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/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_le_iff_le_comap | [] | [
471,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.natDegree_mul_mirror | [
{
"state_after": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\np q : R[X]\ninst✝ : NoZeroDivisors R\nhp : p = 0\n⊢ natDegree (p * mirror p) = 2 * natDegree p\n\ncase neg\nR : Type u_1\ninst✝¹ : Semiring R\np q : R[X]\ninst✝ : NoZeroDivisors R\nhp : ¬p = 0\n⊢ natDegree (p * mirror p) = 2 * natDegree p",
"sta... | [
180,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Std/Data/String/Lemmas.lean | String.dropWhile_eq | [] | [
1108,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1107,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_inv | [] | [
664,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/RepresentationTheory/Maschke.lean | LinearMap.equivariantProjection_condition | [
{
"state_after": "k : Type u\ninst✝¹¹ : CommRing k\nG : Type u\ninst✝¹⁰ : Group G\nV : Type v\ninst✝⁹ : AddCommGroup V\ninst✝⁸ : Module k V\ninst✝⁷ : Module (MonoidAlgebra k G) V\ninst✝⁶ : IsScalarTower k (MonoidAlgebra k G) V\nW : Type w\ninst✝⁵ : AddCommGroup W\ninst✝⁴ : Module k W\ninst✝³ : Module (MonoidAlg... | [
137,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr'_trans | [] | [
560,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.exists_nonlinearRightInverse_of_surjective | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf✝ : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\nf : E →L[𝕜] F\nhsurj : Linear... | [
302,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.spanningCoe_bot | [] | [
588,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Std/Data/List/Lemmas.lean | List.getLast_eq_getLastD | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\nh : a :: l ≠ []\n⊢ getLast (a :: l) h = getLastD l a",
"tactic": "cases l <;> rfl"
}
] | [
465,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
464,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | norm_midpoint_lt_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.79698\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : StrictConvexSpace ℝ E\nx y z : E\na b r : ℝ\nh : ‖x‖ = ‖y‖\n⊢ ‖(1 / 2) • (x + y)‖ < ‖x‖ ↔ x ≠ y",
... | [
245,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_sum | [] | [
382,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_union_mem_openSegment | [
{
"state_after": "case hs₀\nα : Type u_1\nE : Type u_2\nF : Type ?u.218635\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : Measure α\ns✝ : Set E\nf : α → E\ns t : Set... | [
167,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compRight_id | [
{
"state_after": "case H\nR : Type u_1\nM : Type u_2\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type ?u.516867\nM₁ : Type ?u.516870\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type ?u.517479\nM₂ : Type ?u.517482\ninst✝¹⁰ : CommSemiring R₂\ninst✝⁹... | [
629,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
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Mathlib/Order/Filter/Interval.lean | Filter.tendstoIxxClass_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6755\ninst✝ : Preorder α\nl₁ l₁' l₂ l₂' : Filter α\nIxx : α → α → Set α\nh : TendstoIxxClass Ixx l₁ l₂\nh' : TendstoIxxClass Ixx l₁' l₂'\n⊢ Tendsto (fun p => Ixx p.fst p.snd) ((l₁ ⊓ l₁') ×ˢ (l₁ ⊓ l₁')) (smallSets (l₂ ⊓ l₂'))",
"tact... | [
111,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_smul | [] | [
211,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.InitialMonoClass.of_isTerminal | [] | [
543,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | continuous_equivFun_basis | [] | [
280,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_subset_Ioo | [
{
"state_after": "case intro.intro.intro.intro.intro\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.250125\nG : Type ?u.250128\nι : Type ?u.250131\nπ : ι → Type ?u.250136\ninst✝³ : OrderedSemiring 𝕜\ninst✝² : OrderedCancelAddCommMonoid E\ninst✝¹ : Module 𝕜 E\ninst✝ : OrderedSMul 𝕜 E\nx y : E\nh : x < y\na b : 𝕜\... | [
454,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/GroupTheory/Abelianization.lean | Abelianization.lift.of | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf g : Perm α\nhf : f ∈ cycleFactorsFinset g\nhf' : IsCycle f ∧ ∀ (a : α), a ∈ support f → ↑f a = ↑g a\n⊢ cycleType f ≤ cycleType g",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf g : Perm α\nhf : f ∈ cyc... | [
229,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toAddEquiv_toIntLinearEquiv | [] | [
865,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_self_le_mul_self | [] | [
420,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_mul | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Even (m * n) ↔ Even m ∨ Even n",
"tactic": "cases' emod_two_eq_zero_or_one m with h₁ h₁ <;>\ncases' emod_two_eq_zero_or_one n with h₂ h₂ <;>\nsimp [even_iff, h₁, h₂, Int.mul_emod]"
}
] | [
143,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.comp_mono | [] | [
313,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Topology/Category/Profinite/Basic.lean | Profinite.isClosedMap | [] | [
320,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.zigzag_symmetric | [] | [
269,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.nat_ne_top | [] | [
383,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.closure_reProdIm | [
{
"state_after": "no goals",
"state_before": "s t : Set ℝ\n⊢ closure (s ×ℂ t) = closure s ×ℂ closure t",
"tactic": "simpa only [← preimage_eq_preimage equivRealProdClm.symm.toHomeomorph.surjective,\n equivRealProdClm.symm.toHomeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t"
}
] | [
178,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_abs | [] | [
135,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubgroup_injective | [] | [
536,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.id_c | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.image_of_comp | [
{
"state_after": "ι✝ : Type u'\nι'✝ : Type ?u.248228\nR : Type u_3\nK : Type ?u.248234\nM : Type u_4\nM' : Type ?u.248240\nM'' : Type ?u.248243\nV : Type u\nV' : Type ?u.248248\nv : ι✝ → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹... | [
513,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.IsSRGWith.compl_is_regular | [
{
"state_after": "V : Type u\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nn k ℓ μ : ℕ\nh : IsSRGWith G n k ℓ μ\n⊢ IsRegularOfDegree (Gᶜ) (Fintype.card V - 1 - k)",
"state_before": "V : Type u\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝... | [
140,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/GroupTheory/PresentedGroup.lean | PresentedGroup.toGroup.unique | [
{
"state_after": "α : Type u_1\nG : Type u_2\ninst✝ : Group G\nf : α → G\nrels : Set (FreeGroup α)\nh : ∀ (r : FreeGroup α), r ∈ rels → ↑(↑FreeGroup.lift f) r = 1\ng : PresentedGroup rels →* G\nhg : ∀ (x : α), ↑g (PresentedGroup.of x) = f x\nx : PresentedGroup rels\n⊢ ↑g x = ↑(toGroup h) x",
"state_before":... | [
91,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.to_subtype_range' | [] | [
505,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | Commute.exp_left | [] | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.equalizerSubobject_arrow_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf g : X ⟶ Y\ninst✝ : HasEqualizer f g\n⊢ arrow (equalizerSubobject f g) ≫ f = arrow (equalizerSubobject f g) ≫ g",
"tactic": "rw [← equalizerSubobject_arrow, Category.assoc, Category.assoc, equalizer.condition]"
... | [
67,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.dualPairing_apply | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.card_sups_iff | [] | [
79,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/TietzeExtension.lean | ContinuousMap.exists_extension_forall_mem_of_closedEmbedding | [
{
"state_after": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : NormalSpace Y\nf : C(X, ℝ)\nt : Set ℝ\ne : X → Y\nhs : OrdConnected t\nhf : ∀ (x : X), ↑f x ∈ t\nhne : Set.Nonempty t\nhe : ClosedEmbedding e\nh : ℝ ≃o ↑(Ioo (-1) 1)\n⊢ ∃ g, (∀ (y : Y), ↑g y ∈ t) ∧ ↑g... | [
384,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.Integrable.integral_prod_right | [] | [
337,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.liftOnUnits_mk | [] | [
1327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
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] |
Mathlib/Data/Part.lean | Part.one_def | [] | [
700,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_p | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑p‖ = (↑↑p)⁻¹",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑p‖ = (↑p)⁻¹",
"tactic": "rw [← @Rat.cast_coe_nat ℝ _ p]"
},
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑↑p‖ = (↑↑p)⁻¹",
"state_before": "p : ℕ\nhp : Fact (Nat.P... | [
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23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.mem_factors | [] | [
159,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/List/AList.lean | AList.lookup_empty | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_diagonal' | [
{
"state_after": "l : Type ?u.157202\nm : Type u_1\nn : Type ?u.157208\no : Type ?u.157211\nm' : o → Type ?u.157216\nn' : o → Type ?u.157221\nR : Type ?u.157224\nS : Type ?u.157227\nα : Type v\nβ : Type w\nγ : Type ?u.157234\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : DecidableEq m\ninst✝ : NonUnitalNonAs... | [
825,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.toFinsupp_toFreeAbelianGroup | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nf : X →₀ ℤ\n⊢ ↑toFinsupp (↑toFreeAbelianGroup f) = f",
"tactic": "rw [← AddMonoidHom.comp_apply, toFinsupp_comp_toFreeAbelianGroup, AddMonoidHom.id_apply]"
}
] | [
96,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_union_distrib_left | [] | [
1046,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_succ_self | [] | [
87,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/List/Nodup.lean | List.Pairwise.nodup | [] | [
49,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_le_dist_of_mem | [
{
"state_after": "ι : Sort ?u.59705\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : y ∈ s\n⊢ ENNReal.toReal (infEdist x s) ≤ ENNReal.toReal (edist x y)",
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511,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
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Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime | [
{
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405,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.isUnit_iff | [
{
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}
] | [
1271,
87
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1268,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Icc_union_Ico | [] | [
1636,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
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Mathlib/Logic/Function/Iterate.lean | List.foldr_const | [
{
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"tactic": "rw [length_cons, foldr, foldr_const f b l, iterate_succ_apply']"
}
] | [
255,
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253,
1
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Std/Data/Int/DivMod.lean | Int.sub_ediv_of_dvd | [
{
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},
{
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808,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
805,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.add_one_le_ceil_iff | [
{
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"tactic": "rw [← Nat.lt_ceil, Nat.add_one_le_iff]"
}
] | [
289,
41
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288,
1
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Mathlib/Order/CompleteLattice.lean | Prod.snd_sInf | [] | [
1836,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1835,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_add_im | [] | [
113,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.prod_comp | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.sum | [
{
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1800,
31
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1797,
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src/lean/Init/Data/Option/Instances.lean | Option.eq_none_of_isNone | [] | [
18,
19
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Mathlib/Algebra/CovariantAndContravariant.lean | covariant_lt_iff_contravariant_le | [] | [
309,
61
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306,
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Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_blockDiag | [] | [
410,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
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Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.comp_lift | [
{
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"tactic": "simp"
}
] | [
274,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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Mathlib/Combinatorics/Hall/Finite.lean | HallMarriageTheorem.hall_cond_of_erase | [
{
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73,
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53,
1
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_top | [] | [
271,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Std/Logic.lean | and_not_self | [] | [
235,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
235,
9
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurable.measurable_of_complete | [] | [
476,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Deprecated/Subgroup.lean | IsGroupHom.inv_ker_one | [
{
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366,
43
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363,
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Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.restrictNonposSeq_measurableSet | [
{
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208,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_div_pos_iff | [
{
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1996,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1994,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_eq_zero | [
{
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1677,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1676,
1
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Mathlib/Data/Set/Basic.lean | Set.ite_inter | [
{
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"tactic": "rw [ite_inter_inter, ite_same]"
}
] | [
2315,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2314,
1
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Mathlib/Data/Finset/Basic.lean | Finset.range_filter_eq | [
{
"state_after": "case h.e'_2.h.e'_2\nα : Type ?u.433649\nβ : Type ?u.433652\nγ : Type ?u.433655\nn✝ m✝ l n m : ℕ\n⊢ (fun x => x = m) = Eq m\n\ncase h.e'_3.h₁.a\nα : Type ?u.433649\nβ : Type ?u.433652\nγ : Type ?u.433655\nn✝ m✝ l n m : ℕ\n⊢ m < n ↔ m ∈ range n",
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3061,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3057,
1
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Mathlib/Topology/Algebra/UniformGroup.lean | UniformGroup.toUniformSpace_eq | [
{
"state_after": "case a\nG✝ : Type ?u.426706\ninst✝⁴ : CommGroup G✝\ninst✝³ : TopologicalSpace G✝\ninst✝² : TopologicalGroup G✝\nG : Type u_1\nu : UniformSpace G\ninst✝¹ : Group G\ninst✝ : UniformGroup G\n⊢ 𝓤 G = 𝓤 G",
"state_before": "G✝ : Type ?u.426706\ninst✝⁴ : CommGroup G✝\ninst✝³ : TopologicalSpace... | [
736,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
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Mathlib/Data/Finset/Basic.lean | Finset.empty_ssubset | [] | [
653,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.mapFun.nat_cast | [
{
"state_after": "no goals",
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"tact... | [
138,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/BoundedOrder.lean | isBot_bot | [] | [
270,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv_symm_addEquiv | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.one_lt_card | [
{
"state_after": "α : Type u_1\nβ : Type ?u.55273\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ ¬1 < card s ↔ ¬∃ a, a ∈ s ∧ ∃ b, b ∈ s ∧ a ≠ b",
"state_before": "α : Type u_1\nβ : Type ?u.55273\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ 1 < card s ↔ ∃ a, a ∈ s ∧ ∃ b, b ∈ s ∧ a ≠ b",
"tactic": "rw [← not_iff_not]"
},... | [
562,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
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Mathlib/Data/List/Chain.lean | List.Chain'.init | [] | [
327,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.id_c_app | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nX : PresheafedSpace C\nU : (Opens ↑↑X)ᵒᵖ\n⊢ (𝟙 X.presheaf).app U = 𝟙 (X.presheaf.obj U)",
"state_before": "C : Type u_1\ninst✝ : Category C\nX : PresheafedSpace C\nU : (Opens ↑↑X)ᵒᵖ\n⊢ (𝟙 X).c.app U = X.presheaf.map (𝟙 U)",
"tactic": "rw [id_c, map... | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.range_smul_pow_stabilizes | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsArtinian R M\nr : R\nn m : ℕ\nh : n ≤ m\nx : M\nx✝ : x ∈ (fun n => LinearMap.range (r ^ n • LinearMap.id)) m\ny : M\nhy : r ^ m • y = x\n⊢ r ^ n • r ^ (m - n) • y = x",
"state_before": ... | [
291,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Int/Basic.lean | Int.pred_neg_pred | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ pred (-pred a) = -a",
"tactic": "rw [neg_pred, pred_succ]"
}
] | [
168,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_disjoint_append_left_right | [] | [
1399,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1398,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.nil_eval | [
{
"state_after": "no goals",
"state_before": "v : List ℕ\n⊢ eval nil v = pure []",
"tactic": "simp [nil]"
}
] | [
177,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_Ici_subset | [] | [
642,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Algebra/Order/Monoid/Units.lean | Units.max_val | [] | [
58,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_zero_iff' | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\n⊢ orderOf x = 0 ↔ ∀ (n : ℕ), 0 < n → x ^ n ≠ 1",
"tactic": "simp_rw [orderOf_eq_zero_iff, isOfFinOrder_iff_pow_eq_one, not_exists, not_and]"
}
] | [
179,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | lt_div_iff_of_neg' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.148442\nα : Type u_1\nβ : Type ?u.148448\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhc : c < 0\n⊢ a < b / c ↔ b < c * a",
"tactic": "rw [mul_comm, lt_div_iff_of_neg hc]"
}
] | [
749,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_preimage | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.58114\ninst✝ : MeasurableSpace α\nf : α →ₛ β\ng : β → γ\ns : Set γ\n⊢ g ∘ ↑f ⁻¹' s = ↑f ⁻¹' (g ⁻¹' s)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.58114\ninst✝ : MeasurableSpace α\nf : α →ₛ β\ng : β → γ\ns : ... | [
335,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.ae_map_le | [] | [
2492,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2491,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_inj | [] | [
103,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/LinearAlgebra/Matrix/MvPolynomial.lean | Matrix.mvPolynomialX_mapMatrix_aeval | [] | [
72,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_Ioc | [] | [
108,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | subset_tangentCone_prod_right | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\n𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.50038\ninst✝¹ : NormedAddCommGroup G\ninst✝ ... | [
185,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_iff_le_two_or_omega_opow_opow | [
{
"state_after": "case refine'_1\no : Ordinal\nho : Principal (fun x x_1 => x * x_1) o\n⊢ o ≤ 2 ∨ ∃ a, o = ω ^ ω ^ a\n\ncase refine'_2\no : Ordinal\n⊢ (o ≤ 2 ∨ ∃ a, o = ω ^ ω ^ a) → Principal (fun x x_1 => x * x_1) o",
"state_before": "o : Ordinal\n⊢ Principal (fun x x_1 => x * x_1) o ↔ o ≤ 2 ∨ ∃ a, o = ω ^... | [
406,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.coe_prod | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
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