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Mathlib/Algebra/Lie/Nilpotent.lean
LieModule.antitone_lowerCentralSeries
[ { "state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk✝ : ℕ\nN : LieSubmodule R L M\nl k : ℕ\n⊢ l ≤ k → lowerCentralSeries R L M k ≤ lowerCentralS...
[ 137, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 130, 1 ]
Mathlib/Combinatorics/SetFamily/HarrisKleitman.lean
IsLowerSet.nonMemberSubfamily
[ { "state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns✝ : Finset α\na : α\nh : IsLowerSet ↑𝒜\ns t : Finset α\nhts : t ≤ s\n⊢ s ∈ 𝒜 ∧ ¬a ∈ s → t ∈ 𝒜 ∧ ¬a ∈ t", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns✝ : Finset α\na : α\nh : IsLowerSet ↑...
[ 42, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 39, 1 ]
Mathlib/SetTheory/Ordinal/Arithmetic.lean
Ordinal.sup_eq_bsup'
[]
[ 1452, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1450, 1 ]
Mathlib/Data/Polynomial/Coeff.lean
Polynomial.nat_cast_inj
[ { "state_after": "case mp\nR✝ : Type u\nS : Type v\na b : R✝\nn✝ m✝ : ℕ\ninst✝² : Semiring R✝\np q r : R✝[X]\nm n : ℕ\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : CharZero R\n⊢ ↑m = ↑n → m = n\n\ncase mpr\nR✝ : Type u\nS : Type v\na b : R✝\nn✝ m✝ : ℕ\ninst✝² : Semiring R✝\np q r : R✝[X]\nm n : ℕ\nR : Type u_1\ni...
[ 391, 8 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 384, 1 ]
Mathlib/LinearAlgebra/Basic.lean
LinearMap.sub_mem_ker_iff
[ { "state_after": "no goals", "state_before": "R : Type u_2\nR₁ : Type ?u.1341382\nR₂ : Type u_3\nR₃ : Type ?u.1341388\nR₄ : Type ?u.1341391\nS : Type ?u.1341394\nK : Type ?u.1341397\nK₂ : Type ?u.1341400\nM : Type u_1\nM' : Type ?u.1341406\nM₁ : Type ?u.1341409\nM₂ : Type u_4\nM₃ : Type ?u.1341415\nM₄ : Typ...
[ 1488, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1488, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.ae_eq_dirac
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.603087\nγ : Type ?u.603090\nδ : Type u_2\nι : Type ?u.603096\nR : Type ?u.603099\nR' : Type ?u.603102\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nin...
[ 3026, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3025, 1 ]
Mathlib/CategoryTheory/Monoidal/Opposite.lean
CategoryTheory.MonoidalOpposite.unop_injective
[]
[ 55, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 54, 1 ]
Mathlib/Topology/MetricSpace/Infsep.lean
Set.Nontrivial.infsep_eq_iInf
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.65221\ninst✝ : PseudoMetricSpace α\nx y z : α\ns t : Set α\nhs : Set.Nontrivial s\n⊢ infsep s = ⨅ (d : ↑(offDiag s)), uncurry dist ↑d", "tactic": "classical rw [Set.infsep_eq_iInf, if_pos hs]" }, { "state_after": "no goals",...
[ 466, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 464, 1 ]
Mathlib/Data/Polynomial/Basic.lean
Polynomial.eq_zero_of_eq_zero
[ { "state_after": "no goals", "state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nh : 0 = 1\np : R[X]\n⊢ p = 0", "tactic": "rw [← one_smul R p, ← h, zero_smul]" } ]
[ 830, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 829, 1 ]
Mathlib/Data/Set/NAry.lean
Set.image3_mono
[]
[ 239, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.measure_sInf_le
[ { "state_after": "α : Type u_1\nβ : Type ?u.151657\nγ : Type ?u.151660\nδ : Type ?u.151663\nι : Type ?u.151666\nR : Type ?u.151669\nR' : Type ?u.151672\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\nm : Set (Measure α)\nh : μ ∈...
[ 1028, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1026, 9 ]
Mathlib/Topology/Algebra/GroupCompletion.lean
UniformSpace.Completion.denseInducing_toCompl
[]
[ 198, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 197, 1 ]
Mathlib/Algebra/Star/Unitary.lean
unitary.mem_iff_self_mul_star
[]
[ 159, 73 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 158, 1 ]
Mathlib/Topology/MetricSpace/EMetricSpace.lean
edist_triangle_right
[ { "state_after": "α : Type u\nβ : Type v\nX : Type ?u.4940\ninst✝ : PseudoEMetricSpace α\nx y z : α\n⊢ edist x y ≤ edist x z + edist z y", "state_before": "α : Type u\nβ : Type v\nX : Type ?u.4940\ninst✝ : PseudoEMetricSpace α\nx y z : α\n⊢ edist x y ≤ edist x z + edist y z", "tactic": "rw [edist_comm y...
[ 105, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 104, 1 ]
Mathlib/Data/Bool/Basic.lean
Bool.not_ne
[]
[ 223, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 223, 1 ]
Mathlib/Data/Finset/Pointwise.lean
Finset.singletonOneHom_apply
[]
[ 165, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 164, 1 ]
Mathlib/SetTheory/Cardinal/Basic.lean
Cardinal.le_def
[]
[ 269, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 268, 1 ]
Mathlib/LinearAlgebra/Dual.lean
LinearMap.dualMap_id
[ { "state_after": "case h.h\nR : Type u\ninst✝⁴ : CommSemiring R\nM₁ : Type v\nM₂ : Type v'\ninst✝³ : AddCommMonoid M₁\ninst✝² : Module R M₁\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R M₂\nx✝¹ : Dual R M₁\nx✝ : M₁\n⊢ ↑(↑(dualMap id) x✝¹) x✝ = ↑(↑id x✝¹) x✝", "state_before": "R : Type u\ninst✝⁴ : CommSemirin...
[ 218, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 216, 1 ]
Mathlib/Topology/Maps.lean
embedding_id
[]
[ 210, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 209, 1 ]
Mathlib/Tactic/NormNum/Core.lean
Mathlib.Meta.NormNum.IsInt.to_isRat
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : Ring α\nn✝ : ℤ\n⊢ 1 * ↑1 = 1", "tactic": "simp" }, { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : Ring α\nn✝ : ℤ\n⊢ ↑1 * 1 = 1", "tactic": "simp" }, { "state_after": "no goals", "state_be...
[ 160, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 159, 1 ]
Mathlib/Data/Finset/Lattice.lean
Finset.sup'_const
[ { "state_after": "case a\nF : Type ?u.250689\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.250698\nι : Type ?u.250701\nκ : Type ?u.250704\ninst✝ : SemilatticeSup α\ns : Finset β\nH : Finset.Nonempty s\nf : β → α\na : α\n⊢ (sup' s H fun x => a) ≤ a\n\ncase a\nF : Type ?u.250689\nα : Type u_1\nβ : Type u_2\nγ : Type ?...
[ 825, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 820, 1 ]
Mathlib/MeasureTheory/Function/SimpleFunc.lean
MeasureTheory.SimpleFunc.map_map
[]
[ 313, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 312, 1 ]
Mathlib/Data/Set/Lattice.lean
Set.mapsTo_iUnion
[]
[ 1428, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1426, 1 ]
Mathlib/Data/Set/Basic.lean
Set.subsingleton_univ
[]
[ 2376, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2375, 1 ]
Mathlib/Analysis/Asymptotics/Asymptotics.lean
Asymptotics.isLittleO_const_id_comap_norm_atTop
[]
[ 1881, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1879, 1 ]
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean
Projectivization.Subspace.span_coe
[]
[ 115, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 114, 1 ]
Mathlib/CategoryTheory/Subobject/Basic.lean
CategoryTheory.Subobject.ofMkLE_arrow
[ { "state_after": "no goals", "state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝¹ : Category D\nB A : C\nf : A ⟶ B\ninst✝ : Mono f\nX : Subobject B\nh : mk f ≤ X\n⊢ ofMkLE f X h ≫ arrow X = f", "tactic": "simp [ofMkLE]" } ]
[ 369, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 1 ]
Mathlib/RingTheory/Multiplicity.lean
multiplicity.multiplicity_le_multiplicity_iff
[ { "state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b c d : α\nh : ∀ (n : ℕ), a ^ n ∣ b → c ^ n ∣ d\nhab : Finite a b\n⊢ ↑(Part.get (multiplicity a b) (_ : (multiplicity a b).Dom)) ≤ multiplicity c d", "state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : Deci...
[ 245, 96 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Mathlib/RingTheory/WittVector/WittPolynomial.lean
wittPolynomial_vars
[ { "state_after": "p : ℕ\nR : Type u_1\ninst✝³ : CommRing R\ninst✝² : DecidableEq R\nS : Type ?u.157043\ninst✝¹ : CommRing S\nhp : NeZero p\ninst✝ : CharZero R\nn : ℕ\nthis : ∀ (i : ℕ), vars (↑(monomial (single i (p ^ (n - i)))) (↑p ^ i)) = {i}\n⊢ vars (W_ R n) = range (n + 1)", "state_before": "p : ℕ\nR : T...
[ 188, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 177, 1 ]
Mathlib/Algebra/Star/Subalgebra.lean
StarSubalgebra.toSubalgebra_inj
[]
[ 106, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 105, 1 ]
Mathlib/Data/Set/Ncard.lean
Set.exists_smaller_Set
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.133040\ns✝ t : Set α\na b x y : α\nf : α → β\ns : Set α\ni : ℕ\nh₁ : i ≤ ncard s\n⊢ i + ncard ∅ ≤ ncard s", "tactic": "simpa" }, { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.133040\ns✝ t✝ : Set...
[ 603, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 600, 1 ]
Mathlib/Topology/Algebra/Nonarchimedean/Bases.lean
SubmodulesRingBasis.toSubmodulesBasis
[]
[ 377, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 375, 1 ]
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean
Complex.arg_mul_cos_add_sin_mul_I_coe_angle
[ { "state_after": "case h\nr : ℝ\nhr : 0 < r\nθ : ℝ\n⊢ ↑(arg (↑r * (↑(Angle.cos ↑θ) + ↑(Angle.sin ↑θ) * I))) = ↑θ", "state_before": "r : ℝ\nhr : 0 < r\nθ : Angle\n⊢ ↑(arg (↑r * (↑(Angle.cos θ) + ↑(Angle.sin θ) * I))) = θ", "tactic": "induction' θ using Real.Angle.induction_on with θ" }, { "state_...
[ 465, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 460, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
HasDerivWithinAt.ccosh
[]
[ 248, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 246, 1 ]
Mathlib/Analysis/Calculus/Deriv/Add.lean
derivWithin_add
[]
[ 77, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/Algebra/Hom/Ring.lean
NonUnitalRingHom.zero_apply
[]
[ 225, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 224, 1 ]
Mathlib/RingTheory/RootsOfUnity/Complex.lean
IsPrimitiveRoot.nnnorm_eq_one
[]
[ 113, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 111, 1 ]
Mathlib/Order/Filter/Bases.lean
Filter.HasBasis.prod_same_index
[ { "state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.77172\nι : Sort u_3\nι' : Sort ?u.77178\nla : Filter α\npa : ι → Prop\nsa : ι → Set α\nlb : Filter β\npb : ι' → Prop\nsb✝ : ι' → Set β\nf : α → β\np : ι → Prop\nsb : ι → Set β\nhla : HasBasis la p sa\nhlb : HasBasis lb p sb\nh_dir : ∀ {i j : ι}, p i → p ...
[ 916, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 907, 1 ]
Mathlib/Order/Filter/Bases.lean
Filter.HasBasis.ex_mem
[]
[ 279, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 278, 1 ]
Mathlib/Algebra/Associated.lean
associated_eq_eq
[ { "state_after": "case h.h.a\nα : Type u_1\nβ : Type ?u.249344\nγ : Type ?u.249347\nδ : Type ?u.249350\ninst✝¹ : Monoid α\ninst✝ : Unique αˣ\nx✝¹ x✝ : α\n⊢ x✝¹ ~ᵤ x✝ ↔ x✝¹ = x✝", "state_before": "α : Type u_1\nβ : Type ?u.249344\nγ : Type ?u.249347\nδ : Type ?u.249350\ninst✝¹ : Monoid α\ninst✝ : Unique αˣ\n...
[ 702, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 700, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean
BoxIntegral.Prepartition.isSubordinate_toSubordinate
[]
[ 195, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 193, 1 ]
Mathlib/Computability/EpsilonNFA.lean
εNFA.eval_nil
[]
[ 128, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 127, 1 ]
Mathlib/Order/InitialSeg.lean
InitialSeg.init
[]
[ 87, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 86, 1 ]
Mathlib/ModelTheory/Syntax.lean
FirstOrder.Language.Term.relabel_relabel
[ { "state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.5460\nP : Type ?u.5463\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type u_1\nf : α → β\ng : β → γ\n_a✝ : α\n⊢ relabel g (relabel f (var _a✝)) = relabel (g ∘ f) (var _a✝)\n\n...
[ 129, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 125, 1 ]
Mathlib/Analysis/Calculus/ContDiff.lean
contDiffOn_succ_iff_fderiv_apply
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[ 1920, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1916, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
Complex.cos_antiperiodic
[ { "state_after": "no goals", "state_before": "⊢ Function.Antiperiodic cos ↑π", "tactic": "simp [cos_add]" } ]
[ 1200, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1200, 1 ]
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
tsum_dite_left
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.329046\nδ : Type ?u.329049\ninst✝³ : AddCommMonoid α\ninst✝² : TopologicalSpace α\ninst✝¹ : T2Space α\nf g : β → α\na a₁ a₂ : α\nP : Prop\ninst✝ : Decidable P\nx : β → P → α\n⊢ (∑' (b : β), if h : P then x b h else 0) = if...
[ 552, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 550, 1 ]
Mathlib/RingTheory/Adjoin/Tower.lean
Algebra.adjoin_res_eq_adjoin_res
[ { "state_after": "no goals", "state_before": "R : Type u\nS✝ : Type v\nA : Type w\nB : Type u₁\nC : Type u_1\nD : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹⁰ : CommSemiring C\ninst✝⁹ : CommSemiring D\ninst✝⁸ : CommSemiring E\ninst✝⁷ : CommSemiring F\ninst✝⁶ : Algebra C D\ninst✝⁵ : Algebra C E\ninst✝⁴ : Al...
[ 68, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 59, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.OuterMeasure.map_comap
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ✝ : Type ?u.117782\nR : Type ?u.117785\nR' : Type ?u.117788\nms : Set (OuterMeasure α)\nm✝ : OuterMeasure α\nβ : Type u_1\nf : α → β\nm : OuterMeasure β\ns : Set β\n⊢ f '' (f ⁻¹' s) = Subtype.val '' (Subtype.val ⁻¹' s)", "tactic": "simp only [...
[ 594, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 593, 1 ]
Mathlib/Analysis/NormedSpace/Exponential.lean
exp_neg
[]
[ 604, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 603, 1 ]
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
SimpleGraph.Walk.cons_map_snd_darts
[ { "state_after": "no goals", "state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ u :: List.map (fun x => x.snd) (darts p) = support p", "tactic": "induction p <;> simp! [*]" } ]
[ 723, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 722, 1 ]
Mathlib/Computability/TuringMachine.lean
Turing.reaches_total
[]
[ 765, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 763, 1 ]
Mathlib/Order/Filter/Cofinite.lean
Filter.le_cofinite_iff_compl_singleton_mem
[ { "state_after": "ι : Type ?u.2270\nα : Type u_1\nβ : Type ?u.2276\nl : Filter α\nh : ∀ (x : α), {x}ᶜ ∈ l\ns : Set α\nhs : Set.Finite (sᶜ)\n⊢ s ∈ l", "state_before": "ι : Type ?u.2270\nα : Type u_1\nβ : Type ?u.2276\nl : Filter α\n⊢ l ≤ cofinite ↔ ∀ (x : α), {x}ᶜ ∈ l", "tactic": "refine' ⟨fun h x => h (...
[ 100, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 97, 1 ]
Mathlib/Data/Rat/NNRat.lean
NNRat.toNNRat_coe
[]
[ 190, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 189, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.coe_toReal
[]
[ 233, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 233, 9 ]
Mathlib/Analysis/Complex/Schwarz.lean
Complex.abs_deriv_le_one_of_mapsTo_ball
[ { "state_after": "no goals", "state_before": "f : ℂ → ℂ\nc z : ℂ\nR R₁ R₂ : ℝ\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (ball c R)\nhc : f c = c\nh₀ : 0 < R\n⊢ MapsTo f (ball c R) (ball (f c) R)", "tactic": "rwa [hc]" } ]
[ 180, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 178, 1 ]
Mathlib/RingTheory/PowerSeries/Basic.lean
MvPowerSeries.mul_inv_cancel
[ { "state_after": "no goals", "state_before": "σ : Type u_1\nR : Type ?u.1849733\nk : Type u_2\ninst✝ : Field k\nφ : MvPowerSeries σ k\nh : ↑(constantCoeff σ k) φ ≠ 0\n⊢ φ * φ⁻¹ = 1", "tactic": "rw [← invOfUnit_eq φ h, mul_invOfUnit φ (Units.mk0 _ h) rfl]" } ]
[ 986, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 985, 11 ]
Mathlib/Algebra/Homology/ImageToKernel.lean
imageSubobjectMap_comp_imageToKernel
[ { "state_after": "case h\nι : Type ?u.67466\nV : Type u\ninst✝¹⁴ : Category V\ninst✝¹³ : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ninst✝¹² : HasImage f\ng : B ⟶ C\ninst✝¹¹ : HasKernel g\nw : f ≫ g = 0\nA' B' C' : V\nf' : A' ⟶ B'\ninst✝¹⁰ : HasImage f'\ng' : B' ⟶ C'\ninst✝⁹ : HasKernel g'\nw' : f' ≫ g' = 0\nα : ...
[ 263, 11 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 260, 1 ]
Mathlib/Data/Seq/Parallel.lean
Computation.terminates_parallel.aux
[ { "state_after": "α : Type u\nβ : Type v\nlem1 :\n ∀ (l : List (Computation α)) (S : WSeq (Computation α)),\n (∃ a, parallel.aux2 l = Sum.inl a) → Terminates (corec parallel.aux1 (l, S))\n⊢ ∀ {l : List (Computation α)} {S : WSeq (Computation α)} {c : Computation α},\n c ∈ l → Terminates c → Terminates (c...
[ 129, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 59, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Products.lean
CategoryTheory.Limits.piComparison_comp_π
[]
[ 249, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 247, 1 ]
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean
MeasureTheory.SignedMeasure.mutuallySingular_singularPart
[ { "state_after": "α : Type u_1\nβ : Type ?u.301669\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns : SignedMeasure α\nμ : Measure α\n⊢ Measure.singularPart (toJordanDecomposition s).posPart μ + Measure.singularPart (toJordanDecomposition s).negPart μ ⟂ₘ\n VectorMeasure.ennrealToMeasure (toENNRealVectorMeasure μ)...
[ 886, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 881, 8 ]
Mathlib/Topology/Algebra/Affine.lean
AffineMap.homothety_continuous
[ { "state_after": "R : Type u_2\nE : Type ?u.12383\nF : Type u_1\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : TopologicalAddGroup F\ninst✝² : CommRing R\ninst✝¹ : Module R F\ninst✝ : ContinuousConstSMul R F\nx : F\nt : R\n⊢ ↑(homothety x t)...
[ 72, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 66, 1 ]
Mathlib/GroupTheory/Transfer.lean
MonoidHom.ker_transferSylow_isComplement'
[ { "state_after": "G : Type u_1\ninst✝⁴ : Group G\nH : Subgroup G\nA : Type ?u.1410107\ninst✝³ : CommGroup A\nϕ : { x // x ∈ H } →* A\nT : ↑(leftTransversals ↑H)\np : ℕ\nP : Sylow p G\nhP : normalizer ↑P ≤ centralizer ↑P\ninst✝² : Fact (Nat.Prime p)\ninst✝¹ : Finite (Sylow p G)\ninst✝ : FiniteIndex ↑P\nhf : Func...
[ 266, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 254, 1 ]
Mathlib/GroupTheory/Finiteness.lean
Monoid.fg_iff_submonoid_fg
[ { "state_after": "M : Type u_1\nN✝ : Type ?u.43187\ninst✝¹ : Monoid M\ninst✝ : AddMonoid N✝\nN : Submonoid M\n⊢ FG { x // x ∈ N } ↔ Submonoid.FG (Submonoid.map (Submonoid.subtype N) ⊤)", "state_before": "M : Type u_1\nN✝ : Type ?u.43187\ninst✝¹ : Monoid M\ninst✝ : AddMonoid N✝\nN : Submonoid M\n⊢ FG { x // ...
[ 171, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 169, 1 ]
Mathlib/LinearAlgebra/Matrix/Basis.lean
Basis.toMatrix_self
[ { "state_after": "ι : Type u_1\nι' : Type ?u.147575\nκ : Type ?u.147578\nκ' : Type ?u.147581\nR : Type u_2\nM : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nR₂ : Type ?u.147774\nM₂ : Type ?u.147777\ninst✝³ : CommRing R₂\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R₂ M₂\ne : B...
[ 90, 73 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 87, 1 ]
Mathlib/Analysis/LocallyConvex/Bounded.lean
NormedSpace.isVonNBounded_ball
[ { "state_after": "𝕜 : Type u_1\n𝕜' : Type ?u.235860\nE : Type u_2\nE' : Type ?u.235866\nF : Type ?u.235869\nι : Type ?u.235872\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nr : ℝ\n⊢ ∀ (i : ℝ), 0 < i → Absorbs 𝕜 (Seminorm.ball (normSeminorm 𝕜 E) 0 i) (Semi...
[ 279, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 277, 1 ]
src/lean/Init/Classical.lean
Classical.byCases
[]
[ 120, 54 ]
d5348dfac847a56a4595fb6230fd0708dcb4e7e9
https://github.com/leanprover/lean4
[ 119, 1 ]
Mathlib/Topology/Basic.lean
Continuous.continuousAt
[]
[ 1673, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1672, 1 ]
Mathlib/Algebra/GCDMonoid/Basic.lean
CommGroupWithZero.normalize_eq_one
[ { "state_after": "no goals", "state_before": "α : Type ?u.351800\nG₀ : Type u_1\ninst✝¹ : CommGroupWithZero G₀\ninst✝ : DecidableEq G₀\na : G₀\nh0 : a ≠ 0\n⊢ ↑normalize a = 1", "tactic": "simp [normalize_apply, h0]" } ]
[ 1423, 98 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1423, 1 ]
Mathlib/Data/FunLike/Equiv.lean
EquivLike.injective
[]
[ 166, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 165, 11 ]
Mathlib/NumberTheory/PythagoreanTriples.lean
PythagoreanTriple.mul
[ { "state_after": "no goals", "state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\nk : ℤ\n⊢ k * x * (k * x) + k * y * (k * y) = k ^ 2 * (x * x + y * y)", "tactic": "ring" }, { "state_after": "no goals", "state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\nk : ℤ\n⊢ k ^ 2 * (x * x + y *...
[ 83, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 79, 1 ]
Mathlib/Data/List/AList.lean
AList.mem_union
[]
[ 443, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 442, 1 ]
Mathlib/Order/WithBot.lean
WithTop.toDual_le_toDual_iff
[]
[ 808, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 807, 1 ]
Mathlib/Topology/Order/Basic.lean
frontier_Iic_subset
[]
[ 638, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 637, 1 ]
Mathlib/Order/Bounds/Basic.lean
NoMaxOrder.upperBounds_univ
[]
[ 841, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 838, 1 ]
Mathlib/Algebra/Ring/BooleanRing.lean
sub_eq_add
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.8324\nγ : Type ?u.8327\ninst✝ : BooleanRing α\na b : α\n⊢ a - b = a + b", "tactic": "rw [sub_eq_add_neg, add_right_inj, neg_eq]" } ]
[ 108, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 108, 1 ]
Mathlib/LinearAlgebra/Matrix/Hermitian.lean
Matrix.IsHermitian.sub
[]
[ 190, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 188, 1 ]
Mathlib/LinearAlgebra/PiTensorProduct.lean
PiTensorProduct.smul_add
[]
[ 248, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 247, 11 ]
Mathlib/Data/Int/Order/Basic.lean
Int.toNat_pred_coe_of_pos
[ { "state_after": "no goals", "state_before": "a b : ℤ\nn : ℕ\ni : ℤ\nh : 0 < i\n⊢ ↑(toNat i - 1) = i - 1", "tactic": "simp [h, le_of_lt h, push_cast]" } ]
[ 531, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 530, 1 ]
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean
HasDerivWithinAt.clog_real
[ { "state_after": "no goals", "state_before": "α : Type ?u.49835\ninst✝² : TopologicalSpace α\nE : Type ?u.49841\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → ℂ\ns : Set ℝ\nx : ℝ\nf' : ℂ\nh₁ : HasDerivWithinAt f f' s x\nh₂ : 0 < (f x).re ∨ (f x).im ≠ 0\n⊢ HasDerivWithinAt (fun t => log (f ...
[ 134, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 130, 1 ]
Mathlib/Data/Fintype/Card.lean
Fintype.one_lt_card_iff_nontrivial
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.23770\nγ : Type ?u.23773\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ 1 < card α ↔ Nontrivial α", "tactic": "classical\n rw [← not_iff_not]\n push_neg\n rw [not_nontrivial_iff_subsingleton, card_le_one_iff_subsingleton]" }, { ...
[ 575, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 571, 1 ]
Mathlib/Data/List/Count.lean
List.count_singleton'
[ { "state_after": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\na b : α\n⊢ (if a = b then succ (count a []) else count a []) = if a = b then 1 else 0", "state_before": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\na b : α\n⊢ count a [b] = if a = b then 1 else 0", "tactic": "rw [count_cons]" }, ...
[ 228, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 226, 1 ]
Mathlib/Topology/LocallyConstant/Algebra.lean
LocallyConstant.div_apply
[]
[ 141, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 140, 1 ]
Mathlib/Algebra/Hom/NonUnitalAlg.lean
NonUnitalAlgHom.coe_to_mulHom
[]
[ 204, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 203, 1 ]
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean
Euclidean.closedBall_mem_nhds
[]
[ 117, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 116, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.mul_le_of_le_div
[ { "state_after": "α : Type ?u.290686\nβ : Type ?u.290689\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≤ b / c\n⊢ a * c⁻¹⁻¹ ≤ b", "state_before": "α : Type ?u.290686\nβ : Type ?u.290689\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≤ b / c\n⊢ a * c ≤ b", "tactic": "rw [← inv_inv c]" }, { "state_after": "no goals", ...
[ 1599, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1597, 1 ]
Mathlib/Data/Set/Basic.lean
Set.union_diff_cancel'
[]
[ 1826, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1825, 1 ]
Mathlib/Analysis/Calculus/ContDiff.lean
ContDiff.fst
[]
[ 748, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 747, 1 ]
Mathlib/Algebra/GroupWithZero/Defs.lean
zero_ne_mul_self
[]
[ 285, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 285, 1 ]
Mathlib/Analysis/SpecialFunctions/Arsinh.lean
Real.arsinh_eq_zero_iff
[]
[ 161, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 160, 1 ]
Mathlib/Data/Num/Lemmas.lean
PosNum.sub'_one
[ { "state_after": "no goals", "state_before": "a : PosNum\n⊢ sub' a 1 = toZNum (pred' a)", "tactic": "cases a <;> rfl" } ]
[ 819, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 819, 1 ]
Mathlib/CategoryTheory/Monad/Limits.lean
CategoryTheory.Monad.forget_creates_colimits_of_monad_preserves
[]
[ 279, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 277, 1 ]
Mathlib/Data/Nat/Pairing.lean
Set.iInter_unpair
[]
[ 221, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 219, 1 ]
Mathlib/Algebra/Group/Units.lean
divp_divp_eq_divp_mul
[ { "state_after": "no goals", "state_before": "α : Type u\ninst✝ : Monoid α\na b c x : α\nu₁ u₂ : αˣ\n⊢ x /ₚ u₁ /ₚ u₂ = x /ₚ (u₂ * u₁)", "tactic": "simp only [divp, mul_inv_rev, Units.val_mul, mul_assoc]" } ]
[ 483, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 482, 1 ]
Mathlib/Data/Polynomial/Degree/Definitions.lean
Polynomial.leadingCoeff_X_sub_C
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝² : Ring R\ninst✝¹ : Nontrivial R\ninst✝ : Ring S\nr : S\n⊢ leadingCoeff (X - ↑C r) = 1", "tactic": "rw [sub_eq_add_neg, ← map_neg C r, leadingCoeff_X_add_C]" } ]
[ 1506, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1505, 1 ]
Mathlib/Data/Set/Intervals/Basic.lean
Set.Ici_diff_Ioi
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.61203\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ici a \\ Ioi b = Icc a b", "tactic": "rw [diff_eq, compl_Ioi, Ici_inter_Iic]" } ]
[ 1084, 92 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1084, 1 ]
Mathlib/LinearAlgebra/Basis.lean
Basis.forall_coord_eq_zero_iff
[ { "state_after": "no goals", "state_before": "ι : Type u_3\nι' : Type ?u.68644\nR : Type u_1\nR₂ : Type ?u.68650\nK : Type ?u.68653\nM : Type u_2\nM' : Type ?u.68659\nM'' : Type ?u.68662\nV : Type u\nV' : Type ?u.68667\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMono...
[ 224, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 222, 1 ]
Mathlib/Analysis/Asymptotics/Asymptotics.lean
Asymptotics.isLittleO_abs_right
[]
[ 740, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 739, 1 ]
Mathlib/GroupTheory/FreeGroup.lean
FreeGroup.map_inv
[]
[ 1052, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1051, 1 ]
Mathlib/Init/Data/Nat/Lemmas.lean
Nat.bit0_ne_bit1
[]
[ 114, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 113, 11 ]