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Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean
DifferentiableWithinAt.restrictScalars
[]
[ 81, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 79, 1 ]
Mathlib/Data/MvPolynomial/Basic.lean
MvPolynomial.sum_def
[ { "state_after": "no goals", "state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_2\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S₁\np✝ q : MvPolynomial σ R\nA : Type u_1\ninst✝ : AddCommMonoid A\np : MvPolynomial σ R\nb : (σ →₀ ℕ) → R...
[ 592, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 591, 1 ]
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean
CategoryTheory.Presieve.pullbackCompatible_iff
[ { "state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nx : FamilyOfElements P R\ninst✝ : HasPullbacks C\n⊢ FamilyOfElements.Compatible x → FamilyOfElements.PullbackCompatible x\n\ncase mpr\nC : Type u₁\ninst✝¹ : Cat...
[ 172, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 164, 1 ]
Mathlib/Algebra/Module/Submodule/Lattice.lean
AddSubmonoid.toNatSubmodule_toAddSubmonoid
[]
[ 370, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 1 ]
Mathlib/Dynamics/OmegaLimit.lean
nonempty_omegaLimit
[]
[ 329, 101 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 328, 1 ]
Std/Logic.lean
and_congr_right_iff
[ { "state_after": "a b c : Prop\nha : a\nh : b ↔ c\n⊢ b ↔ c", "state_before": "a b c : Prop\nh : a ∧ b ↔ a ∧ c\nha : a\n⊢ b ↔ c", "tactic": "simp [ha] at h" }, { "state_after": "no goals", "state_before": "a b c : Prop\nha : a\nh : b ↔ c\n⊢ b ↔ c", "tactic": "exact h" } ]
[ 220, 60 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 219, 9 ]
Mathlib/Algebra/Star/Subalgebra.lean
StarSubalgebra.map_mono
[]
[ 204, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 203, 1 ]
Mathlib/Analysis/ODE/PicardLindelof.lean
PicardLindelof.continuousOn
[]
[ 115, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 110, 11 ]
Mathlib/Data/Matrix/PEquiv.lean
PEquiv.single_mul_single
[ { "state_after": "no goals", "state_before": "k : Type u_2\nl : Type ?u.73281\nm : Type u_3\nn : Type u_1\nα : Type v\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq k\ninst✝² : DecidableEq m\ninst✝¹ : DecidableEq n\ninst✝ : Semiring α\na : m\nb : n\nc : k\n⊢ toMatrix (single a b) ⬝ toMatrix (single b c) = toMatr...
[ 164, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 161, 1 ]
Mathlib/Data/Set/Prod.lean
Set.univ_pi_eq_empty_iff
[ { "state_after": "no goals", "state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.124745\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\n⊢ pi univ t = ∅ ↔ ∃ i, t i = ∅", "tactic": "simp [← not_nonempty_iff_eq_empty, univ_pi_nonempty_iff]" } ]
[ 700, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 699, 1 ]
Mathlib/GroupTheory/Subgroup/Basic.lean
Subgroup.subsingleton_iff
[ { "state_after": "no goals", "state_before": "G : Type u_1\nG' : Type ?u.194712\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.194721\ninst✝ : AddGroup A\nH K : Subgroup G\nh : Subsingleton G\nx y : Subgroup G\ni : G\n⊢ 1 ∈ x ↔ 1 ∈ y", "tactic": "simp [Subgroup.one_mem]" } ]
[ 1064, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1058, 1 ]
Mathlib/Data/Set/Pointwise/SMul.lean
Set.smul_univ₀'
[]
[ 1068, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1067, 1 ]
Mathlib/LinearAlgebra/Finsupp.lean
Finsupp.iSup_lsingle_range
[ { "state_after": "α : Type u_1\nM : Type u_2\nN : Type ?u.36095\nP : Type ?u.36098\nR : Type u_3\nS : Type ?u.36104\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\nf : α →₀ M\nx...
[ 154, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 151, 1 ]
Mathlib/Algebra/Associated.lean
Associates.mk_one
[]
[ 775, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 774, 1 ]
Mathlib/Order/WithBot.lean
WithTop.map_top
[]
[ 734, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 733, 1 ]
Mathlib/RingTheory/Subsemiring/Basic.lean
Subsemiring.map_id
[]
[ 561, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 560, 1 ]
Mathlib/Data/Nat/Interval.lean
Nat.cauchy_induction_mul
[ { "state_after": "a b c : ℕ\nP : ℕ → Prop\nh : ∀ (n : ℕ), P (n + 1) → P n\nk seed : ℕ\nhk : 1 < k\nhs : P (succ seed)\nhm : ∀ (x : ℕ), seed < x → P x → P (k * x)\nn x✝ : ℕ\nhl : succ seed ≤ x✝\nhP✝ : P x✝\n⊢ x✝ < (fun x x_1 => x * x_1) k x✝", "state_before": "a b c : ℕ\nP : ℕ → Prop\nh : ∀ (n : ℕ), P (n + 1...
[ 376, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 371, 1 ]
Mathlib/Data/Stream/Init.lean
Stream'.map_iterate
[ { "state_after": "case h\nα : Type u\nβ : Type v\nδ : Type w\nf : α → α\na : α\nn : ℕ\n⊢ iterate f (f a) n = map f (iterate f a) n", "state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → α\na : α\n⊢ iterate f (f a) = map f (iterate f a)", "tactic": "funext n" }, { "state_after": "case h.z...
[ 369, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 361, 1 ]
Mathlib/Data/Polynomial/RingDivision.lean
Polynomial.Monic.prime_of_degree_eq_one
[ { "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]\nhp1 : degree p = 1\nhm : Monic p\n⊢ p = X - ↑C (-coeff p 0)", "tactic": "simpa [hm.leadingCoeff] using eq_X_add_C_of_degree_eq_one hp1" } ]
[ 419, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 417, 1 ]
Mathlib/SetTheory/ZFC/Basic.lean
Arity.const_zero
[]
[ 97, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 96, 1 ]
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean
HasSum.mul_eq
[]
[ 162, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 157, 1 ]
Mathlib/CategoryTheory/Limits/ConeCategory.lean
CategoryTheory.Limits.hasColimit_iff_hasInitial_cocone
[]
[ 174, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 171, 1 ]
Std/Data/List/Lemmas.lean
List.erase_cons_head
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\n⊢ List.erase (a :: l) a = l", "tactic": "simp [erase_cons]" } ]
[ 1037, 20 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 1036, 9 ]
Mathlib/FieldTheory/RatFunc.lean
RatFunc.algebraMap_ne_zero
[]
[ 930, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 929, 1 ]
Mathlib/LinearAlgebra/Dual.lean
Submodule.dualAnnihilator_iSup_eq
[]
[ 913, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 911, 1 ]
Mathlib/Data/Set/Countable.lean
Set.Countable.sUnion_iff
[ { "state_after": "no goals", "state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set (Set α)\nhs : Set.Countable s\n⊢ Set.Countable (⋃₀ s) ↔ ∀ (a : Set α), a ∈ s → Set.Countable a", "tactic": "rw [sUnion_eq_biUnion, hs.biUnion_iff]" } ]
[ 205, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 204, 1 ]
Mathlib/Topology/Algebra/Module/Basic.lean
ContinuousLinearMap.coe_coe
[]
[ 522, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 521, 1 ]
Mathlib/Data/Set/Pointwise/SMul.lean
Set.smul_union
[]
[ 202, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 201, 1 ]
Mathlib/Data/Polynomial/Reverse.lean
Polynomial.trailingCoeff_mul
[ { "state_after": "no goals", "state_before": "R✝ : Type ?u.363887\ninst✝² : Semiring R✝\nf : R✝[X]\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : NoZeroDivisors R\np q : R[X]\n⊢ trailingCoeff (p * q) = trailingCoeff p * trailingCoeff q", "tactic": "rw [← reverse_leadingCoeff, reverse_mul_of_domain, leadingCoef...
[ 335, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 332, 1 ]
Mathlib/Algebra/Order/EuclideanAbsoluteValue.lean
AbsoluteValue.IsEuclidean.sub_mod_lt
[]
[ 61, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 60, 1 ]
Mathlib/CategoryTheory/Abelian/DiagramLemmas/Four.lean
CategoryTheory.Abelian.mono_of_epi_of_mono_of_mono
[ { "state_after": "no goals", "state_before": "V : Type u\ninst✝¹ : Category V\ninst✝ : Abelian V\nA B C D A' B' C' D' : V\nf : A ⟶ B\ng : B ⟶ C\nh : C ⟶ D\nf' : A' ⟶ B'\ng' : B' ⟶ C'\nh' : C' ⟶ D'\nα : A ⟶ A'\nβ : B ⟶ B'\nγ : C ⟶ C'\nδ : D ⟶ D'\ncomm₁ : α ≫ f' = f ≫ β\ncomm₂ : β ≫ g' = g ≫ γ\ncomm₃ : γ ≫ h'...
[ 124, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 98, 1 ]
Mathlib/Analysis/Calculus/ContDiff.lean
ContDiffOn.comp_same_univ
[ { "state_after": "case h0\n𝕜 : Type u_1\ninst✝²² : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝²¹ : NormedAddCommGroup D\ninst✝²⁰ : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹⁹ : NormedAddCommGroup E\ninst✝¹⁸ : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹⁷ : NormedAddCommGroup F\ninst✝¹⁶ : NormedSpace 𝕜 F\nG : Type uG\n...
[ 620, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 581, 9 ]
Mathlib/RingTheory/IntegralClosure.lean
IsIntegralClosure.algebraMap_lift
[]
[ 922, 68 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 921, 1 ]
Mathlib/Data/Finsupp/Defs.lean
Finsupp.coe_eq_zero
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.13590\nγ : Type ?u.13593\nι : Type ?u.13596\nM : Type u_2\nM' : Type ?u.13602\nN : Type ?u.13605\nP : Type ?u.13608\nG : Type ?u.13611\nH : Type ?u.13614\nR : Type ?u.13617\nS : Type ?u.13620\ninst✝ : Zero M\nf : α →₀ M\n⊢ ↑f = 0 ↔ f = ...
[ 203, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 203, 1 ]
Mathlib/Logic/Function/Basic.lean
Function.involutive_iff_iter_2_eq_id
[]
[ 875, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 874, 1 ]
Mathlib/RingTheory/IsTensorProduct.lean
Algebra.IsPushout.algHom_ext
[ { "state_after": "case H\nR : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝³³ : AddCommMonoid M\ninst✝³² : AddCommMonoid N\ninst✝³¹ : CommRing R\ninst✝³⁰ : CommRing S\ninst✝²⁹ : Algebra R S\ninst✝²⁸ : Module R M\ninst✝²⁷ : Module R N\ninst✝²⁶ : Module S N\ninst✝²⁵ : IsScalarTower R S N\nf✝ : M →ₗ[R] N\...
[ 533, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 521, 1 ]
Mathlib/LinearAlgebra/Alternating.lean
AlternatingMap.compLinearEquiv_eq_zero_iff
[]
[ 641, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 639, 1 ]
Mathlib/CategoryTheory/Limits/Types.lean
CategoryTheory.Limits.Types.colimit_eq
[ { "state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nj j' : J\nx : F.obj j\nx' : F.obj j'\nw : colimit.ι F j x = colimit.ι F j' x'\n⊢ Quot.mk (Quot.Rel F) { fst := j, snd := x } = Quot.mk (Quot.Rel F) { fst := j', snd := x' }", "state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤...
[ 359, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 355, 1 ]
Mathlib/CategoryTheory/MorphismProperty.lean
CategoryTheory.MorphismProperty.universally_le
[ { "state_after": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.86593\ninst✝ : Category D\nP : MorphismProperty C\nX Y : C\nf : X ⟶ Y\nhf : universally P f\n⊢ P f", "state_before": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.86593\ninst✝ : Category D\nP : MorphismProperty C\n⊢ universally P ≤ P", "tact...
[ 598, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 596, 1 ]
Mathlib/Analysis/NormedSpace/FiniteDimension.lean
FiniteDimensional.complete
[ { "state_after": "𝕜 : Type u\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁶ : AddCommGroup F'\ninst✝⁵ : Module 𝕜 F'\ninst✝⁴ : TopologicalSpace F'\ninst✝³ : T...
[ 370, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 367, 1 ]
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean
Polynomial.natTrailingDegree_C
[]
[ 238, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.ext_iff
[ { "state_after": "no goals", "state_before": "α : Type u\nf g : Filter α\ns t : Set α\n⊢ f = g ↔ ∀ (s : Set α), s ∈ f ↔ s ∈ g", "tactic": "simp only [filter_eq_iff, ext_iff, Filter.mem_sets]" } ]
[ 134, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 133, 11 ]
Mathlib/Topology/Compactification/OnePoint.lean
OnePoint.ultrafilter_le_nhds_infty
[ { "state_after": "no goals", "state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nf : Ultrafilter (OnePoint X)\n⊢ ↑f ≤ 𝓝 ∞ ↔ ∀ (s : Set X), IsClosed s → IsCompact s → ¬some '' s ∈ f", "tactic": "simp only [le_nhds_infty, ← compl_image_coe, Ultrafilter.mem_coe,\n ...
[ 357, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 354, 1 ]
Mathlib/Probability/ProbabilityMassFunction/Basic.lean
Pmf.apply_eq_one_iff
[ { "state_after": "α : Type u_1\nβ : Type ?u.6948\nγ : Type ?u.6951\np : Pmf α\na : α\nh : ↑p a = 1\na' : α\nha' : a' ∈ support p\nha : ¬a' ∈ {a}\n⊢ False", "state_before": "α : Type u_1\nβ : Type ?u.6948\nγ : Type ?u.6951\np : Pmf α\na : α\n⊢ ↑p a = 1 ↔ support p = {a}", "tactic": "refine' ⟨fun h => Set...
[ 132, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 113, 1 ]
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean
Submodule.inner_right_of_mem_orthogonal
[]
[ 70, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 69, 1 ]
Mathlib/Data/Bool/AllAny.lean
List.all_iff_forall_prop
[ { "state_after": "no goals", "state_before": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nl : List α\na : α\n⊢ (all l fun a => decide (p a)) = true ↔ ∀ (a : α), a ∈ l → p a", "tactic": "simp only [all_iff_forall, Bool.of_decide_iff]" } ]
[ 37, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 36, 1 ]
Mathlib/RingTheory/TensorProduct.lean
Algebra.TensorProduct.map_range
[ { "state_after": "case a\nR : Type u\ninst✝⁸ : CommSemiring R\nA : Type v₁\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\nB : Type v₂\ninst✝⁵ : Semiring B\ninst✝⁴ : Algebra R B\nC : Type v₃\ninst✝³ : Semiring C\ninst✝² : Algebra R C\nD : Type v₄\ninst✝¹ : Semiring D\ninst✝ : Algebra R D\nf : A →ₐ[R] B\ng : C →ₐ[R]...
[ 892, 83 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 884, 1 ]
Mathlib/Data/Nat/Choose/Basic.lean
Nat.choose_mul_succ_eq
[ { "state_after": "no goals", "state_before": "case zero\nn : ℕ\n⊢ choose n zero * (n + 1) = choose (n + 1) zero * (n + 1 - zero)", "tactic": "simp" }, { "state_after": "case succ.inl\nn k : ℕ\nhk : k + 1 ≤ n + 1\n⊢ choose n (succ k) * (n + 1) = choose (n + 1) (succ k) * (n + 1 - succ k)\n\ncase ...
[ 235, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 227, 1 ]
Mathlib/Data/List/Range.lean
List.nthLe_range
[]
[ 203, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 202, 1 ]
Mathlib/Algebra/Lie/Submodule.lean
LieIdeal.comap_mono
[ { "state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo...
[ 869, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 866, 1 ]
Mathlib/Data/List/Nodup.lean
List.nodup_nil
[]
[ 39, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 38, 1 ]
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean
AffineSubspace.direction_mk'
[ { "state_after": "case h\nk : 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\np : P\ndirection : Submodule k V\nv : V\n⊢ v ∈ AffineSubspace.direction (mk' p direction) ↔ v ∈ direction", "state_before": "k : Type u_1\nV : Type u_2\...
[ 488, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 480, 1 ]
Mathlib/Algebra/GCDMonoid/Basic.lean
gcd_same
[]
[ 431, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 430, 1 ]
Mathlib/GroupTheory/GroupAction/SubMulAction.lean
SubMulAction.subtype_apply
[]
[ 199, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Finset/NAry.lean
Finset.image_image₂_antidistrib
[ { "state_after": "α : Type u_3\nα' : Type u_6\nβ : Type u_4\nβ' : Type u_5\nγ : Type u_2\nγ' : Type ?u.91719\nδ : Type u_1\nδ' : Type ?u.91725\nε : Type ?u.91728\nε' : Type ?u.91731\nζ : Type ?u.91734\nζ' : Type ?u.91737\nν : Type ?u.91740\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : DecidableEq ...
[ 473, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 469, 1 ]
Mathlib/Algebra/Polynomial/BigOperators.lean
Polynomial.coeff_zero_prod
[ { "state_after": "no goals", "state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R\nf : ι → R[X]\nt : Multiset R[X]\n⊢ coeff (∏ i in s, f i) 0 = ∏ i in s, coeff (f i) 0", "tactic": "simpa using coeff_zero_multiset_prod (s.1.map f)" } ]
[ 235, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 234, 1 ]
Mathlib/LinearAlgebra/Matrix/ToLin.lean
Matrix.toLinAlgEquiv_symm
[]
[ 731, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 729, 1 ]
Mathlib/LinearAlgebra/SesquilinearForm.lean
LinearMap.not_separatingLeft_zero
[]
[ 632, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 630, 1 ]
Mathlib/Algebra/Lie/Submodule.lean
LieIdeal.coe_map_of_surjective
[ { "state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo...
[ 1034, 8 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1021, 1 ]
Mathlib/Data/ZMod/Basic.lean
ZMod.natAbs_valMinAbs_le
[ { "state_after": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\n⊢ ↑(Int.natAbs (valMinAbs x)) * 2 ≤ ↑n", "state_before": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\n⊢ Int.natAbs (valMinAbs x) ≤ n / 2", "tactic": "rw [Nat.le_div_two_iff_mul_two_le]" }, { "state_after": "case inl\nn : ℕ\ninst✝ : NeZero n\nx : ZM...
[ 987, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 981, 1 ]
Mathlib/SetTheory/Game/PGame.lean
PGame.neg_lf_neg_iff
[]
[ 1327, 22 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1326, 1 ]
Mathlib/Algebra/Module/LinearMap.lean
LinearMap.cancel_right
[]
[ 565, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 564, 1 ]
Mathlib/Analysis/InnerProductSpace/Calculus.lean
differentiable_euclidean
[ { "state_after": "𝕜 : Type u_1\nι : Type u_3\nH : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup H\ninst✝¹ : NormedSpace 𝕜 H\ninst✝ : Fintype ι\nf : H → EuclideanSpace 𝕜 ι\nf' : H →L[𝕜] EuclideanSpace 𝕜 ι\nt : Set H\ny : H\n⊢ (∀ (i : ι), Differentiable 𝕜 fun x => (↑(EuclideanSpace.equiv ι 𝕜) ∘...
[ 319, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 317, 1 ]
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
BoxIntegral.TaggedPrepartition.IsSubordinate.mono
[]
[ 283, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 281, 1 ]
Mathlib/Data/Polynomial/Laurent.lean
LaurentPolynomial.algebraMap_apply
[]
[ 146, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 144, 1 ]
Mathlib/Analysis/Complex/ReImTopology.lean
Complex.closure_setOf_im_lt
[ { "state_after": "no goals", "state_before": "a : ℝ\n⊢ closure {z | z.im < a} = {z | z.im ≤ a}", "tactic": "simpa only [closure_Iio] using closure_preimage_im (Iio a)" } ]
[ 123, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 122, 1 ]
Mathlib/Order/Bounds/Basic.lean
lt_isGLB_iff
[]
[ 1055, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1054, 1 ]
Mathlib/RingTheory/Ideal/LocalRing.lean
LocalRing.isField_iff_maximalIdeal_eq
[]
[ 152, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 149, 1 ]
Mathlib/Algebra/GroupWithZero/Units/Basic.lean
Units.val_mk0
[]
[ 197, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 196, 1 ]
Mathlib/Order/Filter/Bases.lean
Filter.isCountablyGenerated_top
[]
[ 1193, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1192, 1 ]
Mathlib/Data/Real/CauSeqCompletion.lean
CauSeq.Completion.mk_mul
[]
[ 103, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 102, 1 ]
Mathlib/SetTheory/ZFC/Basic.lean
ZFSet.nonempty_toSet_iff
[]
[ 759, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 758, 1 ]
Mathlib/MeasureTheory/Measure/VectorMeasure.lean
MeasureTheory.VectorMeasure.restrict_le_restrict_subset
[]
[ 897, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 894, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.empty_or_exists_mem
[]
[ 281, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 280, 1 ]
Mathlib/CategoryTheory/MorphismProperty.lean
CategoryTheory.MorphismProperty.RespectsIso.arrow_mk_iso_iff
[]
[ 171, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 169, 1 ]
Mathlib/SetTheory/ZFC/Basic.lean
PSet.Subset.congr_left
[]
[ 252, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 243, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.ae_restrict_union_eq
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.555132\nγ : Type ?u.555135\nδ : Type ?u.555138\nι : Type ?u.555141\nR : Type ?u.555144\nR' : Type ?u.555147\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t ...
[ 2737, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2735, 1 ]
Mathlib/Topology/MetricSpace/Lipschitz.lean
LipschitzWith.edist_lt_of_edist_lt_div
[]
[ 185, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 181, 1 ]
Mathlib/Data/Set/Function.lean
Set.BijOn.inter_mapsTo
[]
[ 934, 50 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 930, 1 ]
Mathlib/RingTheory/FractionalIdeal.lean
FractionalIdeal.canonicalEquiv_self
[ { "state_after": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type ?u.1037421\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.1037874\ninst✝¹ : CommRing P''\ninst✝ : Algebra R ...
[ 954, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 951, 1 ]
Mathlib/Topology/VectorBundle/Constructions.lean
Bundle.Trivial.trivialization.coordChangeL
[ { "state_after": "case h.h\n𝕜 : Type u_2\nB : Type u_3\nF : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : TopologicalSpace B\nb : B\nv : F\n⊢ ↑(Trivialization.coordChangeL 𝕜 (trivialization B F) (trivialization B F) b) v = ↑(ContinuousLinearEq...
[ 56, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 51, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.inducedOuterMeasure_eq
[]
[ 1591, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1589, 1 ]
Mathlib/Order/PropInstances.lean
Pi.disjoint_iff
[ { "state_after": "case mp\nι : Type u_2\nα' : ι → Type u_1\ninst✝¹ : (i : ι) → PartialOrder (α' i)\ninst✝ : (i : ι) → OrderBot (α' i)\nf g : (i : ι) → α' i\n⊢ Disjoint f g → ∀ (i : ι), Disjoint (f i) (g i)\n\ncase mpr\nι : Type u_2\nα' : ι → Type u_1\ninst✝¹ : (i : ι) → PartialOrder (α' i)\ninst✝ : (i : ι) → Or...
[ 85, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 75, 1 ]
Mathlib/GroupTheory/DoubleCoset.lean
Doset.eq
[ { "state_after": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.26004\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na b : G\n⊢ Setoid.r a b ↔ ∃ h, h ∈ H ∧ ∃ k, k ∈ K ∧ b = h * a * k", "state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.26004\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Sub...
[ 134, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 131, 1 ]
Mathlib/Data/Set/Finite.lean
Multiset.finite_toSet_toFinset
[ { "state_after": "case a\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : DecidableEq α\ns : Multiset α\nx : α\n⊢ x ∈ Finite.toFinset (_ : Set.Finite {x | x ∈ s}) ↔ x ∈ toFinset s", "state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : DecidableEq α\ns : Multiset α\n⊢ Finite.toFin...
[ 556, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 553, 1 ]
Mathlib/Algebra/Algebra/Operations.lean
Submodule.one_le
[ { "state_after": "no goals", "state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n : A\n⊢ 1 ≤ P ↔ 1 ∈ P", "tactic": "simp only [one_eq_span, span_le, Set.singleton_subset_iff, SetLike.mem_coe]" ...
[ 123, 78 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 121, 1 ]
Mathlib/Data/Matrix/Block.lean
Matrix.dotProduct_block
[]
[ 40, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 38, 1 ]
Mathlib/Topology/MetricSpace/Lipschitz.lean
LipschitzWith.mapsTo_ball
[]
[ 371, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 369, 1 ]
Mathlib/SetTheory/Ordinal/FixedPoint.lean
Ordinal.derivFamily_isNormal
[ { "state_after": "ι : Type u\nf✝ : ι → Ordinal → Ordinal\nf : ι → Ordinal → Ordinal\no : Ordinal\n⊢ succ (derivFamily f o) ≤ nfpFamily f (succ (derivFamily f o))", "state_before": "ι : Type u\nf✝ : ι → Ordinal → Ordinal\nf : ι → Ordinal → Ordinal\no : Ordinal\n⊢ derivFamily f o < derivFamily f (succ o)", ...
[ 183, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 181, 1 ]
Mathlib/Data/Polynomial/Derivative.lean
Polynomial.derivative_nat_cast_mul
[ { "state_after": "no goals", "state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Semiring R\nn : ℕ\nf : R[X]\n⊢ ↑derivative (↑n * f) = ↑n * ↑derivative f", "tactic": "simp" } ]
[ 357, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 355, 1 ]
Mathlib/Topology/Algebra/UniformGroup.lean
uniformity_eq_comap_inv_mul_nhds_one
[ { "state_after": "α : Type u_1\nβ : Type ?u.167207\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\n⊢ comap (unop ∘ (fun x => x.snd / x.fst) ∘ fun p => (op p.fst, op p.snd)) (𝓝 1) = comap (fun x => x.fst⁻¹ * x.snd) (𝓝 1)", "state_before": "α : Type u_1\nβ : Type ?u.167207\ninst✝² : Unif...
[ 324, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 320, 1 ]
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean
QuadraticForm.polar_smul
[ { "state_after": "no goals", "state_before": "S : Type u_1\nR : Type u_2\nR₁ : Type ?u.3579\nM : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : CommRing R₁\ninst✝² : AddCommGroup M\ninst✝¹ : Monoid S\ninst✝ : DistribMulAction S R\nf : M → R\ns : S\nx y : M\n⊢ polar (s • f) x y = s • polar f x y", "tactic": "simp o...
[ 104, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 103, 1 ]
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean
MeasureTheory.FiniteMeasure.normalize_testAgainstNN
[ { "state_after": "no goals", "state_before": "Ω : Type u_1\ninst✝¹ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ninst✝ : TopologicalSpace Ω\nnonzero : μ ≠ 0\nf : Ω →ᵇ ℝ≥0\n⊢ testAgainstNN (ProbabilityMeasure.toFiniteMeasure (normalize μ)) f = (mass μ)⁻¹ * testAgainstNN μ f", "tactic": "simp...
[ 408, 93 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 406, 1 ]
Mathlib/Data/Prod/Basic.lean
Prod.swap_prod_mk
[]
[ 178, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 177, 1 ]
Mathlib/Algebra/GradedMonoid.lean
SetLike.mul_mem_graded
[]
[ 520, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 518, 1 ]
Mathlib/Order/Filter/Extr.lean
IsMaxFilter.congr
[]
[ 647, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 645, 1 ]
Mathlib/Init/Logic.lean
decidableEq_inl_refl
[]
[ 333, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 330, 1 ]
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean
AffineMap.coe_mk
[]
[ 118, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/Data/Complex/Exponential.lean
Complex.sin_add_mul_I
[ { "state_after": "no goals", "state_before": "x✝ y✝ x y : ℂ\n⊢ sin (x + y * I) = sin x * cosh y + cos x * sinh y * I", "tactic": "rw [sin_add, cos_mul_I, sin_mul_I, mul_assoc]" } ]
[ 877, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 876, 1 ]
Mathlib/Algebra/Order/Floor.lean
Int.fract_int_add
[ { "state_after": "no goals", "state_before": "F : Type ?u.148716\nα : Type u_1\nβ : Type ?u.148722\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ : α\nm : ℤ\na : α\n⊢ fract (↑m + a) = fract a", "tactic": "rw [add_comm, fract_add_int]" } ]
[ 839, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 839, 1 ]