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start
list
Mathlib/Data/Matrix/Basic.lean
Matrix.bit1_apply_eq
[ { "state_after": "no goals", "state_before": "l : Type ?u.82029\nm : Type ?u.82032\nn : Type u_1\no : Type ?u.82038\nm' : o β†’ Type ?u.82043\nn' : o β†’ Type ?u.82048\nR : Type ?u.82051\nS : Type ?u.82054\nΞ± : Type v\nΞ² : Type w\nΞ³ : Type ?u.82061\ninst✝² : DecidableEq n\ninst✝¹ : AddZeroClass Ξ±\ninst✝ : One Ξ±...
[ 589, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 588, 1 ]
Mathlib/Algebra/Lie/Subalgebra.lean
LieSubalgebra.mem_bot
[]
[ 447, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 446, 1 ]
Mathlib/NumberTheory/PellMatiyasevic.lean
Pell.eq_of_xn_modEq_lem3
[ { "state_after": "a : β„•\na1 : 1 < a\ni n : β„•\nnpos : 0 < n\nj : β„•\nij : i < j + 1\nj2n : j + 1 ≀ 2 * n\njnn : j + 1 β‰  n\nntriv : Β¬(a = 2 ∧ n = 1 ∧ i = 0 ∧ j + 1 = 2)\nk : β„•\nkn : k > n\nk2n : k ≀ 2 * n\nk2nl : 2 * n - k < n :=\n lt_of_add_lt_add_right\n (let_fun this :=\n Eq.mpr (id (tsub_add_cancel_of...
[ 744, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 670, 1 ]
Mathlib/Data/Dfinsupp/Basic.lean
Dfinsupp.coe_sub
[]
[ 321, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 320, 1 ]
Mathlib/RingTheory/Ideal/Operations.lean
Ideal.isPrime_radical
[ { "state_after": "R : Type u\ninst✝ : CommSemiring R\nI : Ideal R\nhi : IsPrimary I\nx y : R\nx✝ : x * y ∈ radical I\nm : β„•\nhxy : x ^ m * y ^ m ∈ I\n⊒ x ∈ radical I ∨ y ∈ radical I", "state_before": "R : Type u\ninst✝ : CommSemiring R\nI : Ideal R\nhi : IsPrimary I\nx y : R\nx✝ : x * y ∈ radical I\nm : β„•\n...
[ 1865, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1860, 1 ]
Mathlib/Topology/LocallyFinite.lean
LocallyFinite.exists_forall_eventually_eq_prod
[ { "state_after": "ΞΉ : Type ?u.9232\nΞΉ' : Type ?u.9235\nΞ± : Type ?u.9238\nX : Type u_2\nY : Type ?u.9244\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf✝ g : ΞΉ β†’ Set X\nΟ€ : X β†’ Sort u_1\nf : β„• β†’ (x : X) β†’ Ο€ x\nU : X β†’ Set X\nhUx : βˆ€ (x : X), U x ∈ 𝓝 x\nhU : βˆ€ (x : X), Set.Finite {i | Set.Nonempty ((...
[ 173, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 158, 1 ]
Mathlib/Data/Fintype/Card.lean
Infinite.exists_superset_card_eq
[ { "state_after": "case zero\nΞ± : Type u_1\nΞ² : Type ?u.80843\nΞ³ : Type ?u.80846\ninst✝ : Infinite Ξ±\ns✝ : Finset Ξ±\nn : β„•\nhn✝ : card s✝ ≀ n\ns : Finset Ξ±\nhn : card s ≀ zero\n⊒ βˆƒ t, s βŠ† t ∧ card t = zero\n\ncase succ\nΞ± : Type u_1\nΞ² : Type ?u.80843\nΞ³ : Type ?u.80846\ninst✝ : Infinite Ξ±\ns✝ : Finset Ξ±\nn✝ : β„•...
[ 1125, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1116, 1 ]
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean
le_mul_self
[ { "state_after": "Ξ± : Type u\ninst✝ : CanonicallyOrderedMonoid Ξ±\na b c d : Ξ±\n⊒ a ≀ a * b", "state_before": "Ξ± : Type u\ninst✝ : CanonicallyOrderedMonoid Ξ±\na b c d : Ξ±\n⊒ a ≀ b * a", "tactic": "rw [mul_comm]" }, { "state_after": "no goals", "state_before": "Ξ± : Type u\ninst✝ : CanonicallyO...
[ 164, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 162, 1 ]
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean
Polynomial.IsEisensteinAt.irreducible
[]
[ 235, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 232, 1 ]
Mathlib/Algebra/Quaternion.lean
Quaternion.sub_im
[]
[ 939, 71 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 939, 16 ]
Mathlib/RingTheory/Derivation/Basic.lean
Derivation.coe_zero
[]
[ 188, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 187, 1 ]
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean
fixedPoints_subgroup_sup
[]
[ 158, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 156, 1 ]
Mathlib/Order/Cover.lean
Covby.Ioo_eq
[]
[ 338, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 337, 1 ]
Mathlib/Topology/LocalHomeomorph.lean
LocalHomeomorph.continuousOn_iff_continuousOn_comp_left
[]
[ 1196, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1192, 1 ]
Mathlib/CategoryTheory/Generator.lean
CategoryTheory.isSeparator_iff_faithful_coyoneda_obj
[]
[ 515, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 512, 1 ]
Mathlib/Order/SupIndep.lean
CompleteLattice.independent_def
[]
[ 256, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 255, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.Measure.le_sum
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\nΞ² : Type ?u.336860\nΞ³ : Type ?u.336863\nΞ΄ : Type ?u.336866\nΞΉ : Type u_2\nR : Type ?u.336872\nR' : Type ?u.336875\nm0 : MeasurableSpace Ξ±\ninst✝¹ : MeasurableSpace Ξ²\ninst✝ : MeasurableSpace Ξ³\nμ✝ μ₁ ΞΌβ‚‚ μ₃ Ξ½ Ξ½' ν₁ Ξ½β‚‚ : Measure Ξ±\ns✝ s' t : Set Ξ±\nΞΌ...
[ 2039, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2038, 1 ]
Mathlib/Data/Multiset/Nodup.lean
Multiset.count_eq_one_of_mem
[]
[ 94, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 92, 1 ]
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean
Subalgebra.mem_prod
[]
[ 1124, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1123, 1 ]
Mathlib/Algebra/BigOperators/Finsupp.lean
Finsupp.prod_ite_eq
[ { "state_after": "Ξ± : Type u_1\nΞΉ : Type ?u.44160\nΞ³ : Type ?u.44163\nA : Type ?u.44166\nB : Type ?u.44169\nC : Type ?u.44172\ninst✝⁢ : AddCommMonoid A\ninst✝⁡ : AddCommMonoid B\ninst✝⁴ : AddCommMonoid C\nt : ΞΉ β†’ A β†’ C\nh0 : βˆ€ (i : ΞΉ), t i 0 = 0\nh1 : βˆ€ (i : ΞΉ) (x y : A), t i (x + y) = t i x + t i y\ns : Finset...
[ 111, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 108, 1 ]
Mathlib/GroupTheory/Sylow.lean
card_sylow_dvd_index
[]
[ 426, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 423, 1 ]
Mathlib/LinearAlgebra/Basic.lean
LinearEquiv.coe_zero
[]
[ 1818, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1817, 1 ]
Mathlib/LinearAlgebra/Span.lean
LinearEquiv.coord_apply_smul
[]
[ 1046, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1045, 1 ]
Mathlib/GroupTheory/FreeGroup.lean
FreeGroup.reduce_toWord
[ { "state_after": "case mk\nΞ± : Type u\nL✝ L₁ Lβ‚‚ L₃ Lβ‚„ : List (Ξ± Γ— Bool)\ninst✝ : DecidableEq Ξ±\nx✝ : FreeGroup Ξ±\nL : List (Ξ± Γ— Bool)\n⊒ reduce (toWord (Quot.mk Red.Step L)) = toWord (Quot.mk Red.Step L)", "state_before": "Ξ± : Type u\nL L₁ Lβ‚‚ L₃ Lβ‚„ : List (Ξ± Γ— Bool)\ninst✝ : DecidableEq Ξ±\n⊒ βˆ€ (x : FreeGrou...
[ 1315, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1313, 1 ]
Mathlib/FieldTheory/Minpoly/Field.lean
minpoly.prime
[ { "state_after": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : IsDomain B\ninst✝ : Algebra A B\nx : B\nhx : IsIntegral A x\n⊒ βˆ€ (a b : A[X]), minpoly A x ∣ a * b β†’ minpoly A x ∣ a ∨ minpoly A x ∣ b", "state_before": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ni...
[ 249, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 244, 1 ]
Mathlib/LinearAlgebra/FiniteDimensional.lean
bot_eq_top_of_rank_eq_zero
[ { "state_after": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nh : Module.rank K V = 0\nthis : FiniteDimensional K V\n⊒ βŠ₯ = ⊀", "state_before": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nh : Module.rank K V ...
[ 669, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 666, 1 ]
Mathlib/Data/List/Basic.lean
List.find?_nil
[]
[ 3237, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3236, 1 ]
Mathlib/Algebra/Lie/Submodule.lean
LieHom.isIdealMorphism_def
[]
[ 923, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 922, 1 ]
Mathlib/Algebra/Tropical/BigOperators.lean
Finset.trop_inf
[ { "state_after": "case h.e'_3\nR : Type u_1\nS : Type u_2\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\ns : Finset S\nf : S β†’ R\n⊒ βˆ‘ i in s, trop (f i) = Multiset.sum (Multiset.map trop (Multiset.map f s.val))", "state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\ns : Fins...
[ 101, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 97, 1 ]
Mathlib/Data/Polynomial/FieldDivision.lean
Polynomial.monic_mul_leadingCoeff_inv
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : β„•\ninst✝ : DivisionRing R\np q : R[X]\nh : p β‰  0\n⊒ Monic (p * ↑C (leadingCoeff p)⁻¹)", "tactic": "rw [Monic, leadingCoeff_mul, leadingCoeff_C,\n mul_inv_cancel (show leadingCoeff p β‰  0 from mt le...
[ 129, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 127, 1 ]
Std/Logic.lean
and_congr
[]
[ 157, 41 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 156, 1 ]
Mathlib/LinearAlgebra/AdicCompletion.lean
adicCompletion.range_eval
[]
[ 254, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 253, 1 ]
Std/Data/List/Init/Lemmas.lean
List.take_length_le
[ { "state_after": "Ξ± : Type u_1\ni : Nat\nl : List Ξ±\nh : length l ≀ i\nthis : take i l ++ drop i l = l\n⊒ take i l = l", "state_before": "Ξ± : Type u_1\ni : Nat\nl : List Ξ±\nh : length l ≀ i\n⊒ take i l = l", "tactic": "have := take_append_drop i l" }, { "state_after": "Ξ± : Type u_1\ni : Nat\nl :...
[ 145, 56 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 143, 1 ]
Mathlib/Analysis/Normed/Group/Quotient.lean
quotient_norm_mk_le'
[]
[ 160, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 159, 1 ]
Mathlib/Data/Complex/Exponential.lean
Real.expNear_sub
[ { "state_after": "no goals", "state_before": "n : β„•\nx r₁ rβ‚‚ : ℝ\n⊒ expNear n x r₁ - expNear n x rβ‚‚ = x ^ n / ↑(Nat.factorial n) * (r₁ - rβ‚‚)", "tactic": "simp [expNear, mul_sub]" } ]
[ 1764, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1762, 1 ]
Mathlib/CategoryTheory/Preadditive/Basic.lean
CategoryTheory.Preadditive.nsmul_comp
[]
[ 170, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 169, 1 ]
Mathlib/Order/CompleteLattice.lean
IsGLB.sInf_eq
[]
[ 220, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 219, 1 ]
Mathlib/Topology/Instances/Matrix.lean
Continuous.matrix_elem
[]
[ 80, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 78, 1 ]
Mathlib/RingTheory/WittVector/WittPolynomial.lean
xInTermsOfW_vars_aux
[ { "state_after": "p : β„•\nR : Type ?u.289237\ninst✝¹ : CommRing R\ninst✝ : DecidableEq R\nhp : Fact (Nat.Prime p)\nn : β„•\n⊒ βˆ€ (n : β„•),\n (βˆ€ (m : β„•), m < n β†’ m ∈ vars (xInTermsOfW p β„š m) ∧ vars (xInTermsOfW p β„š m) βŠ† range (m + 1)) β†’\n n ∈ vars (xInTermsOfW p β„š n) ∧ vars (xInTermsOfW p β„š n) βŠ† range (n + 1)...
[ 283, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 257, 1 ]
Mathlib/Algebra/MonoidAlgebra/Basic.lean
MonoidAlgebra.single_one_mul_apply
[ { "state_after": "no goals", "state_before": "k : Type u₁\nG : Type uβ‚‚\nR : Type ?u.522014\ninst✝¹ : Semiring k\ninst✝ : MulOneClass G\nf : MonoidAlgebra k G\nr : k\nx a : G\n⊒ 1 * a = x ↔ a = x", "tactic": "rw [one_mul]" } ]
[ 589, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 587, 1 ]
Mathlib/Analysis/NormedSpace/OperatorNorm.lean
LinearMap.antilipschitz_of_comap_nhds_le
[ { "state_after": "case intro.intro\nπ•œ : Type u_1\nπ•œβ‚‚ : Type u_2\nπ•œβ‚ƒ : Type ?u.2566867\nE : Type u_3\nEβ‚— : Type ?u.2566873\nF : Type u_4\nFβ‚— : Type ?u.2566879\nG : Type ?u.2566882\nGβ‚— : Type ?u.2566885\n𝓕 : Type ?u.2566888\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedAddComm...
[ 1452, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1432, 1 ]
Mathlib/Data/MvPolynomial/Basic.lean
MvPolynomial.coe_evalβ‚‚Hom
[]
[ 1030, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1029, 1 ]
Mathlib/Analysis/Normed/Group/Hom.lean
NormedAddGroupHom.bounds_nonempty
[]
[ 229, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 226, 1 ]
Mathlib/LinearAlgebra/Span.lean
Submodule.span_int_eq
[ { "state_after": "no goals", "state_before": "R : Type ?u.37777\nRβ‚‚ : Type ?u.37780\nK : Type ?u.37783\nM✝ : Type ?u.37786\nMβ‚‚ : Type ?u.37789\nV : Type ?u.37792\nS : Type ?u.37795\ninst✝⁢ : Semiring R\ninst✝⁡ : AddCommMonoid M✝\ninst✝⁴ : Module R M✝\nx : M✝\np p' : Submodule R M✝\ninst✝³ : Semiring Rβ‚‚\nσ₁₂...
[ 207, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 206, 1 ]
Mathlib/Computability/Primrec.lean
Primrecβ‚‚.compβ‚‚
[]
[ 489, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 487, 1 ]
Mathlib/Data/List/ProdSigma.lean
List.length_product
[ { "state_after": "case nil\nΞ± : Type u_1\nΞ² : Type u_2\nlβ‚‚ : List Ξ²\n⊒ length ([] Γ—Λ’ lβ‚‚) = length [] * length lβ‚‚\n\ncase cons\nΞ± : Type u_1\nΞ² : Type u_2\nlβ‚‚ : List Ξ²\nx : Ξ±\nl₁ : List Ξ±\nIH : length (l₁ Γ—Λ’ lβ‚‚) = length l₁ * length lβ‚‚\n⊒ length ((x :: l₁) Γ—Λ’ lβ‚‚) = length (x :: l₁) * length lβ‚‚", "state_befor...
[ 58, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 53, 1 ]
Mathlib/Data/Polynomial/Laurent.lean
LaurentPolynomial.degree_eq_bot_iff
[ { "state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[T;T⁻¹]\nh : degree f = βŠ₯\n⊒ f = 0", "state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[T;T⁻¹]\n⊒ degree f = βŠ₯ ↔ f = 0", "tactic": "refine' ⟨fun h => _, fun h => by rw [h, degree_zero]⟩" }, { "state_after": "R : Type u_1\ninst✝ : Sem...
[ 495, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 489, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean
BoxIntegral.Prepartition.le_biUnion_iff
[ { "state_after": "case refine'_1\nΞΉ : Type u_1\nI J✝ J₁ Jβ‚‚ : Box ΞΉ\nΟ€ π₁ Ο€β‚‚ : Prepartition I\nx : ΞΉ β†’ ℝ\nΟ€i✝ Ο€i₁ Ο€iβ‚‚ Ο€i : (J : Box ΞΉ) β†’ Prepartition J\nΟ€' : Prepartition I\nH : Ο€' ≀ biUnion Ο€ Ο€i\nJ : Box ΞΉ\nhJ : J ∈ Ο€\n⊒ restrict Ο€' J ≀ Ο€i J\n\ncase refine'_2\nΞΉ : Type u_1\nI J J₁ Jβ‚‚ : Box ΞΉ\nΟ€ π₁ Ο€β‚‚ : Preparti...
[ 565, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 555, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.sup_bind
[]
[ 2766, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2766, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean
Polynomial.Chebyshev.T_real_cos
[ { "state_after": "no goals", "state_before": "R : Type ?u.111481\nA : Type ?u.111484\ninst✝² : CommRing R\ninst✝¹ : CommRing A\ninst✝ : Algebra R A\nΞΈ : ℝ\nn : β„•\n⊒ eval (cos ΞΈ) (T ℝ n) = cos (↑n * ΞΈ)", "tactic": "exact_mod_cast T_complex_cos ΞΈ n" } ]
[ 119, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 119, 1 ]
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean
Submodule.angle_coe
[]
[ 75, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 73, 1 ]
Mathlib/Data/Ordmap/Ordset.lean
Ordnode.Valid'.rotateL_lemmaβ‚‚
[ { "state_after": "no goals", "state_before": "Ξ± : Type ?u.308464\ninst✝ : Preorder Ξ±\na b c : β„•\nH3 : 2 * (b + c) ≀ 9 * a + 3\nh : b < 2 * c\n⊒ b < 3 * a + 1", "tactic": "linarith" } ]
[ 1224, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1223, 1 ]
Mathlib/Data/List/Basic.lean
List.zipLeft'_cons_nil
[]
[ 4052, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 4050, 1 ]
Mathlib/Data/MvPolynomial/Basic.lean
MvPolynomial.evalβ‚‚_pow
[ { "state_after": "R : Type u\nS₁ : Type v\nSβ‚‚ : Type w\nS₃ : Type x\nΟƒ : Type u_1\na a' a₁ aβ‚‚ : R\ne : β„•\nn m : Οƒ\ns : Οƒ β†’β‚€ β„•\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q : MvPolynomial Οƒ R\nf : R β†’+* S₁\ng : Οƒ β†’ S₁\np : MvPolynomial Οƒ R\n⊒ evalβ‚‚ f g 1 = 1", "state_before": "R : Type u\nS₁ : Type...
[ 1015, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1011, 1 ]
Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean
CategoryTheory.Limits.hasColimit_of_coequalizer_and_coproduct
[]
[ 350, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 347, 1 ]
Mathlib/MeasureTheory/Measure/AEDisjoint.lean
MeasureTheory.AEDisjoint.union_left_iff
[ { "state_after": "no goals", "state_before": "ΞΉ : Type ?u.6644\nΞ± : Type u_1\nm : MeasurableSpace Ξ±\nΞΌ : Measure Ξ±\ns t u v : Set Ξ±\n⊒ AEDisjoint ΞΌ (s βˆͺ t) u ↔ AEDisjoint ΞΌ s u ∧ AEDisjoint ΞΌ t u", "tactic": "simp [union_eq_iUnion, and_comm]" } ]
[ 109, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 108, 1 ]
Mathlib/Data/List/Basic.lean
List.getI_append_right
[]
[ 4495, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 4493, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.coe_one
[]
[ 215, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 215, 20 ]
Mathlib/RingTheory/Localization/Basic.lean
IsLocalization.algebraMap_apply_eq_map_map_submonoid
[]
[ 1373, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1369, 1 ]
Mathlib/FieldTheory/Fixed.lean
FixedPoints.coe_algebraMap
[]
[ 127, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 125, 1 ]
Mathlib/Data/Finset/Lattice.lean
Finset.sup'_induction
[ { "state_after": "F : Type ?u.260693\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.260702\nΞΉ : Type ?u.260705\nΞΊ : Type ?u.260708\ninst✝ : SemilatticeSup Ξ±\ns : Finset Ξ²\nH : Finset.Nonempty s\nf : Ξ² β†’ Ξ±\np : Ξ± β†’ Prop\nhp : βˆ€ (a₁ : Ξ±), p a₁ β†’ βˆ€ (aβ‚‚ : Ξ±), p aβ‚‚ β†’ p (a₁ βŠ” aβ‚‚)\nhs : βˆ€ (b : Ξ²), b ∈ s β†’ p (f b)\n⊒ WithBot...
[ 867, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 857, 1 ]
Mathlib/GroupTheory/Subsemigroup/Basic.lean
Subsemigroup.mem_top
[]
[ 199, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Set/Intervals/Monotone.lean
AntitoneOn.Iic
[]
[ 69, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 68, 11 ]
Mathlib/Analysis/Convex/Extreme.lean
inter_extremePoints_subset_extremePoints_of_subset
[]
[ 168, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 166, 1 ]
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean
GeneralizedContinuedFraction.succ_nth_convergent_eq_squashGCF_nth_convergent
[ { "state_after": "case inl\nK : Type u_1\nn : β„•\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : Field K\nnth_part_denom_ne_zero : βˆ€ {b : K}, Stream'.Seq.get? (partialDenominators g) n = some b β†’ b β‰  0\nterminated_at_n : TerminatedAt g n\n⊒ convergents g (n + 1) = convergents (squashGCF g ...
[ 332, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 268, 1 ]
Mathlib/Data/Set/Finite.lean
Set.Finite.of_subsingleton
[]
[ 708, 13 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 707, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean
CategoryTheory.Limits.pushoutCoconeOfRightIso_ΞΉ_app_right
[]
[ 1880, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1879, 1 ]
Mathlib/Analysis/BoxIntegral/Box/Basic.lean
BoxIntegral.Box.distortion_eq_of_sub_eq_div
[ { "state_after": "ΞΉ : Type u_1\nI✝ J✝ : Box ΞΉ\nx y : ΞΉ β†’ ℝ\ninst✝ : Fintype ΞΉ\nI J : Box ΞΉ\nr : ℝ\nh : βˆ€ (i : ΞΉ), upper I i - lower I i = (upper J i - lower J i) / r\n⊒ (Finset.sup Finset.univ fun i =>\n (Finset.sup Finset.univ fun b => ↑Real.nnabs (upper J b - lower J b) / ↑Real.nnabs r) /\n (↑Real...
[ 510, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 499, 1 ]
src/lean/Init/Data/AC.lean
Lean.Data.AC.Context.eq_of_norm
[ { "state_after": "α : Sort u_1\nctx : Context α\na b : Expr\nh✝ : (norm ctx a == norm ctx b) = true\nh : evalList α ctx (norm ctx a) = evalList α ctx (norm ctx b)\n⊒ eval α ctx a = eval α ctx b", "state_before": "α : Sort u_1\nctx : Context α\na b : Expr\nh : (norm ctx a == norm ctx b) = true\n⊒ eval α ctx ...
[ 320, 13 ]
d5348dfac847a56a4595fb6230fd0708dcb4e7e9
https://github.com/leanprover/lean4
[ 317, 1 ]
Mathlib/Analysis/Calculus/TangentCone.lean
uniqueDiffOn_univ
[]
[ 274, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 273, 1 ]
Mathlib/Data/IsROrC/Basic.lean
IsROrC.norm_sq_re_conj_add
[ { "state_after": "no goals", "state_before": "K : Type u_1\nE : Type ?u.7115686\ninst✝ : IsROrC K\nx : K\n⊒ ‖↑(starRingEnd K) x + xβ€– ^ 2 = ↑re (↑(starRingEnd K) x + x) ^ 2", "tactic": "rw [add_comm, norm_sq_re_add_conj]" } ]
[ 770, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 769, 1 ]
Mathlib/Data/List/Perm.lean
List.Perm.inter_left
[ { "state_after": "no goals", "state_before": "Ξ± : Type uu\nΞ² : Type vv\nl₁ lβ‚‚ : List Ξ±\ninst✝ : DecidableEq Ξ±\nl t₁ tβ‚‚ : List Ξ±\np : t₁ ~ tβ‚‚\na : Ξ±\nx✝ : a ∈ l\n⊒ decide (a ∈ t₁) = true ↔ decide (a ∈ tβ‚‚) = true", "tactic": "simpa using p.mem_iff" } ]
[ 1013, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1012, 1 ]
Mathlib/Analysis/SpecialFunctions/Polynomials.lean
Polynomial.abs_isBoundedUnder_iff
[ { "state_after": "π•œ : Type u_1\ninst✝¹ : NormedLinearOrderedField π•œ\nP Q : π•œ[X]\ninst✝ : OrderTopology π•œ\nh : IsBoundedUnder (fun x x_1 => x ≀ x_1) atTop fun x => abs (eval x P)\n⊒ degree P ≀ 0", "state_before": "π•œ : Type u_1\ninst✝¹ : NormedLinearOrderedField π•œ\nP Q : π•œ[X]\ninst✝ : OrderTopology π•œ\...
[ 100, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 94, 1 ]
Mathlib/SetTheory/Ordinal/Arithmetic.lean
Ordinal.not_succ_of_isLimit
[]
[ 257, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 256, 1 ]
Mathlib/Order/CompleteLattice.lean
sSup_le_sSup_of_forall_exists_le
[]
[ 180, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 176, 1 ]
Mathlib/Data/Set/Basic.lean
Set.mem_union_left
[]
[ 738, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 737, 1 ]
Mathlib/NumberTheory/Zsqrtd/Basic.lean
Zsqrtd.sqLe_add_mixed
[ { "state_after": "no goals", "state_before": "d✝ : β„€\nc d x y z w : β„•\nxy : SqLe x c y d\nzw : SqLe z c w d\n⊒ c * (x * z) * (c * (x * z)) ≀ d * (y * w) * (d * (y * w))", "tactic": "simpa [mul_comm, mul_left_comm] using mul_le_mul xy zw (Nat.zero_le _) (Nat.zero_le _)" } ]
[ 440, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 437, 1 ]
Mathlib/Data/Fin/Basic.lean
Fin.succ_le_succ_iff
[]
[ 889, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 888, 1 ]
Mathlib/Algebra/Order/ToIntervalMod.lean
toIcoDiv_add_right'
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\ninst✝ : LinearOrderedAddCommGroup Ξ±\nhΞ± : Archimedean Ξ±\np : Ξ±\nhp : 0 < p\na✝ b✝ c : Ξ±\nn : β„€\na b : Ξ±\n⊒ toIcoDiv hp (a + p) b = toIcoDiv hp a b - 1", "tactic": "simpa only [one_zsmul] using toIcoDiv_add_zsmul' hp a b 1" } ]
[ 305, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 304, 1 ]
Mathlib/Data/Real/Hyperreal.lean
Hyperreal.infinite_omega
[]
[ 811, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 810, 1 ]
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean
TopCat.snd_openEmbedding_of_left_openEmbedding
[ { "state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟢ S\nH : OpenEmbedding ((forget TopCat).map f)\ng : Y ⟢ S\ne_2✝ : (forget TopCat).obj Y = ↑Y\n⊒ (forget TopCat).map pullback.snd =\n ↑(homeoOfIso (asIso pullback.snd)) ∘\n (forget TopCat).map (p...
[ 322, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 316, 1 ]
Mathlib/Data/List/Sigma.lean
List.mem_ext
[]
[ 161, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 159, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.map_subset_map
[]
[ 1328, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1326, 1 ]
Mathlib/Topology/Filter.lean
Filter.nhds_bot
[]
[ 118, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/Logic/Equiv/LocalEquiv.lean
LocalEquiv.symm_symm
[ { "state_after": "case mk\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.24956\nΞ΄ : Type ?u.24959\ne' : LocalEquiv Ξ² Ξ³\ntoFun✝ : Ξ± β†’ Ξ²\ninvFun✝ : Ξ² β†’ Ξ±\nsource✝ : Set Ξ±\ntarget✝ : Set Ξ²\nmap_source'✝ : βˆ€ ⦃x : α⦄, x ∈ source✝ β†’ toFun✝ x ∈ target✝\nmap_target'✝ : βˆ€ ⦃x : β⦄, x ∈ target✝ β†’ invFun✝ x ∈ source✝\nleft_inv'✝...
[ 332, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 330, 1 ]
Mathlib/RingTheory/Polynomial/Basic.lean
Polynomial.mem_degreeLE
[ { "state_after": "R : Type u\nS : Type ?u.4503\ninst✝ : Semiring R\nn : WithBot β„•\nf : R[X]\n⊒ (βˆ€ (i : β„•), ↑i > n β†’ ↑(lcoeff R i) f = 0) ↔ βˆ€ (m : β„•), n < ↑m β†’ coeff f m = 0", "state_before": "R : Type u\nS : Type ?u.4503\ninst✝ : Semiring R\nn : WithBot β„•\nf : R[X]\n⊒ f ∈ degreeLE R n ↔ degree f ≀ n", "...
[ 68, 93 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 67, 1 ]
Mathlib/MeasureTheory/Function/LpSeminorm.lean
MeasureTheory.snorm'_zero
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\nE : Type ?u.911849\nF : Type u_2\nG : Type ?u.911855\nm m0 : MeasurableSpace Ξ±\np : ℝβ‰₯0∞\nq : ℝ\nΞΌ Ξ½ : Measure Ξ±\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhp0_lt : 0 < q\n⊒ snorm' 0 q ΞΌ = 0", "...
[ 187, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 187, 1 ]
Mathlib/Data/Fin/Interval.lean
Fin.card_Ioo
[ { "state_after": "no goals", "state_before": "n : β„•\na b : Fin n\n⊒ card (Ioo a b) = ↑b - ↑a - 1", "tactic": "rw [← Nat.card_Ioo, ← map_valEmbedding_Ioo, card_map]" } ]
[ 95, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 94, 1 ]
Mathlib/Order/RelClasses.lean
IsTrichotomous.swap
[ { "state_after": "no goals", "state_before": "Ξ± : Type u\nΞ² : Type v\nr✝ : Ξ± β†’ Ξ± β†’ Prop\ns : Ξ² β†’ Ξ² β†’ Prop\nr : Ξ± β†’ Ξ± β†’ Prop\ninst✝ : IsTrichotomous Ξ± r\na b : Ξ±\n⊒ Function.swap r a b ∨ a = b ∨ Function.swap r b a", "tactic": "simpa [Function.swap, or_comm, or_left_comm] using trichotomous_of r a b" }...
[ 96, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 95, 1 ]
Mathlib/Logic/Function/Conjugate.lean
Function.Semiconjβ‚‚.isIdempotent_right
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.3743\nf : Ξ± β†’ Ξ²\nga : Ξ± β†’ Ξ± β†’ Ξ±\ngb : Ξ² β†’ Ξ² β†’ Ξ²\ninst✝ : IsIdempotent Ξ± ga\nh : Semiconjβ‚‚ f ga gb\nh_surj : Surjective f\nx : Ξ±\n⊒ gb (f x) (f x) = f x", "tactic": "simp only [← h.eq, @IsIdempotent.idempotent _ ga]" ...
[ 176, 81 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 174, 1 ]
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean
tendsto_atBot_isLUB
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_2\nΞ² : Type ?u.6300\nΞΉ : Type u_1\ninst✝³ : Preorder ΞΉ\ninst✝² : TopologicalSpace Ξ±\ninst✝¹ : Preorder Ξ±\ninst✝ : SupConvergenceClass Ξ±\nf : ΞΉ β†’ Ξ±\na : Ξ±\nh_anti : Antitone f\nha : IsLUB (range f) a\n⊒ Tendsto f atBot (𝓝 a)", "tactic": "convert t...
[ 106, 88 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 105, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.extraction_forall_of_eventually
[]
[ 493, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 491, 1 ]
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean
Polynomial.coeff_eq_zero_of_lt_natTrailingDegree
[ { "state_after": "case h\nR : Type u\nS : Type v\na b : R\nn✝ m : β„•\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : β„•\nh : n < natTrailingDegree p\n⊒ ↑n < trailingDegree p", "state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : β„•\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : β„•\nh : n < natTrailingDegree p\n⊒ coeff...
[ 276, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 269, 1 ]
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean
Subalgebra.rangeS_algebraMap
[ { "state_after": "no goals", "state_before": "R✝ : Type u\nA✝ : Type v\nB : Type w\ninst✝⁷ : CommSemiring R✝\ninst✝⁢ : Semiring A✝\ninst✝⁡ : Algebra R✝ A✝\ninst✝⁴ : Semiring B\ninst✝³ : Algebra R✝ B\nS✝ : Subalgebra R✝ A✝\nα : Type ?u.1950480\nβ : Type ?u.1950483\nR : Type u_1\nA : Type u_2\ninst✝² : CommSe...
[ 1316, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1313, 1 ]
Mathlib/Data/Polynomial/Basic.lean
Polynomial.mul_eq_sum_sum
[ { "state_after": "case a\nR : Type u\na b : R\nm n : β„•\ninst✝ : Semiring R\np q : R[X]\n⊒ (p * q).toFinsupp = (βˆ‘ i in support p, sum q fun j a => ↑(monomial (i + j)) (coeff p i * a)).toFinsupp", "state_before": "R : Type u\na b : R\nm n : β„•\ninst✝ : Semiring R\np q : R[X]\n⊒ p * q = βˆ‘ i in support p, sum q ...
[ 956, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 951, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Combination.lean
Finset.centroid_pair
[ { "state_after": "case pos\nk : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁡ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nΞΉ : Type u_1\ns : Finset ΞΉ\nΞΉβ‚‚ : Type ?u.484128\nsβ‚‚ : Finset ΞΉβ‚‚\ninst✝¹ : DecidableEq ΞΉ\ninst✝ : Invertible 2\np : ΞΉ β†’ P\ni₁ iβ‚‚ : ΞΉ\nh : i₁ = iβ‚‚\...
[ 875, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 864, 1 ]
Mathlib/Topology/MetricSpace/Holder.lean
holderWith_one
[]
[ 95, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 94, 1 ]
Mathlib/Analysis/NormedSpace/OperatorNorm.lean
ContinuousLinearMap.op_nnnorm_le_bound'
[ { "state_after": "no goals", "state_before": "π•œ : Type u_1\nπ•œβ‚‚ : Type u_2\nπ•œβ‚ƒ : Type ?u.621442\nE : Type u_3\nEβ‚— : Type ?u.621448\nF : Type u_4\nFβ‚— : Type ?u.621454\nG : Type ?u.621457\nGβ‚— : Type ?u.621460\n𝓕 : Type ?u.621463\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁢ : SeminormedAddCommGroup Eβ‚—\ninst...
[ 423, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 421, 1 ]
Mathlib/Data/Set/Countable.lean
Set.Countable.prod
[ { "state_after": "Ξ± : Type u\nΞ² : Type v\nΞ³ : Type w\nΞΉ : Sort x\ns : Set Ξ±\nt : Set Ξ²\nhs : Set.Countable s\nht : Set.Countable t\nthis : Countable ↑s\n⊒ Set.Countable (s Γ—Λ’ t)", "state_before": "Ξ± : Type u\nΞ² : Type v\nΞ³ : Type w\nΞΉ : Sort x\ns : Set Ξ±\nt : Set Ξ²\nhs : Set.Countable s\nht : Set.Countable ...
[ 282, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 278, 11 ]
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
ProjectiveSpectrum.zeroLocus_bUnion
[ { "state_after": "no goals", "state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nπ’œ : β„• β†’ Submodule R A\ninst✝ : GradedAlgebra π’œ\ns : Set (Set A)\n⊒ zeroLocus π’œ (⋃ (s' : Set A) (_ : s' ∈ s), s') = β‹‚ (s' : Set A) (_ : s' ∈ s), zeroLocus π’œ s'", ...
[ 270, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 268, 1 ]