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list
Mathlib/Analysis/Normed/Group/Basic.lean
norm_snd_le
[]
[ 2385, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2384, 1 ]
Mathlib/Topology/Order/Basic.lean
IsLUB.frequently_nhds_mem
[]
[ 1971, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1969, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.NeBot.not_disjoint
[]
[ 722, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 721, 1 ]
Mathlib/Algebra/GCDMonoid/Basic.lean
GCDMonoid.prime_of_irreducible
[ { "state_after": "case intro\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nx : α\nhi : Irreducible x\na b : α\nh : x ∣ a * b\ny : α\nhy : x = gcd x a * y\n⊢ x ∣ a ∨ x ∣ b", "state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nx : α\nhi : Irreduc...
[ 892, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 880, 1 ]
Mathlib/Order/Filter/Prod.lean
Filter.bot_coprod
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.57284\nδ : Type ?u.57287\nι : Sort ?u.57290\nf : Filter α\ng l : Filter β\n⊢ Filter.coprod ⊥ l = comap Prod.snd l", "tactic": "simp [Filter.coprod]" } ]
[ 481, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 480, 1 ]
Mathlib/GroupTheory/FreeGroup.lean
FreeGroup.Red.refl
[]
[ 96, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 95, 1 ]
Mathlib/Topology/Order/Basic.lean
nhdsWithin_Ioi_basis'
[]
[ 1627, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1625, 1 ]
Mathlib/Topology/Covering.lean
IsEvenlyCovered.toTrivialization_apply
[ { "state_after": "no goals", "state_before": "E : Type u_2\nX : Type u_3\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalSpace X\nf : E → X\ns : Set X\nx : E\nI : Type u_1\ninst✝ : TopologicalSpace I\nh✝ : IsEvenlyCovered f (f x) I\ne : Trivialization I f := Classical.choose (_ : ∃ t, f x ∈ t.baseSet)\nh ...
[ 63, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 55, 1 ]
Mathlib/Computability/PartrecCode.lean
Nat.Partrec.Code.pair_prim
[]
[ 245, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Mathlib/Order/Directed.lean
directedOn_image
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nι : Sort w\nr r' s✝ : α → α → Prop\ns : Set β\nf : β → α\n⊢ DirectedOn r (f '' s) ↔ DirectedOn (f ⁻¹'o r) s", "tactic": "simp only [DirectedOn, Set.mem_image, exists_exists_and_eq_and, forall_exists_index, and_imp,\n forall_apply_eq_...
[ 80, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 77, 1 ]
Mathlib/CategoryTheory/Iso.lean
CategoryTheory.IsIso.eq_inv_comp
[]
[ 429, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 428, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.OuterMeasure.iUnion_eq_of_caratheodory
[]
[ 1062, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1059, 11 ]
Mathlib/Data/Finset/Basic.lean
Finset.eq_empty_iff_forall_not_mem
[ { "state_after": "α : Type u_1\nβ : Type ?u.20009\nγ : Type ?u.20012\ns : Finset α\nx : α\n⊢ ¬x ∈ ∅", "state_before": "α : Type u_1\nβ : Type ?u.20009\nγ : Type ?u.20012\ns✝ s : Finset α\n⊢ s = ∅ → ∀ (x : α), ¬x ∈ s", "tactic": "rintro rfl x" }, { "state_after": "no goals", "state_before": "...
[ 584, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 582, 1 ]
Mathlib/GroupTheory/Subgroup/Basic.lean
Subgroup.map_le_map_iff
[ { "state_after": "no goals", "state_before": "G : Type u_1\nG' : Type ?u.586626\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.586635\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nH K : Subgroup G\n⊢ map f H ≤ map f K ↔ H ≤ K ⊔ ker f", "tactic": "rw [map_le_iff_le_comap, comap_m...
[ 3077, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3076, 1 ]
Mathlib/Algebra/Hom/Centroid.lean
CentroidHom.coe_copy
[]
[ 157, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/Topology/LocalHomeomorph.lean
Homeomorph.refl_toLocalHomeomorph
[]
[ 1288, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1287, 1 ]
Mathlib/Geometry/Euclidean/Basic.lean
EuclideanGeometry.reflection_mem_of_le_of_mem
[ { "state_after": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns₁ s₂ : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s₁ }\ninst✝ : CompleteSpace { x // x ∈ direction s₁ }\nhle : s₁ ≤ s₂\np : P\nhp : p ∈ s₂\n⊢ ...
[ 639, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 635, 1 ]
Mathlib/Data/Sym/Sym2.lean
Sym2.toRel_symmetric
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.47798\nγ : Type ?u.47801\nr : α → α → Prop\ns : Set (Sym2 α)\nx y : α\n⊢ ToRel s x y → ToRel s y x", "tactic": "simp [eq_swap]" } ]
[ 541, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 541, 1 ]
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean
InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
[ { "state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ ‖x‖ / ‖x + y‖ * ‖x + y‖ = ‖x‖", "state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ Real.cos (angle x (x + y)) * ...
[ 177, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 169, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.attach_val
[]
[ 2407, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2406, 1 ]
Mathlib/Data/Real/EReal.lean
EReal.top_ne_coe
[]
[ 312, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 311, 1 ]
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean
Equiv.Perm.nodup_toList
[ { "state_after": "case pos\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np✝ : Perm α\nx✝ : α\np : Perm α\nx : α\nhx : ↑p x = x\n⊢ Nodup (toList p x)\n\ncase neg\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np✝ : Perm α\nx✝ : α\np : Perm α\nx : α\nhx : ¬↑p x = x\n⊢ Nodup (toList p x)", ...
[ 302, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 272, 1 ]
Mathlib/RingTheory/SimpleModule.lean
IsSimpleModule.nontrivial
[ { "state_after": "R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsSimpleModule R M\nh : ⊥ ≠ ⊤\n⊢ ∃ y, 0 ≠ y", "state_before": "R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsSimpleModule R M\n⊢ ∃ y, 0 ...
[ 61, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 49, 1 ]
Mathlib/Logic/Relation.lean
Relation.TransGen.to_reflTransGen
[ { "state_after": "case single\nα : Type u_1\nβ : Type ?u.18514\nγ : Type ?u.18517\nδ : Type ?u.18520\nr : α → α → Prop\na✝ b✝¹ c d a b✝ b : α\nh : r a b\n⊢ ReflTransGen r a b\n\ncase tail\nα : Type u_1\nβ : Type ?u.18514\nγ : Type ?u.18517\nδ : Type ?u.18520\nr : α → α → Prop\na✝¹ b✝¹ c✝ d a b✝ b c : α\na✝ : Tr...
[ 354, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 351, 1 ]
Mathlib/Computability/Primrec.lean
Primrec.nat_bodd
[ { "state_after": "no goals", "state_before": "α : Type ?u.175087\nβ : Type ?u.175090\nγ : Type ?u.175093\nδ : Type ?u.175096\nσ : Type ?u.175099\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nn : ℕ\n⊢ (id n % 2 == 1) = Nat.bodd n", ...
[ 842, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 840, 1 ]
Mathlib/Data/Fintype/Basic.lean
Fin.univ_castSucc
[ { "state_after": "no goals", "state_before": "α : Type ?u.105001\nβ : Type ?u.105004\nγ : Type ?u.105007\nn : ℕ\n⊢ ¬last n ∈ map castSucc.toEmbedding univ", "tactic": "simp [map_eq_image]" }, { "state_after": "no goals", "state_before": "α : Type ?u.105001\nβ : Type ?u.105004\nγ : Type ?u.10...
[ 843, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 840, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.eventually_pure
[]
[ 1982, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1981, 1 ]
Mathlib/Data/Seq/Seq.lean
Stream'.Seq.destruct_cons
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nf : Stream' (Option α)\nal : IsSeq f\n⊢ instFunctorOption.1\n (fun a' =>\n (a',\n tail\n { val := some a :: ↑{ val := f, property := al },\n property :=\n (_ :\n ∀ {n : ℕ},\n...
[ 247, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 243, 1 ]
Mathlib/Order/Bounds/Basic.lean
IsLeast.insert
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\na✝ b✝ : α\ninst✝ : LinearOrder γ\na b : γ\ns : Set γ\nhs : IsLeast s b\n⊢ IsLeast ({a} ∪ s) (min a b)", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder...
[ 967, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 964, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean
CategoryTheory.Limits.hasEqualizers_of_hasLimit_parallelPair
[]
[ 1178, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1176, 1 ]
Mathlib/MeasureTheory/Integral/Lebesgue.lean
MeasureTheory.lintegral_iUnion_le
[ { "state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1026302\nδ : Type ?u.1026305\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : Countable β\ns : β → Set α\nf : α → ℝ≥0∞\n⊢ (∫⁻ (a : α) in ⋃ (i : β), s i, f a ∂μ) ≤ ∫⁻ (a : α), f a ∂sum fun i => Measure.restrict μ (s i)", "state_before": "α : Type u_2\...
[ 1224, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1221, 1 ]
Mathlib/Data/Set/Prod.lean
Set.offDiag_eq_empty
[ { "state_after": "no goals", "state_before": "α : Type u_1\ns t : Set α\nx : α × α\na : α\n⊢ offDiag s = ∅ ↔ Set.Subsingleton s", "tactic": "rw [← not_nonempty_iff_eq_empty, ← not_nontrivial_iff, offDiag_nonempty.not]" } ]
[ 555, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 554, 1 ]
Mathlib/Logic/Equiv/Fin.lean
finSuccEquiv'_symm_some_below
[]
[ 174, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 172, 1 ]
Mathlib/CategoryTheory/Equivalence.lean
CategoryTheory.Equivalence.essSurj_of_equivalence
[]
[ 689, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 688, 1 ]
Mathlib/Data/Int/Cast/Lemmas.lean
Int.coe_int_dvd
[]
[ 216, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 215, 1 ]
Mathlib/Topology/MetricSpace/Basic.lean
Metric.ball_union_sphere
[]
[ 555, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 554, 1 ]
Mathlib/Algebra/Group/Prod.lean
MonoidHom.comp_coprod
[ { "state_after": "no goals", "state_before": "A : Type ?u.73446\nB : Type ?u.73449\nG : Type ?u.73452\nH : Type ?u.73455\nM : Type u_3\nN : Type u_4\nP : Type u_2\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : CommMonoid P\nf✝ : M →* P\ng✝ : N →* P\nQ : Type u_1\ninst✝ : CommMonoid Q\nh : P →* Q\...
[ 670, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 668, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Basic.lean
fderiv_eq
[]
[ 545, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 544, 1 ]
Mathlib/GroupTheory/GroupAction/SubMulAction.lean
SetLike.forall_smul_mem_iff
[ { "state_after": "no goals", "state_before": "S✝ : Type u'\nT : Type u''\nR✝ : Type u\nM✝ : Type v\ninst✝⁵ : SMul R✝ M✝\ninst✝⁴ : SetLike S✝ M✝\nhS : SMulMemClass S✝ R✝ M✝\ns : S✝\nR : Type u_1\nM : Type u_2\nS : Type u_3\ninst✝³ : Monoid R\ninst✝² : MulAction R M\ninst✝¹ : SetLike S M\ninst✝ : SMulMemClass...
[ 106, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 104, 1 ]
Mathlib/SetTheory/Cardinal/Ordinal.lean
Cardinal.add_one_inj
[]
[ 877, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 876, 1 ]
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean
ContinuousOn.log
[]
[ 403, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 402, 1 ]
Mathlib/RingTheory/UniqueFactorizationDomain.lean
Associates.dvd_count_pow
[ { "state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\na : Associates α\nha : a ≠ 0\np : Associates α\nhp : Irreducible p\nk...
[ 1815, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1812, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Slope.lean
eq_of_slope_eq_zero
[ { "state_after": "no goals", "state_before": "k : Type u_2\nE : Type u_1\nPE : Type u_3\ninst✝³ : Field k\ninst✝² : AddCommGroup E\ninst✝¹ : Module k E\ninst✝ : AddTorsor E PE\nf : k → PE\na b : k\nh : slope f a b = 0\n⊢ f a = f b", "tactic": "rw [← sub_smul_slope_vadd f a b, h, smul_zero, zero_vadd]" ...
[ 82, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 81, 1 ]
Mathlib/Algebra/Order/Monoid/WithTop.lean
WithTop.one_eq_coe
[]
[ 95, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 94, 1 ]
Mathlib/LinearAlgebra/Quotient.lean
Submodule.quotEquivOfEqBot_symm_apply
[]
[ 630, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 628, 1 ]
Mathlib/CategoryTheory/Abelian/Basic.lean
CategoryTheory.Abelian.coimageIsoImage'_hom
[ { "state_after": "no goals", "state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y : C\nf : X ⟶ Y\n⊢ kernel.ι f ≫ factorThruImage f = 0", "tactic": "simp [← cancel_mono (Limits.image.ι f)]" }, { "state_after": "case h\nC : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y : ...
[ 426, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 420, 1 ]
Std/Logic.lean
not_or_intro
[]
[ 293, 83 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 293, 1 ]
Mathlib/Analysis/NormedSpace/AffineIsometry.lean
AffineIsometryEquiv.dist_pointReflection_fixed
[ { "state_after": "no goals", "state_before": "𝕜 : Type u_3\nV : Type u_2\nV₁ : Type ?u.2032361\nV₂ : Type ?u.2032364\nV₃ : Type ?u.2032367\nV₄ : Type ?u.2032370\nP₁ : Type ?u.2032373\nP : Type u_1\nP₂ : Type ?u.2032379\nP₃ : Type ?u.2032382\nP₄ : Type ?u.2032385\ninst✝²¹ : NormedField 𝕜\ninst✝²⁰ : Seminor...
[ 805, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 804, 1 ]
Std/Data/Nat/Gcd.lean
Nat.gcd_mul_right
[ { "state_after": "no goals", "state_before": "m n k : Nat\n⊢ gcd (m * n) (k * n) = gcd m k * n", "tactic": "rw [Nat.mul_comm m n, Nat.mul_comm k n, Nat.mul_comm (gcd m k) n, gcd_mul_left]" } ]
[ 89, 82 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 88, 1 ]
Mathlib/Data/Nat/Factorization/Basic.lean
Nat.factorization_le_of_le_pow
[ { "state_after": "case inl\np b : ℕ\nhb : 0 ≤ p ^ b\n⊢ ↑(factorization 0) p ≤ b\n\ncase inr\nn p b : ℕ\nhb : n ≤ p ^ b\nhn : n ≠ 0\n⊢ ↑(factorization n) p ≤ b", "state_before": "n p b : ℕ\nhb : n ≤ p ^ b\n⊢ ↑(factorization n) p ≤ b", "tactic": "rcases eq_or_ne n 0 with (rfl | hn)" }, { "state_af...
[ 446, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 441, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Basic.lean
HasFDerivAtFilter.isBigO_sub_rev
[]
[ 769, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 763, 1 ]
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean
NonUnitalSubsemiringClass.coeSubtype
[]
[ 73, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 72, 1 ]
Mathlib/Analysis/Convex/Function.lean
concaveOn_const
[]
[ 214, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 213, 1 ]
Mathlib/Order/Heyting/Basic.lean
IsCompl.hnot_eq
[]
[ 1053, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1052, 1 ]
Mathlib/Topology/MetricSpace/Gluing.lean
Metric.glueDist_glued_points
[ { "state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝² : MetricSpace X\ninst✝¹ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\ninst✝ : Nonempty Z\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\np : Z\nthis : (⨅ (q : Z), dist (Φ p) (Φ q) + dist (Ψ p) (Ψ q)) = 0\n⊢ glueDist Φ Ψ ε (Sum.inl (Φ p)) (Sum.inr (Ψ p)) = ε", "s...
[ 90, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 81, 1 ]
Mathlib/Topology/Instances/ENNReal.lean
ENNReal.nhds_coe
[]
[ 89, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/Analysis/NormedSpace/lpSpace.lean
lp.coeFn_sub
[]
[ 385, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 384, 1 ]
Mathlib/Data/Set/Intervals/Pi.lean
Set.pi_univ_Icc
[ { "state_after": "no goals", "state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → Preorder (α i)\nx y✝ y : (i : ι) → α i\n⊢ (y ∈ pi univ fun i => Icc (x i) (y✝ i)) ↔ y ∈ Icc x y✝", "tactic": "simp [Pi.le_def, forall_and]" } ]
[ 47, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 46, 1 ]
Mathlib/Data/Set/Pairwise/Basic.lean
Set.PairwiseDisjoint.elim'
[]
[ 336, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 334, 1 ]
Mathlib/Data/Multiset/Nodup.lean
Multiset.inj_on_of_nodup_map
[]
[ 145, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 143, 1 ]
Mathlib/Topology/ExtendFrom.lean
continuousOn_extendFrom
[ { "state_after": "X : Type u_2\nY : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : RegularSpace Y\nf : X → Y\nA B : Set X\nhB : B ⊆ closure A\nhf : ∀ (x : X), x ∈ B → ∃ y, Tendsto f (𝓝[A] x) (𝓝 y)\nφ : X → Y := extendFrom A f\n⊢ ContinuousOn φ B", "state_before": "X : Type u_2...
[ 84, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 66, 1 ]
Mathlib/LinearAlgebra/TensorProduct.lean
TensorProduct.smul_zero
[]
[ 245, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 244, 11 ]
Mathlib/Data/Multiset/Lattice.lean
Multiset.le_inf
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderTop α\ns : Multiset α\na : α\n⊢ a ≤ inf 0 ↔ ∀ (b : α), b ∈ 0 → a ≤ b", "tactic": "simp" }, { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderT...
[ 147, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 145, 1 ]
Mathlib/Topology/Algebra/ConstMulAction.lean
ContinuousAt.const_smul
[]
[ 100, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 98, 8 ]
Mathlib/LinearAlgebra/Alternating.lean
AlternatingMap.zero_apply
[]
[ 353, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 352, 1 ]
Mathlib/Order/Filter/Pointwise.lean
Filter.vsub_neBot_iff
[]
[ 1113, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1112, 1 ]
Mathlib/Order/Disjointed.lean
disjointed_succ
[]
[ 63, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 62, 1 ]
Mathlib/Data/Set/Intervals/Basic.lean
Set.Ioi_subset_Ici
[]
[ 608, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 607, 1 ]
Mathlib/Topology/UniformSpace/Basic.lean
Uniform.continuous_iff'_left
[]
[ 1966, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1964, 1 ]
Mathlib/Topology/StoneCech.lean
stoneCech_hom_ext
[ { "state_after": "α : Type u\ninst✝⁵ : TopologicalSpace α\nγ : Type u\ninst✝⁴ : TopologicalSpace γ\ninst✝³ : T2Space γ\ninst✝² : CompactSpace γ\nγ' : Type u\ninst✝¹ : TopologicalSpace γ'\ninst✝ : T2Space γ'\nf : α → γ\nhf : Continuous f\ng₁ g₂ : StoneCech α → γ'\nh₁ : Continuous g₁\nh₂ : Continuous g₂\nh : g₁ ∘...
[ 291, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 287, 1 ]
Mathlib/SetTheory/ZFC/Basic.lean
ZFSet.singleton_nonempty
[]
[ 934, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 933, 1 ]
Mathlib/Data/Nat/GCD/Basic.lean
Nat.coprime_add_self_left
[ { "state_after": "no goals", "state_before": "m n : ℕ\n⊢ coprime (m + n) n ↔ coprime m n", "tactic": "rw [coprime, coprime, gcd_add_self_left]" } ]
[ 144, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 143, 1 ]
Mathlib/Data/Complex/Exponential.lean
Complex.sinh_conj
[ { "state_after": "x y : ℂ\n⊢ ↑(starRingEnd ℂ) (exp x - exp (-x)) / 2 = ↑(starRingEnd ℂ) (exp x - exp (-x)) / ↑(starRingEnd ℂ) 2", "state_before": "x y : ℂ\n⊢ sinh (↑(starRingEnd ℂ) x) = ↑(starRingEnd ℂ) (sinh x)", "tactic": "rw [sinh, ← RingHom.map_neg, exp_conj, exp_conj, ← RingHom.map_sub, sinh, map_d...
[ 647, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 644, 1 ]
Mathlib/Algebra/IndicatorFunction.lean
Set.mulSupport_mulIndicator
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.7242\nι : Type ?u.7245\nM : Type u_2\nN : Type ?u.7251\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g : α → M\na x : α\n⊢ x ∈ mulSupport (mulIndicator s f) ↔ x ∈ s ∩ mulSupport f", "tactic": "simp [Function.mem_mulSupport, mulIndi...
[ 151, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 149, 1 ]
Mathlib/Topology/Order/Basic.lean
pi_Iio_mem_nhds
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁷ : TopologicalSpace α\ninst✝⁶ : LinearOrder α\ninst✝⁵ : OrderTopology α\nι : Type u_2\nπ : ι → Type u_1\ninst✝⁴ : Finite ι\ninst✝³ : (i : ι) → LinearOrder (π i)\ninst✝² : (i : ι) → TopologicalSpace (π i)\ninst✝¹ : ∀ (i : ι), OrderTopology (π i)\na b x ...
[ 1488, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1486, 1 ]
Std/Data/List/Lemmas.lean
List.erase_cons
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : b = a\n⊢ List.erase (b :: l) a = if b = a then l else b :: List.erase l a", "tactic": "simp [List.erase, h]" }, { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : Deci...
[ 1034, 62 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1031, 1 ]
Mathlib/Analysis/Convex/Body.lean
ConvexBody.coe_nsmul
[]
[ 113, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 111, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Combination.lean
Finset.affineCombination_apply_const
[ { "state_after": "no goals", "state_before": "k : Type u_1\nV : Type u_4\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.247728\ns₂ : Finset ι₂\nw : ι → k\np : P\nh : ∑ i in s, w i = 1\n⊢ ↑(affineCombination k s fun x...
[ 411, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 409, 1 ]
Mathlib/RingTheory/MatrixAlgebra.lean
MatrixEquivTensor.right_inv
[ { "state_after": "R : Type u\ninst✝⁴ : CommSemiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\nM : Matrix n n A\n⊢ ∑ x : n × n, M x.fst x.snd • Matrix.map (fun i' j' => if x.fst = i' ∧ x.snd = j' then 1 else 0) ↑(algebraMap R A) = M", "st...
[ 129, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 121, 1 ]
Mathlib/Topology/Algebra/Monoid.lean
Continuous.units_map
[]
[ 712, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 710, 1 ]
Mathlib/Topology/DenseEmbedding.lean
DenseEmbedding.separableSpace
[]
[ 265, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 264, 11 ]
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
MeasureTheory.SimpleFunc.snorm'_eq
[ { "state_after": "α : Type u_1\nβ : Type ?u.1108791\nι : Type ?u.1108794\nE : Type ?u.1108797\nF : Type u_2\n𝕜 : Type ?u.1108803\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nμ✝ : Measure α\np✝ : ℝ≥0∞\np : ℝ\nf : α →ₛ F\nμ : Measure α\nh_map : (fun a => ↑‖↑f a‖₊ ^ p)...
[ 310, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 306, 11 ]
Mathlib/GroupTheory/Submonoid/Operations.lean
Submonoid.mem_map_equiv
[]
[ 936, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 934, 1 ]
Mathlib/MeasureTheory/Function/LpSpace.lean
MeasureTheory.Lp.lintegral_rpow_tsum_coe_nnnorm_sub_le_tsum
[ { "state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.8169395\nG : Type ?u.8169398\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 : ℕ → α → E\nhf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ\np : ℝ\nhp1...
[ 1396, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1364, 9 ]
Mathlib/FieldTheory/Subfield.lean
Subfield.mem_iSup_of_directed
[ { "state_after": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\nι : Sort u_1\nhι : Nonempty ι\nS : ι → Subfield K\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : K\n⊢ (x ∈ ⨆ (i : ι), S i) → ∃ i, x ∈ S i", "state_before": "K : Type u\nL : Type v\nM : Type w\ninst✝² : F...
[ 834, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 818, 1 ]
Mathlib/Topology/Basic.lean
ContinuousAt.congr
[]
[ 1603, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1601, 1 ]
Mathlib/GroupTheory/Subgroup/Basic.lean
SubgroupClass.inclusion_mk
[]
[ 326, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 325, 1 ]
Mathlib/Data/Vector/Basic.lean
Vector.tail_nil
[]
[ 182, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 181, 1 ]
Mathlib/Data/Set/NAry.lean
Set.image2_comm
[ { "state_after": "no goals", "state_before": "α : Type u_2\nα' : Type ?u.40713\nβ : Type u_3\nβ' : Type ?u.40719\nγ : Type u_1\nγ' : Type ?u.40725\nδ : Type ?u.40728\nδ' : Type ?u.40731\nε : Type ?u.40734\nε' : Type ?u.40737\nζ : Type ?u.40740\nζ' : Type ?u.40743\nν : Type ?u.40746\nf f' : α → β → γ\ng✝ g' ...
[ 317, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 316, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.natDegree_pow
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn✝ : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np✝ q p : R[X]\nn : ℕ\nhp0 : p = 0\nhn0 : n = 0\n⊢ natDegree (p ^ n) = n * natDegree p", "tactic": "simp [hp0, hn0]" }, { "state_after": "R : Type u\nS...
[ 159, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 153, 1 ]
Mathlib/Topology/Algebra/Order/Compact.lean
IsCompact.continuous_sInf
[]
[ 409, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 407, 1 ]
Mathlib/Algebra/GroupWithZero/Divisibility.lean
dvd_and_not_dvd_iff
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\nx y : α\nx✝ : x ∣ y ∧ ¬y ∣ x\nd : α\nhd : y = x * d\nhyx : ¬y ∣ x\nhx0 : x = 0\n⊢ False", "tactic": "simp [hx0] at hyx" }, { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : Cance...
[ 98, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 85, 1 ]
Mathlib/Data/List/Sublists.lean
List.sublists_nil
[]
[ 108, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 107, 1 ]
Std/Classes/LawfulMonad.lean
SatisfiesM.bind_pre
[]
[ 180, 51 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 178, 11 ]
Mathlib/GroupTheory/Torsion.lean
Monoid.not_isTorsionFree_iff
[ { "state_after": "no goals", "state_before": "G : Type u_1\nH : Type ?u.209046\ninst✝ : Monoid G\n⊢ ¬IsTorsionFree G ↔ ∃ g, g ≠ 1 ∧ IsOfFinOrder g", "tactic": "simp_rw [IsTorsionFree, Ne.def, not_forall, Classical.not_not, exists_prop]" } ]
[ 369, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 1 ]
Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean
Ideal.hasBasis_nhds_adic
[ { "state_after": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nx : R\nthis : TopologicalSpace R := adicTopology I\n⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (fun y => x + y) '' ↑(I ^ n)", "state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nx : R\n⊢ HasBasis (𝓝 x) (fun _n => True) fun n => (...
[ 115, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 110, 1 ]
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean
StructureGroupoid.liftPropWithinAt_self
[]
[ 226, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 225, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Basic.lean
support_fderiv_subset
[ { "state_after": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\n⊢ f =ᶠ[𝓝 x] 0 → fderiv 𝕜 f x = 0", "state_before": "𝕜 : Type u_3\nE : Type...
[ 1156, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1154, 1 ]
Mathlib/GroupTheory/Perm/Basic.lean
Equiv.mul_swap_eq_swap_mul
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nf : Perm α\nx y : α\n⊢ f * swap x y = swap (↑f x) (↑f y) * f", "tactic": "rw [swap_mul_eq_mul_swap, Perm.inv_apply_self, Perm.inv_apply_self]" } ]
[ 530, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 529, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_atBot_add_const_right
[]
[ 826, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 824, 1 ]