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Mathlib/GroupTheory/SpecificGroups/Dihedral.lean
DihedralGroup.r_mul_sr
[]
[ 88, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 87, 1 ]
Mathlib/RingTheory/GradedAlgebra/Basic.lean
GradedRing.mem_support_iff
[]
[ 127, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 125, 1 ]
Mathlib/CategoryTheory/Arrow.lean
CategoryTheory.Arrow.inv_left_hom_right
[ { "state_after": "no goals", "state_before": "T : Type u\ninst✝¹ : Category T\nf g : Arrow T\nsq : f ⟶ g\ninst✝ : IsIso sq\n⊢ inv sq.left ≫ f.hom ≫ sq.right = g.hom", "tactic": "simp only [w, IsIso.inv_comp_eq]" } ]
[ 222, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 221, 1 ]
Mathlib/Data/Polynomial/Degree/Definitions.lean
Polynomial.card_supp_le_succ_natDegree
[ { "state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\n⊢ card (support p) ≤ card (range (natDegree p + 1))", "state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\n⊢ card (support p) ≤ natDegree p + 1", "tactic": ...
[ 494, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 492, 1 ]
Mathlib/Analysis/Asymptotics/Theta.lean
Asymptotics.IsLittleO.trans_isTheta
[]
[ 112, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 110, 1 ]
Mathlib/Data/List/Basic.lean
List.lookmap_cons_some
[ { "state_after": "ι : Type ?u.343019\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option α\na b : α\nl : List α\nh : f a = some b\n⊢ (match f a with\n | some b => b :: l\n | none => lookmap.go f l (Array.push #[] a)) =\n b :: l", "state_before": "ι : Type ?u.343019\nα : ...
[ 3303, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3300, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean
midpoint_vsub_left
[]
[ 109, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 108, 1 ]
Std/Data/Int/DivMod.lean
Int.mod_add_div'
[ { "state_after": "m k : Int\n⊢ mod m k + k * div m k = m", "state_before": "m k : Int\n⊢ mod m k + div m k * k = m", "tactic": "rw [Int.mul_comm]" }, { "state_after": "no goals", "state_before": "m k : Int\n⊢ mod m k + k * div m k = m", "tactic": "apply mod_add_div" } ]
[ 393, 39 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 392, 1 ]
Mathlib/Logic/Encodable/Basic.lean
Encodable.mem_decode₂
[]
[ 201, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 200, 1 ]
Mathlib/RingTheory/Ideal/Cotangent.lean
Ideal.map_toCotangent_ker
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nS' : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : CommSemiring S\ninst✝⁴ : Algebra S R\ninst✝³ : CommSemiring S'\ninst✝² : Algebra S' R\ninst✝¹ : Algebra S S'\ninst✝ : IsScalarTower S S' R\nI : Ideal R\n⊢ Submodule.map (Submodule.subtype I) (Lin...
[ 70, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 68, 1 ]
Mathlib/GroupTheory/Sylow.lean
Sylow.coe_subtype
[]
[ 137, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 136, 1 ]
Mathlib/Dynamics/OmegaLimit.lean
omegaLimit_subset_of_tendsto
[ { "state_after": "τ : Type u_1\nα : Type u_3\nβ : Type u_2\nι : Type ?u.22929\ninst✝ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\nm : τ → τ\nf₁ f₂ : Filter τ\nhf : Tendsto m f₁ f₂\nu : Set τ\nhu : u ∈ f₂\n⊢ closure (image2 (fun t x => ϕ (m t) x) (m ⁻¹' u) s) ⊆ closure (image2 ϕ u s)", ...
[ 81, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 77, 1 ]
Mathlib/Data/Polynomial/Monic.lean
Polynomial.Monic.natDegree_eq_zero_iff_eq_one
[ { "state_after": "case mp\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhp : Monic p\nh : natDegree p = 0\n⊢ p = 1\n\ncase mpr\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhp : Monic p\nh : p = 1\n⊢ natDegree p = 0", "sta...
[ 164, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 155, 1 ]
Mathlib/Data/Set/Image.lean
Set.mem_range_of_mem_image
[]
[ 704, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 703, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean
CategoryTheory.IsKernelPair.cancel_right_of_mono
[ { "state_after": "no goals", "state_before": "C : Type u\ninst✝¹ : Category C\nR X Y Z : C\nf : X ⟶ Y\na b : R ⟶ X\nf₁ : X ⟶ Y\nf₂ : Y ⟶ Z\ninst✝ : Mono f₂\nbig_k : IsKernelPair (f₁ ≫ f₂) a b\n⊢ a ≫ f₁ = b ≫ f₁", "tactic": "rw [← cancel_mono f₂, assoc, assoc, big_k.w]" } ]
[ 136, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 134, 1 ]
Mathlib/LinearAlgebra/PiTensorProduct.lean
PiTensorProduct.lift.unique
[]
[ 429, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 427, 1 ]
Std/Data/Int/Lemmas.lean
Int.eq_succ_of_zero_lt
[ { "state_after": "a : Int\nh✝ : 0 < a\nn : Nat\nh : ↑(n + 1) = a\n⊢ a = ↑(succ n)", "state_before": "a : Int\nh✝ : 0 < a\nn : Nat\nh : ↑(1 + n) = a\n⊢ a = ↑(succ n)", "tactic": "rw [Nat.add_comm] at h" }, { "state_after": "no goals", "state_before": "a : Int\nh✝ : 0 < a\nn : Nat\nh : ↑(n + 1...
[ 588, 47 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 586, 1 ]
Mathlib/Data/FunLike/Basic.lean
FunLike.congr
[]
[ 217, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 216, 11 ]
Mathlib/Analysis/Analytic/Basic.lean
FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp
[ { "state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np✝ : FormalMultilinearSerie...
[ 369, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 362, 1 ]
Mathlib/Analysis/SpecificLimits/Normed.lean
tsum_geometric_of_norm_lt_1
[]
[ 302, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 301, 1 ]
Mathlib/Data/Finset/Lattice.lean
Finset.max_le
[]
[ 1232, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1230, 11 ]
Mathlib/Algebra/GroupPower/Order.lean
one_lt_pow_iff
[]
[ 250, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 249, 1 ]
Mathlib/Algebra/BigOperators/Finprod.lean
finprod_mem_mul_diff'
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.362387\nι : Type ?u.362390\nG : Type ?u.362393\nM : Type u_2\nN : Type ?u.362399\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\nhst : s ⊆ t\nht : Set.Finite (t ∩ mulSupport f)\n⊢ ((∏ᶠ (i : α) (_ : i ∈ s...
[ 1035, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1033, 1 ]
Mathlib/Algebra/Algebra/Hom.lean
AlgHom.id_comp
[]
[ 354, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 353, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.iInf_sets_eq_finite
[ { "state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.101230\nι✝ : Sort x\nf✝ g : Filter α\ns t : Set α\nι : Type u_1\nf : ι → Filter α\n⊢ Directed (fun x x_1 => x ≥ x_1) fun t => ⨅ (i : ι) (_ : i ∈ t), f i", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.101230\nι✝ : S...
[ 839, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 836, 1 ]
Mathlib/Data/Finset/Lattice.lean
Finset.sup_erase_bot
[ { "state_after": "F : Type ?u.58882\nα : Type u_1\nβ : Type ?u.58888\nγ : Type ?u.58891\nι : Type ?u.58894\nκ : Type ?u.58897\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ns✝ s₁ s₂ : Finset β\nf g : β → α\na✝ : α\ninst✝ : DecidableEq α\ns : Finset α\na : α\nha : a ∈ s\n⊢ id a ≤ sup (erase s ⊥) id", "stat...
[ 191, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 187, 1 ]
Mathlib/Data/List/Sublists.lean
List.sublistsAux_eq_bind
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nr : List (List α)\n⊢ sublistsAux a [] = List.bind [] fun l => [l, a :: l]", "tactic": "simp [sublistsAux]" }, { "state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nr✝ r : List (List α)\nl : List α\nih...
[ 140, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 133, 1 ]
Mathlib/Data/Finset/LocallyFinite.lean
Finset.uIcc_subset_Icc
[ { "state_after": "ι : Type ?u.185526\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nha : a₂ ≤ a₁ ∧ a₁ ≤ b₂\nhb : a₂ ≤ b₁ ∧ b₁ ≤ b₂\n⊢ [[a₁, b₁]] ⊆ Icc a₂ b₂", "state_before": "ι : Type ?u.185526\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : LocallyFiniteOrder α\na a₁ ...
[ 940, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 938, 1 ]
Std/Data/Rat/Lemmas.lean
Rat.maybeNormalize_eq
[ { "state_after": "num : Int\nden g : Nat\nden_nz : den / g ≠ 0\nreduced : Nat.coprime (Int.natAbs (Int.div num ↑g)) (den / g)\n⊢ (if hg : g = 1 then mk' num den else mk' (Int.div num ↑g) (den / g)) = mk' (Int.div num ↑g) (den / g)", "state_before": "num : Int\nden g : Nat\nden_nz : den / g ≠ 0\nreduced : Na...
[ 13, 8 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 8, 9 ]
Mathlib/GroupTheory/Commensurable.lean
Commensurable.eq
[]
[ 118, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 115, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.roots_X_pow
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn✝ : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nn : ℕ\n⊢ roots (X ^ n) = n • {0}", "tactic": "rw [roots_pow, roots_X]" } ]
[ 717, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 716, 1 ]
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
MeasureTheory.AEFinStronglyMeasurable.mul
[]
[ 1877, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1874, 11 ]
Mathlib/Computability/Primrec.lean
PrimrecPred.not
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.132671\nγ : Type ?u.132674\nδ : Type ?u.132677\nσ : Type ?u.132680\ninst✝⁵ : Primcodable α\ninst✝⁴ : Primcodable β\ninst✝³ : Primcodable γ\ninst✝² : Primcodable δ\ninst✝¹ : Primcodable σ\np : α → Prop\ninst✝ : DecidablePred p\nhp : Prim...
[ 729, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 727, 1 ]
Mathlib/Data/Ordmap/Ordset.lean
Ordnode.Valid'.glue_aux
[ { "state_after": "case nil\nα : Type u_1\ninst✝ : Preorder α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhr : Valid' o₁ r o₂\nhl : Valid' o₁ nil o₂\nsep : All (fun x => All (fun y => x < y) r) nil\nbal : BalancedSz (size nil) (size r)\n⊢ Valid' o₁ (glue nil r) o₂ ∧ size (glue nil r) = size nil + size r\n\nc...
[ 1449, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1419, 1 ]
Mathlib/Dynamics/PeriodicPts.lean
Function.IsPeriodicPt.isFixedPt
[]
[ 82, 5 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 81, 11 ]
Mathlib/Topology/Category/TopCat/Limits/Products.lean
TopCat.piIsoPi_hom_apply
[ { "state_after": "J : Type v\ninst✝ : SmallCategory J\nι : Type v\nα : ι → TopCatMax\ni : ι\nx : ↑(∏ α)\nthis : (piIsoPi α).inv ≫ Pi.π α i = piπ α i\n⊢ (forget TopCat).map (piIsoPi α).hom x i = (forget TopCat).map (Pi.π α i) x", "state_before": "J : Type v\ninst✝ : SmallCategory J\nι : Type v\nα : ι → TopCa...
[ 86, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 82, 1 ]
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean
MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero
[]
[ 478, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 474, 1 ]
Mathlib/Data/Polynomial/UnitTrinomial.lean
Polynomial.IsUnitTrinomial.irreducible_of_coprime
[ { "state_after": "p q✝ : ℤ[X]\nhp : IsUnitTrinomial p\nh : ∀ (q : ℤ[X]), q ∣ p → q ∣ mirror p → IsUnit q\nq : ℤ[X]\nhpq : p * mirror p = q * mirror q\n⊢ q = p ∨ q = -p ∨ q = mirror p ∨ q = -mirror p", "state_before": "p q : ℤ[X]\nhp : IsUnitTrinomial p\nh : ∀ (q : ℤ[X]), q ∣ p → q ∣ mirror p → IsUnit q\n⊢ I...
[ 345, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 313, 1 ]
Mathlib/RingTheory/Finiteness.lean
RingHom.Finite.of_surjective
[]
[ 688, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 686, 1 ]
Mathlib/Data/List/Cycle.lean
Cycle.toFinset_toMultiset
[]
[ 805, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 804, 1 ]
Mathlib/Topology/Maps.lean
QuotientMap.comp
[ { "state_after": "no goals", "state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.137449\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ng : β → γ\nf : α → β\nhg : QuotientMap g\nhf : QuotientMap f\n⊢ inst✝¹ = coinduced (g...
[ 297, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 296, 11 ]
Mathlib/Algebra/Hom/Group.lean
NeZero.of_injective
[ { "state_after": "α : Type ?u.1488\nβ : Type ?u.1491\nM✝ : Type ?u.1494\nN : Type ?u.1497\nP : Type ?u.1500\nG : Type ?u.1503\nH : Type ?u.1506\nF : Type u_3\nR : Type u_1\nM : Type u_2\ninst✝³ : Zero R\nr : R\ninst✝² : NeZero r\ninst✝¹ : Zero M\ninst✝ : ZeroHomClass F R M\nf : F\nhf : Function.Injective ↑f\n⊢ ...
[ 121, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/Data/Polynomial/Mirror.lean
Polynomial.mirror_trailingCoeff
[ { "state_after": "no goals", "state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\n⊢ trailingCoeff (mirror p) = leadingCoeff p", "tactic": "rw [leadingCoeff, trailingCoeff, mirror_natTrailingDegree, coeff_mirror,\n revAt_le (Nat.le_add_left _ _), add_tsub_cancel_right]" } ]
[ 156, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 154, 1 ]
Mathlib/Algebra/Order/Hom/Ring.lean
OrderRingHom.coe_id
[]
[ 276, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 275, 1 ]
Mathlib/Data/Dfinsupp/Basic.lean
Dfinsupp.comapDomain_apply
[]
[ 1318, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1316, 1 ]
Mathlib/CategoryTheory/IsConnected.lean
CategoryTheory.induct_on_objects
[ { "state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : IsPreconnected J\np : Set J\nj₀ : J\nh0 : j₀ ∈ p\nh1 : ∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)\nj : J\naux : ∀ (j₁ j₂ : J), (j₁ ⟶ j₂) → { down := j₁ ∈ p } = { down := j₂ ∈ p } :=\n fun j₁ j₂ f => congrArg ULift.u...
[ 157, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 153, 1 ]
Mathlib/Data/Matrix/Hadamard.lean
Matrix.hadamard_assoc
[]
[ 73, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 72, 1 ]
Mathlib/Topology/Constructions.lean
openEmbedding_inl
[]
[ 910, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 909, 1 ]
Mathlib/Data/MvPolynomial/Expand.lean
MvPolynomial.rename_expand
[ { "state_after": "no goals", "state_before": "σ : Type u_1\nτ : Type u_3\nR : Type u_2\nS : Type ?u.281360\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : σ → τ\np : ℕ\nφ : MvPolynomial σ R\n⊢ ↑(rename f) (↑(expand p) φ) = ↑(expand p) (↑(rename f) φ)", "tactic": "simp [expand, bind₁_rename, rename...
[ 89, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 87, 1 ]
Mathlib/Analysis/Convex/Quasiconvex.lean
AntitoneOn.quasiconcaveOn
[]
[ 201, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 200, 1 ]
Mathlib/Data/Complex/Exponential.lean
Complex.sinh_mul_I
[ { "state_after": "no goals", "state_before": "x y : ℂ\n⊢ sinh (x * I) = sin x * I", "tactic": "rw [← mul_right_inj' (two_ne_zero' ℂ), two_sinh, ← mul_assoc, two_sin, mul_assoc, I_mul_I,\n mul_neg_one, neg_sub, neg_mul_eq_neg_mul]" } ]
[ 814, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 812, 1 ]
Mathlib/CategoryTheory/Sites/CompatiblePlus.lean
CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv
[ { "state_after": "no goals", "state_before": "C : Type u\ninst✝⁸ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁷ : Category D\nE : Type w₂\ninst✝⁶ : Category E\nF : D ⥤ E\ninst✝⁵ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁴ : ∀ (α β : Ty...
[ 221, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 220, 1 ]
Mathlib/Analysis/LocallyConvex/Basic.lean
Balanced.sub
[ { "state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.43430\nE : Type u_2\nι : Sort ?u.43436\nκ : ι → Sort ?u.43441\ninst✝² : SeminormedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns s₁ s₂ t t₁ t₂ : Set E\nhs : Balanced 𝕜 s\nht : Balanced 𝕜 t\n⊢ Balanced 𝕜 (s + -t)", "state_before": "𝕜 : Type u_1\n𝕝 ...
[ 248, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 246, 1 ]
Mathlib/Data/Real/Basic.lean
Real.mk_eq
[]
[ 306, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 305, 1 ]
Mathlib/Topology/Order/Hom/Esakia.lean
PseudoEpimorphism.cancel_left
[ { "state_after": "no goals", "state_before": "F : Type ?u.72756\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.72768\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\ng : PseudoEpimorphism β γ\nf₁ f₂ : PseudoEpimorphism α β\nhg : Injective ↑g\nh : comp g f₁ = comp g...
[ 219, 81 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 217, 1 ]
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean
IsBoundedBilinearMap.map_sub_left
[]
[ 391, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 389, 1 ]
Mathlib/Topology/Instances/AddCircle.lean
AddCircle.coe_nsmul
[]
[ 155, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 154, 1 ]
Mathlib/SetTheory/Cardinal/Basic.lean
Cardinal.lift_iSup_le_lift_iSup
[ { "state_after": "α β : Type u\nι : Type v\nι' : Type v'\nf : ι → Cardinal\nf' : ι' → Cardinal\nhf : BddAbove (range f)\nhf' : BddAbove (range f')\ng : ι → ι'\nh : ∀ (i : ι), lift (f i) ≤ lift (f' (g i))\n⊢ (⨆ (i : ι), lift (f i)) ≤ ⨆ (i : ι'), lift (f' i)", "state_before": "α β : Type u\nι : Type v\nι' : T...
[ 1217, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1213, 1 ]
Mathlib/MeasureTheory/Integral/Lebesgue.lean
MeasureTheory.lintegral_eq_top_of_measure_eq_top_pos
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.963625\nγ : Type ?u.963628\nδ : Type ?u.963631\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : AEMeasurable f\nhμf : 0 < ↑↑μ {x | f x = ⊤}\n⊢ ⊤ = ⊤ * ↑↑μ {x | ⊤ ≤ f x}", "tactic": "simp [mul_eq_top, hμf.ne.symm]" } ]
[ 844, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 839, 1 ]
Mathlib/Order/Category/LinOrdCat.lean
linOrdCat_dual_comp_forget_to_latCat
[]
[ 104, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 102, 1 ]
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean
MeasurableEquiv.symm_mulRight
[]
[ 157, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/Data/Matrix/Kronecker.lean
Matrix.add_kronecker
[]
[ 307, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 305, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_atTop_atTop_of_monotone
[]
[ 1299, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1294, 1 ]
Mathlib/MeasureTheory/Function/LpSeminorm.lean
MeasureTheory.exists_Lp_half
[ { "state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.3035161\nG : Type ?u.3035164\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np δ : ℝ≥0∞\nhδ : δ ≠ 0\nthis : Tendsto (fun η => LpAddConst p * (η + η)...
[ 852, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 836, 1 ]
Mathlib/CategoryTheory/Limits/Opposites.lean
CategoryTheory.Limits.hasProductsOfShape_of_opposite
[]
[ 359, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 356, 1 ]
Mathlib/ModelTheory/Substructures.lean
FirstOrder.Language.Hom.eq_of_eqOn_dense
[]
[ 895, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 894, 1 ]
Mathlib/Data/List/ProdSigma.lean
List.mem_product
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type u_2\nl₁ : List α\nl₂ : List β\na : α\nb : β\n⊢ (a, b) ∈ l₁ ×ˢ l₂ ↔ a ∈ l₁ ∧ b ∈ l₂", "tactic": "simp_all [SProd.sprod, product, mem_bind, mem_map, Prod.ext_iff, exists_prop, and_left_comm,\n exists_and_left, exists_eq_left, exists_eq_...
[ 50, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 47, 1 ]
Mathlib/RingTheory/Ideal/LocalRing.lean
isUnit_of_map_unit
[]
[ 246, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 245, 1 ]
Mathlib/NumberTheory/Padics/PadicIntegers.lean
PadicInt.padic_norm_e_of_padicInt
[ { "state_after": "no goals", "state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz : ℤ_[p]\n⊢ ‖↑z‖ = ‖z‖", "tactic": "simp [norm_def]" } ]
[ 301, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 301, 1 ]
Mathlib/Data/Matrix/Basic.lean
RingHom.mapMatrix_id
[]
[ 1537, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1536, 1 ]
Mathlib/Topology/Sequences.lean
continuous_iff_seqContinuous
[]
[ 232, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 230, 1 ]
Mathlib/Algebra/BigOperators/Basic.lean
Multiset.disjoint_finset_sum_right
[ { "state_after": "no goals", "state_before": "ι : Type ?u.902298\nβ✝ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β✝\nβ : Type u_1\ni : Finset β\nf : β → Multiset α\na : Multiset α\n⊢ Disjoint a (Finset.sum i f) ↔ ∀ (b : β), b ∈ i → Disjoint a (f b)", "tactic": "simpa only [d...
[ 2087, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2085, 1 ]
Mathlib/Data/Set/Intervals/ProjIcc.lean
Set.strictMonoOn_projIcc
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.10840\ninst✝ : LinearOrder α\na b : α\nh : a ≤ b\nx✝ x : α\nhx : x ∈ Icc a b\ny : α\nhy : y ∈ Icc a b\nhxy : x < y\n⊢ projIcc a b h x < projIcc a b h y", "tactic": "simpa only [projIcc_of_mem, hx, hy]" } ]
[ 100, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 99, 1 ]
Mathlib/Data/Set/Prod.lean
Set.offDiag_inter
[ { "state_after": "α : Type u_1\ns t : Set α\nx✝ : α × α\na : α\nx : α × α\n⊢ (x.fst ∈ s ∧ x.fst ∈ t) ∧ (x.snd ∈ s ∧ x.snd ∈ t) ∧ x.fst ≠ x.snd ↔\n (x.fst ∈ s ∧ x.snd ∈ s ∧ x.fst ≠ x.snd) ∧ x.fst ∈ t ∧ x.snd ∈ t ∧ x.fst ≠ x.snd", "state_before": "α : Type u_1\ns t : Set α\nx✝ : α × α\na : α\nx : α × α\n⊢ ...
[ 599, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 596, 1 ]
Mathlib/Algebra/BigOperators/Pi.lean
Prod.fst_prod
[]
[ 134, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 133, 1 ]
Mathlib/Algebra/MonoidAlgebra/Basic.lean
AddMonoidAlgebra.lift_single
[ { "state_after": "no goals", "state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.2710730\ninst✝⁵ : CommSemiring k\ninst✝⁴ : AddMonoid G\nA : Type u₃\ninst✝³ : Semiring A\ninst✝² : Algebra k A\nB : Type ?u.2710767\ninst✝¹ : Semiring B\ninst✝ : Algebra k B\nF : Multiplicative G →* A\na : G\nb : k\n⊢ ↑(↑(li...
[ 1995, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1993, 1 ]
Mathlib/SetTheory/Ordinal/Arithmetic.lean
Ordinal.add_mul_limit
[]
[ 2492, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2491, 1 ]
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean
contDiffOn_ext_coord_change
[]
[ 1253, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1250, 1 ]
Mathlib/Order/Minimal.lean
inter_maximals_subset
[]
[ 169, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 168, 1 ]
Mathlib/Data/Multiset/LocallyFinite.lean
Multiset.left_not_mem_Ioc
[]
[ 135, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 134, 1 ]
Mathlib/Analysis/InnerProductSpace/Basic.lean
inner_self_conj
[]
[ 648, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 648, 1 ]
Mathlib/Topology/Order/Basic.lean
exists_countable_dense_no_bot_top
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderTopology α\ninst✝² : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf : α → β\ninst✝¹ : SeparableSpace α\ninst✝ : Nontrivial α\n⊢ ∃ s, Set.Countable s ∧ D...
[ 2614, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2612, 1 ]
Mathlib/RingTheory/Coprime/Basic.lean
IsCoprime.mul_add_left_left
[ { "state_after": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime (x + y * z) y", "state_before": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime (y * z + x) y", "tactic": "rw [add_comm]" }, { "state_after": "no goals", "state_be...
[ 305, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 303, 1 ]
Mathlib/GroupTheory/Perm/Support.lean
Equiv.Perm.mem_support
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx : α\n⊢ x ∈ support f ↔ ↑f x ≠ x", "tactic": "rw [support, mem_filter, and_iff_right (mem_univ x)]" } ]
[ 294, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 293, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.comap_sup
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.256139\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\n⊢ comap m (g₁ ⊔ g₂) = comap m g₁ ⊔ comap m g₂", "tactic": "rw [sup_eq_iSup, comap_iSup, iSup_bool_eq, Boo...
[ 2244, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2243, 1 ]
Mathlib/ModelTheory/Order.lean
FirstOrder.Language.realize_denselyOrdered_iff
[ { "state_after": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝ : Preorder M\n⊢ (∀ (a a_1 : M),\n Fin.snoc (Fin.snoc default a) a_1 0 < Fin.snoc (Fin.snoc default a) a_1 1 →\n ∃ a_3,\n Fin.snoc (Fin.snoc (Fin.snoc default a) a_1) a_3 0 < Fin.snoc (Fin.snoc (Fin.snoc default a) a_1) a_...
[ 271, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 264, 1 ]
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
tsum_eq_zero_add'
[ { "state_after": "no goals", "state_before": "α : Type ?u.460879\nβ : Type ?u.460882\nγ : Type ?u.460885\nδ : Type ?u.460888\ninst✝⁶ : AddCommGroup α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalAddGroup α\nf✝ g : β → α\na a₁ a₂ : α\nM : Type u_1\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\n...
[ 976, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 973, 1 ]
Mathlib/Algebra/Associated.lean
Prime.associated_of_dvd
[]
[ 615, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 613, 1 ]
Mathlib/Order/Monotone/Basic.lean
strictMono_nat_of_lt_succ
[]
[ 999, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 998, 1 ]
Mathlib/Order/Antisymmetrization.lean
liftFun_antisymmRel
[]
[ 212, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 9 ]
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean
CircleDeg1Lift.commute_iff_commute
[]
[ 278, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 277, 1 ]
Mathlib/Analysis/Calculus/Deriv/Basic.lean
derivWithin_congr
[ { "state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nhs : EqOn f₁ f s\nhx : ...
[ 612, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 609, 1 ]
Mathlib/Topology/SubsetProperties.lean
isCompact_of_finite_subcover
[ { "state_after": "α : Type u\nβ : Type v\nι : Type ?u.25315\nπ : ι → Type ?u.25320\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nf : Filter α\nhf : NeBot f\nhfs : f ≤ 𝓟 s\nh : ∀ (a : α), a ∈ s → ¬ClusterPt a f\n⊢ Exists fun {ι} =>\n ∃ U, (∀ (i : ι), IsOpen (U i)) ∧ (s ⊆ ⋃ (i : ι), U...
[ 334, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 322, 1 ]
Mathlib/GroupTheory/Perm/List.lean
List.formPerm_apply_of_not_mem
[ { "state_after": "case nil\nα : Type u_1\nβ : Type ?u.3357\ninst✝ : DecidableEq α\nl : List α\nx✝ x : α\nh : ¬x ∈ []\n⊢ ↑(formPerm []) x = x\n\ncase cons\nα : Type u_1\nβ : Type ?u.3357\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ x y : α\nl : List α\nh : ¬x ∈ y :: l\n⊢ ↑(formPerm (y :: l)) x = x", "state_before...
[ 83, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 76, 1 ]
Mathlib/Order/Disjoint.lean
Disjoint.sup_left
[]
[ 197, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 196, 1 ]
Mathlib/Logic/Basic.lean
exists_unique_iff_exists
[]
[ 733, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 731, 9 ]
Mathlib/LinearAlgebra/SModEq.lean
SModEq.sub_mem
[ { "state_after": "no goals", "state_before": "R : Type u_1\ninst✝⁴ : Ring R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nU U₁ U₂ : Submodule R M\nx x₁ x₂ y y₁ y₂ z z₁ z₂ : M\nN : Type ?u.30171\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nV V₁ V₂ : Submodule R N\n⊢ x ≡ y [SMOD U] ↔ x - y ∈ U...
[ 48, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 48, 1 ]
Mathlib/Algebra/Quaternion.lean
Quaternion.add_imI
[]
[ 890, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 890, 9 ]
Mathlib/Tactic/Sat/FromLRAT.lean
Sat.Clause.reify_and
[]
[ 200, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Std/Data/Nat/Gcd.lean
Nat.lcm_comm
[ { "state_after": "no goals", "state_before": "m n : Nat\n⊢ lcm m n = lcm n m", "tactic": "rw [lcm, lcm, Nat.mul_comm n m, gcd_comm n m]" } ]
[ 183, 48 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 182, 1 ]