file_path
stringlengths
11
79
full_name
stringlengths
2
100
traced_tactics
list
end
list
commit
stringclasses
4 values
url
stringclasses
4 values
start
list
Mathlib/Algebra/Module/LocalizedModule.lean
IsLocalizedModule.iso_symm_apply'
[ { "state_after": "no goals", "state_before": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_3\nM' : Type u_2\nM'' : Type ?u.688815\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] ...
[ 836, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 830, 1 ]
Mathlib/Data/Nat/Choose/Central.lean
Nat.centralBinom_pos
[]
[ 45, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 44, 1 ]
Mathlib/LinearAlgebra/SesquilinearForm.lean
LinearMap.IsAdjointPair.mul
[]
[ 465, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 463, 1 ]
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean
NonUnitalSubsemiring.coe_sInf
[]
[ 433, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 431, 1 ]
Mathlib/Algebra/Order/Ring/Lemmas.lean
mul_le_iff_le_one_right
[ { "state_after": "no goals", "state_before": "α : Type u_1\na b c d : α\ninst✝⁴ : MulOneClass α\ninst✝³ : Zero α\ninst✝² : Preorder α\ninst✝¹ : PosMulMono α\ninst✝ : PosMulMonoRev α\na0 : 0 < a\n⊢ a * b ≤ a ↔ a * b ≤ a * 1", "tactic": "rw [mul_one]" } ]
[ 628, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 627, 1 ]
Mathlib/Topology/Maps.lean
QuotientMap.of_quotientMap_compose
[ { "state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.137691\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ng : β → γ\nf : α → β\nhf : Continuous f\nhg : Continuous g\nhgf : QuotientMap (g ∘ f)\n⊢ coinduced g (coinduced f ins...
[ 305, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 300, 11 ]
Mathlib/Data/PNat/Xgcd.lean
PNat.gcd_b_eq
[]
[ 531, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 530, 1 ]
Mathlib/Order/CompleteLattice.lean
iInf_subtype''
[]
[ 1220, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1219, 1 ]
Mathlib/Data/Set/Pointwise/SMul.lean
Set.preimage_smul_inv
[]
[ 904, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 903, 1 ]
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean
intervalIntegral.continuousOn_primitive_Icc
[ { "state_after": "ι : Type ?u.18353564\n𝕜 : Type ?u.18353567\nE : Type u_1\nF : Type ?u.18353573\nA : Type ?u.18353576\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\na b b₀ b₁ b₂ : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → E\ninst✝ : NoAtoms μ\nh_int : IntegrableOn f (Icc a...
[ 1216, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1210, 1 ]
Mathlib/Analysis/Calculus/FDerivAnalytic.lean
AnalyticAt.differentiableAt
[]
[ 57, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 56, 1 ]
Mathlib/NumberTheory/LucasLehmer.lean
LucasLehmer.residue_eq_zero_iff_sMod_eq_zero
[ { "state_after": "p : ℕ\nw : 1 < p\n⊢ sZMod p (p - 2) = 0 ↔ sMod p (p - 2) = 0", "state_before": "p : ℕ\nw : 1 < p\n⊢ lucasLehmerResidue p = 0 ↔ sMod p (p - 2) = 0", "tactic": "dsimp [lucasLehmerResidue]" }, { "state_after": "p : ℕ\nw : 1 < p\n⊢ ↑(sMod p (p - 2)) = 0 ↔ sMod p (p - 2) = 0", "...
[ 163, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 149, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.OuterMeasure.le_boundedBy'
[ { "state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\nμ : OuterMeasure α\n⊢ ∀ (a : Set α), ↑μ a ≤ m a ↔ Set.Nonempty a → ↑μ a ≤ m a", "state_before": "α : Type u_1\nm : Set α → ℝ≥0∞\nμ : OuterMeasure α\n⊢ μ ≤ boundedBy m ↔ ∀ (s : Set α), Set.Nonempty s → ↑μ s ≤ m s", "tactic": "rw [le_boundedBy, forall_cong...
[ 882, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 878, 1 ]
Mathlib/LinearAlgebra/Finsupp.lean
Finsupp.supported_comap_lmapDomain
[ { "state_after": "α : Type u_2\nM : Type u_3\nN : Type ?u.243431\nP : Type ?u.243434\nR : Type u_4\nS : Type ?u.243440\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nα' : Type ...
[ 472, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 467, 1 ]
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean
QuaternionGroup.card
[ { "state_after": "n : ℕ\ninst✝ : NeZero n\n⊢ n + n + (n + n) = 4 * n", "state_before": "n : ℕ\ninst✝ : NeZero n\n⊢ Fintype.card (QuaternionGroup n) = 4 * n", "tactic": "rw [← Fintype.card_eq.mpr ⟨fintypeHelper⟩, Fintype.card_sum, ZMod.card, two_mul]" }, { "state_after": "no goals", "state_be...
[ 179, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 177, 1 ]
Mathlib/RingTheory/RootsOfUnity/Complex.lean
IsPrimitiveRoot.arg
[ { "state_after": "n : ℕ\nζ : ℂ\nh : ∃ i, i < n ∧ ∃ x, Complex.exp (2 * ↑Real.pi * Complex.I * (↑i / ↑n)) = ζ\nhn : n ≠ 0\n⊢ ∃ i, Complex.arg ζ = ↑i / ↑n * (2 * Real.pi) ∧ IsCoprime i ↑n ∧ Int.natAbs i < n", "state_before": "n : ℕ\nζ : ℂ\nh : IsPrimitiveRoot ζ n\nhn : n ≠ 0\n⊢ ∃ i, Complex.arg ζ = ↑i / ↑n * ...
[ 189, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 135, 1 ]
Mathlib/RepresentationTheory/Action.lean
Action.neg_hom
[]
[ 402, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 401, 1 ]
Mathlib/MeasureTheory/Function/L1Space.lean
MeasureTheory.Integrable.toL1_neg
[]
[ 1385, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1384, 1 ]
Mathlib/RingTheory/Polynomial/Basic.lean
Ideal.mem_ofPolynomial
[]
[ 488, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 487, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Mul.lean
HasStrictFDerivAt.mul
[ { "state_after": "case h.e'_10.h.e'_6\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type ?u.681201\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type ?u.681296\ninst✝⁷ : NormedAddCommGroup G\ninst✝⁶ : NormedSp...
[ 294, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 290, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_bit0_atTop
[]
[ 677, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 676, 15 ]
Mathlib/Computability/Reduce.lean
ManyOneDegree.liftOn_eq
[]
[ 394, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 392, 11 ]
Mathlib/Algebra/Support.lean
Function.range_subset_insert_image_mulSupport
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ : Type ?u.7733\nA : Type ?u.7736\nB : Type ?u.7739\nM : Type u_1\nN : Type ?u.7745\nP : Type ?u.7748\nR : Type ?u.7751\nS : Type ?u.7754\nG : Type ?u.7757\nM₀ : Type ?u.7760\nG₀ : Type ?u.7763\nι : Sort ?u.7766\ninst✝² : One M\ninst✝¹ : One N\nin...
[ 126, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 123, 1 ]
Mathlib/Data/PFunctor/Univariate/Basic.lean
PFunctor.W.mk_dest
[ { "state_after": "case mk\nP : PFunctor\nα β : Type u\na✝ : P.A\nf✝ : B P a✝ → WType P.B\n⊢ mk (dest (WType.mk a✝ f✝)) = WType.mk a✝ f✝", "state_before": "P : PFunctor\nα β : Type u\np : W P\n⊢ mk (dest p) = p", "tactic": "cases p" }, { "state_after": "no goals", "state_before": "case mk\nP ...
[ 118, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 118, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.restrict_iUnion_ae
[ { "state_after": "no goals", "state_before": "α : Type u_2\nβ : Type ?u.359713\nγ : Type ?u.359716\nδ : Type ?u.359719\nι : Type u_1\nR : Type ?u.359725\nR' : Type ?u.359728\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\n...
[ 2164, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2162, 1 ]
Mathlib/Order/Cover.lean
Wcovby.covby_of_not_le
[]
[ 289, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 288, 1 ]
Mathlib/Analysis/Asymptotics/Asymptotics.lean
Asymptotics.isBigOWith_const_const
[ { "state_after": "α : Type u_2\nβ : Type ?u.273806\nE : Type u_3\nF : Type ?u.273812\nG : Type ?u.273815\nE' : Type ?u.273818\nF' : Type ?u.273821\nG' : Type ?u.273824\nE'' : Type ?u.273827\nF'' : Type u_1\nG'' : Type ?u.273833\nR : Type ?u.273836\nR' : Type ?u.273839\n𝕜 : Type ?u.273842\n𝕜' : Type ?u.273845\...
[ 1248, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1241, 1 ]
Mathlib/Algebra/Algebra/Operations.lean
Submodule.pow_induction_on_right
[]
[ 498, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 493, 11 ]
Std/Data/Rat/Lemmas.lean
Rat.mkRat_zero
[ { "state_after": "no goals", "state_before": "n : Int\n⊢ mkRat n 0 = 0", "tactic": "simp [mkRat_def]" } ]
[ 99, 70 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 99, 9 ]
Mathlib/Init/Data/Nat/Bitwise.lean
Nat.div2_val
[ { "state_after": "n : ℕ\n⊢ n % 2 + 2 * div2 n = n", "state_before": "n : ℕ\n⊢ div2 n = n / 2", "tactic": "refine'\n Nat.eq_of_mul_eq_mul_left (by decide)\n (Nat.add_left_cancel (Eq.trans _ (Nat.mod_add_div n 2).symm))" }, { "state_after": "no goals", "state_before": "n : ℕ\n⊢ n % 2 + 2 *...
[ 144, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 140, 1 ]
Mathlib/Algebra/DirectSum/Basic.lean
DirectSum.toAddMonoid_of
[]
[ 207, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 206, 1 ]
Mathlib/Data/List/Rdrop.lean
List.rdrop_concat_succ
[ { "state_after": "no goals", "state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\n⊢ rdrop (l ++ [x]) (n + 1) = rdrop l n", "tactic": "simp [rdrop_eq_reverse_drop_reverse]" } ]
[ 67, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 66, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.roots_X
[ { "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]\n⊢ roots X = {0}", "tactic": "rw [← roots_X_sub_C, C_0, sub_zero]" } ]
[ 655, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 655, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Independent.lean
affineIndependent_iff_eq_of_fintype_affineCombination_eq
[ { "state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ninst✝ : Fintype ι\np : ι → P\n⊢ (∀ (s1 s2 : Finset ι) (w1 w2 : ι → k),\n ∑ i in s1, w1 i = 1 →\n ∑ i in s2, w2 i = 1 →\n ↑(Finse...
[ 253, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 239, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_const_mul_atTop_iff_pos
[ { "state_after": "ι : Type ?u.217364\nι' : Type ?u.217367\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.217376\ninst✝¹ : LinearOrderedSemifield α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\ninst✝ : NeBot l\nh : Tendsto f l atTop\nhrf : Tendsto (fun x => r * f x) l atTop\nhr : r ≤ 0\n⊢ False", "state_before": "ι : ...
[ 1022, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1018, 1 ]
Mathlib/Algebra/Group/Basic.lean
inv_mul_eq_one
[ { "state_after": "no goals", "state_before": "α : Type ?u.55705\nβ : Type ?u.55708\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ a⁻¹ * b = 1 ↔ a = b", "tactic": "rw [mul_eq_one_iff_eq_inv, inv_inj]" } ]
[ 721, 87 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 721, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean
Complex.sin_add_two_pi
[]
[ 1149, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1148, 1 ]
Mathlib/ModelTheory/Definability.lean
FirstOrder.Language.DefinableSet.mem_inf
[]
[ 329, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 328, 1 ]
Mathlib/Topology/ContinuousOn.lean
continuousOn_singleton
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.318436\nδ : Type ?u.318439\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\na : α\n⊢ ContinuousWithinAt f {a} a", "tactic": "simpa only [Con...
[ 673, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 670, 1 ]
Mathlib/Data/Complex/Exponential.lean
Real.sin_sq_add_cos_sq
[ { "state_after": "no goals", "state_before": "x y : ℝ\n⊢ ↑(sin x ^ 2 + cos x ^ 2) = ↑1", "tactic": "simp [sin_sq_add_cos_sq]" } ]
[ 1243, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1242, 8 ]
Mathlib/ModelTheory/Semantics.lean
FirstOrder.Language.Term.realize_varsToConstants
[ { "state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.19079\nP : Type ?u.19082\ninst✝⁴ : Structure L M\ninst✝³ : Structure L N\ninst✝² : Structure L P\nα : Type u'\nβ : Type v'\ninst✝¹ : Structure (L[[α]]) M\ninst✝ : LHom.IsExpansionOn (lhomWithConstants L α) M\nv : β → M\nab : α ⊕ β\...
[ 192, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 182, 1 ]
Mathlib/Algebra/Star/Order.lean
star_mul_self_nonneg'
[ { "state_after": "no goals", "state_before": "R : Type u\ninst✝² : NonUnitalSemiring R\ninst✝¹ : PartialOrder R\ninst✝ : StarOrderedRing R\nr : R\n⊢ 0 ≤ r * star r", "tactic": "simpa only [star_star] using star_mul_self_nonneg (star r)" } ]
[ 161, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 160, 1 ]
Mathlib/Data/List/Basic.lean
List.lookmap_of_forall_not
[]
[ 3327, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3326, 1 ]
Mathlib/Order/Hom/Basic.lean
OrderIso.map_top
[]
[ 1183, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1182, 1 ]
Mathlib/Data/Set/Pointwise/SMul.lean
Set.mem_inv_smul_set_iff
[ { "state_after": "no goals", "state_before": "F : Type ?u.107575\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.107584\ninst✝¹ : Group α\ninst✝ : MulAction α β\ns t A B : Set β\na : α\nx : β\n⊢ x ∈ a⁻¹ • A ↔ a • x ∈ A", "tactic": "simp only [← image_smul, mem_image, inv_smul_eq_iff, exists_eq_right]" } ]
[ 892, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 891, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean
CategoryTheory.Limits.IsZero.of_epi_eq_zero
[ { "state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : Epi 0\n⊢ IsZero Y", "state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : Epi f\nh : f = 0...
[ 212, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 1 ]
Mathlib/Data/Set/Image.lean
Set.forall_range_iff
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.62770\nγ : Type ?u.62773\nι : Sort u_2\nι' : Sort ?u.62779\nf : ι → α\ns t : Set α\np : α → Prop\n⊢ (∀ (a : α), a ∈ range f → p a) ↔ ∀ (i : ι), p (f i)", "tactic": "simp" } ]
[ 660, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 660, 1 ]
Mathlib/Data/Stream/Init.lean
Stream'.corec_def
[]
[ 375, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 374, 1 ]
Mathlib/Data/FunLike/Embedding.lean
EmbeddingLike.comp_injective
[]
[ 158, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/SetTheory/Game/PGame.lean
PGame.sub_congr
[]
[ 1785, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1784, 1 ]
Mathlib/Order/SymmDiff.lean
bihimp_eq_bot
[ { "state_after": "no goals", "state_before": "ι : Type ?u.90223\nα : Type u_1\nβ : Type ?u.90229\nπ : ι → Type ?u.90234\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ⇔ b = ⊥ ↔ IsCompl a b", "tactic": "rw [bihimp_eq', ← compl_sup, sup_eq_bot_iff, compl_eq_bot, isCompl_iff, disjoint_iff,\n codisjoint_iff]"...
[ 765, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 763, 1 ]
Mathlib/Data/Dfinsupp/Multiset.lean
Multiset.toDfinsupp_support
[]
[ 67, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 66, 1 ]
Mathlib/GroupTheory/Subgroup/Pointwise.lean
AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀
[]
[ 536, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 534, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
Real.hasStrictDerivAt_cos
[]
[ 604, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 603, 1 ]
Mathlib/Data/Set/Prod.lean
Set.eval_image_univ_pi
[]
[ 820, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 818, 1 ]
Mathlib/Data/List/Sort.lean
List.perm_mergeSort
[ { "state_after": "no goals", "state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\n⊢ mergeSort r [] ~ []", "tactic": "simp [mergeSort]" }, { "state_after": "no goals", "state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\na : α\n⊢ mergeSort r [a] ~ [a]", ...
[ 399, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 389, 1 ]
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean
MeasureTheory.Integrable.integral_prod_left
[]
[ 332, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 325, 1 ]
Mathlib/Analysis/NormedSpace/LinearIsometry.lean
LinearIsometryEquiv.symm_apply_apply
[]
[ 748, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 747, 1 ]
Std/Data/RBMap/Alter.lean
Std.RBNode.cmpEq.RootOrdered_congr
[]
[ 250, 64 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 246, 1 ]
Mathlib/Logic/Basic.lean
Decidable.forall_or_right
[ { "state_after": "no goals", "state_before": "ι : Sort ?u.22270\nα : Sort ?u.22275\nκ : ι → Sort ?u.22272\np✝ q✝ : α → Prop\nq : Prop\np : α → Prop\ninst✝ : Decidable q\n⊢ (∀ (x : α), p x ∨ q) ↔ (∀ (x : α), p x) ∨ q", "tactic": "simp [or_comm, Decidable.forall_or_left]" } ]
[ 853, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 852, 11 ]
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean
Ordinal.CNF_of_lt
[ { "state_after": "no goals", "state_before": "b o : Ordinal\nho : o ≠ 0\nhb : o < b\n⊢ CNF b o = [(0, o)]", "tactic": "simp only [CNF_ne_zero ho, log_eq_zero hb, opow_zero, div_one, mod_one, CNF_zero]" } ]
[ 112, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 111, 1 ]
Mathlib/NumberTheory/PellMatiyasevic.lean
Pell.pellZd_add
[ { "state_after": "no goals", "state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\n⊢ pellZd a1 (m + (n + 1)) = pellZd a1 m * pellZd a1 (n + 1)", "tactic": "rw [← add_assoc, pellZd_succ, pellZd_succ, pellZd_add _ n, ← mul_assoc]" } ]
[ 363, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 361, 1 ]
Mathlib/Order/Cover.lean
covby_iff_wcovby_and_not_le
[]
[ 305, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 304, 1 ]
Mathlib/Topology/MetricSpace/ShrinkingLemma.lean
exists_locallyFinite_iUnion_eq_ball_radius_lt
[]
[ 128, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 122, 1 ]
Mathlib/GroupTheory/Submonoid/Membership.lean
Submonoid.mul_mem_sup
[]
[ 252, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 251, 1 ]
Mathlib/Order/Bounded.lean
Set.unbounded_lt_Ici
[]
[ 297, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 296, 1 ]
Mathlib/Algebra/Group/Basic.lean
div_mul_eq_div_mul_one_div
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.42444\nG : Type ?u.42447\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / (b * c) = a / b * (1 / c)", "tactic": "simp" } ]
[ 580, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 580, 1 ]
Mathlib/Data/Seq/Computation.lean
Computation.exists_of_mem_bind
[]
[ 852, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 848, 1 ]
Mathlib/Data/Set/Basic.lean
Set.univ_eq_true_false
[ { "state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nx : Prop\n⊢ x = True ∨ x = False", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nx : Prop\n⊢ x ∈ {True, False}", "tactic": "rw [mem_insert_iff, mem...
[ 2639, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2636, 1 ]
Mathlib/Analysis/Normed/Group/Quotient.lean
quotient_norm_mk_eq
[ { "state_after": "M : Type u_1\nN : Type ?u.113147\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nm : M\n⊢ (⨅ (y : ↑↑S), dist (-m) ↑y) = ⨅ (a : ↑↑S), ‖m + ↑a‖", "state_before": "M : Type u_1\nN : Type ?u.113147\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedA...
[ 168, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 164, 1 ]
Mathlib/Algebra/Algebra/Operations.lean
Submodule.iSup_mul
[]
[ 358, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 357, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.restrict_apply'
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.283030\nγ : Type ?u.283033\nδ : Type ?u.283036\nι : Type ?u.283039\nR : Type ?u.283042\nR' : Type ?u.283045\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ...
[ 1562, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1560, 1 ]
Mathlib/RingTheory/Subsemiring/Basic.lean
RingHom.coe_rangeSRestrict
[]
[ 1171, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1170, 1 ]
Mathlib/Analysis/NormedSpace/lpSpace.lean
lp.single_apply_ne
[ { "state_after": "no goals", "state_before": "α : Type u_1\nE : α → Type u_2\np✝ q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type ?u.862305\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), BoundedSMul 𝕜 (E i)\ninst✝ : DecidableEq α\np : ℝ≥0∞\ni : α\na : E i\n...
[ 1012, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1010, 11 ]
Mathlib/Analysis/Normed/Group/AddTorsor.lean
dist_vadd_vadd_le
[ { "state_after": "no goals", "state_before": "α : Type ?u.18232\nV : Type u_2\nP : Type u_1\nW : Type ?u.18241\nQ : Type ?u.18244\ninst✝⁵ : SeminormedAddCommGroup V\ninst✝⁴ : PseudoMetricSpace P\ninst✝³ : NormedAddTorsor V P\ninst✝² : NormedAddCommGroup W\ninst✝¹ : MetricSpace Q\ninst✝ : NormedAddTorsor W Q...
[ 175, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 172, 1 ]
Mathlib/Topology/Bornology/Hom.lean
LocallyBoundedMap.comp_assoc
[]
[ 181, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 179, 1 ]
Mathlib/Analysis/SpecificLimits/Normed.lean
NormedField.continuousAt_zpow
[ { "state_after": "α : Type ?u.63999\nβ : Type ?u.64002\nι : Type ?u.64005\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nm : ℤ\nx : 𝕜\n⊢ ContinuousAt (fun x => x ^ m) x → x ≠ 0 ∨ 0 ≤ m", "state_before": "α : Type ?u.63999\nβ : Type ?u.64002\nι : Type ?u.64005\n𝕜 : Type u_1\ninst✝ : NontriviallyNormed...
[ 84, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 79, 1 ]
Mathlib/Algebra/GroupPower/Ring.lean
pow_eq_zero_of_le
[ { "state_after": "no goals", "state_before": "R : Type ?u.11506\nS : Type ?u.11509\nM : Type u_1\ninst✝ : MonoidWithZero M\nx : M\nn m : ℕ\nhn : n ≤ m\nhx : x ^ n = 0\n⊢ x ^ m = 0", "tactic": "rw [← tsub_add_cancel_of_le hn, pow_add, hx, mul_zero]" } ]
[ 54, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 53, 1 ]
Mathlib/GroupTheory/SemidirectProduct.lean
SemidirectProduct.mul_right
[]
[ 80, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 80, 1 ]
Mathlib/CategoryTheory/StructuredArrow.lean
CategoryTheory.CostructuredArrow.mk_left
[]
[ 302, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 301, 1 ]
Mathlib/Algebra/DirectSum/Decomposition.lean
DirectSum.decompose_of_mem_same
[ { "state_after": "no goals", "state_before": "ι : Type u_3\nR : Type ?u.121042\nM : Type u_1\nσ : Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddCommMonoid M\ninst✝² : SetLike σ M\ninst✝¹ : AddSubmonoidClass σ M\nℳ : ι → σ\ninst✝ : Decomposition ℳ\nx : M\ni : ι\nhx : x ∈ ℳ i\n⊢ ↑(↑(↑(decompose ℳ) x) i) = x",...
[ 122, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 121, 1 ]
Mathlib/Algebra/MonoidAlgebra/Grading.lean
AddMonoidAlgebra.mem_grade_iff
[ { "state_after": "M : Type u_2\nι : Type ?u.6758\nR : Type u_1\ninst✝¹ : DecidableEq M\ninst✝ : CommSemiring R\nm : M\na : AddMonoidAlgebra R M\n⊢ a ∈ grade R m ↔ ↑a.support ⊆ {m}", "state_before": "M : Type u_2\nι : Type ?u.6758\nR : Type u_1\ninst✝¹ : DecidableEq M\ninst✝ : CommSemiring R\nm : M\na : AddM...
[ 71, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 69, 1 ]
Mathlib/Analysis/Analytic/Basic.lean
HasFPowerSeriesOnBall.congr
[ { "state_after": "case h.e'_6\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.402679\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\nf g : E ...
[ 434, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 427, 1 ]
Mathlib/Data/Vector/Basic.lean
Vector.prod_set
[ { "state_after": "n : ℕ\nα : Type u_1\nβ : Type ?u.60631\nγ : Type ?u.60634\ninst✝ : Monoid α\nv : Vector α n\ni : Fin n\na : α\n⊢ (List.prod (List.take (↑i) (toList v)) * if ↑i < List.length (toList v) then a else 1) *\n List.prod (List.drop (↑i + 1) (toList v)) =\n List.prod (toList (take (↑i) v)) * a...
[ 616, 11 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 613, 1 ]
Mathlib/LinearAlgebra/LinearPMap.lean
LinearPMap.sup_le
[]
[ 373, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 11 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.natDegree_eq_zero_of_isUnit
[ { "state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\nh : IsUnit p\n✝ : Nontrivial R\n⊢ natDegree p = 0", "state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q : R[X]\...
[ 216, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 211, 1 ]
Mathlib/Algebra/Ring/Equiv.lean
RingEquiv.map_ne_one_iff
[]
[ 510, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 509, 1 ]
Mathlib/Analysis/Calculus/FDerivSymmetric.lean
Convex.second_derivative_within_at_symmetric_of_mem_interior
[ { "state_after": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ (x : E), x ∈ interior s → HasFDerivAt f (f' x) x\nx : E\nx...
[ 256, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 236, 1 ]
Mathlib/Algebra/Lie/Basic.lean
LieModuleHom.map_add
[]
[ 736, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 735, 1 ]
Std/Data/Int/Lemmas.lean
Int.natAbs_add_le
[ { "state_after": "a b : Int\n⊢ ∀ (a b : Nat), natAbs (subNatNat a (succ b)) ≤ succ (a + b)", "state_before": "a b : Int\n⊢ natAbs (a + b) ≤ natAbs a + natAbs b", "tactic": "suffices ∀ a b : Nat, natAbs (subNatNat a b.succ) ≤ (a + b).succ by\n match a, b with\n | (a:Nat), (b:Nat) => simp\n | (a:Nat), ...
[ 1349, 27 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1334, 1 ]
Mathlib/Data/Multiset/Fintype.lean
Multiset.prod_eq_prod_coe
[ { "state_after": "case e_a\nα : Type u_1\ninst✝¹ : DecidableEq α\nm✝ : Multiset α\ninst✝ : CommMonoid α\nm : Multiset α\n⊢ m = map (fun x => x.fst) Finset.univ.val", "state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\nm✝ : Multiset α\ninst✝ : CommMonoid α\nm : Multiset α\n⊢ prod m = ∏ x : ToType m, x.fst...
[ 266, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 263, 1 ]
Mathlib/Algebra/Module/Injective.lean
Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension
[]
[ 327, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 324, 1 ]
Mathlib/LinearAlgebra/Finsupp.lean
LinearMap.map_finsupp_total
[]
[ 1154, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1151, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean
CategoryTheory.IsPullback.isoPullback_hom_snd
[ { "state_after": "C : Type u₁\ninst✝¹ : Category C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\ninst✝ : HasPullback f g\n⊢ (limit.isoLimitCone { cone := PullbackCone.mk fst snd (_ : fst ≫ f = snd ≫ g), isLimit := isLimit h }).inv ≫\n pullback.snd =\n snd", ...
[ 298, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 295, 1 ]
Mathlib/Algebra/Free.lean
Magma.AssocQuotient.map_of
[]
[ 438, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 438, 1 ]
Mathlib/Algebra/GroupPower/Lemmas.lean
MonoidHom.ext_mnat
[ { "state_after": "no goals", "state_before": "α : Type ?u.345545\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Monoid M\nf g : Multiplicative ℕ →* M\nh : ↑f (↑Multiplicative.ofAdd 1) = ↑g (↑Multiplicative.ofAdd 1)\nn : Multiplicative ℕ\n⊢ ↑f n = ↑...
[ 902, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 900, 1 ]
Mathlib/RingTheory/Valuation/Basic.lean
AddValuation.map_add
[]
[ 682, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 681, 1 ]
Mathlib/GroupTheory/Congruence.lean
Con.coe_mk'
[]
[ 874, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 873, 1 ]
Mathlib/CategoryTheory/Equivalence.lean
CategoryTheory.Equivalence.inverse_inv
[]
[ 582, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 581, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
measure_Ioo_lt_top
[]
[ 4602, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 4601, 1 ]