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list
Mathlib/Data/Nat/Totient.lean
Nat.totient_gcd_mul_totient_mul
[ { "state_after": "a b : ℕ\nshuffle : ∀ (a1 a2 b1 b2 c1 c2 : ℕ), b1 ∣ a1 → b2 ∣ a2 → a1 / b1 * c1 * (a2 / b2 * c2) = a1 * a2 / (b1 * b2) * (c1 * c2)\n⊢ φ (gcd a b) * φ (a * b) = φ a * φ b * gcd a b", "state_before": "a b : ℕ\n⊢ φ (gcd a b) * φ (a * b) = φ a * φ b * gcd a b", "tactic": "have shuffle :\n ...
[ 349, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 333, 1 ]
Mathlib/Algebra/Algebra/Equiv.lean
AlgEquiv.map_finsupp_sum
[]
[ 239, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Std/Data/Int/Lemmas.lean
Int.ofNat_succ
[]
[ 37, 61 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 37, 1 ]
Mathlib/Logic/Equiv/LocalEquiv.lean
LocalEquiv.trans_assoc
[ { "state_after": "no goals", "state_before": "α : Type u_3\nβ : Type u_4\nγ : Type u_1\nδ : Type u_2\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ne'' : LocalEquiv γ δ\n⊢ (LocalEquiv.trans (LocalEquiv.trans e e') e'').source = (LocalEquiv.trans e (LocalEquiv.trans e' e'')).source", "tactic": "simp [trans_so...
[ 744, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 742, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean
CategoryTheory.Limits.hasTerminal_of_unique
[]
[ 325, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 324, 1 ]
Mathlib/CategoryTheory/Closed/Cartesian.lean
CategoryTheory.CartesianClosed.curry_natural_left
[]
[ 182, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 180, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.erase_add_left_pos
[]
[ 1052, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1051, 1 ]
Mathlib/LinearAlgebra/FreeModule/PID.lean
Ideal.smithCoeffs_ne_zero
[ { "state_after": "ι : Type u_1\nR : Type u_2\ninst✝⁸ : CommRing R\ninst✝⁷ : IsDomain R\ninst✝⁶ : IsPrincipalIdealRing R\nM : Type ?u.391806\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nb✝ : ι → M\nS : Type u_3\ninst✝³ : CommRing S\ninst✝² : IsDomain S\ninst✝¹ : Algebra R S\ninst✝ : Finite ι\nb : Basis ι R S\n...
[ 623, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 618, 1 ]
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean
Complex.hasStrictFDerivAt_cpow
[ { "state_after": "p : ℂ × ℂ\nhp : 0 < p.fst.re ∨ p.fst.im ≠ 0\nA : p.fst ≠ 0\n⊢ HasStrictFDerivAt (fun x => x.fst ^ x.snd)\n ((p.snd * p.fst ^ (p.snd - 1)) • ContinuousLinearMap.fst ℂ ℂ ℂ +\n (p.fst ^ p.snd * log p.fst) • ContinuousLinearMap.snd ℂ ℂ ℂ)\n p", "state_before": "p : ℂ × ℂ\nhp : 0 < p...
[ 45, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 34, 1 ]
Mathlib/RingTheory/Localization/Integral.lean
IsLocalization.scaleRoots_commonDenom_mem_lifts
[ { "state_after": "R : Type u_2\ninst✝⁹ : CommRing R\nM : Submonoid R\nS : Type ?u.399271\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nP : Type ?u.399527\ninst✝⁶ : CommRing P\nRₘ : Type u_1\nSₘ : Type ?u.399536\ninst✝⁵ : CommRing Rₘ\ninst✝⁴ : CommRing Sₘ\ninst✝³ : Algebra R Rₘ\ninst✝² : IsLocalization M Rₘ\ninst✝...
[ 286, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 266, 1 ]
Mathlib/Data/Set/Ncard.lean
Set.ncard_ne_zero_of_mem
[]
[ 117, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 116, 1 ]
Mathlib/Algebra/Order/Floor.lean
Int.fract_div_intCast_eq_div_intCast_mod
[ { "state_after": "case inl\nF : Type ?u.196930\nα : Type ?u.196933\nβ : Type ?u.196936\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\nz : ℤ\na : α\nk : Type u_1\ninst✝¹ : LinearOrderedField k\ninst✝ : FloorRing k\nb : k\nm : ℤ\n⊢ fract (↑m / ↑0) = ↑(m % ↑0) / ↑0\n\ncase inr\nF : Type ?u.196930\nα : Type ?...
[ 1082, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1051, 1 ]
Mathlib/Algebra/Order/Hom/Monoid.lean
OrderMonoidHom.toOrderHom_injective
[ { "state_after": "no goals", "state_before": "F : Type ?u.78754\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.78763\nδ : Type ?u.78766\ninst✝⁷ : Preorder α\ninst✝⁶ : Preorder β\ninst✝⁵ : Preorder γ\ninst✝⁴ : Preorder δ\ninst✝³ : MulOneClass α\ninst✝² : MulOneClass β\ninst✝¹ : MulOneClass γ\ninst✝ : MulOneClass δ...
[ 362, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 361, 1 ]
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
SimpleGraph.Walk.darts_bypass_subset
[ { "state_after": "no goals", "state_before": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v u✝ : V\n⊢ darts (bypass nil) ⊆ darts nil", "tactic": "simp!" }, { "state_after": "case cons\nV : Type u\nV' : T...
[ 1425, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1416, 1 ]
Std/Data/Array/Init/Lemmas.lean
Array.foldrM_push
[ { "state_after": "no goals", "state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝ : Monad m\nf : α → β → m β\ninit : β\narr : Array α\na : α\n⊢ foldrM f init (push arr a) (size (push arr a)) = do\n let init ← f a init\n foldrM f init arr (size arr)", "tactic": "simp [foldrM_...
[ 80, 51 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 78, 1 ]
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean
BilinForm.mul_toMatrix'_mul
[ { "state_after": "no goals", "state_before": "R : Type ?u.740707\nM✝ : Type ?u.740710\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M✝\ninst✝¹⁶ : Module R M✝\nR₁ : Type ?u.740746\nM₁ : Type ?u.740749\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type ?u.741361\n...
[ 260, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 257, 1 ]
Mathlib/Order/PFilter.lean
Order.PFilter.top_mem
[]
[ 142, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 142, 9 ]
Mathlib/SetTheory/Ordinal/Basic.lean
Ordinal.type_preimage_aux
[ { "state_after": "no goals", "state_before": "α✝ : Type ?u.30166\nβ✝ : Type ?u.30169\nγ : Type ?u.30172\nr✝ : α✝ → α✝ → Prop\ns : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nf : β ≃ α\n⊢ (type fun x y => r (↑f x) (↑f y)) = type r", "tactic": "convert (RelIs...
[ 308, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 306, 1 ]
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean
BilinForm.mul_toMatrix
[ { "state_after": "no goals", "state_before": "R : Type ?u.1715810\nM✝ : Type ?u.1715813\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M✝\ninst✝¹⁸ : Module R M✝\nR₁ : Type ?u.1715849\nM₁ : Type ?u.1715852\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\nin...
[ 412, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 410, 1 ]
Mathlib/Order/SymmDiff.lean
compl_bihimp_compl
[]
[ 753, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 752, 1 ]
Mathlib/SetTheory/Cardinal/Basic.lean
Cardinal.mk_eq_nat_iff
[ { "state_after": "no goals", "state_before": "α✝ β α : Type u\nn : ℕ\n⊢ (#α) = ↑n ↔ Nonempty (α ≃ Fin n)", "tactic": "rw [← lift_mk_fin, ← lift_uzero (#α), lift_mk_eq']" } ]
[ 1465, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1464, 1 ]
Mathlib/Topology/Algebra/Group/Basic.lean
tendsto_inv_nhdsWithin_Ici
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalGroup G\ninst✝³ : TopologicalSpace α\nf : α → G\ns : Set α\nx : α\ninst✝² : TopologicalSpace H\ninst✝¹ : OrderedCommGroup H\ninst✝ : ContinuousInv ...
[ 585, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 584, 1 ]
Mathlib/Data/IsROrC/Basic.lean
IsROrC.ofReal_sum
[]
[ 237, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 235, 1 ]
Mathlib/Algebra/ModEq.lean
AddCommGroup.ModEq.add_zsmul
[]
[ 136, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 135, 11 ]
Mathlib/Combinatorics/Additive/Energy.lean
Finset.multiplicativeEnergy_pos
[]
[ 90, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean
DihedralGroup.orderOf_sr
[ { "state_after": "case hg\nn : ℕ\ni : ZMod n\n⊢ sr i ^ 2 = 1\n\ncase hg1\nn : ℕ\ni : ZMod n\n⊢ sr i ≠ 1", "state_before": "n : ℕ\ni : ZMod n\n⊢ orderOf (sr i) = 2", "tactic": "apply orderOf_eq_prime" }, { "state_after": "no goals", "state_before": "case hg\nn : ℕ\ni : ZMod n\n⊢ sr i ^ 2 = 1"...
[ 159, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 154, 1 ]
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean
Complex.hasDerivAt_exp
[ { "state_after": "𝕜 : Type ?u.55\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : NormedAlgebra 𝕜 ℂ\nx : ℂ\n⊢ (fun h => exp (x + h) - exp x - h • exp x) =o[𝓝 0] fun h => h", "state_before": "𝕜 : Type ?u.55\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : NormedAlgebra 𝕜 ℂ\nx : ℂ\n⊢ HasDerivAt exp (exp x) x",...
[ 41, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 35, 1 ]
Mathlib/Topology/Instances/ENNReal.lean
summable_sigma_of_nonneg
[ { "state_after": "case intro\nα : Type u_2\nβ✝ : Type ?u.346013\nγ : Type ?u.346016\nβ : α → Type u_1\nf : (x : α) × β x → ℝ≥0\n⊢ (Summable fun i => ↑(f i)) ↔\n (∀ (x : α), Summable fun y => (fun i => ↑(f i)) { fst := x, snd := y }) ∧\n Summable fun x => ∑' (y : β x), (fun i => ↑(f i)) { fst := x, snd :...
[ 1336, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1333, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean
BoxIntegral.Prepartition.distortion_biUnion
[]
[ 688, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 686, 1 ]
Mathlib/RingTheory/Subring/Basic.lean
Subring.toSubsemiring_strictMono
[]
[ 261, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 260, 1 ]
Mathlib/Analysis/Convex/Side.lean
AffineSubspace.sOppSide_vadd_right_iff
[ { "state_after": "no goals", "state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.156301\nP : Type u_3\nP' : Type ?u.156307\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns...
[ 327, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 325, 1 ]
Mathlib/Algebra/BigOperators/Finsupp.lean
MonoidHom.coe_finsupp_prod
[]
[ 263, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 261, 1 ]
Mathlib/Topology/Constructions.lean
Filter.Eventually.prod_inl_nhds
[]
[ 475, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 473, 1 ]
Mathlib/Data/PNat/Factors.lean
PrimeMultiset.prod_dvd_iff
[ { "state_after": "u v : PrimeMultiset\nh : PNat.factorMultiset (prod u) ≤ v ↔ prod u ∣ prod v := PNat.factorMultiset_le_iff'\n⊢ prod u ∣ prod v ↔ u ≤ v", "state_before": "u v : PrimeMultiset\n⊢ prod u ∣ prod v ↔ u ≤ v", "tactic": "let h := @PNat.factorMultiset_le_iff' u.prod v" }, { "state_after...
[ 354, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 351, 1 ]
Mathlib/Data/List/Lex.lean
List.nil_lt_cons
[]
[ 183, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 182, 1 ]
Mathlib/Data/List/MinMax.lean
List.maximum_cons
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.101376\ninst✝ : LinearOrder α\nl✝ : List α\na✝ m a : α\nl : List α\n⊢ maximum [a] = max (↑a) (maximum [])", "tactic": "simp [@max_eq_left (WithBot α) _ _ _ bot_le]" }, { "state_after": "no goals", "state_before": "α : Ty...
[ 376, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 374, 1 ]
Mathlib/RingTheory/RootsOfUnity/Complex.lean
IsPrimitiveRoot.arg_eq_zero_iff
[]
[ 124, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 121, 1 ]
Mathlib/Data/Polynomial/Coeff.lean
Polynomial.support_trinomial
[ { "state_after": "R : Type u\nS : Type v\na b : R\nn✝ m✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nx y z : R\nhx : x ≠ 0\nhy : y ≠ 0\nhz : z ≠ 0\n⊢ {k, m, n} ⊆ support (↑C x * X ^ k + ↑C y * X ^ m + ↑C z * X ^ n)", "state_before": "R : Type u\nS : Type v\na b : R\nn✝ m✝ : ℕ...
[ 212, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 205, 1 ]
Mathlib/Topology/Homotopy/Path.lean
Path.Homotopic.hcomp
[]
[ 295, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 293, 1 ]
Mathlib/FieldTheory/Subfield.lean
Subfield.map_iSup
[]
[ 793, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 791, 1 ]
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean
Pmf.support_filter
[]
[ 289, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 288, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.OuterMeasure.restrict_le_self
[]
[ 602, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 601, 1 ]
Mathlib/Data/Polynomial/FieldDivision.lean
Polynomial.leadingCoeff_map
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Field R\np q : R[X]\ninst✝ : DivisionRing k\nf : R →+* k\n⊢ leadingCoeff (map f p) = ↑f (leadingCoeff p)", "tactic": "simp only [← coeff_natDegree, coeff_map f, natDegree_map]" } ]
[ 290, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 288, 1 ]
Mathlib/Data/ZMod/Basic.lean
ZMod.addOrderOf_one
[]
[ 105, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 104, 1 ]
Mathlib/SetTheory/Ordinal/Basic.lean
RelIso.ordinal_lift_type_eq
[]
[ 673, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 669, 1 ]
Mathlib/Analysis/InnerProductSpace/Basic.lean
Dfinsupp.inner_sum
[ { "state_after": "no goals", "state_before": "𝕜 : Type u_3\nE : Type u_4\nF : Type ?u.1509183\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\ndec : DecidableEq ι\nα : ι →...
[ 556, 93 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 553, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_iff_seq_tendsto
[ { "state_after": "ι : Type ?u.364855\nι' : Type ?u.364858\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.364867\nf : α → β\nk : Filter α\nl : Filter β\ninst✝ : IsCountablyGenerated k\nH : ∀ (x : ℕ → α), Tendsto x atTop k → Tendsto (f ∘ x) atTop l\ns : Set β\nhs : s ∈ l\n⊢ s ∈ map f k", "state_before": "ι : Type ?...
[ 1826, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1817, 1 ]
Mathlib/RingTheory/UniqueFactorizationDomain.lean
UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvd
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\na p : α\nha0 : a ≠ 0\nhp : Irreducible p\nx✝ : p ∣ a\nb : α\nhb : a = p * b\nhb0 : b = 0\n⊢ False", "tactic": "sim...
[ 639, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 623, 1 ]
Mathlib/Data/Set/Basic.lean
Set.ite_same
[]
[ 2267, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2266, 1 ]
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean
conformalAt_const_smul
[]
[ 70, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 69, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.coe_singleton
[]
[ 334, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 333, 1 ]
Mathlib/Topology/Algebra/Module/FiniteDimension.lean
ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply
[]
[ 498, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 496, 1 ]
Mathlib/Data/Int/Order/Basic.lean
Int.neg_emod_two
[ { "state_after": "a b : ℤ\nn : ℕ\ni : ℤ\n⊢ (-i - i) % 2 = 0", "state_before": "a b : ℤ\nn : ℕ\ni : ℤ\n⊢ -i % 2 = i % 2", "tactic": "apply Int.emod_eq_emod_iff_emod_sub_eq_zero.mpr" }, { "state_after": "case h.e'_2.h.e'_5\na b : ℤ\nn : ℕ\ni : ℤ\n⊢ -i - i = 2 * -i", "state_before": "a b : ℤ\nn...
[ 294, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 291, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean
CategoryTheory.Limits.hasBinaryCoproducts_of_hasColimit_pair
[]
[ 983, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 981, 1 ]
Mathlib/Data/Set/Function.lean
Set.MapsTo.inter_inter
[]
[ 487, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 486, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean
midpoint_add_self
[ { "state_after": "no goals", "state_before": "R : Type u_2\nV : Type u_1\nV' : Type ?u.112580\nP : Type ?u.112583\nP' : Type ?u.112586\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTor...
[ 207, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 204, 1 ]
Mathlib/MeasureTheory/Integral/SetToL1.lean
MeasureTheory.L1.SimpleFunc.setToL1S_nonneg
[ { "state_after": "α : Type u_1\nE : Type ?u.738601\nF : Type ?u.738604\nF' : Type ?u.738607\nG : Type ?u.738610\n𝕜 : Type ?u.738613\np : ℝ≥0∞\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedAddCommGroup F'\ninst✝⁷ : NormedSpac...
[ 855, 96 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 845, 1 ]
Mathlib/Data/Polynomial/HasseDeriv.lean
Polynomial.hasseDeriv_X
[ { "state_after": "no goals", "state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nhk : 1 < k\n⊢ ↑(hasseDeriv k) X = 0", "tactic": "rw [← monomial_one_one_eq_X, hasseDeriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,\n MulZeroClass.zero_mul, monomial_zero_right]" } ]
[ 144, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 142, 1 ]
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
SimpleGraph.Walk.rotate_edges
[]
[ 1224, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1222, 1 ]
Mathlib/Algebra/Module/LinearMap.lean
LinearMap.id_comp
[]
[ 559, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 558, 1 ]
Mathlib/Data/Finset/Pointwise.lean
Finset.Nonempty.of_vsub_left
[]
[ 1496, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1495, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
HasStrictDerivAt.cosh
[]
[ 857, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 855, 1 ]
Mathlib/GroupTheory/Submonoid/Operations.lean
Submonoid.mrange_inr'
[]
[ 1305, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1304, 1 ]
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
Units.mul_right_eq_zero
[ { "state_after": "no goals", "state_before": "α : Type ?u.1597\nM₀ : Type u_1\nG₀ : Type ?u.1603\nM₀' : Type ?u.1606\nG₀' : Type ?u.1609\nF : Type ?u.1612\nF' : Type ?u.1615\ninst✝ : MonoidWithZero M₀\nu : M₀ˣ\na : M₀\nh : ↑u * a = 0\n⊢ a = 0", "tactic": "simpa using mul_eq_zero_of_right (↑u⁻¹) h" } ]
[ 46, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 45, 1 ]
Mathlib/Data/Set/Pointwise/ListOfFn.lean
Set.mem_list_prod
[ { "state_after": "case h\nF : Type ?u.8458\nα : Type u_1\nβ : Type ?u.8464\nγ : Type ?u.8467\ninst✝ : Monoid α\ns t : Set α\na✝ : α\nm n✝ : ℕ\na : α\nn : ℕ\nf : Fin n → Set α\n⊢ a ∈ List.prod (List.ofFn f) ↔\n ∃ l', List.prod (List.map (fun x => ↑x.snd) l') = a ∧ List.map Sigma.fst l' = List.ofFn f", "st...
[ 50, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 39, 1 ]
Mathlib/Order/Filter/Partial.lean
Filter.rcomap'_compose
[]
[ 181, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 180, 1 ]
Mathlib/RingTheory/Polynomial/Content.lean
Polynomial.content_X_pow
[ { "state_after": "case zero\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\n⊢ content (X ^ Nat.zero) = 1\n\ncase succ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nk : ℕ\nhi : content (X ^ k) = 1\n⊢ content (X ^ Nat.succ k) = 1", ...
[ 141, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 138, 1 ]
Mathlib/Algebra/Module/Submodule/Bilinear.lean
Submodule.map₂_iSup_right
[ { "state_after": "ι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\ns : Submodule R M\nt : ι → Submodule ...
[ 164, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 160, 1 ]
Mathlib/Analysis/LocallyConvex/Polar.lean
LinearMap.polar_weak_closed
[ { "state_after": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\ninst✝⁴ : NormedCommRing 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nB : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜\ns : Set E\n⊢ IsClosed (⋂ (x : E) (_ : x ∈ s), {y | ‖↑(↑B x) y‖ ≤ 1})", "state_before": "𝕜 : Type ...
[ 131, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 127, 1 ]
Mathlib/Data/Polynomial/Div.lean
Polynomial.modByMonic_eq_of_not_monic
[]
[ 211, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 1 ]
Mathlib/Algebra/Order/Floor.lean
Nat.ceil_le_floor_add_one
[ { "state_after": "F : Type ?u.46418\nα : Type u_1\nβ : Type ?u.46424\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn : ℕ\na : α\n⊢ a ≤ ↑⌊a⌋₊ + 1", "state_before": "F : Type ?u.46418\nα : Type u_1\nβ : Type ?u.46424\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn :...
[ 299, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 297, 1 ]
Mathlib/Algebra/Order/Floor.lean
Nat.ceil_congr
[]
[ 1505, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1504, 1 ]
Mathlib/Order/Filter/Bases.lean
Filter.Tendsto.basis_both
[]
[ 893, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 890, 1 ]
Mathlib/LinearAlgebra/Matrix/ToLin.lean
LinearMap.toMatrix'_mul
[]
[ 406, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 404, 1 ]
Mathlib/LinearAlgebra/Dfinsupp.lean
Submodule.mem_iSup_iff_exists_dfinsupp
[]
[ 358, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 355, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.rootSet_finite
[]
[ 915, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 913, 1 ]
Mathlib/Order/Monotone/Basic.lean
Antitone.strictAnti_iff_injective
[]
[ 884, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 883, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean
CategoryTheory.Limits.WidePushout.arrow_ι
[ { "state_after": "no goals", "state_before": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type u_1\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → B ⟶ objs j\ninst✝ : HasWidePushout B objs arrows\nj : J\n⊢ arrows j ≫ ι arrows j = head arrows", "tactic": "apply colimit.w (WidePushoutSh...
[ 401, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 400, 1 ]
Mathlib/Data/Fin/Tuple/Basic.lean
Fin.tail_init_eq_init_tail
[ { "state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq✝ : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni✝ : Fin n\ny : α (↑castSucc i✝)\nz : α (last n)\nβ : Type u_1\nq : Fin (n + 2) → β\ni : Fin n\n⊢ tail (init q) i = init (tail q) i", "state_before": "m n : ℕ\nα : Fi...
[ 577, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 574, 1 ]
Mathlib/Topology/Sheaves/Stalks.lean
TopCat.Presheaf.stalkSpecializes_stalkPushforward
[ { "state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y Z : TopCat\nf : X ⟶ Y\nF : Presheaf C X\nx y : ↑X\nh : x ⤳ y\n⊢ stalkSpecializes (f _* F) (_ : ↑f x ⤳ ↑f y) ≫ stalkPushforward C f F x =\n stalkPushforward C f F y ≫ stalkSpecializes F h", "state_before": "C : Type u\ninst✝¹ : ...
[ 374, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 367, 1 ]
Mathlib/Order/CompleteLattice.lean
iSup_const_le
[]
[ 1036, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1035, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean
CategoryTheory.section_comp_right
[]
[ 88, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 87, 1 ]
Mathlib/Topology/UnitInterval.lean
unitInterval.one_minus_nonneg
[ { "state_after": "no goals", "state_before": "x : ↑I\n⊢ 0 ≤ 1 - ↑x", "tactic": "simpa using x.2.2" } ]
[ 145, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 145, 1 ]
Mathlib/Data/Real/Hyperreal.lean
Hyperreal.InfinitePos.pos
[]
[ 437, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 437, 1 ]
Mathlib/RingTheory/Polynomial/Basic.lean
Polynomial.eval_eq_sum_degreeLTEquiv
[ { "state_after": "R : Type u\nS : Type ?u.35049\ninst✝ : Semiring R\nn : ℕ\np : R[X]\nhp : p ∈ degreeLT R n\nx : R\n⊢ (sum p fun e a => a * x ^ e) = ∑ x_1 : Fin n, ↑(degreeLTEquiv R n) { val := p, property := hp } x_1 * x ^ ↑x_1", "state_before": "R : Type u\nS : Type ?u.35049\ninst✝ : Semiring R\nn : ℕ\np ...
[ 183, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 180, 1 ]
Mathlib/MeasureTheory/Covering/LiminfLimsup.lean
blimsup_thickening_mul_ae_eq
[ { "state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : MeasureTheory.Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nM : ℝ\nhM : 0 < M\nr : ℕ → ℝ\nhr : Tends...
[ 287, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 271, 1 ]
Mathlib/Analysis/SpecialFunctions/Integrals.lean
intervalIntegral.mul_integral_comp_sub_mul
[]
[ 297, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 295, 1 ]
Mathlib/Data/Set/Intervals/Basic.lean
Set.Ici_inter_Ici
[ { "state_after": "case h\nα : Type u_1\nβ : Type ?u.180404\ninst✝ : SemilatticeSup α\na b x : α\n⊢ x ∈ Ici a ∩ Ici b ↔ x ∈ Ici (a ⊔ b)", "state_before": "α : Type u_1\nβ : Type ?u.180404\ninst✝ : SemilatticeSup α\na b : α\n⊢ Ici a ∩ Ici b = Ici (a ⊔ b)", "tactic": "ext x" }, { "state_after": "no...
[ 1742, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1740, 1 ]
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean
CircleDeg1Lift.mono
[]
[ 154, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 154, 9 ]
Mathlib/Data/Real/Basic.lean
Real.ofCauchy_one
[]
[ 120, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 119, 1 ]
Mathlib/Order/Filter/Germ.lean
Filter.Germ.map'_coe
[]
[ 175, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 173, 1 ]
Mathlib/RingTheory/WittVector/Basic.lean
WittVector.mapFun.sub
[ { "state_after": "no goals", "state_before": "p : ℕ\nR : Type u_2\nS : Type u_1\nT : Type ?u.158070\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.158085\nβ : Type ?u.158088\nf : R →+* S\nx y : 𝕎 R\n⊢ mapFun (↑f) (x - y) = mapFun (↑f) x - mapFun (↑f) y",...
[ 118, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 118, 1 ]
Mathlib/AlgebraicTopology/SimplexCategory.lean
SimplexCategory.eq_id_of_mono
[ { "state_after": "x : SimplexCategory\ni : x ⟶ x\ninst✝ : Mono i\n⊢ IsIso i", "state_before": "x : SimplexCategory\ni : x ⟶ x\ninst✝ : Mono i\n⊢ i = 𝟙 x", "tactic": "suffices IsIso i by\n apply eq_id_of_isIso" }, { "state_after": "case hf\nx : SimplexCategory\ni : x ⟶ x\ninst✝ : Mono i\n⊢ Func...
[ 720, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 713, 1 ]
Mathlib/Algebra/Order/Floor.lean
Int.preimage_fract
[ { "state_after": "case h\nF : Type ?u.178920\nα : Type u_1\nβ : Type ?u.178926\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\ns : Set α\nx : α\n⊢ x ∈ fract ⁻¹' s ↔ x ∈ ⋃ (m : ℤ), (fun x => x - ↑m) ⁻¹' (s ∩ Ico 0 1)", "state_before": "F : Type ?u.178920\nα : Type u_1\nβ : Type ?u.178926\ni...
[ 998, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 991, 1 ]
Mathlib/Algebra/Quaternion.lean
QuaternionAlgebra.imJ_star
[]
[ 626, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 625, 1 ]
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean
AffineMap.coe_fst
[]
[ 350, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 349, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean
Real.arccos_neg
[ { "state_after": "no goals", "state_before": "x : ℝ\n⊢ arccos (-x) = π - arccos x", "tactic": "rw [← add_halves π, arccos, arcsin_neg, arccos, add_sub_assoc, sub_sub_self, sub_neg_eq_add]" } ]
[ 408, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 407, 1 ]
Mathlib/Order/Bounds/Basic.lean
IsLUB.dual
[]
[ 163, 4 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 162, 1 ]
Mathlib/MeasureTheory/Function/L1Space.lean
MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top
[ { "state_after": "α : Type u_1\nβ : Type ?u.731151\nγ : Type ?u.731154\nδ : Type ?u.731157\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ≥0∞\nhf : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\nthis :\n ∀ (x : α), ↑‖ENNReal.toReal (f x)‖₊ ...
[ 272, 8 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 260, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.ae_restrict_eq
[ { "state_after": "case a\nα : Type u_1\nβ : Type ?u.587542\nγ : Type ?u.587545\nδ : Type ?u.587548\nι : Type ?u.587551\nR : Type ?u.587554\nR' : Type ?u.587557\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t✝ : Set α\nhs : MeasurableSet s...
[ 2906, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2902, 1 ]