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/MeasureTheory/Measure/Lebesgue/EqHaar.lean
MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one
[ { "state_after": "case intro.intro.intro.intro\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2304193\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Norme...
[ 852, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 838, 1 ]
Mathlib/Data/Polynomial/Laurent.lean
LaurentPolynomial.T_mul
[]
[ 329, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 328, 1 ]
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_le
[ { "state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.345549\nι : Type ?u.345552\ninst✝⁵ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\nf✝ g✝ : α → β\ninst✝² : Preorder β\ninst✝¹ : OrderClosedTopology β\ninst✝ : PseudoMetrizableSpace β\nf g : α...
[ 1537, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1530, 1 ]
Mathlib/Data/Set/Pairwise/Basic.lean
Set.pairwiseDisjoint_insert
[]
[ 274, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 271, 1 ]
Mathlib/RingTheory/Ideal/QuotientOperations.lean
Ideal.quotientMap_injective'
[ { "state_after": "R : Type u\nS : Type v\nF : Type w\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\nR₁ : Type ?u.1390678\nR₂ : Type ?u.1390681\nA : Type ?u.1390684\nB : Type ?u.1390687\ninst✝⁶ : CommSemiring R₁\ninst✝⁵ : CommSemiring R₂\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : Algebra R₁ A\ninst✝¹ : Alge...
[ 405, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 400, 1 ]
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean
intervalIntegral.integral_comp_sub_right
[ { "state_after": "no goals", "state_before": "ι : Type ?u.14957297\n𝕜 : Type ?u.14957300\nE : Type u_1\nF : Type ?u.14957306\nA : Type ?u.14957309\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (x - d)) = ∫ (x : ℝ) ...
[ 852, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 851, 1 ]
Mathlib/Order/Filter/NAry.lean
Filter.map₂_inf_subset_right
[]
[ 177, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 176, 1 ]
Mathlib/Data/Set/Intervals/Instances.lean
Set.Icc.one_sub_mem
[ { "state_after": "α : Type ?u.24560\ninst✝¹ : OrderedSemiring α\nβ : Type u_1\ninst✝ : OrderedRing β\nt : β\nht : 0 ≤ t ∧ t ≤ 1\n⊢ 0 ≤ 1 - t ∧ 1 - t ≤ 1", "state_before": "α : Type ?u.24560\ninst✝¹ : OrderedSemiring α\nβ : Type u_1\ninst✝ : OrderedRing β\nt : β\nht : t ∈ Icc 0 1\n⊢ 1 - t ∈ Icc 0 1", "ta...
[ 168, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 166, 1 ]
Mathlib/Analysis/Convex/Side.lean
AffineEquiv.wOppSide_map_iff
[]
[ 135, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 133, 1 ]
Std/Data/Nat/Lemmas.lean
Nat.add_mod
[ { "state_after": "no goals", "state_before": "a b n : Nat\n⊢ (a + b) % n = (a % n + b % n) % n", "tactic": "rw [add_mod_mod, mod_add_mod]" } ]
[ 792, 32 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 791, 1 ]
Mathlib/Algebra/BigOperators/Multiset/Basic.lean
Multiset.prod_le_prod_of_rel_le
[ { "state_after": "case zero\nι : Type ?u.127230\nα : Type u_1\nβ : Type ?u.127236\nγ : Type ?u.127239\ninst✝ : OrderedCommMonoid α\ns t : Multiset α\na : α\n⊢ prod 0 ≤ prod 0\n\ncase cons\nι : Type ?u.127230\nα : Type u_1\nβ : Type ?u.127236\nγ : Type ?u.127239\ninst✝ : OrderedCommMonoid α\ns t : Multiset α\na ...
[ 400, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 396, 1 ]
Mathlib/Data/Polynomial/Module.lean
PolynomialModule.single_apply
[]
[ 90, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 89, 1 ]
Mathlib/Data/Multiset/Dedup.lean
Multiset.dedup_subset
[]
[ 62, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 61, 1 ]
Mathlib/CategoryTheory/Adjunction/Limits.lean
CategoryTheory.Adjunction.has_colimits_of_equivalence
[]
[ 161, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 159, 1 ]
Mathlib/SetTheory/Ordinal/Arithmetic.lean
Ordinal.sup_succ_le_lsub
[ { "state_after": "case refine'_1\nα : Type ?u.322882\nβ : Type ?u.322885\nγ : Type ?u.322888\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\nh : succ (sup f) ≤ lsub f\n⊢ ∃ i, f i = sup f\n\ncase refine'_2\nα : Type ?u.322882\nβ : Type ?u.322885\nγ : Type ?u.322888\nr : α → α ...
[ 1631, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1624, 1 ]
Mathlib/Order/Heyting/Basic.lean
Disjoint.le_sdiff_of_le_left
[]
[ 711, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 710, 1 ]
Mathlib/Topology/MetricSpace/HausdorffDistance.lean
Metric.closure_eq_iInter_thickening
[ { "state_after": "ι : Sort ?u.145496\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns t : Set α\nx : α\nE : Set α\n⊢ cthickening 0 E = ⋂ (δ : ℝ) (_ : 0 < δ), thickening δ E", "state_before": "ι : Sort ?u.145496\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns t : Set α\nx :...
[ 1378, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1375, 1 ]
Mathlib/Data/Fin/Basic.lean
Fin.eta
[ { "state_after": "case mk\nn m val✝ : ℕ\nisLt✝ : val✝ < n\nh : ↑{ val := val✝, isLt := isLt✝ } < n\n⊢ { val := ↑{ val := val✝, isLt := isLt✝ }, isLt := h } = { val := val✝, isLt := isLt✝ }", "state_before": "n m : ℕ\na : Fin n\nh : ↑a < n\n⊢ { val := ↑a, isLt := h } = a", "tactic": "cases a" }, { ...
[ 176, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 175, 11 ]
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
MeasureTheory.StronglyMeasurable.stronglyMeasurable_of_measurableSpace_le_on
[ { "state_after": "α✝ : Type ?u.231002\nβ : Type ?u.231005\nγ : Type ?u.231008\nι : Type ?u.231011\ninst✝² : Countable ι\nf✝ g : α✝ → β\nα : Type u_1\nE : Type u_2\nm m₂ : MeasurableSpace α\ninst✝¹ : TopologicalSpace E\ninst✝ : Zero E\ns : Set α\nf : α → E\nhs_m : MeasurableSet s\nhs : ∀ (t : Set α), MeasurableS...
[ 944, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 910, 1 ]
src/lean/Init/Data/Nat/Basic.lean
Nat.mul_comm
[]
[ 176, 91 ]
d5348dfac847a56a4595fb6230fd0708dcb4e7e9
https://github.com/leanprover/lean4
[ 174, 11 ]
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean
AEMeasurable.coe_nnreal_real
[]
[ 1776, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1774, 1 ]
Mathlib/Order/UpperLower/Basic.lean
LowerSet.mem_iSup₂_iff
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.77303\nγ : Type ?u.77306\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\nS : Set (LowerSet α)\ns t : LowerSet α\na : α\nf : (i : ι) → κ i → LowerSet α\n⊢ (a ∈ ⨆ (i : ι) (j : κ i), f i j) ↔ ∃ i j, a ∈ f i j", "tactic": "simp_rw [mem_i...
[ 765, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 764, 1 ]
Mathlib/Algebra/GroupWithZero/Power.lean
SemiconjBy.zpow_right₀
[ { "state_after": "no goals", "state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na x y : G₀\nh : SemiconjBy a x y\nn : ℕ\n⊢ SemiconjBy a (x ^ ↑n) (y ^ ↑n)", "tactic": "simp [h.pow_right n]" }, { "state_after": "no goals", "state_before": "G₀ : Type u_1\ninst✝ : GroupWithZero G₀\na x y ...
[ 120, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/Analysis/NormedSpace/FiniteDimension.lean
Basis.op_norm_le
[ { "state_after": "no goals", "state_before": "𝕜 : Type u\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁶ : AddCommGroup F'\ninst✝⁵ : Module 𝕜 F'\ninst✝⁴ :...
[ 296, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 293, 1 ]
Mathlib/RingTheory/RootsOfUnity/Basic.lean
IsPrimitiveRoot.zmodEquivZpowers_apply_coe_int
[ { "state_after": "M : Type ?u.2827809\nN : Type ?u.2827812\nG : Type ?u.2827815\nR : Type u_1\nS : Type ?u.2827821\nF : Type ?u.2827824\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ninst✝¹ : DivisionCommMonoid G\nk l : ℕ\ninst✝ : CommRing R\nζ : Rˣ\nh : IsPrimitiveRoot ζ k\ni : ℤ\n⊢ ↑(↑(AddMonoidHom.liftOfRigh...
[ 708, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 705, 1 ]
Mathlib/Algebra/AddTorsor.lean
vsub_vadd
[]
[ 89, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/Analysis/SpecialFunctions/Exp.lean
Complex.continuousOn_exp
[]
[ 81, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 80, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.inv_lt_inv'
[]
[ 1506, 92 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1506, 21 ]
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean
Filter.BoundedAtFilter.neg
[]
[ 101, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 99, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Star.lean
differentiableOn_star_iff
[]
[ 88, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 86, 1 ]
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean
InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two
[ { "state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : sin (angle x y) = 1\n⊢ angle x y = π / 2", "state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ sin (angle x y) = 1 ↔ angle x y = π / 2", "tactic"...
[ 374, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 371, 1 ]
Mathlib/Logic/Relation.lean
Acc.TransGen
[ { "state_after": "case intro\nα : Type u_1\nβ : Type ?u.22046\nγ : Type ?u.22049\nδ : Type ?u.22052\nr : α → α → Prop\na b c d x : α\nh✝ : ∀ (y : α), r y x → Acc r y\nH : ∀ (y : α), r y x → Acc (Relation.TransGen r) y\n⊢ Acc (Relation.TransGen r) x", "state_before": "α : Type u_1\nβ : Type ?u.22046\nγ : Typ...
[ 443, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 439, 1 ]
Mathlib/Data/Set/Intervals/OrdConnected.lean
Set.ordConnected_singleton
[ { "state_after": "α✝ : Type ?u.6443\nβ : Type ?u.6446\ninst✝² : Preorder α✝\ninst✝¹ : Preorder β\ns t : Set α✝\nα : Type u_1\ninst✝ : PartialOrder α\na : α\n⊢ OrdConnected (Icc a a)", "state_before": "α✝ : Type ?u.6443\nβ : Type ?u.6446\ninst✝² : Preorder α✝\ninst✝¹ : Preorder β\ns t : Set α✝\nα : Type u_1\...
[ 178, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 175, 1 ]
Mathlib/Data/MvPolynomial/Basic.lean
MvPolynomial.eval₂_monomial
[ { "state_after": "no goals", "state_before": "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 : MvPolynomial σ R\nf : R →+* S₁\ng : σ → S₁\n⊢ (↑f 0 * Finsupp.prod s fun n e => g n ^ e) = 0", ...
[ 962, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 961, 1 ]
Mathlib/SetTheory/Cardinal/Basic.lean
Cardinal.mk_subtype_of_equiv
[]
[ 2157, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2155, 1 ]
Mathlib/Data/Nat/Factorial/Basic.lean
Nat.ascFactorial_zero
[]
[ 236, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 235, 1 ]
Mathlib/Algebra/Order/ToIntervalMod.lean
toIocMod_eq_iff
[ { "state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ (c ∈ Set.Ioc a (a + p) ∧ ∃ z, b = c + z • p) → toIocMod hp a b = c", "state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b ...
[ 191, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 184, 1 ]
Mathlib/Analysis/Normed/Group/Basic.lean
lipschitzWith_one_nnnorm'
[]
[ 1111, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1110, 1 ]
Mathlib/MeasureTheory/Measure/Stieltjes.lean
StieltjesFunction.measure_univ
[ { "state_after": "f : StieltjesFunction\nl u : ℝ\nhfl : Tendsto (↑f) atBot (𝓝 l)\nhfu : Tendsto (↑f) atTop (𝓝 u)\n⊢ Tendsto (fun x => ↑↑(StieltjesFunction.measure f) (Iic x)) atTop (𝓝 (ofReal (u - l)))", "state_before": "f : StieltjesFunction\nl u : ℝ\nhfl : Tendsto (↑f) atBot (𝓝 l)\nhfu : Tendsto (↑f) ...
[ 609, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 605, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.sdiff_insert_insert_of_mem_of_not_mem
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.269252\nγ : Type ?u.269255\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na b : α\ns t : Finset α\nx : α\nhxs : x ∈ s\nhxt : ¬x ∈ t\n⊢ insert x (s \\ insert x t) = s \\ t", "tactic": "rw [sdiff_insert, insert_erase (mem_sdiff.mpr ⟨hx...
[ 2313, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2311, 1 ]
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
Real.abs_log_mul_self_rpow_lt
[ { "state_after": "x✝ y z x t : ℝ\nh1 : 0 < x\nh2 : x ≤ 1\nht : 0 < t\n⊢ abs (log x * x ^ t) * t < 1", "state_before": "x✝ y z x t : ℝ\nh1 : 0 < x\nh2 : x ≤ 1\nht : 0 < t\n⊢ abs (log x * x ^ t) < 1 / t", "tactic": "rw [lt_div_iff ht]" }, { "state_after": "x✝ y z x t : ℝ\nh1 : 0 < x\nh2 : x ≤ 1\nh...
[ 622, 73 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 618, 1 ]
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean
MeasureTheory.integrable_of_intervalIntegral_norm_bounded
[ { "state_after": "ι : Type u_2\nE : Type u_1\nμ : Measure ℝ\nl : Filter ι\ninst✝² : NeBot l\ninst✝¹ : IsCountablyGenerated l\ninst✝ : NormedAddCommGroup E\na b : ι → ℝ\nf : ℝ → E\nI : ℝ\nhfi : ∀ (i : ι), IntegrableOn f (Ioc (a i) (b i))\nha : Tendsto a l atBot\nhb : Tendsto b l atTop\nh : ∀ᶠ (i : ι) in l, (∫ (x...
[ 527, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 520, 1 ]
Mathlib/Algebra/Star/Subalgebra.lean
StarAlgHom.ext_of_adjoin_eq_top
[]
[ 749, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 748, 1 ]
Mathlib/Data/Polynomial/Basic.lean
Polynomial.monomial_left_inj
[ { "state_after": "no goals", "state_before": "R : Type u\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\na : R\nha : a ≠ 0\ni j : ℕ\n⊢ ↑(monomial i) a = ↑(monomial j) a ↔ i = j", "tactic": "rw [← ofFinsupp_single, ← ofFinsupp_single, ofFinsupp.injEq, Finsupp.single_left_inj ha]" } ]
[ 918, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 915, 1 ]
Mathlib/Data/MvPolynomial/Division.lean
MvPolynomial.modMonomial_X
[]
[ 199, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Polynomial/Monic.lean
Polynomial.not_monic_zero
[]
[ 427, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 426, 1 ]
Mathlib/MeasureTheory/Group/Arithmetic.lean
AEMeasurable.const_smul'
[]
[ 661, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 659, 1 ]
Mathlib/Order/Monotone/Basic.lean
StrictMonoOn.le_iff_le
[]
[ 776, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 773, 1 ]
Mathlib/Algebra/Algebra/Basic.lean
Module.ker_algebraMap_end
[]
[ 637, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 635, 1 ]
Mathlib/Topology/Order.lean
generateFrom_sUnion
[]
[ 960, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 958, 1 ]
Mathlib/Algebra/GroupPower/Basic.lean
mul_pow
[]
[ 259, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 258, 1 ]
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean
MeasureTheory.Measure.rnDeriv_restrict
[ { "state_after": "α : Type u_1\nβ : Type ?u.62355\nm : MeasurableSpace α\nμ ν✝ ν : Measure α\ninst✝ : SigmaFinite ν\ns : Set α\nhs : MeasurableSet s\n⊢ rnDeriv (withDensity ν (indicator s 1)) ν =ᶠ[ae ν] indicator s 1", "state_before": "α : Type u_1\nβ : Type ?u.62355\nm : MeasurableSpace α\nμ ν✝ ν : Measure...
[ 383, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 380, 1 ]
Mathlib/Analysis/InnerProductSpace/Calculus.lean
ContDiffOn.norm_sq
[]
[ 202, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 201, 1 ]
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean
MeasureTheory.withDensityᵥ_smul
[ { "state_after": "case pos\nα : Type u_3\nβ : Type ?u.41128\nm : MeasurableSpace α\nμ ν : Measure α\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\nf✝ g : α → E\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : SMulCommClass...
[ 126, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 116, 1 ]
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean
ZMod.χ₄_nat_eq_if_mod_four
[ { "state_after": "no goals", "state_before": "n : ℕ\n⊢ ↑χ₄ ↑n = if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1", "tactic": "exact_mod_cast χ₄_int_eq_if_mod_four n" } ]
[ 79, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 77, 1 ]
Mathlib/Topology/LocallyConstant/Basic.lean
LocallyConstant.unflip_flip
[]
[ 443, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 442, 1 ]
Mathlib/Algebra/Hom/Group.lean
MonoidWithZeroHom.toZeroHom_injective
[]
[ 1245, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1243, 1 ]
Std/Control/ForInStep/Lemmas.lean
ForInStep.bindList_cons
[]
[ 25, 76 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 23, 9 ]
Mathlib/LinearAlgebra/Matrix/Charpoly/Minpoly.lean
charpoly_leftMulMatrix
[ { "state_after": "case inl\nR : Type u\ninst✝⁶ : CommRing R\nn : Type v\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\nN : Type w\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\nS : Type u_1\ninst✝¹ : Ring S\ninst✝ : Algebra R S\nh : PowerBasis R S\nh✝ : Subsingleton R\n⊢ charpoly (↑(leftMulMatrix h.basis) h.gen) ...
[ 97, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/Data/Real/EReal.lean
EReal.coe_eq_coe_iff
[]
[ 113, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 112, 11 ]
Mathlib/MeasureTheory/Decomposition/Jordan.lean
MeasureTheory.SignedMeasure.toJordanDecomposition_smul
[ { "state_after": "case a\nα : Type u_1\nβ : Type ?u.75261\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nr : ℝ≥0\n⊢ toSignedMeasure (toJordanDecomposition (r • s)) = toSignedMeasure (r • toJordanDecomposition s)", "state_before": "α : Type u_1\nβ : Type ?u.75261\ninst✝ : MeasurableSpace α\ns : SignedMeasu...
[ 469, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 466, 1 ]
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean
eq_on_inv₀
[ { "state_after": "case inl\nα : Type ?u.15847\nM₀ : Type ?u.15850\nG₀ : Type u_3\nM₀' : Type u_1\nG₀' : Type ?u.15859\nF : Type ?u.15862\nF' : Type u_2\ninst✝⁵ : MonoidWithZero M₀\ninst✝⁴ : GroupWithZero G₀\ninst✝³ : Nontrivial M₀\ninst✝² : MonoidWithZero M₀'\ninst✝¹ : MonoidWithZeroHomClass F G₀ M₀\ninst✝ : Mo...
[ 226, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 223, 1 ]
Mathlib/Order/Partition/Equipartition.lean
Finpartition.Set.Subsingleton.isEquipartition
[]
[ 48, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 46, 1 ]
Mathlib/Topology/SubsetProperties.lean
IsIrreducible.image
[]
[ 1877, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1875, 1 ]
Mathlib/FieldTheory/Adjoin.lean
IntermediateField.adjoin.finrank
[ { "state_after": "F : Type ?u.870038\ninst✝⁶ : Field F\nE : Type ?u.870044\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\nα : E\nK : Type u_1\ninst✝³ : Field K\ninst✝² : Algebra F K\nL : Type u_2\ninst✝¹ : Field L\ninst✝ : Algebra K L\nx : L\nhx : IsIntegral K x\n⊢ (powerBasis hx).dim = natDegree (minpoly K x)", ...
[ 875, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 872, 1 ]
Mathlib/Order/Hom/Basic.lean
OrderIso.trans_apply
[]
[ 906, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 905, 1 ]
Mathlib/Topology/Basic.lean
le_nhds_lim
[]
[ 1522, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1521, 1 ]
Mathlib/NumberTheory/PellMatiyasevic.lean
Pell.xn_modEq_x4n_add
[ { "state_after": "a : ℕ\na1 : 1 < a\nn j : ℕ\n⊢ xn a1 (4 * n + j) + xn a1 (2 * n + j) ≡ 0 [MOD xn a1 n]", "state_before": "a : ℕ\na1 : 1 < a\nn j : ℕ\n⊢ xn a1 (4 * n + j) + xn a1 (2 * n + j) ≡ xn a1 j + xn a1 (2 * n + j) [MOD xn a1 n]", "tactic": "refine' @ModEq.trans _ _ 0 _ _ (by rw [add_comm]; exact ...
[ 636, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 632, 1 ]
Mathlib/MeasureTheory/MeasurableSpaceDef.lean
MeasurableSet.ite
[]
[ 222, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 220, 11 ]
Mathlib/Algebra/Group/Defs.lean
npow_eq_pow
[]
[ 623, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 622, 1 ]
Mathlib/Order/Monotone/Basic.lean
strictMonoOn_id
[]
[ 520, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 520, 1 ]
Mathlib/SetTheory/Game/PGame.lean
PGame.zero_lt_neg_iff
[ { "state_after": "no goals", "state_before": "x : PGame\n⊢ 0 < -x ↔ x < 0", "tactic": "rw [lt_neg_iff, neg_zero]" } ]
[ 1392, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1392, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Prod.lean
HasFDerivAtFilter.fst
[]
[ 154, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 152, 11 ]
Mathlib/ModelTheory/LanguageMap.lean
FirstOrder.Language.LHom.map_constants_comp_sumInl
[ { "state_after": "no goals", "state_before": "L : Language\nL' : Language\nM : Type w\ninst✝ : Structure L M\nα : Type w'\nβ : Type u_1\nf : α → β\n⊢ comp (lhomWithConstantsMap L f) LHom.sumInl = lhomWithConstants L β", "tactic": "ext <;> rfl" } ]
[ 528, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 527, 1 ]
Mathlib/MeasureTheory/Integral/SetIntegral.lean
ContinuousOn.integral_sub_linear_isLittleO_ae
[]
[ 1041, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1033, 1 ]
Mathlib/Topology/Algebra/Module/Basic.lean
ContinuousLinearMap.pi_eq_zero
[ { "state_after": "R : Type u_1\ninst✝⁹ : Semiring R\nM : Type u_2\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nM₂ : Type ?u.693068\ninst✝⁵ : TopologicalSpace M₂\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Module R M₂\nι : Type u_4\nφ : ι → Type u_3\ninst✝² : (i : ι) → TopologicalSpace (...
[ 1228, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1226, 1 ]
Mathlib/GroupTheory/FreeGroup.lean
FreeGroup.lift_eq_prod_map
[ { "state_after": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\ninst✝ : Group β\nf : α → β\nx : FreeGroup α\n⊢ ↑(MonoidHom.comp prod (map f)) x = ↑prod (↑(map f) x)\n\ncase hg\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nβ : Type v\ninst✝ : Group β\nf : α → β\nx : FreeGroup α\n⊢ ∀ (x : α), ↑(MonoidH...
[ 930, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 927, 1 ]
Mathlib/Topology/Instances/TrivSqZeroExt.lean
TrivSqZeroExt.hasSum_inl
[]
[ 151, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 149, 1 ]
Mathlib/Data/Set/Prod.lean
Set.univ_pi_eq_empty
[]
[ 680, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 679, 1 ]
Mathlib/Data/Fintype/Powerset.lean
Fintype.card_finset
[]
[ 29, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 28, 1 ]
Mathlib/Analysis/Convex/Exposed.lean
IsExposed.sInter
[ { "state_after": "case empty.h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : TopologicalSpace 𝕜\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : TopologicalSpace E\ninst✝¹ : Module 𝕜 E\nl : E →L[𝕜] 𝕜\nA B C : Set E\nX : Finset E\nx : E\ninst✝ : ContinuousAdd 𝕜\nhF : Finset.Nonempty ∅\nhAF : ∀ (B : Set...
[ 168, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 158, 1 ]
Mathlib/Data/Set/Basic.lean
SetCoe.forall
[]
[ 187, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 186, 1 ]
Mathlib/Analysis/Normed/Group/Basic.lean
Real.nnnorm_coe_nat
[]
[ 1733, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1732, 1 ]
Mathlib/Computability/Reduce.lean
ManyOneDegree.of_le_of
[]
[ 440, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 439, 1 ]
Mathlib/Algebra/Lie/Basic.lean
LieEquiv.apply_symm_apply
[]
[ 621, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 620, 1 ]
Mathlib/Topology/Order/Basic.lean
frontier_le_subset_eq
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\nf g : β → α\ninst✝ : TopologicalSpace β\nhf : Continuous f\nhg : Continuous g\n⊢ {b | f b ≤ g b} ∩ closure ({b | f b ≤ g b}ᶜ) ⊆ {b | f b = g b}", "state_before": "α : Ty...
[ 634, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 629, 1 ]
Mathlib/LinearAlgebra/Matrix/Adjugate.lean
Matrix.adjugate_conjTranspose
[ { "state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA : Matrix n n α\n⊢ map (adjugate A)ᵀ star = adjugate (map Aᵀ star)", "state_before": "m : Type u\nn : Type v\nα : Type w\nin...
[ 454, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 451, 1 ]
Mathlib/Data/Real/Hyperreal.lean
Hyperreal.gt_of_tendsto_zero_of_neg
[ { "state_after": "f : ℕ → ℝ\nhf : Tendsto f atTop (𝓝 0)\nr : ℝ\nhr : r < 0\n⊢ -↑(-r) < ofSeq f", "state_before": "f : ℕ → ℝ\nhf : Tendsto f atTop (𝓝 0)\nr : ℝ\nhr : r < 0\n⊢ ↑r < ofSeq f", "tactic": "rw [← neg_neg r, coe_neg]" }, { "state_after": "no goals", "state_before": "f : ℕ → ℝ\nhf ...
[ 214, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 212, 1 ]
Mathlib/Topology/UniformSpace/Basic.lean
nhdsSet_diagonal_le_uniformity
[]
[ 931, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 930, 1 ]
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean
ContinuousMonoidHom.embedding_toContinuousMap
[]
[ 288, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 286, 1 ]
Mathlib/Combinatorics/SetFamily/Shadow.lean
Finset.shadow_singleton_empty
[]
[ 80, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 79, 1 ]
Mathlib/Algebra/Category/Ring/Constructions.lean
CommRingCat.pushoutCocone_inr
[ { "state_after": "R A B : CommRingCat\nf : R ⟶ A\ng : R ⟶ B\nthis : Algebra ↑R ↑A := RingHom.toAlgebra f\n⊢ B ⟶ (pushoutCocone f g).pt", "state_before": "R A B : CommRingCat\nf : R ⟶ A\ng : R ⟶ B\n⊢ B ⟶ (pushoutCocone f g).pt", "tactic": "letI := f.toAlgebra" }, { "state_after": "R A B : CommRin...
[ 72, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 67, 1 ]
Mathlib/Topology/Algebra/Order/Compact.lean
IsCompact.sSup_mem
[]
[ 164, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 163, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.eq_zero_of_isEmpty
[]
[ 766, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 765, 1 ]
Mathlib/SetTheory/Cardinal/Cofinality.lean
Ordinal.nfpFamily_lt_ord_lift
[ { "state_after": "case refine'_1\nα : Type ?u.32966\nr : α → α → Prop\nι : Type u\nf : ι → Ordinal → Ordinal\nc : Ordinal\nhc : ℵ₀ < cof c\nhc' : Cardinal.lift (#ι) < cof c\nhf : ∀ (i : ι) (b : Ordinal), b < c → f i b < c\na : Ordinal\nha : a < c\n⊢ Cardinal.lift (max ℵ₀ (#ι)) < cof c\n\ncase refine'_2\nα : Typ...
[ 389, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 380, 1 ]
Mathlib/Topology/Maps.lean
inducing_id
[]
[ 75, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/Algebra/Field/Basic.lean
inv_add_inv
[]
[ 218, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 217, 1 ]
Mathlib/Data/List/Intervals.lean
List.Ico.pred_singleton
[ { "state_after": "m : ℕ\nh : 0 < m\n⊢ range' (m - 1) (m - (m - 1)) = [m - 1]", "state_before": "m : ℕ\nh : 0 < m\n⊢ Ico (m - 1) m = [m - 1]", "tactic": "dsimp [Ico]" }, { "state_after": "m : ℕ\nh : 0 < m\n⊢ range' (m - 1) (succ 0) = [m - 1]", "state_before": "m : ℕ\nh : 0 < m\n⊢ range' (m - ...
[ 141, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 138, 1 ]
Mathlib/Topology/Compactification/OnePoint.lean
OnePoint.compl_range_coe
[]
[ 136, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 135, 1 ]
Mathlib/Analysis/Asymptotics/Asymptotics.lean
Asymptotics.IsBigO.const_mul_left
[]
[ 1456, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1454, 1 ]