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 |
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.sup | [] | [
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642,
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Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.coe_nsmul | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
11
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Mathlib/Data/Set/Finite.lean | Set.Finite.fin_param | [] | [
1088,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_eq_top | [
{
"state_after": "no goals",
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"tactic": "rw [isUnit_iff_dvd_one, ← span_singleton_le_span_singleton, span_singleton_one, eq_top_iff]"
}
] | [
522,
94
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521,
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Mathlib/Topology/SubsetProperties.lean | isClopen_empty | [] | [
1561,
88
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1561,
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.bind_zero_right' | [] | [
173,
20
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172,
1
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Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.reflexive | [] | [
109,
25
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108,
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Mathlib/Data/Finset/Basic.lean | Finset.union_subset_union | [] | [
1381,
39
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofMkLE_comp_ofLE | [
{
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423,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
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Mathlib/LinearAlgebra/Vandermonde.lean | Matrix.det_vandermonde_eq_zero_iff | [
{
"state_after": "case mp\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nv : Fin n → R\n⊢ det (vandermonde v) = 0 → ∃ i j, v i = v j ∧ i ≠ j\n\ncase mpr\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nv : Fin n → R\n⊢ (∃ i j, v i = v j ∧ i ≠ j) → det (vandermonde v) = 0",
"sta... | [
151,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/Algebra/CovariantAndContravariant.lean | covariant_flip_mul_iff | [
{
"state_after": "no goals",
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] | [
320,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_union | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.535752\nι : Type ?u.535755\ninst✝ : PseudoMetricSpace α\ns : Set α\nx y z : α\nt : Set α\nxs : x ∈ s\nyt : y ∈ t\n⊢ ENNReal.toReal (EMetric.diam (s ∪ t)) ≤\n ENNReal.toReal (EMetric.diam s) + ENNReal.toReal (edist x y) + ENNReal.toReal (EMetric.diam t)",
... | [
2705,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2698,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.symm_apply_le | [] | [
994,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.uncurry_curryLeft | [] | [
1382,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
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Mathlib/LinearAlgebra/Basis.lean | Basis.ext' | [
{
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288,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiffWithinAt_prod' | [] | [
1410,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.nat_add | [] | [
245,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Algebra/Module/Basic.lean | smul_eq_zero | [] | [
618,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_eq_zero_of_unbounded | [
{
"state_after": "no goals",
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}
] | [
2687,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousOn.lean | IsOpen.ite' | [
{
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1220,
38
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1214,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_iInf_comap_of_surjective | [] | [
1592,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1591,
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Mathlib/Data/Matrix/Hadamard.lean | Matrix.hadamard_comm | [] | [
68,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.smul_mem_of_zero_mem | [
{
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356,
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_matrix_trace | [
{
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108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/List/Basic.lean | List.tail_cons | [] | [
311,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
311,
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Mathlib/CategoryTheory/FintypeCat.lean | FintypeCat.Skeleton.ext | [] | [
144,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/Order/Disjoint.lean | disjoint_iff | [] | [
129,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Algebra/Group/Prod.lean | MonoidHom.prod_apply | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Ideal/Prod.lean | Ideal.prod.ext_iff | [
{
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"tactic": "simp only [← idealProdEquiv_symm_apply, idealProdEquiv.symm.injective.eq_iff, ... | [
109,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.congr_apply | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
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Mathlib/Data/Set/Intervals/Monotone.lean | iUnion_Ioo_of_mono_of_isGLB_of_isLUB | [] | [
195,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
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Mathlib/Logic/Basic.lean | not_xor | [
{
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"tactic": "simp only [not_and, Xor', not_or, not_not, ← iff_iff_implies_and_implies]"
}
] | [
476,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_one | [
{
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_pos_iff_support_of_nonneg_ae | [
{
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1243,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Irrational.lean | Irrational.div_rat | [
{
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},
{
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424,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.basisAux_tmul | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Separation.lean | eq_of_forall_symmetric | [
{
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160,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_eq_zero | [
{
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},
{
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82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Basic.lean | Convex.inter | [] | [
98,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAtFilter_id | [
{
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995,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | lt_csSup_of_lt | [] | [
630,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Logic.lean | and_not_self_iff | [] | [
239,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
239,
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_eq_iSup_of_singleton_spans | [
{
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Mathlib/Order/Height.lean | Set.chainHeight_eq_top_iff | [
{
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Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_commutator_eq_bot_of_rotate | [
{
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ofSet_toLocalEquiv | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sym/Sym2.lean | Sym2.IsDiag.mem_range_diag | [
{
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457,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.continuous_symm | [] | [
236,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_vsub_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nV : Type u_1\nV' : Type ?u.44515\nP : Type u_2\nP' : Type ?u.44521\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\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... | [
114,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/Data/Rel.lean | Rel.core_comp | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nr : Rel α β\ns : Rel β γ\nt : Set γ\nx : α\n⊢ x ∈ core (r • s) t ↔ x ∈ core r (core s t)",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nr : Rel α β\ns : Rel β γ\nt : Set γ\n⊢ core (r • s) t = core r (core s t)",
"tactic": ... | [
245,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_Ico_right | [] | [
263,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.sInf_glb | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\nS : Set (LieSubmodule R L M)\nh : ∀ {N N' : Li... | [
437,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_smul_left_image | [] | [
232,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_Icc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.5978\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Icc a₁ b₁ ⊆ Icc a₂ b₂",
"tactic": "simpa [← coe_subset] using Set.Icc_subset_Icc ha hb"
}
] | [
163,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Constructions.lean | ULift.closedEmbedding_down | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.564674\nδ : Type ?u.564677\nε : Type ?u.564680\nζ : Type ?u.564683\ninst✝ : TopologicalSpace α\n⊢ IsClosed (range down)",
"tactic": "simp only [ULift.down_surjective.range_eq, isClosed_univ]"
}
] | [
1595,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1593,
1
] |
Mathlib/Algebra/Associated.lean | associated_iff_eq | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.248864\nγ : Type ?u.248867\nδ : Type ?u.248870\ninst✝¹ : Monoid α\ninst✝ : Unique αˣ\nx y : α\n⊢ x ~ᵤ y → x = y\n\ncase mpr\nα : Type u_1\nβ : Type ?u.248864\nγ : Type ?u.248867\nδ : Type ?u.248870\ninst✝¹ : Monoid α\ninst✝ : Unique αˣ\nx y : α\n⊢ x = y → x ~... | [
697,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.valid_zero | [] | [
151,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
151,
9
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_finset_sup | [
{
"state_after": "R : Type ?u.1093501\nR' : Type ?u.1093504\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1093510\n𝕜₃ : Type ?u.1093513\n𝕝 : Type ?u.1093516\nE : Type u_2\nE₂ : Type ?u.1093522\nE₃ : Type ?u.1093525\nF : Type ?u.1093528\nG : Type ?u.1093531\nι : Type u_3\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCommGroup E\ni... | [
873,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_conjTranspose_mul_self | [
{
"state_after": "l : Type ?u.244698\nm : Type u_1\nn : Type u_2\no : Type ?u.244707\nR : Type u_3\nm_fin : Fintype m\ninst✝⁵ : Fintype n\ninst✝⁴ : Fintype o\ninst✝³ : Fintype m\ninst✝² : Field R\ninst✝¹ : PartialOrder R\ninst✝ : StarOrderedRing R\nA : Matrix m n R\n⊢ finrank R { x // x ∈ LinearMap.range (mulVe... | [
210,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.symm_apply_apply | [] | [
179,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.unit_isSquare_iff | [
{
"state_after": "case intro\nK : Type ?u.1100843\nR : Type ?u.1100846\nF : Type u_1\ninst✝¹ : Field F\ninst✝ : Fintype F\nhF : ringChar F ≠ 2\na g : Fˣ\nhg : ∀ (x : Fˣ), x ∈ Subgroup.zpowers g\n⊢ IsSquare a ↔ a ^ (Fintype.card F / 2) = 1",
"state_before": "K : Type ?u.1100843\nR : Type ?u.1100846\nF : Type... | [
556,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | pow_le_of_le_one | [] | [
677,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_neg | [] | [
504,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.traverse_def | [
{
"state_after": "case mk\nF G : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : Applicative G\nα β : Type u\nf : α → F β\nx : α\nxs : List α\n⊢ Vector.traverse f (x ::ᵥ { val := xs, property := (_ : List.length xs = List.length xs) }) =\n Seq.seq (cons <$> f x) fun x => Vector.traverse f { val := xs, prope... | [
660,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
11
] |
Mathlib/Data/Set/Basic.lean | Set.inter_inter_distrib_left | [] | [
1082,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.le_of_lt_add_one | [] | [
205,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Std/Data/List/Lemmas.lean | List.prefix_or_prefix_of_prefix | [] | [
1669,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1667,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.limsup_measure_closed_le_iff_liminf_measure_open_ge | [
{
"state_after": "case mp\nΩ : Type u_2\ninst✝⁴ : MeasurableSpace Ω\ninst✝³ : TopologicalSpace Ω\ninst✝² : OpensMeasurableSpace Ω\nι : Type u_1\nL : Filter ι\nμ : Measure Ω\nμs : ι → Measure Ω\ninst✝¹ : IsProbabilityMeasure μ\ninst✝ : ∀ (i : ι), IsProbabilityMeasure (μs i)\n⊢ (∀ (F : Set Ω), IsClosed F → limsup... | [
190,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_of | [] | [
135,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | PreErgodic.measure_self_or_compl_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\nhf : PreErgodic f\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ ↑↑μ s = 0 ∨ ↑↑μ (sᶜ) = 0",
"tactic": "simpa using hf.ae_empty_or_univ hs hs'"
}
] | [
69,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMin.hasFDerivAt_eq_zero | [
{
"state_after": "case h\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\nh : IsLocalMin f a\nhf : HasFDerivAt f f' a\ny : E\n⊢ ↑f' y = ↑0 y",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →... | [
193,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate'_length_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\n⊢ rotate' l (length l * 0) = l",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate' l (length l * (n + 1)) = rotate' (rotate' l (length l * n)) (length (rotate' l (le... | [
100,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Connected.lean | IsConnected.biUnion_of_chain | [] | [
281,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | fderivWithin_inv | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter 𝕜\nx_ne_zero : x ≠ 0\nhxs : Uniq... | [
130,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Computability/Reduce.lean | toNat_manyOneEquiv | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : Type v\ninst✝³ : Primcodable β\ninst✝² : Inhabited β\nγ : Type w\ninst✝¹ : Primcodable γ\ninst✝ : Inhabited γ\np : Set α\n⊢ ManyOneEquiv (toNat p) p",
"tactic": "simp [ManyOneEquiv]"
}
] | [
357,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_self_sub_mul_self_eq | [
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ a * a - b * b = (a + b) * (a - b)",
"tactic": "rw [Nat.mul_sub_left_distrib, Nat.right_distrib, Nat.right_distrib,\n Nat.mul_comm b a, Nat.add_comm (a*a) (a*b), Nat.add_sub_add_left]"
}
] | [
419,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
417,
11
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_ofInvolutive | [] | [
603,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | isLittleO_pow_pow_of_lt_left | [] | [
100,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inter_div_subset | [] | [
720,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.mul_transpose_self_isDiag_iff_hasOrthogonalRows | [] | [
196,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/NhdsSet.lean | Continuous.tendsto_nhdsSet | [] | [
148,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.of_isIso_fac_left | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nf✝ g✝ : X✝ ⟶ Y✝\nh✝ : Y✝ ⟶ Z✝\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nh : X ⟶ Z\ninst✝ : IsIso f\nhh : IsIso (f ≫ g)\nw : f ≫ g = h\n⊢ IsIso g",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nf✝ g✝ : X✝ ⟶ Y✝\nh✝ : Y✝ ⟶ Z✝\nX Y Z : C... | [
458,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.idCoverLifting | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝² : Category C\nD : Type ?u.741\ninst✝¹ : Category D\nE : Type ?u.748\ninst✝ : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nU✝ : C\nS✝ : Sieve ((𝟭 C).obj U✝)\nh : S✝ ∈ GrothendieckTopology.si... | [
84,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.bit0_of_bit0 | [] | [
229,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_integral_piecewise | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nι : Type ?u.1474570\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ η : { x // x ∈ kernel α β }\ns : Set α\nhs : MeasurableSet s\ninst✝³ : DecidablePred fun x => x ∈ s\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E... | [
669,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Order/Concept.lean | Concept.ext' | [
{
"state_after": "case mk.mk\nι : Sort ?u.6130\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.6139\nκ : ι → Sort ?u.6144\nr : α → β → Prop\ns s₁✝ s₂ : Set α\nt t₁✝ t₂ : Set β\nd : Concept α β r\ns₁ : Set α\nt₁ : Set β\nclosure_fst✝ : intentClosure r (s₁, t₁).fst = (s₁, t₁).snd\nh₁ : extentClosure r (s₁, t₁).snd = (s₁... | [
204,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.re_add_im | [] | [
298,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | dNext_eq | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf✝ g : C ⟶ D\nh k : D ⟶ E\ni✝ : ι\nf : (i j : ι) → X C i ⟶ X D j\ni : ι\nw : ComplexShape.Rel c i (ComplexShape.next c i)\n⊢ ↑(dNext i) f = d C i (ComplexShape.next c i) ≫ ... | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Lattice.lean | left_eq_inf | [] | [
444,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.biUnion' | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\nι : Type u_1\ns : Set ι\nt : (i : ι) → i ∈ s → Set α\nht : ∀ (i : ι) (hi : i ∈ s), Set.Finite (t i hi)\na✝ : Fintype ↑s\n⊢ Set.Finite (⋃ (i : ι) (h : i ∈ s), t i h)",
"state_before": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type... | [
800,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.surj_on_of_inj_on_of_card_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ns t✝ : Finset α\nf✝ : α → β\nn : ℕ\nt : Finset β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂\nhst : card t ≤ card s\n⊢ ∀ (b : β),... | [
372,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.smul_mem_pointwise_smul | [] | [
377,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Part.lean | Part.map_id' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.49680\nγ : Type ?u.49683\nf : α → α\nH : ∀ (x : α), f x = x\no : Part α\n⊢ map id o = o",
"state_before": "α : Type u_1\nβ : Type ?u.49680\nγ : Type ?u.49683\nf : α → α\nH : ∀ (x : α), f x = x\no : Part α\n⊢ map f o = o",
"tactic": "rw [show f = id from funext... | [
593,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Topology/Basic.lean | not_isOpen_singleton | [] | [
1325,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1324,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isDetecting_op_iff | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\n𝒢 : Set C\nh𝒢 : IsDetecting (Set.op 𝒢)\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), G ∈ 𝒢 → ∀ (h : X ⟶ G), ∃! h', f ≫ h' = h\n⊢ IsIso f\n\ncase refine'_2\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Categ... | [
128,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.ne_zero_iff | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q p : MvPolynomial σ R\n⊢ (¬∀ (d : σ →₀ ℕ), coeff d p = 0) ↔ ∃ d, coeff d p ≠ 0",
"state_before": "R : Type u\nS₁ : Type v\nS₂ :... | [
815,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_succ | [] | [
85,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Combinatorics/Catalan.lean | catalan_eq_centralBinom_div | [
{
"state_after": "n : ℕ\n⊢ ↑(catalan n) = ↑(Nat.centralBinom n) / (↑n + 1)",
"state_before": "n : ℕ\n⊢ catalan n = Nat.centralBinom n / (n + 1)",
"tactic": "suffices (catalan n : ℚ) = Nat.centralBinom n / (n + 1) by\n have h := Nat.succ_dvd_centralBinom n\n exact_mod_cast this"
},
{
"state_aft... | [
141,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.250745\nα : Type u_1\nβ : Type ?u.250751\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\n⊢ round 1 = 1",
"tactic": "simp [round]"
}
] | [
1343,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.inv_mk | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
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