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Mathlib/Data/Polynomial/EraseLead.lean
Polynomial.eraseLead_add_C_mul_X_pow
[ { "state_after": "no goals", "state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\n⊢ eraseLead f + ↑C (leadingCoeff f) * X ^ natDegree f = f", "tactic": "rw [C_mul_X_pow_eq_monomial, eraseLead_add_monomial_natDegree_leadingCoeff]" } ]
[ 74, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 72, 1 ]
Mathlib/Algebra/Invertible.lean
invOf_eq_right_inv
[]
[ 151, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 150, 1 ]
Mathlib/Data/Quot.lean
Setoid.ext
[ { "state_after": "α✝ : Sort ?u.8\nβ : Sort ?u.11\nα : Sort u_1\nr : α → α → Prop\niseqv✝¹ : Equivalence r\np : α → α → Prop\niseqv✝ : Equivalence p\nEq : ∀ (a b : α), Setoid.r a b ↔ Setoid.r a b\nthis : r = p\n⊢ { r := r, iseqv := iseqv✝¹ } = { r := p, iseqv := iseqv✝ }", "state_before": "α✝ : Sort ?u.8\nβ ...
[ 33, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 28, 1 ]
Mathlib/Data/Sum/Basic.lean
Sum.getRight_swap
[ { "state_after": "no goals", "state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.23345\nδ : Type ?u.23348\nx : α ⊕ β\n⊢ getRight (swap x) = getLeft x", "tactic": "cases x <;> rfl" } ]
[ 381, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 381, 1 ]
Mathlib/GroupTheory/Perm/Fin.lean
Fin.cycleRange_of_le
[ { "state_after": "case zero\ni j : Fin (Nat.succ Nat.zero)\nh : j ≤ i\n⊢ ↑(cycleRange i) j = if j = i then 0 else j + 1\n\ncase succ\nn✝ : ℕ\ni j : Fin (Nat.succ (Nat.succ n✝))\nh : j ≤ i\n⊢ ↑(cycleRange i) j = if j = i then 0 else j + 1", "state_before": "n : ℕ\ni j : Fin (Nat.succ n)\nh : j ≤ i\n⊢ ↑(cycle...
[ 187, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 172, 1 ]
Mathlib/Analysis/SpecialFunctions/Exponential.lean
hasStrictDerivAt_exp_zero
[]
[ 212, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 211, 1 ]
Mathlib/Topology/MetricSpace/HausdorffDistance.lean
Metric.ball_infDist_compl_subset
[]
[ 546, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 545, 1 ]
Mathlib/Logic/Encodable/Basic.lean
Encodable.choose_spec
[]
[ 592, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 591, 1 ]
Mathlib/Analysis/Calculus/LHopital.lean
HasDerivAt.lhopital_zero_right_on_Ico
[ { "state_after": "case refine'_1\na b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\nhgg' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt g (g' x) x\nhcf : ContinuousOn f (Ico a b)\nhcg : ContinuousOn g (Ico a b)\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → g' x ≠ 0\nhfa : f ...
[ 108, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 99, 1 ]
Mathlib/Combinatorics/SimpleGraph/Prod.lean
SimpleGraph.boxProd_neighborSet
[ { "state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9830\nG : SimpleGraph α\nH : SimpleGraph β\nx : α × β\na' : α\nb' : β\n⊢ (a', b') ∈ neighborSet (G □ H) x ↔ (a', b') ∈ neighborSet G x.fst ×ˢ {x.snd} ∪ {x.fst} ×ˢ neighborSet H x.snd", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ...
[ 75, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 71, 1 ]
Mathlib/Topology/SubsetProperties.lean
IsCompact.elim_nhds_subcover
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nι : Type ?u.14579\nπ : ι → Type ?u.14584\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t✝ : Set α\nhs : IsCompact s\nU : α → Set α\nhU : ∀ (x : α), x ∈ s → U x ∈ 𝓝 x\nt : Finset ↑s\nht : s ⊆ ⋃ (x : ↑s) (_ : x ∈ t), U ↑x\n⊢ ...
[ 213, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 207, 1 ]
Mathlib/Combinatorics/Young/YoungDiagram.lean
YoungDiagram.transpose_eq_iff_eq_transpose
[ { "state_after": "case mpr\nν : YoungDiagram\n⊢ transpose (transpose ν) = ν", "state_before": "case mpr\nμ ν : YoungDiagram\n⊢ μ = transpose ν → transpose μ = ν", "tactic": "rintro rfl" }, { "state_after": "no goals", "state_before": "case mpr\nν : YoungDiagram\n⊢ transpose (transpose ν) = ν...
[ 231, 11 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 228, 1 ]
Mathlib/Algebra/RingQuot.lean
RingQuot.lift_unique
[ { "state_after": "case w.a\nR : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr✝ : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\nf : R →+* T\nr : R → R → Prop\nw : ∀ ⦃x y : R⦄, r x y → ↑f x = ↑f y\ng : RingQuot r →+* T\nh : RingHom.c...
[ 470, 11 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 467, 1 ]
Mathlib/Data/Complex/Module.lean
Complex.reLm_coe
[]
[ 266, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 265, 1 ]
Mathlib/Analysis/Convex/Between.lean
mem_vsub_const_affineSegment
[ { "state_after": "no goals", "state_before": "R : Type u_3\nV : Type u_1\nV' : Type ?u.55686\nP : Type u_2\nP' : Type ?u.55692\ninst✝⁶ : OrderedRing 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'\nx y z p : P\n...
[ 139, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 137, 1 ]
Mathlib/ModelTheory/Substructures.lean
FirstOrder.Language.Substructure.closure_eq_of_le
[]
[ 297, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 296, 1 ]
Mathlib/Algebra/CubicDiscriminant.lean
Cubic.coeff_eq_c
[]
[ 116, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 115, 1 ]
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean
Real.rpow_def_of_nonpos
[ { "state_after": "case inr\nx : ℝ\nhx : x ≤ 0\ny : ℝ\nh : ¬x = 0\n⊢ (↑x ^ ↑y).re = exp (log x * y) * cos (y * π)", "state_before": "x : ℝ\nhx : x ≤ 0\ny : ℝ\n⊢ x ^ y = if x = 0 then if y = 0 then 1 else 0 else exp (log x * y) * cos (y * π)", "tactic": "split_ifs with h <;> simp [rpow_def, *]" }, { ...
[ 92, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 90, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C
[]
[ 1125, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1121, 1 ]
Mathlib/CategoryTheory/Sites/Grothendieck.lean
CategoryTheory.GrothendieckTopology.top_mem
[]
[ 125, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 124, 1 ]
Mathlib/Data/Finset/Card.lean
Finset.exists_intermediate_set
[ { "state_after": "case intro\nα : Type u_1\nβ : Type ?u.43518\ns t : Finset α\nf : α → β\nn : ℕ\nA B : Finset α\ni : ℕ\nh₁ : i + card B ≤ card A\nh₂ : B ⊆ A\nk : ℕ\nh : i + card B + k = card A\n⊢ ∃ C, B ⊆ C ∧ C ⊆ A ∧ card C = i + card B", "state_before": "α : Type u_1\nβ : Type ?u.43518\ns t : Finset α\nf :...
[ 486, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 466, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean
BoxIntegral.BoxAdditiveMap.coe_injective
[]
[ 77, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 76, 1 ]
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean
DoubleCentralizer.neg_fst
[]
[ 273, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 272, 1 ]
Mathlib/Data/List/Basic.lean
List.splitOn_intercalate
[ { "state_after": "ι : Type ?u.310123\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nxs ys : List α\nls : List (List α)\nf : List α → List α\ninst✝ : DecidableEq α\nx : α\nhx : ∀ (l : List α), l ∈ ls → ¬x ∈ l\nhls : ls ≠ []\n⊢ splitOn x (join (intersperse [x] ls)) = ls", "stat...
[ 3024, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3000, 1 ]
Mathlib/ModelTheory/Basic.lean
FirstOrder.Language.empty_card
[ { "state_after": "no goals", "state_before": "L : Language\nL' : Language\n⊢ card Language.empty = 0", "tactic": "simp [card_eq_card_functions_add_card_relations]" } ]
[ 240, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 240, 1 ]
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
SimpleGraph.Walk.toDeleteEdges_cons
[]
[ 1795, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1791, 1 ]
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean
MeasureTheory.Measure.prod_dirac
[ { "state_after": "α : Type u_1\nα' : Type ?u.4489185\nβ : Type u_2\nβ' : Type ?u.4489191\nγ : Type ?u.4489194\nE : Type ?u.4489197\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ...
[ 558, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 555, 1 ]
Mathlib/MeasureTheory/Function/SimpleFunc.lean
MeasureTheory.SimpleFunc.const_lintegral
[ { "state_after": "α : Type u_1\nβ : Type ?u.889363\nγ : Type ?u.889366\nδ : Type ?u.889369\nm : MeasurableSpace α\nμ ν : Measure α\nc : ℝ≥0∞\n⊢ ∑ x in SimpleFunc.range (const α c), x * ↑↑μ (↑(const α c) ⁻¹' {x}) = c * ↑↑μ univ", "state_before": "α : Type u_1\nβ : Type ?u.889363\nγ : Type ?u.889366\nδ : Type...
[ 1094, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1090, 1 ]
Mathlib/GroupTheory/SchurZassenhaus.lean
Subgroup.SchurZassenhausInduction.step1
[ { "state_after": "G : Type u\ninst✝² : Group G\ninst✝¹ : Fintype G\nN : Subgroup G\ninst✝ : Normal N\nh1 : Nat.coprime (Fintype.card { x // x ∈ N }) (index N)\nh2 :\n ∀ (G' : Type u) [inst : Group G'] [inst_1 : Fintype G'],\n Fintype.card G' < Fintype.card G →\n ∀ {N' : Subgroup G'} [inst_2 : Normal N'...
[ 196, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 176, 9 ]
Mathlib/Data/Polynomial/Degree/Definitions.lean
Polynomial.as_sum_range
[]
[ 429, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 428, 1 ]
Mathlib/LinearAlgebra/Projection.lean
Submodule.prodEquivOfIsCompl_symm_apply_right
[ { "state_after": "no goals", "state_before": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.90945\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.91461\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.92424\ni...
[ 130, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 128, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.div_mul_cancel
[ { "state_after": "no goals", "state_before": "α : Type ?u.252386\nβ : Type ?u.252389\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh0 : a ≠ 0\nhI : a ≠ ⊤\n⊢ b / a * a = b", "tactic": "rw [div_eq_mul_inv, mul_assoc, ENNReal.inv_mul_cancel h0 hI, mul_one]" } ]
[ 1392, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1391, 11 ]
Mathlib/GroupTheory/Subsemigroup/Basic.lean
Subsemigroup.closure_empty
[]
[ 422, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 421, 1 ]
Mathlib/Topology/UnitInterval.lean
unitInterval.symm_one
[ { "state_after": "no goals", "state_before": "⊢ ↑(σ 1) = ↑0", "tactic": "simp [symm]" } ]
[ 116, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 115, 1 ]
Mathlib/Algebra/Field/Basic.lean
toLex_rat_cast
[]
[ 409, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 408, 1 ]
Mathlib/LinearAlgebra/Finsupp.lean
Finsupp.lsingle_apply
[]
[ 123, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 122, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.mapₗ_apply_of_measurable
[ { "state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.176472\nδ : Type ?u.176475\nι : Type ?u.176478\nR : Type ?u.176481\nR' : Type ?u.176484\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\nf : α → β\nhf : Measurable f\nμ : ...
[ 1167, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1164, 1 ]
Mathlib/Topology/Algebra/ConstMulAction.lean
continuousWithinAt_const_smul_iff₀
[]
[ 306, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 304, 1 ]
Mathlib/Algebra/BigOperators/Finsupp.lean
MulEquiv.map_finsupp_prod
[]
[ 232, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 230, 11 ]
Mathlib/RingTheory/UniqueFactorizationDomain.lean
WfDvdMonoid.iff_wellFounded_associates
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\n⊢ WfDvdMonoid α → WellFounded fun x x_1 => x < x_1", "tactic": "apply WfDvdMonoid.wellFounded_associates" } ]
[ 151, 87 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 149, 1 ]
Mathlib/RingTheory/Localization/Module.lean
LinearIndependent.iff_fractionRing
[]
[ 159, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/Computability/Partrec.lean
Computable.subtype_mk
[]
[ 712, 5 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 709, 1 ]
Mathlib/Data/Stream/Init.lean
Stream'.mem_const
[]
[ 239, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 238, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean
CategoryTheory.Limits.WidePullback.π_arrow
[ { "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) → objs j ⟶ B\ninst✝ : HasWidePullback B objs arrows\nj : J\n⊢ π arrows j ≫ arrows j = base arrows", "tactic": "apply limit.w (WidePullbackSh...
[ 326, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 325, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.tendsto_const_mul_atTop_iff
[ { "state_after": "case inl\nι : Type ?u.233433\nι' : Type ?u.233436\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.233445\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nhr : r < 0\n⊢ Tendsto (fun x => r * f x) l atTop ↔ 0 < r ∧ Tendsto f l atTop ∨ r < 0 ∧ Tendsto f l atBot\n\ncase in...
[ 1124, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1119, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.zero_inter
[]
[ 1759, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1758, 1 ]
Mathlib/RingTheory/Ideal/QuotientOperations.lean
Ideal.quotientKerAlgEquivOfRightInverse.apply
[]
[ 320, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 317, 1 ]
Mathlib/Data/Polynomial/Expand.lean
Polynomial.expand_eq_sum
[ { "state_after": "no goals", "state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q : ℕ\nf : R[X]\n⊢ ↑(expand R p) f = sum f fun e a => ↑C a * (X ^ p) ^ e", "tactic": "simp [expand, eval₂]" } ]
[ 50, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 49, 1 ]
Mathlib/Order/Filter/Germ.lean
Filter.Germ.liftPred_const_iff
[]
[ 308, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 307, 1 ]
Mathlib/LinearAlgebra/Basic.lean
Submodule.range_subtype
[ { "state_after": "no goals", "state_before": "R : Type u_2\nR₁ : Type ?u.1533316\nR₂ : Type ?u.1533319\nR₃ : Type ?u.1533322\nR₄ : Type ?u.1533325\nS : Type ?u.1533328\nK : Type ?u.1533331\nK₂ : Type ?u.1533334\nM : Type u_1\nM' : Type ?u.1533340\nM₁ : Type ?u.1533343\nM₂ : Type ?u.1533346\nM₃ : Type ?u.153...
[ 1622, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1622, 1 ]
Mathlib/Data/List/Sigma.lean
List.mem_keys_kunion
[ { "state_after": "case nil\nα : Type u\nβ : α → Type v\nl l₁ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl₂ : List (Sigma β)\n⊢ a ∈ keys (kunion [] l₂) ↔ a ∈ keys [] ∨ a ∈ keys l₂\n\ncase cons\nα : Type u\nβ : α → Type v\nl l₁ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nhead✝ : Sigma β\ntail✝ : ...
[ 706, 73 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 702, 1 ]
Mathlib/Data/Set/Intervals/Basic.lean
Set.Ioi_diff_Ici
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.61989\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioi a \\ Ici b = Ioo a b", "tactic": "rw [diff_eq, compl_Ici, Ioi_inter_Iio]" } ]
[ 1092, 92 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1092, 1 ]
Mathlib/Topology/UniformSpace/Basic.lean
uniformity_prod
[]
[ 1571, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1567, 1 ]
Mathlib/Analysis/LocallyConvex/StrongTopology.lean
ContinuousLinearMap.strongTopology.locallyConvexSpace
[ { "state_after": "R : Type u_2\n𝕜₁ : Type u_4\n𝕜₂ : Type u_5\nE : Type u_1\nF : Type u_3\ninst✝¹³ : AddCommGroup E\ninst✝¹² : TopologicalSpace E\ninst✝¹¹ : AddCommGroup F\ninst✝¹⁰ : TopologicalSpace F\ninst✝⁹ : TopologicalAddGroup F\ninst✝⁸ : OrderedSemiring R\ninst✝⁷ : NormedField 𝕜₁\ninst✝⁶ : NormedField �...
[ 62, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 53, 1 ]
Mathlib/Topology/UniformSpace/Basic.lean
Filter.Tendsto.uniformity_symm
[]
[ 496, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 494, 1 ]
Std/Data/Rat/Lemmas.lean
Rat.divInt_mul_left
[ { "state_after": "no goals", "state_before": "n d a : Int\na0 : a ≠ 0\n⊢ a * n /. (a * d) = n /. d", "tactic": "if d0 : d = 0 then simp [d0] else\nsimp [divInt_eq_iff (Int.mul_ne_zero a0 d0) d0, Int.mul_assoc, Int.mul_left_comm]" }, { "state_after": "no goals", "state_before": "n d a : Int\n...
[ 145, 84 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 143, 1 ]
Mathlib/Data/Real/NNReal.lean
NNReal.iInf_mul
[ { "state_after": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (⨅ (i : ι), ↑(f i)) * ↑a = ⨅ (i : ι), ↑(f i * a)", "state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ iInf f * a = ⨅ (i : ι), f i * a", "tactic": "rw [← NNReal.coe_eq, NNReal.coe_mul, coe_iInf, coe_iInf]" }, { "state_after": "no g...
[ 955, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 953, 1 ]
Mathlib/AlgebraicTopology/DoldKan/Normalized.lean
AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex
[ { "state_after": "no goals", "state_before": "A : Type u_2\ninst✝¹ : Category A\ninst✝ : Abelian A\nX✝ X : SimplicialObject A\n⊢ PInfty ≫ PInftyToNormalizedMooreComplex X = PInftyToNormalizedMooreComplex X", "tactic": "aesop_cat" } ]
[ 93, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 92, 1 ]
Mathlib/Data/List/Zip.lean
List.lt_length_right_of_zipWith
[ { "state_after": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.19964\nε : Type ?u.19967\nf : α → β → γ\ni : ℕ\nl : List α\nl' : List β\nh : i < length l ∧ i < length l'\n⊢ i < length l'", "state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.19964\nε : Type ?u.19967\nf : α → β → γ\ni :...
[ 100, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 97, 1 ]
Mathlib/Algebra/DirectSum/Module.lean
DirectSum.smul_apply
[]
[ 60, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 59, 1 ]
Mathlib/RingTheory/ChainOfDivisors.lean
DivisorChain.element_of_chain_not_isUnit_of_index_ne_zero
[]
[ 92, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/Topology/Category/TopCat/EpiMono.lean
TopCat.epi_iff_surjective
[ { "state_after": "X Y : TopCat\nf : X ⟶ Y\n⊢ Epi f ↔ Epi ((forget TopCat).map f)", "state_before": "X Y : TopCat\nf : X ⟶ Y\n⊢ Epi f ↔ Function.Surjective ((forget TopCat).map f)", "tactic": "suffices Epi f ↔ Epi ((forget TopCat).map f) by\n rw [this, CategoryTheory.epi_iff_surjective]" }, { "s...
[ 36, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 30, 1 ]
Mathlib/Tactic/NormNum/Core.lean
Mathlib.Meta.NormNum.IsRat.neg_to_eq
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : DivisionRing α\nn d : ℕ\ninv✝ : Invertible ↑d\n⊢ ↑(Int.negOfNat n) * ⅟↑d = -(↑n / ↑d)", "tactic": "simp [div_eq_mul_inv]" } ]
[ 167, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 165, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Independent.lean
weightedVSub_mem_vectorSpan_pair
[ { "state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw w₁ w₂ : ι → k\ns : Finset ι\nhw : ∑ i in s, w i = 0\nhw₁ : ∑ i in s, w₁ i = 1\nhw₂ : ∑ i in s, w₂ i = 1\n⊢ (∃ ...
[ 522, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 499, 1 ]
Mathlib/Data/Multiset/FinsetOps.lean
Multiset.cons_ndinter_of_mem
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α\na : α\ns t : Multiset α\nh : a ∈ t\n⊢ ndinter (a ::ₘ s) t = a ::ₘ ndinter s t", "tactic": "simp [ndinter, h]" } ]
[ 234, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 233, 1 ]
Mathlib/Init/Function.lean
Function.comp_const_right
[]
[ 60, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 60, 1 ]
Mathlib/Topology/Inseparable.lean
Inseparable.mem_closed_iff
[]
[ 369, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 1 ]
Mathlib/Topology/Instances/ENNReal.lean
ENNReal.tsum_comm
[]
[ 823, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 822, 11 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.Rel.mono
[ { "state_after": "case zero\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.439427\nδ : Type ?u.439430\nr✝ : α → β → Prop\np✝ : γ → δ → Prop\nr p : α → β → Prop\ns : Multiset α\nt : Multiset β\nh : ∀ (a : α), a ∈ 0 → ∀ (b : β), b ∈ 0 → r a b → p a b\n⊢ Rel p 0 0\n\ncase cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.43...
[ 2699, 92 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2692, 1 ]
Mathlib/Topology/Separation.lean
regularSpace_sInf
[ { "state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α\na : α\ns : Set α\nX : Type u_1\nT : Set (TopologicalSpace X)\nh : ∀ (t : TopologicalSpace X), t ∈ T → RegularSpace X\nx✝ : TopologicalSpace X := sInf T\n⊢ RegularSpace X", "state_before": "α : Type u\nβ : Type v\n...
[ 1617, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1606, 1 ]
Mathlib/Algebra/GroupPower/Lemmas.lean
abs_add_eq_add_abs_le
[ { "state_after": "case inl.inl\nα : Type u_1\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✝ : LinearOrderedAddCommGroup α\na b : α\nhle : a ≤ b\na0 : 0 ≤ a\nb0 : 0 ≤ b\n⊢ abs (a + b) = abs a + abs b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0\n\ncase inl.inr\nα : Ty...
[ 483, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 469, 1 ]
Mathlib/Topology/UniformSpace/Completion.lean
UniformSpace.Completion.ext'
[]
[ 527, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 524, 1 ]
Mathlib/Data/Ordmap/Ordset.lean
Ordnode.all_node4L
[ { "state_after": "no goals", "state_before": "α : Type u_1\nP : α → Prop\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ All P (node4L l x m y r) ↔ All P l ∧ P x ∧ All P m ∧ P y ∧ All P r", "tactic": "cases m <;> simp [node4L, all_node', All, all_node3L, and_assoc]" } ]
[ 509, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 507, 1 ]
Mathlib/Init/Data/Nat/Bitwise.lean
Nat.bodd_add_div2
[ { "state_after": "n : ℕ\n⊢ (bif bodd n then 0 else 1) + (bif bodd n then succ (div2 n) else div2 n) * 2 = succ n", "state_before": "n : ℕ\n⊢ (bif bodd (succ n) then 1 else 0) + 2 * div2 (succ n) = succ n", "tactic": "simp" }, { "state_after": "n : ℕ\n⊢ (bif bodd n then 0 else 1) + (bif bodd n th...
[ 137, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 130, 1 ]
Mathlib/SetTheory/Ordinal/Basic.lean
Ordinal.out_nonempty_iff_ne_zero
[]
[ 285, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 284, 1 ]
Mathlib/FieldTheory/IntermediateField.lean
IntermediateField.range_val
[]
[ 508, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 507, 1 ]
Mathlib/MeasureTheory/Function/LpSeminorm.lean
MeasureTheory.snorm'_add_le_of_le_one
[ { "state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2557321\nG : Type ?u.2557324\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : AEStronglyMeasurable f μ\nhq0 : 0 ≤ q\nhq1 : q ≤ 1\n⊢ ...
[ 766, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 757, 1 ]
Mathlib/Order/Circular.lean
Set.compl_cIoo
[ { "state_after": "case h\nα : Type u_1\ninst✝ : CircularOrder α\na b x✝ : α\n⊢ x✝ ∈ cIoo a bᶜ ↔ x✝ ∈ cIcc b a", "state_before": "α : Type u_1\ninst✝ : CircularOrder α\na b : α\n⊢ cIoo a bᶜ = cIcc b a", "tactic": "ext" }, { "state_after": "case h\nα : Type u_1\ninst✝ : CircularOrder α\na b x✝ : α...
[ 381, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 378, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.FiniteAtFilter.filter_mono_ae
[]
[ 4125, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 4124, 1 ]
Mathlib/Algebra/Algebra/Basic.lean
Module.algebraMap_end_apply
[]
[ 631, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 630, 1 ]
Mathlib/MeasureTheory/Measure/VectorMeasure.lean
MeasureTheory.VectorMeasure.AbsolutelyContinuous.zero
[]
[ 1111, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1110, 1 ]
Mathlib/Data/TypeVec.lean
TypeVec.typevecCasesNil₂_appendFun
[]
[ 381, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 379, 1 ]
Mathlib/Order/Filter/Extr.lean
IsMinOn.on_preimage
[]
[ 416, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 414, 1 ]
Mathlib/Topology/MetricSpace/Basic.lean
Metric.continuousAt_iff'
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nX : Type ?u.127935\nι : Type ?u.127938\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\n⊢ ContinuousAt f b ↔ ∀ (ε : ℝ), ε > 0 → ∀ᶠ (x : β) in 𝓝 b, dist (f x) (f b) < ε", ...
[ 1080, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1078, 1 ]
Mathlib/Order/BoundedOrder.lean
OrderBot.ext
[ { "state_after": "case mk\nα✝ : Type u\nβ : Type v\nγ : Type ?u.25434\nδ : Type ?u.25437\nα : Type u_1\ninst✝ : PartialOrder α\nB : OrderBot α\ntoBot✝ : Bot α\nha : ∀ (a : α), ⊥ ≤ a\n⊢ mk ha = B", "state_before": "α✝ : Type u\nβ : Type v\nγ : Type ?u.25434\nδ : Type ?u.25437\nα : Type u_1\ninst✝ : PartialOr...
[ 447, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 442, 1 ]
Mathlib/Order/LiminfLimsup.lean
Filter.eventually_lt_of_limsup_lt
[]
[ 1134, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1130, 1 ]
Mathlib/Analysis/Calculus/MeanValue.lean
Convex.norm_image_sub_le_of_norm_deriv_le
[]
[ 672, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 668, 1 ]
Mathlib/Algebra/Order/Ring/WithTop.lean
WithTop.mul_lt_top'
[ { "state_after": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : Zero α\ninst✝¹ : Mul α\ninst✝ : LT α\na b : WithTop α\nha : a ≠ ⊤\nhb : b ≠ ⊤\n⊢ a * b ≠ ⊤", "state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : Zero α\ninst✝¹ : Mul α\ninst✝ : LT α\na b : WithTop α\nha : a < ⊤\nhb : b < ⊤\n⊢ a * b...
[ 72, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 70, 1 ]
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean
PrimeSpectrum.le_vanishingIdeal_zeroLocus
[]
[ 218, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 217, 1 ]
Mathlib/Order/Filter/SmallSets.lean
Filter.HasBasis.smallSets
[]
[ 50, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 48, 1 ]
Mathlib/Topology/Order/Basic.lean
countable_of_isolated_left'
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n⊢ Set.Countable {x | ∃ y, y < x ∧ Ioo y x = ∅}", "tactic": "simpa only [← covby_iff_Ioo_eq] using countable_...
[ 1432, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1430, 1 ]
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure
[ { "state_after": "case h₁\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nt : Set (ProjectiveSpectrum 𝒜)\n⊢ zeroLocus 𝒜 ↑(vanishingIdeal t) ⊆ closure t\n\ncase h₂\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiri...
[ 371, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 363, 1 ]
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean
GromovHausdorff.HD_optimalGHDist_le
[]
[ 438, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 435, 9 ]
Mathlib/Topology/Order/Basic.lean
exists_Ico_subset_of_mem_nhds
[]
[ 1245, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1241, 1 ]
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean
tendsto_log_mul_rpow_nhds_zero
[ { "state_after": "no goals", "state_before": "r : ℝ\nhr : 0 < r\nx : ℝ\nhx : x ∈ Set.Ioi 0\n⊢ log x / x ^ (-r) = (fun x => log x * x ^ r) x", "tactic": "rw [rpow_neg hx.out.le, div_inv_eq_mul]" } ]
[ 336, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 333, 1 ]
Mathlib/Logic/Equiv/Set.lean
Equiv.Set.insert_symm_apply_inr
[]
[ 296, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 294, 1 ]
Mathlib/Topology/UniformSpace/CompactConvergence.lean
ContinuousMap.self_mem_compactConvNhd
[]
[ 106, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 105, 1 ]
Mathlib/Topology/Algebra/UniformGroup.lean
TopologicalGroup.tendstoLocallyUniformlyOn_iff
[]
[ 650, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 644, 1 ]
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean
intervalIntegral.integral_comp_mul_add
[ { "state_after": "no goals", "state_before": "ι : Type ?u.14872189\n𝕜 : Type ?u.14872192\nE : Type u_1\nF : Type ?u.14872198\nA : Type ?u.14872201\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nhc : c ≠ 0\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (c * x + ...
[ 755, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 753, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.Superset.trans
[]
[ 359, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 358, 1 ]