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/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_iff_nat_mul_le | [] | [
266,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centroid_eq_centerMass | [] | [
256,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/AddTorsor.lean | Prod.snd_vadd | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Computability/Ackermann.lean | ack_three | [
{
"state_after": "case zero\n\n⊢ ack 3 zero = 2 ^ (zero + 3) - 3\n\ncase succ\nn : ℕ\nIH : ack 3 n = 2 ^ (n + 3) - 3\n⊢ ack 3 (succ n) = 2 ^ (succ n + 3) - 3",
"state_before": "n : ℕ\n⊢ ack 3 n = 2 ^ (n + 3) - 3",
"tactic": "induction' n with n IH"
},
{
"state_after": "no goals",
"state_befo... | [
106,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.p_nonnunit | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nthis : (↑p)⁻¹ < 1\n⊢ ↑p ∈ nonunits ℤ_[p]",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ↑p ∈ nonunits ℤ_[p]",
"tactic": "have : (p : ℝ)⁻¹ < 1 := inv_lt_one <| by exact_mod_cast hp.1.one_lt"
},
{
"state_after": "no goals",
"state_before"... | [
596,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.separatingLeft_toLinearMap₂_iff | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2748126\nR₁ : Type u_2\nR₂ : Type ?u.2748132\nM✝ : Type ?u.2748135\nM₁ : Type u_3\nM₂ : Type ?u.2748141\nM₁' : Type ?u.2748144\nM₂' : Type ?u.2748147\nn : Type ?u.2748150\nm : Type ?u.2748153\nn' : Type ?u.2748156\nm' : Type ?u.2748159\nι : Type u_1\... | [
712,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_smul | [] | [
592,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Init/Algebra/Order.lean | le_refl | [] | [
55,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.comp_id | [] | [
342,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Deprecated/Group.lean | IsMonoidHom.map_mul' | [] | [
173,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_range | [
{
"state_after": "case h\nα : Type u\nf : α → ZFSet\nx✝ : ZFSet\n⊢ x✝ ∈ toSet (range f) ↔ x✝ ∈ Set.range f",
"state_before": "α : Type u\nf : α → ZFSet\n⊢ toSet (range f) = Set.range f",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\nα : Type u\nf : α → ZFSet\nx✝ : ... | [
1282,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_integral_bounded_of_nonneg_ae | [] | [
468,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_mono_subtype | [] | [
996,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.spanSingleton_div_self | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.45600\nA : Type ?u.45603\nK : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing A\ninst✝⁸ : Field K\ninst✝⁷ : IsDomain A\nR₁ : Type u_2\ninst✝⁶ : CommRing R₁\ninst✝⁵ : IsDomain R₁\ninst✝⁴ : Algebra R₁ K\ninst✝³ : IsFractionRing R₁ K\nI J : Fractional... | [
164,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Basic.lean | tendsto_atTop_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝² : TopologicalSpace α\ninst✝¹ : Nonempty β\ninst✝ : SemilatticeSup β\nf : β → α\na : α\n⊢ (∀ (ib : Set α), a ∈ ib ∧ IsOpen ib → ∃ ia, True ∧ ∀ (x : β), x ∈ Ici ia → f x ∈ ib... | [
1033,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasStrictFDerivAt_pi' | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type ?u.395005\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nG : Type ?u.395100\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : NormedSpace 𝕜 G\nG' : Type ?u... | [
383,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_eq_map_pullback' | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nA : C\nf₁ f₂ : MonoOver A\n⊢ (inf.obj (Quotient.mk'' f₁)).obj (Quotient.mk'' f₂) =\n (map (MonoOver.arrow f₁)).obj ((pullback (MonoOver.arrow f₁)).obj (Quotient.mk'' f₂))",
"st... | [
467,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Finset.summable | [] | [
185,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add_eq_of_lt_left | [
{
"state_after": "K : Type ?u.2215047\nF : Type ?u.2215050\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.2215062\nΓ''₀ : Type ?u.2215065\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx y z : R\nh : ↑v y < ↑v... | [
331,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderiv_snd | [] | [
316,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.norm_eq_abs | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_self_div_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.25591\nM₀ : Type ?u.25594\nG₀ : Type u_1\nM₀' : Type ?u.25600\nG₀' : Type ?u.25603\nF : Type ?u.25606\nF' : Type ?u.25609\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\n⊢ a * a / a = a",
"tactic": "rw [div_eq_mul_inv, mul_self_mul_inv a]"
}
] | [
375,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Trident.IsLimit.hom_ext | [] | [
304,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.of_sub_of | [] | [
333,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.ext | [] | [
87,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_sup | [] | [
498,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.cosh_le_cosh | [] | [
731,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_apply_left | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a < a + p ∧ ∃ z, a = a + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ toIc... | [
207,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.lift_comp_of | [
{
"state_after": "R : Type u\nX : Type v\ninst✝² : CommRing R\nL : Type w\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nF : FreeLieAlgebra R X →ₗ⁅R⁆ L\n⊢ ↑(lift R) (↑(lift R).symm F) = F",
"state_before": "R : Type u\nX : Type v\ninst✝² : CommRing R\nL : Type w\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nF ... | [
266,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_lt_iff | [] | [
729,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
11
] |
Mathlib/Topology/Instances/RatLemmas.lean | Rat.dense_compl_compact | [] | [
50,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Subtype.nndist_eq | [] | [
1647,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1646,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eventually_right_inverse' | [] | [
253,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | bddBelow_range_of_tendsto_atTop_atTop | [] | [
128,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean | AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : CommRing R\nf : R[X]\nx : PrimeSpectrum R\n⊢ x ∈ imageOfDf f ↔ x ∈ ↑(PrimeSpectrum.comap C) '' zeroLocus {f}ᶜ",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nf : R[X]\n⊢ imageOfDf f = ↑(PrimeSpectrum.comap C) '' zeroLocus {f}ᶜ",
"tactic": "ext x"
},... | [
69,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | NoZeroSMulDivisors.trans | [
{
"state_after": "R✝ : Type ?u.984855\ninst✝²⁰ : CommSemiring R✝\nA✝ : Type ?u.984861\ninst✝¹⁹ : Semiring A✝\ninst✝¹⁸ : Algebra R✝ A✝\nM✝ : Type ?u.984890\ninst✝¹⁷ : AddCommMonoid M✝\ninst✝¹⁶ : Module A✝ M✝\ninst✝¹⁵ : Module R✝ M✝\ninst✝¹⁴ : IsScalarTower R✝ A✝ M✝\nN : Type ?u.986785\ninst✝¹³ : AddCommMonoid N\... | [
892,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.sum_mem | [] | [
236,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_disj_union | [] | [
2794,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2792,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.AEFinStronglyMeasurable.ae_eq_of_forall_set_integral_eq | [
{
"state_after": "α : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf g : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → IntegrableOn f s\nhg_int_finite : ∀ (s : Set α... | [
471,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basisDivisor_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\n⊢ basisDivisor x y ≠ 0 ↔ x ≠ y",
"tactic": "rw [Ne.def, basisDivisor_eq_zero_iff]"
}
] | [
148,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.independent_pair | [
{
"state_after": "case mp\nα : Type u_2\nβ : Type ?u.54428\nι : Type u_1\nι' : Type ?u.54434\ninst✝ : CompleteLattice α\ns : Set α\nhs : SetIndependent s\nt : ι → α\nht : Independent t\ni j : ι\nhij : i ≠ j\nhuniv : ∀ (k : ι), k = i ∨ k = j\n⊢ Independent t → Disjoint (t i) (t j)\n\ncase mpr\nα : Type u_2\nβ : ... | [
334,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.trans_left | [] | [
958,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.atom_pf | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ a = a ^ Nat.rawCast 1 * Nat.rawCast 1 + 0",
"tactic": "simp"
}
] | [
865,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_multiset_prod | [] | [
1109,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/CategoryTheory/Sites/Adjunction.lean | CategoryTheory.Sheaf.adjunctionToTypes_unit_app_val | [
{
"state_after": "C : Type u\ninst✝⁹ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁸ : Category D\nE : Type w₂\ninst✝⁷ : Category E\nF : D ⥤ E\nG✝ : E ⥤ D\ninst✝⁶ : (X : C) → (S : Cover J X) → (P : Cᵒᵖ ⥤ D) → PreservesLimit (MulticospanIndex.multicospan (Cover.index S P)) F\ninst✝⁵ : ConcreteCateg... | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Order/WithBot.lean | WithTop.lt_iff_exists_coe_btwn | [] | [
1354,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.finset_sum_coeff | [] | [
109,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.mkPiField_apply_one_eq_self | [] | [
902,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Data/Setoid/Partition.lean | Finpartition.isPartition_parts | [] | [
316,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix'_toLinearMapₛₗ₂' | [] | [
259,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_subset_smul_finset_iff | [] | [
1970,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1969,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_le_one_of_ge | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.148913\nα : Type u_1\nβ : Type ?u.148919\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nh : b ≤ a\nhb : b ≤ 0\n⊢ a / b ≤ 1",
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] | [
753,
94
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752,
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Mathlib/Data/Finset/Pointwise.lean | Finset.mul_eq_one_iff | [
{
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1005,
75
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Mathlib/LinearAlgebra/Lagrange.lean | Polynomial.eq_zero_of_degree_lt_of_eval_index_eq_zero | [
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88,
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Mathlib/Computability/Language.lean | Language.map_id | [
{
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171,
64
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.ext | [] | [
924,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_C_of_degree_eq_zero | [] | [
627,
38
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626,
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Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.HasBinaryBiproduct.of_hasBinaryCoproduct | [] | [
433,
91
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429,
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Mathlib/Data/Set/Image.lean | Subtype.preimage_coe_compl | [] | [
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47
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Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_self | [] | [
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33
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1550,
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Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.NatTrans.rightDerived_id | [
{
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142,
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Mathlib/Algebra/Module/Basic.lean | rat_cast_smul_eq | [] | [
545,
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543,
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Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.units_inv_symm_left_iff | [] | [
147,
45
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146,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_smul_right | [
{
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.nnnorm | [] | [
1471,
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1469,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_def | [] | [
263,
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262,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.smul_apply | [] | [
317,
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316,
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Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_mul_left | [] | [
120,
32
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Mathlib/Algebra/Ring/BooleanRing.lean | mul_self | [] | [
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25
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.forall_measure_preimage_mul_right_iff | [
{
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201,
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Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_def | [] | [
1107,
10
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1105,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | Prod.edist_eq | [] | [
464,
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Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_pi | [
{
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126,
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Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.exists_forall_norm_le | [
{
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73
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Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.ofNat_toNat | [
{
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147,
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Mathlib/Topology/Algebra/Order/Field.lean | tendsto_inv_zero_atTop | [
{
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.sum_elim_comp_relabelAux | [
{
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.csin | [] | [
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61
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Mathlib/Data/Bool/Basic.lean | Bool.coe_bool_iff | [
{
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142,
68
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142,
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Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.monoidalPreadditive_of_faithful | [
{
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_on_segment' | [
{
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.orthonormal | [
{
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453,
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448,
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.mapEquiv_trans | [
{
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123,
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119,
1
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.comp_liftAddHom | [
{
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504,
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498,
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Mathlib/Algebra/IndicatorFunction.lean | Set.prod_mulIndicator_subset_of_eq_one | [
{
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597,
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584,
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_init | [] | [
1703,
28
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1701,
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.X_divMonomial | [] | [
172,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.Continuous.mul | [] | [
90,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Order/Directed.lean | directedOn_of_sup_mem | [] | [
129,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Order/OmegaCompletePartialOrder.lean | CompleteLattice.inf_continuous' | [] | [
535,
40
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533,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | Differentiable.const_smul | [] | [
101,
69
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100,
1
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Mathlib/Order/Filter/Extr.lean | IsExtrOn.comp_mapsTo | [] | [
441,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
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Mathlib/Order/BooleanAlgebra.lean | sdiff_lt | [
{
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"tactic": "refine'... | [
324,
32
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321,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_normalClosure | [] | [
2468,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2467,
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Icc | [] | [
482,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
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Mathlib/NumberTheory/Divisors.lean | Nat.image_snd_divisorsAntidiagonal | [
{
"state_after": "n : ℕ\n⊢ image (Prod.snd ∘ ↑(Equiv.toEmbedding (Equiv.prodComm ℕ ℕ))) (divisorsAntidiagonal n) = divisors n",
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"tactic": "rw [← map_swap_divisorsAntidiagonal, map_eq_image, image_image]"
},
{
"state... | [
260,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.map_adj | [] | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
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Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_of_mem_incidenceSet | [
{
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"tactic": "rw [incMatrix_apply, Set.indicator_of_mem h, Pi.one_apply]"
}
] | [
99,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/Topology/SubsetProperties.lean | IsCompact.inter_right | [
{
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118,
29
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112,
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Mathlib/Data/Sign.lean | sign_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x < x_1\na : α\nha : a < 0\n⊢ ↑sign a = -1",
"tactic": "rwa [sign_apply, if_neg <| asymm ha, if_pos]"
}
] | [
328,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
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