicative F\nf : β → γ\nx : F (α → β)\ny : F α\n⊢ (Seq.seq (pure f) fun x_1 => Seq.seq x fun x => y) = Seq.seq (Seq.seq (pure fun x => f ∘ x) fun x_1 => x) fun x => y",
"state_before": "α β γ : Type u\nF : Type u ... | [
77,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.not_mem_of_ortho | [
{
"state_after": "G : Type u''\nS : Type u'\nR : Type u\nM : Type v\nι : Type w\ninst✝³ : Ring R\ninst✝² : IsDomain R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nb : ι → M\nx : M\nN : Submodule R M\northo : ∀ (c : R) (y : M), y ∈ N → c • x + y = 0 → c = 0\nhx : x ∈ N\n⊢ False",
"state_before": "G : Type u... | [
608,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_map₂_antidistrib_left | [] | [
388,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.ker_incl | [
{
"state_after": "case h\nR : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³... | [
1132,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.twoBlockTriangular_det' | [
{
"state_after": "α : Type ?u.96201\nβ : Type ?u.96204\nm : Type u_1\nn : Type ?u.96210\no : Type ?u.96213\nm' : α → Type ?u.96218\nn' : α → Type ?u.96223\nR : Type v\ninst✝⁵ : CommRing R\nM✝ N : Matrix m m R\nb : m → α\ninst✝⁴ : DecidableEq m\ninst✝³ : Fintype m\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nM :... | [
196,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/NumberTheory/Fermat4.lean | Fermat42.mul | [
{
"state_after": "a b c k : ℤ\nhk0 : k ≠ 0\n⊢ a ≠ 0 ∧ b ≠ 0 ∧ a ^ 4 + b ^ 4 = c ^ 2 ↔ k * a ≠ 0 ∧ k * b ≠ 0 ∧ (k * a) ^ 4 + (k * b) ^ 4 = (k ^ 2 * c) ^ 2",
"state_before": "a b c k : ℤ\nhk0 : k ≠ 0\n⊢ Fermat42 a b c ↔ Fermat42 (k * a) (k * b) (k ^ 2 * c)",
"tactic": "delta Fermat42"
},
{
"state_... | [
57,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.coe_reindex | [] | [
608,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
11
] |
Mathlib/Order/Closure.lean | ClosureOperator.mem_closed_iff | [] | [
174,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_add_eq_ite | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\na b : Fin n\n⊢ ↑(a + b) = if n ≤ ↑a + ↑b then ↑a + ↑b - n else ↑a + ↑b",
"tactic": "rw [Fin.val_add, Nat.add_mod_eq_ite, Nat.mod_eq_of_lt (show ↑a < n from a.2),\n Nat.mod_eq_of_lt (show ↑b < n from b.2)]"
}
] | [
712,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Order/Bounds/Basic.lean | lub_Iio_le | [] | [
551,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_disjoint_of_coprime | [
{
"state_after": "no goals",
"state_before": "a b : ℕ\nhab : coprime a b\n⊢ _root_.Disjoint (factorization a).support (factorization b).support",
"tactic": "simpa only [support_factorization] using\n disjoint_toFinset_iff_disjoint.mpr (coprime_factors_disjoint hab)"
}
] | [
784,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.comp_assoc | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.succ_succ_nth_convergent'_aux_eq_succ_nth_convergent'_aux_squashSeq | [
{
"state_after": "case none\nK : Type u_1\nn : ℕ\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\ns_succ_nth_eq : Stream'.Seq.get? s (n + 1) = none\n⊢ convergents'Aux s (n + 2) = convergents'Aux (squashSeq s n) (n + 1)\n\ncase some\nK : Type u_1\nn : ℕ\ng : GeneralizedConti... | [
186,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.surjective | [] | [
335,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
11
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.map_sup | [] | [
1205,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Data/List/Lex.lean | List.Lex.imp | [] | [
148,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.neg_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\na : A\nx : R\n⊢ x ∈ -σ a ↔ x ∈ σ (-a)",
"tactic": "simp only [mem_neg, mem_iff, map_neg, ← neg_add', IsUnit.neg_iff, sub_neg_eq_add]"
}
] | [
311,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_ofNatMultiset | [
{
"state_after": "no goals",
"state_before": "v : Multiset ℕ\nh : ∀ (p : ℕ), p ∈ v → Nat.Prime p\n⊢ ↑(prod (ofNatMultiset v h)) = Multiset.prod v",
"tactic": "rw [coe_prod, to_ofNatMultiset]"
}
] | [
170,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/Order/Interval.lean | Interval.length_zero | [] | [
701,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_normSq_add | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.795476\nT : Type ?u.795479\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ ↑(↑normSq (a + b)) = ↑(↑normSq a) + a * star b + b * star a + ↑(↑normSq b)",
"tactic": "simp only [star_add, ← self_mul_star, mul_add, add_mul, add_assoc, ... | [
1239,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_cancel_left | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ lxor' n (lxor' n m) = m",
"tactic": "rw [← lxor'_assoc, lxor'_self, zero_lxor']"
}
] | [
248,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.le_cof_type | [
{
"state_after": "case intro.intro\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nc : Cardinal\nH : ∀ (S : Set α), Unbounded r S → c ≤ (#↑S)\nS : Set α\nh : Unbounded r S\n⊢ c ≤ (#↑S)",
"state_before": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nc : Cardinal\n⊢ (∀ (S : Set α), Unbou... | [
167,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/Convex/Between.lean | not_sbtw_self | [] | [
353,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_odd | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns : Stream' α\n⊢ nth (tail s) (2 * n) = nth s (2 * n + 1)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns : Stream' α\n⊢ nth (odd s) n = nth s (2 * n + 1)",
"tactic": "rw [odd_eq, nth_even]"
},
{
"state_after": "no goal... | [
511,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_imI | [] | [
148,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.range_top_of_surjective | [] | [
1220,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mrange_eq_map | [] | [
1058,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.iff_addGroup_fg | [] | [
551,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_lt_tsum | [] | [
1281,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\n⊢ ↑(interpolate {i} v) r = ↑C (r i)",
"tactic": "rw [interpolate_apply, sum_singleton, basis_singleton, mul_one]"
}
] | [
315,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_zpow | [
{
"state_after": "case ofNat\nx✝ y x : ℝ\na✝ : ℕ\n⊢ log (x ^ Int.ofNat a✝) = ↑(Int.ofNat a✝) * log x\n\ncase negSucc\nx✝ y x : ℝ\na✝ : ℕ\n⊢ log (x ^ Int.negSucc a✝) = ↑(Int.negSucc a✝) * log x",
"state_before": "x✝ y x : ℝ\nn : ℤ\n⊢ log (x ^ n) = ↑n * log x",
"tactic": "induction n"
},
{
"state_... | [
263,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_neg | [
{
"state_after": "case h\nR : Type u_1\ninst✝¹⁶ : Ring R\nR₂ : Type u_2\ninst✝¹⁵ : Ring R₂\nR₃ : Type u_3\ninst✝¹⁴ : Ring R₃\nM : Type u_6\ninst✝¹³ : TopologicalSpace M\ninst✝¹² : AddCommGroup M\nM₂ : Type u_4\ninst✝¹¹ : TopologicalSpace M₂\ninst✝¹⁰ : AddCommGroup M₂\nM₃ : Type u_5\ninst✝⁹ : TopologicalSpace M₃... | [
1401,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_apply | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
1160,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
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