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Mathlib/Algebra/BigOperators/Order.lean
Fintype.prod_strict_mono'
[]
[ 701, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 698, 1 ]
Mathlib/Algebra/ContinuedFractions/Translations.lean
GeneralizedContinuedFraction.part_num_none_iff_s_none
[ { "state_after": "no goals", "state_before": "α : Type u_1\ng : GeneralizedContinuedFraction α\nn : ℕ\n⊢ Stream'.Seq.get? (partialNumerators g) n = none ↔ Stream'.Seq.get? g.s n = none", "tactic": "cases s_nth_eq : g.s.get? n <;> simp [partialNumerators, s_nth_eq]" } ]
[ 44, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 43, 1 ]
Mathlib/Analysis/Calculus/MeanValue.lean
image_norm_le_of_norm_deriv_right_lt_deriv_boundary'
[]
[ 278, 80 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 272, 1 ]
Mathlib/Data/PNat/Defs.lean
PNat.coe_injective
[]
[ 155, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 154, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean
Complex.deriv_tan
[ { "state_after": "x : ℂ\nh : cos x = 0\nthis : ¬DifferentiableAt ℂ tan x\n⊢ deriv tan x = ↑1 / cos x ^ 2", "state_before": "x : ℂ\nh : cos x = 0\n⊢ deriv tan x = ↑1 / cos x ^ 2", "tactic": "have : ¬DifferentiableAt ℂ tan x := mt differentiableAt_tan.1 (Classical.not_not.2 h)" }, { "state_after":...
[ 74, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 70, 1 ]
Mathlib/Algebra/GCDMonoid/Finset.lean
Finset.gcd_mul_right
[ { "state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.37723\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\na : α\n⊢ (gcd ∅ fun x => f x * a) = gcd ∅ f * ↑normalize a\n\ncase refine'_2\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.37723\ninst✝¹ ...
[ 261, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 255, 8 ]
Mathlib/Order/Hom/Basic.lean
OrderEmbedding.eq_iff_eq
[]
[ 662, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 661, 1 ]
Mathlib/RingTheory/FiniteType.lean
AddMonoidAlgebra.support_gen_of_gen
[ { "state_after": "R : Type u_2\nM : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : AddMonoid M\nS : Set (AddMonoidAlgebra R M)\nhS : adjoin R S = ⊤\n⊢ ⊤ ≤ adjoin R (⋃ (f : AddMonoidAlgebra R M) (_ : f ∈ S), of' R M '' ↑f.support)", "state_before": "R : Type u_2\nM : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Ad...
[ 359, 49 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 350, 1 ]
Mathlib/Order/Filter/Extr.lean
isMinOn_univ_iff
[]
[ 143, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 142, 1 ]
Mathlib/RingTheory/SimpleModule.lean
JordanHolderModule.iso_trans
[]
[ 222, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 221, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq
[ { "state_after": "case refine'_1\nθ ψ : Angle\n⊢ θ = ψ → sign θ = sign ψ ∧ abs (toReal θ) = abs (toReal ψ)\n\ncase refine'_2\nθ ψ : Angle\nh : sign θ = sign ψ ∧ abs (toReal θ) = abs (toReal ψ)\n⊢ θ = ψ", "state_before": "θ ψ : Angle\n⊢ θ = ψ ↔ sign θ = sign ψ ∧ abs (toReal θ) = abs (toReal ψ)", "tactic"...
[ 962, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 944, 1 ]
Mathlib/MeasureTheory/Measure/VectorMeasure.lean
MeasureTheory.VectorMeasure.AbsolutelyContinuous.mk
[ { "state_after": "α : Type u_1\nβ : Type ?u.622187\nm : MeasurableSpace α\nL : Type ?u.622193\nM : Type u_3\nN : Type u_2\ninst✝⁵ : AddCommMonoid L\ninst✝⁴ : TopologicalSpace L\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\nv : VectorMeasure α M\nw ...
[ 1092, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1088, 1 ]
Mathlib/Computability/Primrec.lean
Nat.Primrec'.encode
[ { "state_after": "v : Vector ℕ 0\n⊢ 0 = encode nil", "state_before": "v : Vector ℕ 0\n⊢ 0 = encode v", "tactic": "rw [v.eq_nil]" }, { "state_after": "no goals", "state_before": "v : Vector ℕ 0\n⊢ 0 = encode nil", "tactic": "rfl" } ]
[ 1486, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1483, 11 ]
Mathlib/Analysis/NormedSpace/LinearIsometry.lean
LinearIsometry.toContinuousLinearMap_injective
[]
[ 347, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 345, 1 ]
Mathlib/Data/Fintype/BigOperators.lean
Fintype.card_fun
[ { "state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.12409\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ card β ^ Finset.card univ = card β ^ card α", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.12409\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ car...
[ 152, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 150, 1 ]
Mathlib/Order/CompleteLattice.lean
isLUB_sSup
[]
[ 148, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 147, 1 ]
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean
SimpleGraph.Subgraph.deleteEdges_spanningCoe_eq
[ { "state_after": "case Adj.h.h.a\nι : Sort ?u.243913\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns : Set (Sym2 V)\nx✝¹ x✝ : V\n⊢ SimpleGraph.Adj (SimpleGraph.deleteEdges (Subgraph.spanningCoe G') s) x✝¹ x✝ ↔\n SimpleGraph.Adj (Subgraph.spanningCoe (deleteEdges G' s)) x✝¹ x✝", "state_befo...
[ 1061, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1058, 1 ]
Mathlib/RingTheory/DedekindDomain/Ideal.lean
multiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_multiplicity
[ { "state_after": "no goals", "state_before": "R : Type u_1\nA : Type ?u.1418572\nK : Type ?u.1418575\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing A\ninst✝⁸ : Field K\ninst✝⁷ : IsDomain A\ninst✝⁶ : IsDomain R\ninst✝⁵ : IsPrincipalIdealRing R\ninst✝⁴ : DecidableEq R\ninst✝³ : DecidableEq (Ideal R)\ninst✝² : Norma...
[ 1496, 45 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1490, 1 ]
Mathlib/Topology/Bornology/Hom.lean
LocallyBoundedMap.id_apply
[]
[ 156, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 155, 1 ]
Mathlib/Topology/ContinuousOn.lean
OpenEmbedding.map_nhdsWithin_preimage_eq
[ { "state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.370133\nδ : Type ?u.370136\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : OpenEmbedding f\ns : Set β\nx : α\n⊢ 𝓝[s ∩ range f] f x = 𝓝[s] f x", "state_before": "α :...
[ 1095, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1091, 1 ]
Mathlib/Data/Matrix/Notation.lean
Matrix.eta_fin_two
[ { "state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nA : Matrix (Fin 2) (Fin 2) α\ni j : Fin 2\n⊢ A i j = ↑of ![![A 0 0, A 0 1], ![A 1 0, A 1 1]] i j", "state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nA : Matrix (Fin ...
[ 425, 38 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 423, 1 ]
Mathlib/Topology/LocallyConstant/Basic.lean
LocallyConstant.eq_const
[]
[ 393, 51 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 392, 1 ]
Mathlib/Analysis/Asymptotics/Asymptotics.lean
Asymptotics.isBigO_refl
[]
[ 568, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 567, 1 ]
Mathlib/Analysis/Normed/Group/Basic.lean
ContinuousAt.nnnorm'
[]
[ 1224, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1223, 1 ]
Mathlib/Order/PrimeIdeal.lean
Order.Ideal.PrimePair.F_isPrime
[ { "state_after": "P : Type u_1\ninst✝ : Preorder P\nIF : Ideal.PrimePair P\n⊢ IsIdeal ↑IF.I", "state_before": "P : Type u_1\ninst✝ : Preorder P\nIF : Ideal.PrimePair P\n⊢ IsIdeal (↑IF.Fᶜ)", "tactic": "rw [IF.compl_F_eq_I]" }, { "state_after": "no goals", "state_before": "P : Type u_1\ninst✝ ...
[ 238, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 234, 1 ]
Mathlib/MeasureTheory/Measure/OuterMeasure.lean
MeasureTheory.OuterMeasure.map_apply
[]
[ 458, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 457, 1 ]
Mathlib/RingTheory/PowerSeries/Basic.lean
PowerSeries.coeff_of_lt_order
[ { "state_after": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nn : ℕ\nh : ↑(coeff R n) φ ≠ 0\n⊢ order φ ≤ ↑n", "state_before": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nn : ℕ\nh : ↑n < order φ\n⊢ ↑(coeff R n) φ = 0", "tactic": "contrapose! h" }, { "state_after": "no goals", ...
[ 2275, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2273, 1 ]
Std/Logic.lean
iff_false_intro
[]
[ 73, 66 ]
e68aa8f5fe47aad78987df45f99094afbcb5e936
https://github.com/leanprover/std4
[ 73, 1 ]
Mathlib/Analysis/PSeries.lean
Real.not_summable_nat_cast_inv
[ { "state_after": "this : ¬Summable fun n => (↑n ^ ↑1)⁻¹\n⊢ ¬Summable fun n => (↑n)⁻¹", "state_before": "⊢ ¬Summable fun n => (↑n)⁻¹", "tactic": "have : ¬Summable (fun n => ((n : ℝ) ^ ((1 : ℕ) : ℝ))⁻¹ : ℕ → ℝ) :=\n mt (Real.summable_nat_pow_inv (p := 1)).1 (lt_irrefl 1)" }, { "state_after": "cas...
[ 252, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 247, 1 ]
Mathlib/Data/Nat/Sqrt.lean
Nat.sqrt_one
[]
[ 165, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 164, 1 ]
Mathlib/RingTheory/ChainOfDivisors.lean
coe_factor_orderIso_map_eq_one_iff
[ { "state_after": "M : Type u_1\ninst✝¹ : CancelCommMonoidWithZero M\nN : Type u_2\ninst✝ : CancelCommMonoidWithZero N\nm u : Associates M\nn : Associates N\nhu' : u ≤ m\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\nhu : ↑(↑d { val := u, property := hu' }) = 1\n⊢ ↑(↑(OrderIso.symm d)\n { val := ↑(↑d { val := u, prop...
[ 246, 58 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 238, 1 ]
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean
MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
[ { "state_after": "case inl\nΩ : Type u_1\ninst✝ : Nonempty Ω\nm0 : MeasurableSpace Ω\ns : Set Ω\n⊢ (fun s => ENNReal.toNNReal (↑↑↑0 s)) s = mass 0 * (fun s => ENNReal.toNNReal (↑↑↑(normalize 0) s)) s\n\ncase inr\nΩ : Type u_1\ninst✝ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ns : Set Ω\nh : μ ≠ 0...
[ 346, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 336, 1 ]
Mathlib/CategoryTheory/Sites/Sheaf.lean
CategoryTheory.isSheaf_iff_isSheaf_of_type
[ { "state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\nJ : GrothendieckTopology C\nA : Type u₂\ninst✝ : Category A\nP : Cᵒᵖ ⥤ Type w\n⊢ Presheaf.IsSheaf J P → Presieve.IsSheaf J P\n\ncase mpr\nC : Type u₁\ninst✝¹ : Category C\nJ : GrothendieckTopology C\nA : Type u₂\ninst✝ : Category A\nP : Cᵒᵖ ⥤ Type w\n...
[ 358, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 340, 1 ]
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean
CategoryTheory.Limits.BinaryBicone.toCone_π_app_right
[]
[ 1008, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1007, 1 ]
Mathlib/CategoryTheory/Monoidal/Category.lean
CategoryTheory.MonoidalCategory.id_tensor_comp
[ { "state_after": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W X Y Z : C\nf : W ⟶ X\ng : X ⟶ Y\n⊢ 𝟙 Z ⊗ f ≫ g = 𝟙 Z ≫ 𝟙 Z ⊗ f ≫ g", "state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\n...
[ 235, 7 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 233, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.not_nonempty_empty
[]
[ 557, 91 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 557, 1 ]
Mathlib/Analysis/NormedSpace/Basic.lean
Filter.Tendsto.zero_smul_isBoundedUnder_le
[]
[ 101, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 98, 1 ]
Mathlib/Data/Int/Basic.lean
Int.neg_nat_succ
[]
[ 174, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 174, 1 ]
Mathlib/MeasureTheory/Function/AEEqFun.lean
MeasureTheory.AEEqFun.lintegral_add
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.1576020\nγ : Type ?u.1576023\nδ : Type ?u.1576026\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf✝ g✝ : α →ₘ[μ] ℝ≥0∞\nf : α → ℝ≥0∞\nhf : AEStronglyMea...
[ 868, 82 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 867, 1 ]
Mathlib/Data/Rat/Defs.lean
Rat.coe_int_num_of_den_eq_one
[ { "state_after": "a b c q : ℚ\nhq : q.den = 1\n⊢ ↑q.num = q.num /. ↑1", "state_before": "a b c q : ℚ\nhq : q.den = 1\n⊢ ↑q.num = q", "tactic": "conv_rhs => rw [← @num_den q, hq]" }, { "state_after": "a b c q : ℚ\nhq : q.den = 1\n⊢ q.num /. 1 = q.num /. ↑1", "state_before": "a b c q : ℚ\nhq :...
[ 517, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 514, 1 ]
Mathlib/Algebra/BigOperators/Basic.lean
Finset.prod_boole
[ { "state_after": "case inl\nι : Type ?u.870155\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoidWithZero β\ns : Finset α\np : α → Prop\ninst✝ : DecidablePred p\nh : ∀ (i : α), i ∈ s → p i\n⊢ (∏ i in s, if p i then 1 else 0) = 1\n\ncase inr\nι : Type ?u.870155\nβ :...
[ 1919, 19 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1910, 1 ]
Mathlib/Analysis/Calculus/ContDiff.lean
ContDiffWithinAt.fderivWithin'
[]
[ 1006, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1001, 1 ]
src/lean/Init/Data/Nat/Basic.lean
Nat.add_sub_of_le
[ { "state_after": "no goals", "state_before": "a b : Nat\nh : a ≤ b\n⊢ a + (b - a) = b", "tactic": "induction a with\n| zero => simp\n| succ a ih =>\n have hne : b - a ≠ 0 := Nat.sub_ne_zero_of_lt h\n have : a ≤ b := Nat.le_of_succ_le h\n rw [sub_succ, Nat.succ_add, ← Nat.add_succ, Nat.succ_pred hne, ...
[ 581, 76 ]
d5348dfac847a56a4595fb6230fd0708dcb4e7e9
https://github.com/leanprover/lean4
[ 575, 1 ]
Mathlib/Algebra/MonoidAlgebra/Basic.lean
AddMonoidAlgebra.single_eq_zero
[]
[ 1211, 90 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1211, 1 ]
Mathlib/RingTheory/Valuation/ValuationRing.lean
ValuationRing.range_algebraMap_eq
[ { "state_after": "case h\nA : Type u\ninst✝⁵ : CommRing A\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra A K\ninst✝² : IsDomain A\ninst✝¹ : ValuationRing A\ninst✝ : IsFractionRing A K\nx✝ : K\n⊢ x✝ ∈ Valuation.integer (valuation A K) ↔ x✝ ∈ RingHom.range (algebraMap A K)", "state_before": "A : Type u\ninst...
[ 241, 35 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 240, 1 ]
Mathlib/SetTheory/Ordinal/Principal.lean
Ordinal.mul_omega_dvd
[ { "state_after": "no goals", "state_before": "a : Ordinal\na0 : 0 < a\nha : a < ω\nb : Ordinal\n⊢ a * (ω * b) = ω * b", "tactic": "rw [← mul_assoc, mul_omega a0 ha]" } ]
[ 410, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 409, 1 ]
Mathlib/Data/PEquiv.lean
PEquiv.bot_apply
[]
[ 303, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 302, 1 ]
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean
MeasureTheory.Lp.simpleFunc.uniformEmbedding
[]
[ 763, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 762, 11 ]
Mathlib/Topology/Instances/NNReal.lean
NNReal.iInf_real_pos_eq_iInf_nnreal_pos
[]
[ 230, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 228, 1 ]
Mathlib/MeasureTheory/Measure/AEMeasurable.lean
aemeasurable_restrict_of_measurable_subtype
[]
[ 303, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 301, 1 ]
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean
ModularGroup.coe_T_zpow
[ { "state_after": "case hz\n\n⊢ ↑(T ^ 0) = ↑of ![![1, 0], ![0, 1]]\n\ncase hp\nn : ℕ\nh : ↑(T ^ ↑n) = ↑of ![![1, ↑n], ![0, 1]]\n⊢ ↑(T ^ (↑n + 1)) = ↑of ![![1, ↑n + 1], ![0, 1]]\n\ncase hn\nn : ℕ\nh : ↑(T ^ (-↑n)) = ↑of ![![1, -↑n], ![0, 1]]\n⊢ ↑(T ^ (-↑n - 1)) = ↑of ![![1, -↑n - 1], ![0, 1]]", "state_before"...
[ 375, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 367, 1 ]
Mathlib/Data/Real/CauSeqCompletion.lean
CauSeq.lim_inv
[ { "state_after": "no goals", "state_before": "α : Type u_1\ninst✝³ : LinearOrderedField α\nβ : Type u_2\ninst✝² : Field β\nabv : β → α\ninst✝¹ : IsAbsoluteValue abv\ninst✝ : IsComplete β abv\nf : CauSeq β abv\nhf : ¬LimZero f\n⊢ lim f ≠ 0", "tactic": "rwa [← lim_eq_zero_iff] at hf" }, { "state_a...
[ 440, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 417, 1 ]
Mathlib/Data/Set/Pointwise/SMul.lean
Set.pairwiseDisjoint_smul_iff
[]
[ 868, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 866, 1 ]
Mathlib/SetTheory/Cardinal/Ordinal.lean
Cardinal.mk_finsupp_nat
[ { "state_after": "no goals", "state_before": "α : Type u\ninst✝ : Nonempty α\n⊢ (#α →₀ ℕ) = max (#α) ℵ₀", "tactic": "simp" } ]
[ 1068, 86 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1068, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.subset_insert_iff
[ { "state_after": "α : Type u_1\nβ : Type ?u.217477\nγ : Type ?u.217480\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ (∀ ⦃x : α⦄, x ∈ s → ¬x = a → x ∈ t) ↔ ∀ ⦃x : α⦄, x ≠ a → x ∈ s → x ∈ t", "state_before": "α : Type u_1\nβ : Type ?u.217477\nγ : Type ?u.217480\ninst✝ : Decidable...
[ 1991, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1989, 1 ]
Mathlib/Algebra/Symmetrized.lean
SymAlg.sym_eq_one_iff
[]
[ 246, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 245, 1 ]
Mathlib/Data/Set/Lattice.lean
Set.seq_singleton
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.269744\nι : Sort ?u.269747\nι' : Sort ?u.269750\nι₂ : Sort ?u.269753\nκ : ι → Sort ?u.269758\nκ₁ : ι → Sort ?u.269763\nκ₂ : ι → Sort ?u.269768\nκ' : ι' → Sort ?u.269773\ns : Set (α → β)\na : α\n⊢ ∀ (x : β), x ∈ seq s {a} ↔...
[ 1975, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1974, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.restrict_trim
[ { "state_after": "α : Type u_1\nβ : Type ?u.3499198\nγ : Type ?u.3499201\nδ : Type ?u.3499204\nι : Type ?u.3499207\nR : Type ?u.3499210\nR' : Type ?u.3499213\nm m0 : MeasurableSpace α\nμ✝ : Measure α\ns : Set α\nhm : m ≤ m0\nμ : Measure α\nhs : MeasurableSet s\nt : Set α\nht : MeasurableSet t\n⊢ ↑↑(Measure.rest...
[ 4416, 67 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 4411, 1 ]
Mathlib/Data/Bool/Basic.lean
Bool.ofNat_le_ofNat
[ { "state_after": "n m : ℕ\nh : n ≤ m\n⊢ (!decide (n = 0)) ≤ !decide (m = 0)", "state_before": "n m : ℕ\nh : n ≤ m\n⊢ ofNat n ≤ ofNat m", "tactic": "simp only [ofNat, ne_eq, _root_.decide_not]" }, { "state_after": "no goals", "state_before": "n m : ℕ\nh : n ≤ m\n⊢ (!decide (n = 0)) ≤ !decide ...
[ 390, 84 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 383, 1 ]
Mathlib/MeasureTheory/Integral/SetToL1.lean
MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left'
[]
[ 916, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 913, 1 ]
Mathlib/Algebra/Lie/Basic.lean
LieHom.coe_one
[]
[ 368, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 367, 1 ]
Mathlib/Topology/Algebra/Order/T5.lean
Set.ordT5Nhd_mem_nhdsSet
[ { "state_after": "X : Type u_1\ninst✝² : LinearOrder X\ninst✝¹ : TopologicalSpace X\ninst✝ : OrderTopology X\na b c : X\ns t : Set X\nhd : Disjoint s (closure t)\nx : X\nhx : x ∈ s\n⊢ x ∈ closure tᶜ", "state_before": "X : Type u_1\ninst✝² : LinearOrder X\ninst✝¹ : TopologicalSpace X\ninst✝ : OrderTopology X...
[ 90, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 85, 1 ]
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean
SimpleGraph.singletonSubgraph_fst_le_subgraphOfAdj
[ { "state_after": "case right\nι : Sort ?u.226800\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nu v : V\nh : Adj G u v\n⊢ ∀ ⦃v_1 w : V⦄, ⊥ → u = v_1 ∧ v = w ∨ u = w ∧ v = v_1", "state_before": "ι : Sort ?u.226800\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nu v : V\nh : A...
[ 971, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 968, 1 ]
Mathlib/Algebra/Module/Torsion.lean
Module.IsTorsionBySet.mk_smul
[]
[ 531, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 528, 1 ]
Mathlib/GroupTheory/Subsemigroup/Operations.lean
Subsemigroup.map_strictMono_of_injective
[]
[ 438, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 437, 1 ]
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean
Monotone.le_csInf_image
[ { "state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.98153\nι : Sort ?u.98156\ninst✝¹ : Preorder α\ninst✝ : ConditionallyCompleteLattice β\nf : α → β\nh_mono : Monotone f\ns : Set α\nhs : Set.Nonempty s\nB : α\nhB : B ∈ lowerBounds s\nf' : αᵒᵈ → βᵒᵈ := f\n⊢ f B ≤ sInf (f '' s)", "state_before": "α : Ty...
[ 1268, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1264, 1 ]
Mathlib/Data/Finset/Functor.lean
Finset.bind_def
[]
[ 163, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 162, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean
Real.lt_arcsin_iff_sin_lt'
[]
[ 192, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 190, 1 ]
Mathlib/Data/Polynomial/DenomsClearable.lean
denomsClearable_zero
[ { "state_after": "no goals", "state_before": "R : Type u_2\nK : Type u_1\ninst✝¹ : Semiring R\ninst✝ : CommSemiring K\ni : R →+* K\na✝ b : R\nbi : K\nN : ℕ\na : R\nbu : bi * ↑i b = 1\n⊢ ↑i 0 = ↑i b ^ N * eval (↑i a * bi) (Polynomial.map i 0)", "tactic": "simp only [eval_zero, RingHom.map_zero, MulZeroCl...
[ 48, 89 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 46, 1 ]
Mathlib/RingTheory/Polynomial/RationalRoot.lean
num_dvd_of_is_root
[ { "state_after": "case h.e'_4\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : UniqueFactorizationMonoid A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\np : A[X]\nr : K\nhr : ↑(aeval r) p = 0\n⊢ coeff (scaleRoots p ↑(den A r)) 0 = coeff (scaleRoots p ↑(den A...
[ 91, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 74, 1 ]
Mathlib/RingTheory/Ideal/Operations.lean
Submodule.smul_iSup
[]
[ 229, 24 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 228, 1 ]
Mathlib/Data/Finset/Basic.lean
Finset.ssubset_iff_subset_ne
[]
[ 424, 28 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 423, 1 ]
Mathlib/Algebra/Order/Floor.lean
Nat.ceil_one
[ { "state_after": "no goals", "state_before": "F : Type ?u.52302\nα : Type u_1\nβ : Type ?u.52308\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢ ⌈1⌉₊ = 1", "tactic": "rw [← Nat.cast_one, ceil_natCast]" } ]
[ 328, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 328, 1 ]
Mathlib/RingTheory/Ideal/Basic.lean
Ideal.add_mem_iff_right
[]
[ 664, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 663, 11 ]
Mathlib/Data/Set/Ncard.lean
Set.pred_ncard_le_ncard_diff_singleton
[ { "state_after": "case inl\nα : Type u_1\nβ : Type ?u.18254\ns✝ t : Set α\na✝ b x y : α\nf : α → β\ns : Set α\na : α\nhs : Set.Finite s\n⊢ ncard s - 1 ≤ ncard (s \\ {a})\n\ncase inr\nα : Type u_1\nβ : Type ?u.18254\ns✝ t : Set α\na✝ b x y : α\nf : α → β\ns : Set α\na : α\nhs : Set.Infinite s\n⊢ ncard s - 1 ≤ nc...
[ 217, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 210, 1 ]
Mathlib/Order/Lattice.lean
le_sup_left'
[]
[ 138, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 137, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Add.lean
DifferentiableOn.neg
[]
[ 438, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 437, 1 ]
Mathlib/Data/Finset/Interval.lean
Finset.Ico_eq_image_ssubsets
[ { "state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\nu : Finset α\n⊢ u ∈ Ico s t ↔ u ∈ image ((fun x x_1 => x ∪ x_1) s) (ssubsets (t \\ s))", "state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\n⊢ Ico s t = image ((fun x x_1 => x ∪ x_1) s) (ss...
[ 95, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 88, 1 ]
Mathlib/Tactic/Ring/Basic.lean
Mathlib.Tactic.Ring.neg_congr
[ { "state_after": "u : Lean.Level\nR✝ : Type ?u.398334\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\na' : R\n⊢ -a' = -a'", "state_before": "u : Lean.Level\nR✝ : Type ?u.398334\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_...
[ 974, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 973, 1 ]
Mathlib/Algebra/Order/Ring/Lemmas.lean
mul_le_mul_of_nonneg_left
[]
[ 156, 72 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 155, 1 ]
Mathlib/Order/OrderIsoNat.lean
RelEmbedding.coe_natGt
[]
[ 57, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 56, 1 ]
Mathlib/MeasureTheory/Measure/Content.lean
MeasureTheory.Content.innerContent_of_isCompact
[]
[ 141, 95 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 139, 1 ]
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean
MeasureTheory.SignedMeasure.rnDeriv_sub
[ { "state_after": "α : Type u_1\nβ : Type ?u.655633\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t✝ s t : SignedMeasure α\nμ : Measure α\ninst✝¹ : HaveLebesgueDecomposition s μ\ninst✝ : HaveLebesgueDecomposition t μ\nhst : HaveLebesgueDecomposition (s + -t) μ\n⊢ rnDeriv (s - t) μ =ᶠ[ae μ] rnDeriv s μ - rnDeriv t...
[ 1185, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1180, 1 ]
Mathlib/Topology/LocalExtr.lean
isLocalExtrOn_const
[]
[ 199, 21 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 198, 1 ]
Mathlib/Data/Set/Basic.lean
Set.union_subset
[]
[ 825, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 824, 1 ]
Mathlib/RingTheory/MvPolynomial/Basic.lean
MvPolynomial.coe_basisMonomials
[]
[ 119, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 117, 1 ]
Mathlib/MeasureTheory/Integral/SetIntegral.lean
MeasureTheory.MeasurePreserving.set_integral_image_emb
[]
[ 512, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 509, 1 ]
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean
Summable.sigma'
[]
[ 418, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 416, 1 ]
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean
SimpleGraph.isUniform_singleton
[ { "state_after": "α : Type u_2\n𝕜 : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\na b : α\nhε : 0 < ε\ns' : Finset α\nhs' : s' ⊆ {a}\nt' : Finset α\nht' : t' ⊆ {b}\nhs : ↑(card {a}) * ε ≤ ↑(card s')\nht : ↑(card {b}) * ε ≤ ↑(card t')\n⊢ abs (↑(...
[ 91, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 82, 1 ]
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean
csInf_Ici
[]
[ 724, 23 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 723, 1 ]
Mathlib/Data/Matrix/Basic.lean
Matrix.submatrix_one_equiv
[]
[ 2496, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2494, 1 ]
Mathlib/Analysis/Calculus/Deriv/Pow.lean
hasDerivWithinAt_pow
[]
[ 71, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 69, 1 ]
Mathlib/Data/Finset/Card.lean
Finset.strongDownwardInduction_eq
[ { "state_after": "no goals", "state_before": "α : Type u_1\nβ : Type ?u.88956\ns✝ t : Finset α\nf : α → β\nn : ℕ\np : Finset α → Sort u_2\nH : (t₁ : Finset α) → ({t₂ : Finset α} → card t₂ ≤ n → t₁ ⊂ t₂ → p t₂) → card t₁ ≤ n → p t₁\ns : Finset α\n⊢ strongDownwardInduction H s = H s fun {t} ht x => strongDown...
[ 690, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 686, 1 ]
Mathlib/Data/Num/Lemmas.lean
Num.mem_ofZNum'
[ { "state_after": "no goals", "state_before": "α : Type ?u.860822\nm : Num\np : PosNum\n⊢ pos p = m ↔ ZNum.pos p = toZNum m", "tactic": "cases m <;> constructor <;> intro h <;> try cases h <;> rfl" }, { "state_after": "no goals", "state_before": "case pos.mpr\nα : Type ?u.860822\np a✝ : PosNu...
[ 1285, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1280, 1 ]
Mathlib/RingTheory/Finiteness.lean
Module.finite_def
[]
[ 537, 31 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 535, 1 ]
Mathlib/Data/PNat/Prime.lean
PNat.Coprime.mul_right
[ { "state_after": "k m n : ℕ+\n⊢ coprime ↑k ↑m → coprime ↑k ↑n → coprime ↑k ↑(m * n)", "state_before": "k m n : ℕ+\n⊢ Coprime k m → Coprime k n → Coprime k (m * n)", "tactic": "repeat' rw [← coprime_coe]" }, { "state_after": "k m n : ℕ+\n⊢ coprime ↑k ↑m → coprime ↑k ↑n → coprime (↑k) (↑m * ↑n)", ...
[ 186, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 183, 1 ]
Mathlib/Algebra/Order/Sub/Canonical.lean
tsub_inj_left
[]
[ 55, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 54, 1 ]
Mathlib/Algebra/Category/Ring/Basic.lean
CategoryTheory.Iso.commRingIsoToRingEquiv_symm_toRingHom
[ { "state_after": "case a\nX Y : CommRingCat\ni : X ≅ Y\nx✝ : ↑Y\n⊢ ↑(RingEquiv.toRingHom (RingEquiv.symm (commRingCatIsoToRingEquiv i))) x✝ = ↑i.inv x✝", "state_before": "X Y : CommRingCat\ni : X ≅ Y\n⊢ RingEquiv.toRingHom (RingEquiv.symm (commRingCatIsoToRingEquiv i)) = i.inv", "tactic": "ext" }, {...
[ 490, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 487, 1 ]
Mathlib/Data/Nat/Prime.lean
Nat.minFac_pos
[ { "state_after": "no goals", "state_before": "n : ℕ\n⊢ 0 < minFac n", "tactic": "by_cases n1 : n = 1 <;> [exact n1.symm ▸ (by decide); exact (minFac_prime n1).pos]" }, { "state_after": "no goals", "state_before": "n : ℕ\nn1 : n = 1\n⊢ 0 < minFac 1", "tactic": "decide" } ]
[ 344, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 343, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
deriv_sin
[]
[ 849, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 847, 1 ]