file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_mul | [
{
"state_after": "no goals",
"state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\n⊢ adjugate A ⬝ A = (Aᵀ ⬝ adjugate Aᵀ)ᵀ",
"tactic": "rw [← adjugate_transpose, ← transpose_mul, t... | [
302,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | isHausdorff_iff | [] | [
66,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Mathlib/Topology/UniformSpace/Basic.lean | comp_mem_uniformity_sets | [] | [
460,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isAdjointPair_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.296180\nR₂ : Type ?u.296183\nR₃ : Type ?u.296186\nM : Type u_2\nM₁ : Type u_3\nM₂ : Type ?u.296195\nMₗ₁ : Type ?u.296198\nMₗ₁' : Type ?u.296201\nMₗ₂ : Type ?u.296204\nMₗ₂' : Type ?u.296207\nK : Type ?u.296210\nK₁ : Type ?u.296213\nK₂ :... | [
447,
101
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Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.liftR_iff | [
{
"state_after": "case mp\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nr : {i : Fin2 n} → α i → α i → Prop\nx y : F α\n⊢ LiftR (fun {i} => r) x y →\n ∃ a f₀ f₁,\n x = abs { fst := a, snd := f₀ } ∧\n y = abs { fst := a, snd := f₁ } ∧ ∀ (i : Fin2 n) (j : MvPFun... | [
160,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.exists_irreducible | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\n⊢ ∃ ϖ, maximalIdeal R = span {ϖ}",
"state_before": "R : Type u\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\n⊢ ∃ ϖ, Irreducible ϖ",
"tactic": "simp_rw [irreducible_iff_u... | [
113,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.lift.unique | [] | [
742,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
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Mathlib/Data/List/Basic.lean | List.of_mem_filter | [
{
"state_after": "no goals",
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"tactic": "simpa only [filter_cons_of_pos _ pb] using ain"
},
{
... | [
3536,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3530,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.range_total | [
{
"state_after": "case h\nα : Type u_3\nM : Type u_1\nN : Type ?u.330103\nP : Type ?u.330106\nR : Type u_2\nS : Type ?u.330112\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R P... | [
620,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.copy_eq | [] | [
921,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
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Mathlib/Computability/Encoding.lean | Computability.Encoding.card_le_card_list | [] | [
247,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Algebra/Star/Basic.lean | star_sub | [] | [
301,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Pi.nat_apply | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mul_def | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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] |
Mathlib/Data/Set/Lattice.lean | Set.not_mem_of_not_mem_sUnion | [] | [
1036,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.map_some_eraseNone | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14880\ninst✝ : DecidableEq (Option α)\ns : Finset (Option α)\n⊢ map Embedding.some (↑eraseNone s) = erase s none",
"tactic": "rw [map_eq_image, Embedding.some_apply, image_some_eraseNone]"
}
] | [
153,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.div_rpow | [] | [
120,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Homology/Single.lean | CochainComplex.single₀_map_f_0 | [] | [
381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitLower_ne_splitUpper | [
{
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153,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
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Mathlib/Logic/Nonempty.lean | Nonempty.map | [] | [
142,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | rel_act_of_rel_of_rel_act | [] | [
201,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
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] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.srange_fst | [] | [
913,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | zero_ne_one_or_forall_eq_0 | [] | [
141,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Std/Data/List/Basic.lean | List.takeWhile₂_eq_takeWhile₂TR | [
{
"state_after": "case h.h.h.h.h\nα : Type u_2\nβ : Type u_1\nR : α → β → Bool\nas : List α\nbs : List β\n⊢ takeWhile₂ R as bs = takeWhile₂TR R as bs",
"state_before": "⊢ @takeWhile₂ = @takeWhile₂TR",
"tactic": "funext α β R as bs"
},
{
"state_after": "case h.h.h.h.h\nα : Type u_2\nβ : Type u_1\... | [
1054,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1048,
10
] |
Mathlib/Order/SymmDiff.lean | symmDiff_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.20047\nα : Type u_1\nβ : Type ?u.20053\nπ : ι → Type ?u.20058\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c d a b : α\nh : a ≤ b\n⊢ a ∆ b = b \\ a",
"tactic": "rw [symmDiff, sdiff_eq_bot_iff.2 h, bot_sup_eq]"
}
] | [
142,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Finsupp.toDfinsupp_neg | [] | [
166,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_rename | [] | [
273,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_singleton_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.25381\nβ : Type u_3\nβ' : Type ?u.25387\nγ : Type u_1\nγ' : Type ?u.25393\nδ : Type ?u.25396\nδ' : Type ?u.25399\nε : Type ?u.25402\nε' : Type ?u.25405\nζ : Type ?u.25408\nζ' : Type ?u.25411\nν : Type ?u.25414\nf f' : α → β → γ\ng g' :... | [
197,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_nat_cast | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_eq | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.congr_right | [] | [
367,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.summable_of_sum_range_le | [
{
"state_after": "α : Type ?u.314365\nβ : Type ?u.314368\nγ : Type ?u.314371\nf : ℕ → ℝ≥0\nc : ℝ≥0\nh : ∀ (n : ℕ), ∑ i in Finset.range n, f i ≤ c\nH : Tendsto (fun n => ∑ i in Finset.range n, f i) atTop atTop\n⊢ False",
"state_before": "α : Type ?u.314365\nβ : Type ?u.314368\nγ : Type ?u.314371\nf : ℕ → ℝ≥0... | [
1151,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
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Mathlib/ModelTheory/Quotients.lean | FirstOrder.Language.funMap_quotient_mk' | [
{
"state_after": "L : Language\nM : Type u_3\ns : Setoid M\nps : Prestructure L s\nn : ℕ\nf : Functions L n\nx : Fin n → M\n⊢ Quotient.map (funMap f) (_ : ∀ (x y : Fin n → M), x ≈ y → funMap f x ≈ funMap f y)\n (Quotient.finChoice fun i => Quotient.mk s (x i)) =\n Quotient.mk s (funMap f x)",
"state... | [
65,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.Nat.cast_ringChar | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : NonAssocSemiring R\n⊢ ↑(ringChar R) = 0",
"tactic": "rw [ringChar.spec]"
}
] | [
243,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.lift_comp | [
{
"state_after": "case C0\nα✝ : Type u\nβ✝ : Type v\nγ✝ : Type w\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : AddCommGroup γ\nf : α → β\ng : β → γ\nx : FreeAbelianGroup α\n⊢ ↑(↑lift (g ∘ f)) 0 = ↑(↑lift g) (↑(map f) 0)\n\ncase C1\nα✝ : Type u\nβ✝ : Type v\nγ✝ : Type w\nα : Type u_1\nβ : Type u_2\nγ : Type... | [
371,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.comp_restrict | [] | [
1159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
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Mathlib/Data/Real/EReal.lean | EReal.top_add_coe | [] | [
664,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivaryOn_comm | [] | [
417,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.IsFiniteKernel.bound_lt_top | [] | [
137,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/Constructions.lean | quotientMap_quot_mk | [] | [
1143,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.div_right | [] | [
86,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_apply | [] | [
342,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.pred_mk_succ' | [] | [
1531,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.subset_iff | [] | [
400,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_coe | [] | [
1202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_lintegral_nnnorm_bounded | [
{
"state_after": "α : Type u_2\nι : Type u_1\nE : Type u_3\ninst✝³ : MeasurableSpace α\nμ : Measure α\nl : Filter ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NeBot l\ninst✝ : IsCountablyGenerated l\nφ : ι → Set α\nhφ : AECover μ l φ\nf : α → E\nI : ℝ\nhfm : AEStronglyMeasurable f μ\nhbounded : ∀ᶠ (i : ι) in l, (... | [
412,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ppow_succ | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nk x : ℕ\n⊢ ↑(ppow f (k + 1)) x = ↑(pmul f (ppow f k)) x",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nk : ℕ\n⊢ ppow f (k + 1) = pmul f (ppow f k)",
"tactic": "ext x"
},
{
"state... | [
565,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.coe_submonoidClass_iff | [
{
"state_after": "M✝ : Type ?u.1875140\nN✝ : Type ?u.1875143\nG : Type ?u.1875146\nR : Type ?u.1875149\nS : Type ?u.1875152\nF : Type ?u.1875155\ninst✝⁵ : CommMonoid M✝\ninst✝⁴ : CommMonoid N✝\ninst✝³ : DivisionCommMonoid G\nk l : ℕ\nζ✝ : M✝\nf : F\nh : IsPrimitiveRoot ζ✝ k\nM : Type u_1\nB : Type u_2\ninst✝² :... | [
409,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpowersHom_symm_apply | [] | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.gc | [] | [
139,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.mapBiprod_inv | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_one_ne_zero | [] | [
302,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
302,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.toSubmonoid_strictMono | [] | [
467,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_int_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Ring R\nn : ℤ\n⊢ natTrailingDegree ↑n = 0",
"tactic": "simp only [← C_eq_int_cast, natTrailingDegree_C]"
}
] | [
473,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_three | [
{
"state_after": "case h.h\nm k : ℕ\n⊢ hyperoperation 3 m k = m ^ k",
"state_before": "⊢ hyperoperation 3 = fun x x_1 => x ^ x_1",
"tactic": "ext (m k)"
},
{
"state_after": "case h.h.zero\nm : ℕ\n⊢ hyperoperation 3 m Nat.zero = m ^ Nat.zero\n\ncase h.h.succ\nm bn : ℕ\nbih : hyperoperation 3 m bn... | [
93,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.one_mem | [] | [
343,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
11
] |
Mathlib/GroupTheory/Perm/Fin.lean | sign_finRotate | [
{
"state_after": "case zero\n\n⊢ ↑sign (finRotate (Nat.zero + 1)) = (-1) ^ Nat.zero\n\ncase succ\nn : ℕ\nih : ↑sign (finRotate (n + 1)) = (-1) ^ n\n⊢ ↑sign (finRotate (Nat.succ n + 1)) = (-1) ^ Nat.succ n",
"state_before": "n : ℕ\n⊢ ↑sign (finRotate (n + 1)) = (-1) ^ n",
"tactic": "induction' n with n i... | [
111,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_coe_linearMap_eq_linearProj | [] | [
856,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.inv_right_iff | [] | [
207,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.mul_iSup_le | [
{
"state_after": "ι : Sort u_1\nf : ι → ℝ≥0\na g : ℝ≥0\nh : ι → ℝ≥0\nH : ∀ (j : ι), g * h j ≤ a\n⊢ (⨆ (i : ι), g * h i) ≤ a",
"state_before": "ι : Sort u_1\nf : ι → ℝ≥0\na g : ℝ≥0\nh : ι → ℝ≥0\nH : ∀ (j : ι), g * h j ≤ a\n⊢ g * iSup h ≤ a",
"tactic": "rw [mul_iSup]"
},
{
"state_after": "no goals... | [
979,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply | [] | [
438,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.finrank_submodule | [
{
"state_after": "K : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : ℙ K V\n⊢ finrank K { x // x ∈ Submodule.span K {Projectivization.rep v} } = 1",
"state_before": "K : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Modul... | [
143,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_eq_iSup_norm | [] | [
259,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_trans | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type ?u.142397\nM : Type u_4\nM' : Type ?u.142403\nN : Type ?u.142406\nP : Type ?u.142409\nG : Type ?u.142412\nH : Type ?u.142415\nR : Type ?u.142418\nS : Type ?u.142421\ninst✝ : Zero M\nf : α ≃ β\ng : β ≃ γ\nl : α →₀ M\nx : γ\n⊢ ↑(equivMap... | [
337,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_im | [
{
"state_after": "no goals",
"state_before": "d n : ℤ\n⊢ (↑n).im = 0",
"tactic": "cases n <;> rfl"
}
] | [
303,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_of_isEmpty | [
{
"state_after": "case h\nR : Type u_2\ninst✝⁵ : StrictOrderedCommSemiring R\nM : Type u_3\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nN : Type ?u.31631\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nι : Type u_1\ninst✝ : IsEmpty ι\nf : M ≃ₗ[R] M\ng : AlternatingMap R M R ι\nhg : g ≠ 0\n⊢ ↑(map ι f) (rayOf... | [
112,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomain.exists_representative_mod_finset | [
{
"state_after": "R : Type u_2\nA : Type ?u.1294364\nK : Type ?u.1294367\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : IsDomain R\ninst✝ : IsDedekindDomain R\nι : Type u_1\ns : Finset ι\nP : ι → Ideal R\ne : ι → ℕ\nprime : ∀ (i : ι), i ∈ s → Prime (P i)\ncoprime : ∀ ... | [
1384,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_eq_true | [] | [
665,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_eq_zero | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ toNNReal r = 0 ↔ r ≤ 0",
"tactic": "simpa [-toNNReal_pos] using not_iff_not.2 (@toNNReal_pos r)"
}
] | [
622,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_top | [] | [
380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_mulVec_single | [
{
"state_after": "case h\nl : Type ?u.878832\nm : Type ?u.878835\nn : Type u_1\no : Type ?u.878841\nm' : o → Type ?u.878846\nn' : o → Type ?u.878851\nR : Type u_2\nS : Type ?u.878857\nα : Type v\nβ : Type w\nγ : Type ?u.878864\ninst✝³ : NonUnitalNonAssocSemiring α\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nin... | [
1803,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioc | [] | [
485,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.smul | [] | [
1500,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1498,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_copy | [] | [
652,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.rev_symm | [] | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | memℓp_infty | [] | [
101,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_apply | [] | [
1171,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_left_distrib | [] | [
212,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.support_factorization | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (factorization n).support = toFinset (factors n)",
"tactic": "simp [factorization]"
}
] | [
133,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Memℒp.exists_hasCompactSupport_snorm_sub_le | [
{
"state_after": "α : Type u_1\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : NormalSpace α\ninst✝⁴ : BorelSpace α\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\ninst✝² : NormedSpace ℝ E\ninst✝¹ : LocallyCompactSpace α\ninst✝ : Measure.Regular μ\nhp : p ≠ ⊤\nf : α → E... | [
193,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/ZMod/Quotient.lean | MulAction.zpowersQuotientStabilizerEquiv_symm_apply | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_ne_zero_coe | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : IsWellOrder ι fun x x_1 => x < x_1\nf : ι → E\nn : ι\nh₀ : LinearIndependent 𝕜 (f ∘ Subtype.val)\nh ... | [
227,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.mk | [] | [
920,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.of_map | [] | [
131,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | Measurable.map_prod_mk_left | [
{
"state_after": "case h\nα : Type u_2\nα' : Type ?u.2479556\nβ : Type u_1\nβ' : Type ?u.2479562\nγ : Type ?u.2479565\nE : Type ?u.2479568\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : MeasureTheory.Measure α... | [
203,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.nat_cast_toProd | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.continuous_coeRingHom | [] | [
150,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.biInter | [] | [
178,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.set_range_subset | [] | [
585,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Algebra/Category/ModuleCat/Colimits.lean | ModuleCat.Colimits.quot_zero | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.trStmts₁_self | [
{
"state_after": "no goals",
"state_before": "case ret\nk✝ : Cont'\n⊢ Λ'.ret k✝ ∈ trStmts₁ (Λ'.ret k✝)",
"tactic": "first |apply Finset.mem_singleton_self|apply Finset.mem_insert_self"
},
{
"state_after": "no goals",
"state_before": "case ret\nk✝ : Cont'\n⊢ Λ'.ret k✝ ∈ trStmts₁ (Λ'.ret k✝)",... | [
1756,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1755,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.iSup_span | [] | [
599,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.union | [] | [
1005,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_mul_equiv | [] | [
2503,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2500,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_pow | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_mul_le_mul_inf'_of_nonneg | [] | [
1912,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1909,
1
] |
Mathlib/GroupTheory/Perm/ViaEmbedding.lean | Equiv.Perm.viaEmbeddingHom_injective | [] | [
52,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_inj | [] | [
562,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Data/Finset/Slice.lean | Finset.eq_of_mem_slice | [] | [
156,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.mulLeft_symm | [
{
"state_after": "case H\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\na x✝ : G\n⊢ ↑(Homeomorph.symm (Homeomorph.mulLeft a)) x✝ = ↑(Homeomorph.mulLeft a⁻¹) x✝",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² ... | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
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