file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_on_segment | [] | [
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41
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652,
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Mathlib/Data/Real/EReal.lean | EReal.range_coe | [
{
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347,
39
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Mathlib/Order/RelClasses.lean | ssubset_or_eq_of_subset | [] | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_sum_of_ne_finset_zero | [] | [
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Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.toLinearPMap_graph_eq | [
{
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Mathlib/LinearAlgebra/Isomorphisms.lean | Submodule.quotientQuotientEquivQuotientAux_mk | [] | [
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Mathlib/Dynamics/PeriodicPts.lean | MulAction.zpow_smul_eq_iff_minimalPeriod_dvd | [
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | MeasurableEmbedding.aemeasurable_comp_iff | [
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Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.not_nhds_le_map | [] | [
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ioc | [] | [
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.dTo_eq_zero | [] | [
417,
16
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Mathlib/Order/Basic.lean | le_of_le_of_eq | [] | [
175,
19
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_le_iff | [] | [
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13
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Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.Symmetrify.lift_spec | [
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_nonempty_self | [
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Mathlib/Topology/Separation.lean | exists_subset_nhds_of_isCompact | [] | [
1288,
81
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Mathlib/Analysis/Calculus/Darboux.lean | convex_image_hasDerivAt | [
{
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.ker_liftQ_eq_bot | [
{
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Mathlib/Topology/ContinuousOn.lean | antitone_continuousOn | [] | [
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Mathlib/Topology/Separation.lean | Set.pairwiseDisjoint_nhds | [] | [
896,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.singletonMonoidHom_apply | [] | [
923,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_C_mul | [
{
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"tactic": "... | [
363,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
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Mathlib/Data/Int/Parity.lean | Int.isCompl_even_odd | [
{
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64,
42
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Mathlib/Data/PFun.lean | PFun.preimage_subset_dom | [] | [
439,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
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Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.reindex_apply | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/GroupTheory/OrderOfElement.lean | pow_eq_pow_iff_modEq | [
{
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Mathlib/Order/Hom/Set.lean | OrderIso.image_eq_preimage | [] | [
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.toList_formPerm_nontrivial | [
{
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364,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.exists_multiset_of_mem_closure | [
{
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48
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378,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_comap | [] | [
1624,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1623,
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_prodMap | [
{
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224,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_u_le | [] | [
107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Data/Set/Basic.lean | Set.nontrivial_of_exists_ne | [] | [
2486,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2484,
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Mathlib/Data/Set/Basic.lean | Disjoint.inter_left' | [] | [
2965,
16
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2964,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.volume_eq_prod | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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Mathlib/Data/Finset/Sups.lean | Finset.disjSups_inter_subset_left | [
{
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"tactic": "simpa only [disjSups, inter_product, filter_inter_dis... | [
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92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_pow | [] | [
412,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app | [] | [
526,
6
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524,
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Mathlib/Algebra/Support.lean | Function.compl_mulSupport | [] | [
64,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Semicontinuous.lean | Continuous.upperSemicontinuous | [] | [
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49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_nonneg | [
{
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_sub | [] | [
285,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_attach | [] | [
1547,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
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Mathlib/SetTheory/ZFC/Basic.lean | Arity.const_succ_apply | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Order/Bounds/Basic.lean | BddAbove.dual | [] | [
147,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Data/List/Basic.lean | List.lookmap.go_append | [
{
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"tactic": "cases l with\n| nil => rfl\n| cons hd tl =>\n rw [lookmap, go, ... | [
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20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/SymmDiff.lean | bihimp_bihimp_bihimp_comm | [
{
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}
] | [
641,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_spec | [] | [
479,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Mathlib/Topology/Separation.lean | exists_open_singleton_of_open_finite | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T0Space α\ns : Finset α\nhne : Set.Nonempty ↑s\nho : IsOpen ↑s\n⊢ ∃ x, x ∈ ↑s ∧ IsOpen {x}",
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315,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_diff_null' | [] | [
224,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_inl | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_eq_empty | [] | [
635,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
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Mathlib/Order/Synonym.lean | OrderDual.ofDual_le_ofDual | [] | [
104,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_ball' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.186781\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ y ∈ ball x ε ↔ edist x y < ε",
"tactic": "rw [edist_comm, mem_ball]"
}
] | [
534,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.bijective | [] | [
2018,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2017,
11
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ico | [] | [
652,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_notin_image_support | [] | [
300,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym2_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na✝ b : α\nm : Sym2 α\na : α\n⊢ Finset.sym2 {a} = {Sym2.diag a}",
"tactic": "rw [Finset.sym2, singleton_product_singleton, image_singleton, Sym2.diag, Quotient.mk']"
}
] | [
98,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/Instances/Matrix.lean | summable_matrix_diagonal | [] | [
357,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.finitaryExtensive_of_preserves_and_reflects | [] | [
576,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.isClosed_iff_zeroLocus | [
{
"state_after": "no goals",
"state_before": "R : 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\nZ : Set (ProjectiveSpectrum 𝒜)\n⊢ IsClosed Z ↔ ∃ s, Z = zeroLocus 𝒜 s",
"tactic": "rw [← isOpen_compl_iff, isO... | [
355,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.eq_inv_iff_eq | [] | [
111,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Embedding.to_isometry | [] | [
289,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.clm_comp | [] | [
892,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_normalizer_eq_of_injective_of_le_range | [
{
"state_after": "case a\nG : Type u_2\nG' : Type ?u.624266\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.624275\ninst✝² : AddGroup A\nN✝ : Type ?u.624281\ninst✝¹ : Group N✝\nf✝ : G →* N✝\nN : Type u_1\ninst✝ : Group N\nH : Subgroup G\nf : N →* G\nhf : Injective ↑f\nh : normalizer H ≤ range f\n⊢ map f (coma... | [
3223,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3214,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_smul | [] | [
1288,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.mod_add_div | [
{
"state_after": "m k : ℕ+\nh₀ : ↑m % ↑k + ↑k * (↑m / ↑k) = ↑m := Nat.mod_add_div ↑m ↑k\n⊢ ↑(mod m k) + ↑k * div m k = ↑m",
"state_before": "m k : ℕ+\n⊢ ↑(mod m k) + ↑k * div m k = ↑m",
"tactic": "let h₀ := Nat.mod_add_div (m : ℕ) (k : ℕ)"
},
{
"state_after": "m k : ℕ+\nh₀ : ↑m % ↑k + ↑k * (↑m /... | [
362,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.mk_dest | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nx : Fix F α\n⊢ (mk ∘ dest) x = x",
"state_before": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nx : Fix F α\n⊢ mk (dest x) = x",
"tactic": "change (Fix.mk ∘ F... | [
297,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.eq_spanSingleton_of_principal | [
{
"state_after": "no goals",
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1333,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.lt_le_top | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.toSubalgebra_lt_toSubalgebra | [] | [
601,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.iso_symm_apply_aux | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type ?u.678047\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : IsL... | [
826,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_toAddSubmonoid | [] | [
494,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_eq_zero' | [] | [
324,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_add | [] | [
172,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin.algebraMap_mem | [] | [
307,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_self | [
{
"state_after": "R : Type u_3\ninst✝⁷ : CommSemiring R\nl : Type ?u.1718698\nm : Type u_1\nn : Type u_2\ninst✝⁶ : Fintype n\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq n\nM₁ : Type u_5\nM₂ : Type u_4\ninst✝³ : AddCommMonoid M₁\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₁\ninst✝ : Module R M₂\nv₁ : Basis n R ... | [
618,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Arrow.from_middle_condition | [] | [
643,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Data/Rat/Sqrt.lean | Rat.exists_mul_self | [
{
"state_after": "no goals",
"state_before": "x : ℚ\nx✝ : ∃ q, q * q = x\nn : ℚ\nhn : n * n = x\n⊢ sqrt x * sqrt x = x",
"tactic": "rw [← hn, sqrt_eq, abs_mul_abs_self]"
}
] | [
37,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_singleton | [
{
"state_after": "F : Type ?u.135470\nα : Type u_1\nβ : Type ?u.135476\n𝕜 : Type ?u.135479\nE : Type ?u.135482\ninst✝³ : DecidableEq α\ninst✝² : Monoid α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid β\ns t : Finset α\nn : ℕ\na : α\n⊢ MulSalemSpencer ↑{a}",
"state_before": "F : Type ?u.135470\nα : Type u_1\nβ : ... | [
376,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.singleton_product_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.71755\ns s' : Finset α\nt t' : Finset β\na✝ : α\nb✝ : β\na : α\nb : β\n⊢ {a} ×ˢ {b} = {(a, b)}",
"tactic": "simp only [product_singleton, Function.Embedding.coeFn_mk, map_singleton]"
}
] | [
231,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.natTrans_hcomp_injective | [
{
"state_after": "case w.h\nC : Type u_1\ninst✝¹ : Category C\nW : MorphismProperty C\nD : Type u_4\ninst✝ : Category D\nG✝ : C ⥤ D\nhG : MorphismProperty.IsInvertedBy W G✝\nF G : MorphismProperty.Localization W ⥤ D\nτ₁ τ₂ : F ⟶ G\nh : 𝟙 (MorphismProperty.Q W) ◫ τ₁ = 𝟙 (MorphismProperty.Q W) ◫ τ₂\nX : Morphis... | [
320,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Subtype.lean | Subtype.val_injective | [] | [
126,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Algebra/Module/Simple.lean | LinearMap.isClosed_or_dense_ker | [
{
"state_after": "case inl\nR : Type u\nM : Type v\nN : Type w\ninst✝⁹ : Ring R\ninst✝⁸ : TopologicalSpace R\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R M\ninst✝³ : ContinuousSMul R M\ninst✝² : Module R N\ninst✝¹ : ContinuousAdd M\ninst✝ : IsSimpleModule R N... | [
37,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_lt_iff | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nX : Type ?u.391436\nι : Type ?u.391439\ninst✝² : PseudoMetricSpace α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoMetricSpace (π b)\nf g : (b : β) → π b\nr : ℝ≥0\nhr : 0 < ↑r\n⊢ dist f g < ↑r ↔ ∀ (b : β), dist (f b) (g b) < ↑r",
"state_... | [
2002,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1999,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.of_injective | [] | [
155,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.hasStrictFDerivAt | [] | [
1968,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1966,
1
] |
Mathlib/Topology/Basic.lean | continuousAt_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.165904\nδ : Type ?u.165907\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf g : α → β\nx : α\nh : f =ᶠ[𝓝 x] g\n⊢ ContinuousAt f x ↔ ContinuousAt g x",
"tactic": "simp only [Cont... | [
1598,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_le_of_colorable | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn : ℕ\nhc : Colorable G n\n⊢ sInf {n | Colorable G n} ≤ n",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nn : ℕ\nhc : Colorable G n\n⊢ chromaticNumber G ≤ n",
"tactic": "rw [chromaticNumber]"
... | [
257,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Std/Data/List/Basic.lean | List.takeWhile_eq_takeWhileTR | [
{
"state_after": "case h.h.h\nα : Type u_1\np : α → Bool\nl : List α\n⊢ takeWhile p l = takeWhileTR p l",
"state_before": "⊢ @takeWhile = @takeWhileTR",
"tactic": "funext α p l"
},
{
"state_after": "case h.h.h\nα : Type u_1\np : α → Bool\nl : List α\n⊢ takeWhile p l = takeWhileTR.go p l l #[]",
... | [
165,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
156,
10
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_sub_iff_le | [
{
"state_after": "case zero\nn m : ℕ\na b : Fin zero\n⊢ ↑(a - b) = ↑a - ↑b ↔ b ≤ a\n\ncase succ\nn m n✝ : ℕ\na b : Fin (Nat.succ n✝)\n⊢ ↑(a - b) = ↑a - ↑b ↔ b ≤ a",
"state_before": "n✝ m n : ℕ\na b : Fin n\n⊢ ↑(a - b) = ↑a - ↑b ↔ b ≤ a",
"tactic": "cases n"
},
{
"state_after": "case succ\nn m n✝... | [
1968,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1960,
1
] |
Mathlib/RingTheory/Localization/Ideal.lean | IsLocalization.bot_lt_comap_prime | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommRing S\ninst✝² : Algebra R S\ninst✝¹ : IsLocalization M S\ninst✝ : IsDomain R\nhM : M ≤ R⁰\np : Ideal S\nhpp : Ideal.IsPrime p\nhp0 : p ≠ ⊥\nthis : IsDomain S\n⊢ ⊥ < Ideal.comap (algebraMap R S) p",
"state_befor... | [
218,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.norm_sq_eq_inner' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.54916\n𝕜 : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf : { x // x ∈ Lp E 2 }\nh_two : ENNReal.toReal 2 = 2\n⊢ ‖f‖ ^ 2 = ↑IsROrC.... | [
185,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
9
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mkHom_f_0 | [] | [
1098,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.supports_run | [
{
"state_after": "no goals",
"state_before": "K : Type u_2\ninst✝² : DecidableEq K\nΓ : K → Type u_3\nΛ : Type u_1\ninst✝¹ : Inhabited Λ\nσ : Type u_4\ninst✝ : Inhabited σ\nS : Finset Λ\nk : K\ns : StAct k\nq : Stmt₂\n⊢ TM2.SupportsStmt S (stRun s q) ↔ TM2.SupportsStmt S q",
"tactic": "cases s <;> rfl"
... | [
2463,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2461,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_iff_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a / b ≤ c ↔ a ≤ b * c",
"tactic": "rw [div_le_iff_le_mul, mul_comm]"
}
] | [
819,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.bound | [
{
"state_after": "α : Type ?u.786208\nβ : Type ?u.786211\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 4096 ≤ N\n⊢ 2 / (1 - 2 / exp 1) ≤ ↑N ^ (1 / ↑(nValue N))",
"state_before": "α : Type ?u.786208\nβ : Type ?u.786211\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 4096 ≤ N\n⊢ ↑N ^ (1 / ↑(nValue N)) / exp 1 < ↑(dValue N)",
"tact... | [
482,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | pow_mem_closedBall | [
{
"state_after": "𝓕 : Type ?u.832658\n𝕜 : Type ?u.832661\nα : Type ?u.832664\nι : Type ?u.832667\nκ : Type ?u.832670\nE : Type u_1\nF : Type ?u.832676\nG : Type ?u.832679\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nn : ℕ\nh : ‖a / b‖ ≤ r\n⊢ ‖(a / b) ^ n‖ ≤... | [
1567,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.leInfCone_π_app_none | [] | [
606,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_lt_mul_right | [] | [
276,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
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