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/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Localization.whiskeringLeftFunctor'_eq | [] | [
262,
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Mathlib/Data/Complex/Exponential.lean | Real.exp_approx_end | [
{
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp_smul_const | [] | [
424,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.isRegular_aleph_succ | [
{
"state_after": "α : Type ?u.147903\nr : α → α → Prop\no : Ordinal\n⊢ IsRegular (succ (aleph o))",
"state_before": "α : Type ?u.147903\nr : α → α → Prop\no : Ordinal\n⊢ IsRegular (aleph (succ o))",
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},
{
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1013,
43
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1011,
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval | [] | [
294,
44
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.fieldRange_le | [
{
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Mathlib/Init/CcLemmas.lean | and_eq_of_eq_false_right | [] | [
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Mathlib/Data/Real/Irrational.lean | exists_irrational_btwn | [] | [
666,
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Mathlib/Data/Finset/Pointwise.lean | Finset.coe_prod | [] | [
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52
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980,
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Mathlib/NumberTheory/FermatPsp.lean | FermatPsp.frequently_atTop_fermatPsp | [
{
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},
{
"state_after": "case intro\nb : ℕ\nh : 1 ≤ b\nn p : ℕ\nhp : FermatPsp p b... | [
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390,
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Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_range | [
{
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374,
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Mathlib/Order/Filter/Basic.lean | Filter.pure_seq_eq_map | [
{
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Mathlib/Data/Nat/ModEq.lean | Nat.add_div_eq_of_add_mod_lt | [
{
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Mathlib/Order/Basic.lean | Ne.not_le_or_not_le | [] | [
437,
42
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.compLinearMap_id | [] | [
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19
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Mathlib/LinearAlgebra/Ray.lean | SameRay.pos_smul_right | [] | [
141,
28
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Mathlib/Data/List/Rotate.lean | List.IsRotated.map | [
{
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"tactic": "obtain ⟨n, ... | [
557,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
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Mathlib/GroupTheory/Complement.lean | Subgroup.mem_leftTransversals_iff_existsUnique_quotient_mk''_eq | [
{
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Mathlib/GroupTheory/IsFreeGroup.lean | IsFreeGroup.lift_symm_apply | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/UpperLower/Hom.lean | LowerSet.iicInfHom_apply | [] | [
89,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | Matrix.toEuclideanLin_piLp_equiv_symm | [] | [
989,
6
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | modelWithCorners_prod_coe_symm | [] | [
464,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.tan_angle_sub_of_inner_eq_zero | [
{
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302,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineMap.lineMap_mem | [
{
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40
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Mathlib/Algebra/Group/Basic.lean | div_mul_div_cancel' | [
{
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"tactic": "rw [← mul_div_assoc, div_mul_cancel']"
}
] | [
804,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Iio | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | mem_pairSelfAdjointMatricesSubmodule | [
{
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638,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/MvPolynomial/Cardinal.lean | MvPolynomial.cardinal_mk_eq_lift | [] | [
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Mathlib/Topology/PathConnected.lean | Path.symm_cast | [] | [
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Mathlib/Data/Finset/Basic.lean | Finset.erase_insert_eq_erase | [
{
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"tactic": "simp (config := { contextual := true }) only [mem_erase, mem_insert, an... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_add_right | [
{
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"tacti... | [
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47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2953,
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_ofSubtype | [] | [
800,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
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Mathlib/Topology/Algebra/Order/LeftRight.lean | nhds_left'_le_nhds_ne | [] | [
48,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_inter_Iio | [] | [
1780,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.le_N | [
{
"state_after": "α : Type ?u.783410\nβ : Type ?u.783413\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 2 ≤ N\nthis : (2 * dValue N - 1) ^ nValue N ≤ (2 * dValue N) ^ nValue N\n⊢ (2 * dValue N - 1) ^ nValue N ≤ N",
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432,
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.neg_negPart | [] | [
119,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_lt_arsinh | [] | [
156,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_le | [] | [
98,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Instances/NNReal.lean | NNReal.nhds_zero | [
{
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"tactic": "simp only [bot_lt_iff_ne_bot]"
},
{
... | [
137,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.coe_coe | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.bddAbove_range_comp | [
{
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{
"st... | [
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34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Part.lean | Part.mem_map | [] | [
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.topEquiv_toMonoidHom | [] | [
807,
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806,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_eq_zero_iff | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd | [
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324,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | lt_of_tsub_lt_tsub_left_of_le | [] | [
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69
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_inter | [
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1
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Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.denseRange_coe | [] | [
418,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovary_const_right | [] | [
102,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_eq_nfpFamily | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.coe_ne_one | [] | [
155,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.differentiableAt | [] | [
505,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_limRatio | [
{
"state_after": "case h\nα : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.2273791\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\n... | [
274,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_mul | [] | [
677,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encodek₂ | [] | [
230,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.min | [] | [
595,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.coe_mk | [] | [
1014,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.isRegular_compl | [] | [
78,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Constructions.lean | isOpen_pi_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.248072\nδ : Type ?u.248075\nε : Type ?u.248078\nζ : Type ?u.248081\nι : Type u_1\nπ : ι → Type u_2\nκ : Type ?u.248092\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf : α → (i : ι) → π i\ns : Set ((a : ι) → π a)\n⊢ (∀ (a : (a : ι) →... | [
1312,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.reindex_refl | [
{
"state_after": "case a\nι : Type u_1\nι₂ : Type ?u.505120\nι₃ : Type ?u.505123\nR : Type u_2\ninst✝⁷ : CommSemiring R\nR₁ : Type ?u.505132\nR₂ : Type ?u.505135\ns : ι → Type ?u.505140\ninst✝⁶ : (i : ι) → AddCommMonoid (s i)\ninst✝⁵ : (i : ι) → Module R (s i)\nM : Type u_3\ninst✝⁴ : AddCommMonoid M\ninst✝³ : M... | [
528,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.comp_id | [] | [
1146,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.scaleRoots.isWeaklyEisensteinAt | [
{
"state_after": "R : Type u\nA : Type ?u.108344\ninst✝¹ : CommRing R\ninst✝ : CommRing A\np : R[X]\nx : R\nP : Ideal R\nhP : x ∈ P\nn✝ : ℕ\ni : n✝ < natDegree (scaleRoots p x)\n⊢ coeff (scaleRoots p x) n✝ ∈ P",
"state_before": "R : Type u\nA : Type ?u.108344\ninst✝¹ : CommRing R\ninst✝ : CommRing A\np : R[... | [
170,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Int/Interval.lean | Int.card_Ioc | [
{
"state_after": "a b : ℤ\n⊢ card (map (Function.Embedding.trans Nat.castEmbedding (addLeftEmbedding (a + 1))) (range (toNat (b - a)))) =\n toNat (b - a)",
"state_before": "a b : ℤ\n⊢ card (Ioc a b) = toNat (b - a)",
"tactic": "change (Finset.map _ _).card = _"
},
{
"state_after": "no goals",... | [
121,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.den_mem | [] | [
515,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.exists_forall_ge' | [] | [
302,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuousAt_mul_const | [] | [
408,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
11
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittOne_zero_eq_one | [
{
"state_after": "case a\np : ℕ\nR : Type ?u.44782\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(map (Int.castRingHom ℚ)) (wittOne p 0) = ↑(map (Int.castRingHom ℚ)) 1",
"state_before": "p : ℕ\nR : Type ?u.44782\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ wittOne p 0 = 1",
"tactic": "apply MvPoly... | [
243,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/CategoryTheory/Comma.lean | CategoryTheory.Comma.comp_right | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.coe_support_append | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\np' : Walk G v w\n⊢ ↑(support (append p p')) = {u} + ↑(List.tail (support p)) + ↑(List.tail (support p'))",
"tactic": "rw [support... | [
634,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_op_nnnorm | [] | [
483,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Prepartition.measure_iUnion_toReal | [
{
"state_after": "ι : Type u_1\ninst✝¹ : Finite ι\nI : Box ι\nπ : Prepartition I\nμ : MeasureTheory.Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\n⊢ ∀ (b : Box ι), b ∈ π.boxes → MeasurableSet ↑b\n\nι : Type u_1\ninst✝¹ : Finite ι\nI : Box ι\nπ : Prepartition I\nμ : MeasureTheory.Measure (ι → ℝ)\ninst✝ : IsL... | [
92,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.bddAbove_range_approx | [] | [
175,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_left | [
{
"state_after": "case mp\nC : Type u_2\ninst✝ : Category C\nA✝ B✝ B'✝ X✝ Y✝ Y' : C\ni✝ : A✝ ⟶ B✝\ni'✝ : B✝ ⟶ B'✝\np✝ : X✝ ⟶ Y✝\np' : Y✝ ⟶ Y'\nA B A' B' X Y : C\ni : A ⟶ B\ni' : A' ⟶ B'\ne : Arrow.mk i ≅ Arrow.mk i'\np : X ⟶ Y\na✝ : HasLiftingProperty i p\n⊢ HasLiftingProperty i' p\n\ncase mpr\nC : Type u_2\nin... | [
141,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_tProd_elim | [
{
"state_after": "case pos\nα : Type ?u.370700\nβ : Type ?u.370703\nγ : Type ?u.370706\nδ : Type u_1\nδ' : Type ?u.370712\nι : Sort uι\ns t u : Set α\nπ : δ → Type u_2\ninst✝¹ : (x : δ) → MeasurableSpace (π x)\ninst✝ : DecidableEq δ\ni : δ\nis : List δ\nj : δ\nhj : j ∈ i :: is\nhji : j = i\n⊢ Measurable fun v =... | [
961,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.coe_mk | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_eq' | [
{
"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✝² : CommSemiring R\ninst✝¹ : CommSemiring S₁\np q : MvPolynomial σ R\nf✝ : R →+* S₁\ng✝ : σ → S₁\ninst✝ : Fintype σ\ng : R →+* S₁\nX : σ → S₁\nf : MvPolynomial σ R\n⊢ ∑ x in suppor... | [
945,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.empty_eq | [] | [
507,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_len_sup | [
{
"state_after": "case a\nα : Type u_1\ns t : Finset α\ninst✝ : DecidableEq α\nu : Finset α\nn : ℕ\nhn : n < card u\n⊢ sup (powersetLen (Nat.succ n) u) id ≤ u\n\ncase a\nα : Type u_1\ns t : Finset α\ninst✝ : DecidableEq α\nu : Finset α\nn : ℕ\nhn : n < card u\n⊢ u ≤ sup (powersetLen (Nat.succ n) u) id",
"st... | [
319,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Analysis/Calculus/Deriv/Star.lean | HasStrictDerivAt.star | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nf : 𝕜 → F\ninst✝⁴ : StarRing 𝕜\ninst✝³ : TrivialStar 𝕜\ninst✝² : StarAddMonoid F\ninst✝¹ : ContinuousStar F\ninst✝ : StarModule 𝕜 F\nf' : ... | [
54,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
18
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_eq_one | [] | [
758,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.mem_orthogonal | [] | [
57,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_le_norm_of_ae_le | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.423171\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : { x // x ∈ Lp E p }\ng : { x // x ∈ Lp F p }\nh : ∀ᵐ (x : α) ∂μ, ‖↑↑f x‖ ≤ ‖... | [
381,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_isGreatest | [] | [
194,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.IsLimit.hom_ext | [] | [
422,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Topology/Instances/Sign.lean | continuousAt_sign_of_ne_zero | [
{
"state_after": "case inl\nα : Type u_1\ninst✝³ : Zero α\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na : α\nh : a ≠ 0\nh_neg : a < 0\n⊢ ContinuousAt (↑SignType.sign) a\n\ncase inr\nα : Type u_1\ninst✝³ : Zero α\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : Ord... | [
56,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.mk_set_nat | [
{
"state_after": "no goals",
"state_before": "⊢ (#Set ℕ) = 𝔠",
"tactic": "simp"
}
] | [
94,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.botEquiv_symm | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Algebra/Associated.lean | Irreducible.associated_of_dvd | [] | [
605,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/GroupTheory/CommutingProbability.lean | commProb_le_one | [
{
"state_after": "M : Type u_1\ninst✝¹ : Mul M\ninst✝ : Finite M\n⊢ ↑(Nat.card { p // p.fst * p.snd = p.snd * p.fst }) ≤ ↑(Nat.card M) ^ 2",
"state_before": "M : Type u_1\ninst✝¹ : Mul M\ninst✝ : Finite M\n⊢ commProb M ≤ 1",
"tactic": "refine' div_le_one_of_le _ (sq_nonneg (Nat.card M : ℚ))"
},
{
... | [
58,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.reindex_refl | [] | [
877,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.and_le_left | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x y : Bool), (x && y) ≤ x",
"tactic": "decide"
}
] | [
355,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Std/Data/List/Init/Lemmas.lean | List.all_nil | [] | [
36,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
36,
9
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_sInf | [] | [
429,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MulEquiv.coe_subgroupMap_apply | [] | [
3469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3467,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.neg_strictAnti | [] | [
794,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.cons | [] | [
1119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.finite_def | [] | [
61,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.isCycle_of_prime_order | [
{
"state_after": "case intro\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh1 : Nat.Prime (orderOf σ)\nh2 : Finset.card (support σ) < 2 * orderOf σ\nn : ℕ\nhn : cycleType σ = replicate (n + 1) (orderOf σ)\n⊢ IsCycle σ",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : Decid... | [
221,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.ediv_dvd_ediv | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b c : ℤ\naz : a = 0\n⊢ a * b / a ∣ a * b * c / a",
"tactic": "simp [az]"
},
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b c : ℤ\naz : ¬a = 0\n⊢ b ∣ b * c",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b c : ℤ\naz : ¬a = 0\n⊢ a * b / a ∣ a *... | [
358,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.zero_ne_one_of_proper | [] | [
280,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
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