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/Order/Hom/CompleteLattice.lean | sInfHom.dual_comp | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
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Mathlib/GroupTheory/Submonoid/Operations.lean | OneMemClass.coe_eq_one | [] | [
530,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
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Mathlib/Order/Lattice.lean | SemilatticeSup.dual_dual | [] | [
378,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_injective | [] | [
113,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Algebra/Order/WithZero.lean | inv_lt_inv₀ | [] | [
212,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/Algebra/Module/Torsion.lean | Submodule.supIndep_torsionBy | [
{
"state_after": "case h.e'_6.h\nR : Type u_3\nM : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ns : Set R\na : R\nι : Type u_1\np : ι → Ideal R\nS : Finset ι\nhp : Set.Pairwise ↑S fun i j => p i ⊔ p j = ⊤\nq : ι → R\nhq : Set.Pairwise (↑S) (IsCoprime on q)\ninst✝ : Decidable... | [
465,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.IsNClique.not_cliqueFree | [] | [
167,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.range | [
{
"state_after": "case intro.intro\nα : Type u_2\nβ : Type ?u.36838\nγ : Type ?u.36841\nι : Type u_1\nι' : Type ?u.36847\nr p q : α → α → Prop\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\ns t : Set ι\nf g✝ : ι → α\ng : ↑s → ι\nhg : ∀ (i : ↑s), f (g i) ≤ f ↑i\nht : PairwiseDisjoint s f\nx y : ↑s\nhxy : g x ≠ g ... | [
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87
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.congr_arg | [] | [
588,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_two_right | [
{
"state_after": "case zero\n\n⊢ choose zero 2 = zero * (zero - 1) / 2\n\ncase succ\nn : ℕ\nih : choose n 2 = n * (n - 1) / 2\n⊢ choose (succ n) 2 = succ n * (succ n - 1) / 2",
"state_before": "n : ℕ\n⊢ choose n 2 = n * (n - 1) / 2",
"tactic": "induction' n with n ih"
},
{
"state_after": "case s... | [
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20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Disjoint.lean | eq_top_of_bot_isCompl | [] | [
634,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
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Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullbackIsoProdSubtype_inv_fst_apply | [] | [
110,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_pow | [] | [
1279,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
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Mathlib/Topology/Order/Basic.lean | frontier_Iio' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na✝ b : α\ns : Set α\na : α\nha : Set.Nonempty (Iio a)\n⊢ frontier (Iio a) = {a}",
"tactic": "simp [frontier, closure_... | [
2355,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.sup_apply | [] | [
315,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
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Mathlib/Topology/LocalExtr.lean | IsLocalExtr.on | [] | [
102,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.inclusion_inclusion | [
{
"state_after": "case mk\nG : Type u_2\nG' : Type ?u.63896\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.63905\ninst✝⁴ : AddGroup A\nM : Type ?u.63911\nS : Type u_1\ninst✝³ : DivInvMonoid M\ninst✝² : SetLike S M\nhSM : SubgroupClass S M\nH K : S\ninst✝¹ : SetLike S G\ninst✝ : SubgroupClass S G\nL : S\nhHK ... | [
341,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
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Mathlib/Analysis/Calculus/MeanValue.lean | norm_image_sub_le_of_norm_deriv_right_le_segment | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.31247\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → E\na b : ℝ\nf' : ℝ → E\nC : ℝ\nhf : ContinuousOn f (Icc a b)\nhf' : ∀ (x : ℝ), x ∈ Ico a b → HasDerivWithinAt f (f' x) (Ici x) x\nbound : ∀ ... | [
353,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.105796\nR : Type ?u.105799\nR' : Type ?u.105802\nms : Set (OuterMeasure α)\nm✝ : OuterMeasure α\nι : Sort u_1\ns : Set α\nm : ι → OuterMeasure α\n⊢ ↑(restrict s) (⨆ (i : ι), m i) = ⨆ (i : ι), ↑(restrict s) (m i)",
"tactic": "simp [r... | [
590,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_le_comap | [] | [
683,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
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Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.shiftFunctor_map_apply | [] | [
156,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
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Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_vsub_center | [] | [
47,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_right_right_iff | [] | [
352,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | measurable_id | [] | [
546,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_eq_zero_of_le | [] | [
88,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.withBotCongr_trans | [] | [
1359,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1357,
1
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Mathlib/Order/Hom/Bounded.lean | BotHom.sup_apply | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.nondegenerate_of_anisotropic | [
{
"state_after": "S : Type ?u.480390\nR : Type u_1\nR₁ : Type ?u.480396\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : Invertible 2\nQ : QuadraticForm R M\nhB : Anisotropic Q\nx : M\nhx : ∀ (n : M), bilin (↑associated' Q) x n = 0\n⊢ ↑Q x = bilin (↑associated' Q) x x",
... | [
909,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_norm_iff | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2312369\nG : Type ?u.2312372\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → E\nhf : AEStronglyMeasurable f μ\nh : Memℒp (fun x => ‖f x‖) p\n... | [
692,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.30865\nP : Type ?u.30868\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS✝ : Substructure L M\ns : Set M\nS : Substructure L M :=\n { carrier := range (Term.realize Subtype.val),\n fun_mem :=\n (_ :\n ∀ {n : ℕ} (f :... | [
310,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_zero | [] | [
570,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
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] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.nullHomotopicMap'_comp | [
{
"state_after": "case h\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g✝ : C ⟶ D\nh k : D ⟶ E\ni : ι\nhom : (i j : ι) → ComplexShape.Rel c j i → (X C i ⟶ X D j)\ng : D ⟶ E\nn : ι\n⊢ Hom.f (nullHomotopicMap' hom ≫ g) n = Hom.f (nullH... | [
288,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid A\ninst✝¹ : Mul A\ninst✝ : SMulWithZero R A\na₁ a₂ : A\n⊢ a₁ * a₂ = 0 • a₂ + 0 • a₁ + a₁ * a₂",
"tactic": "simp only [zero_smul, zero_add]"
}
] | [
412,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
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Mathlib/Algebra/Group/Prod.lean | Prod.fst_one | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.ascFactorial_eq_div | [
{
"state_after": "n k : ℕ\n⊢ n ! * ascFactorial n k = n ! * ((n + k)! / n !)",
"state_before": "n k : ℕ\n⊢ ascFactorial n k = (n + k)! / n !",
"tactic": "apply mul_left_cancel₀ n.factorial_ne_zero"
},
{
"state_after": "n k : ℕ\n⊢ (n + k)! = n ! * ((n + k)! / n !)",
"state_before": "n k : ℕ\n... | [
274,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
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] |
Mathlib/Data/List/MinMax.lean | List.maximum_concat | [
{
"state_after": "α : Type u_1\nβ : Type ?u.92933\ninst✝ : LinearOrder α\nl✝ : List α\na✝ m a : α\nl : List α\n⊢ Option.rec (some a) (fun val => if val < a then some a else some val) (argmax (fun a => a) l) =\n max (argmax (fun a => a) l) ↑a",
"state_before": "α : Type u_1\nβ : Type ?u.92933\ninst✝ : Lin... | [
351,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
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] |
Std/Data/Nat/Lemmas.lean | Nat.add_lt_add_iff_lt_left | [] | [
81,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
80,
11
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.id | [] | [
330,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
11
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.image.mk | [] | [
1240,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.bicomp_mono | [] | [
298,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
8
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.coe_setPreimage | [] | [
924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.exists_seq_strictAnti_tendsto_of_not_mem | [] | [
2162,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2159,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.le_iff | [] | [
762,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.inv_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a : α\nha : 0 < a\n⊢ (Ioi a)⁻¹ = Ioo 0 a⁻¹",
"tactic": "rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]"
}
] | [
772,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
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Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.equiv | [
{
"state_after": "case intro.intro\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\ne : A ≃ₐ[R] B\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] A\nhf : Surjective ↑f ∧ Ideal.FG (RingHom.ker ↑f)\n⊢ FinitePresentation R B"... | [
100,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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] |
src/lean/Init/SimpLemmas.lean | implies_true | [] | [
98,
90
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
98,
9
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_col_mul_row | [
{
"state_after": "case h\nl : Type ?u.281699\nm : Type ?u.281702\nn : Type u_1\no : Type ?u.281708\nm' : o → Type ?u.281713\nn' : o → Type ?u.281718\nR : Type ?u.281721\nS : Type ?u.281724\nα : Type v\nβ : Type w\nγ : Type ?u.281731\ninst✝ : NonUnitalNonAssocSemiring α\na b : n → α\nx✝ : n\n⊢ diag (col a ⬝ row ... | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Cauchy.lean | Ultrafilter.cauchy_of_totallyBounded | [] | [
539,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
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] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasStrictDerivAt_iff_hasStrictFDerivAt | [] | [
214,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsRefl.neg | [] | [
870,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_ne_top | [] | [
321,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
9
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Mathlib/Data/PNat/Basic.lean | PNat.bit0_le_bit0 | [] | [
210,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_closedBall_mul_of_pos | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1987762\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
445,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeFun_mapEquiv | [] | [
823,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.mul_comp | [] | [
1523,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_subset_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.22547\nγ : Type ?u.22550\nι : Type ?u.22553\nM : Type u_2\nM' : Type ?u.22559\nN : Type ?u.22562\nP : Type ?u.22565\nG : Type ?u.22568\nH : Type ?u.22571\nR : Type ?u.22574\nS : Type ?u.22577\ninst✝ : Zero M\ns : Set α\nf : α →₀ M\n⊢ (∀ (x : α), ↑f x ≠ 0 → x ∈ s) ↔ ∀ ... | [
244,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns✝ s₁ s₂ : Finset β\nf : β → α\ninst✝ : DecidableEq β\ng : γ → β\ns : Finset γ\n⊢ lcm (image g s) f = lcm s (f ∘ g)",
"tactic": "classical inductio... | [
118,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/Order/BoundedOrder.lean | min_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.43317\nδ : Type ?u.43320\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\na b : α\n⊢ min a b = ⊥ ↔ a = ⊥ ∨ b = ⊥",
"tactic": "simp only [← inf_eq_min, ← le_bot_iff, inf_le_iff]"
}
] | [
868,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodUnique_symm_apply | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | IsLocalization.Away.AwayMap.lift_comp | [] | [
88,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RepresentationTheory/Maschke.lean | LinearMap.sumOfConjugatesEquivariant_apply | [] | [
116,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.monotone_zpow | [] | [
1931,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1930,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_real_iff_eq | [] | [
372,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/List/Basic.lean | List.length_eraseP_add_one | [
{
"state_after": "ι : Type ?u.424384\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ : List α\np : α → Bool\nl : List α\na : α\nal : a ∈ l\npa : p a = true\nw✝ : α\nl₁ l₂ : List α\nleft✝¹ : ∀ (b : α), b ∈ l₁ → ¬p b = true\nleft✝ : p w✝ = true\nh₁ : l = l₁ ++ w✝ :: l₂\nh₂ : eraseP p l = l₁ ++ l₂\n⊢ leng... | [
3696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3692,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.nndist_self_conj | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.129445\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz : ℂ\n⊢ nndist z (↑(starRingEnd ℂ) z) = 2 * ↑Real.nnabs z.im",
"tactic": "rw [nndist_comm, nndist_conj_self]"
}
] | [
143,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Topology/Partial.lean | ptendsto_nhds | [] | [
42,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_normalizer_eq | [
{
"state_after": "case hf\nG : Type u_1\nG' : Type ?u.626768\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.626777\ninst✝¹ : AddGroup A\nN✝ : Type ?u.626783\ninst✝ : Group N✝\nf : G →* N✝\nH N : Subgroup G\nh : normalizer H ≤ N\n⊢ Injective ↑(Subgroup.subtype N)\n\ncase h\nG : Type u_1\nG' : Type ?u.626768\n... | [
3232,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3228,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_of_mod_lt | [] | [
488,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
487,
1
] |
Std/Data/Option/Lemmas.lean | Option.to_list_none | [] | [
220,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
220,
9
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.const_mul | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type ?u.263867\n... | [
258,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator.coeFn_eq_comp | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/List/Sigma.lean | List.mem_dlookup_iff | [] | [
236,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.sum_pow_mul_eq_add_pow | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α✝\na✝ : α✝\nb✝ : β\nf g : α✝ → β\ninst✝¹ : CommSemiring β\nα : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\na b : R\ns : Finset α\n⊢ ∑ t in powerset s, a ^ card t * b ^ (card s - card t) = ∑ t in powerset s, (∏ a_1 in t, a) * ∏ a in s ... | [
211,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.atBot_mul_neg | [
{
"state_after": "𝕜 : Type u_1\nα : Type u_2\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x => (Neg.neg ∘ f) x * g x) l atBot\n⊢ Tendsto (fun x => f x... | [
106,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Std/Logic.lean | and_congr_right' | [] | [
169,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
169,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.Paths.lift_spec | [
{
"state_after": "case h_obj\nV : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category C\nφ : V ⥤q C\n⊢ ∀ (X : V), (of ⋙q (lift φ).toPrefunctor).obj X = φ.obj X\n\ncase h_map\nV : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category C\nφ : V ⥤q C\n⊢ ∀ (X Y : V) (f : X ⟶ Y),\n (of ⋙q (lift φ).toPr... | [
103,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/Algebra/Order/SMul.lean | smul_pos_iff_of_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.45479\n𝕜 : Type ?u.45482\nR : Type u_1\nM : Type u_2\nN : Type ?u.45491\ninst✝³ : OrderedSemiring R\ninst✝² : OrderedAddCommMonoid M\ninst✝¹ : SMulWithZero R M\ninst✝ : OrderedSMul R M\ns : Set M\na b : M\nc : R\nhc : 0 < c\n⊢ 0 < c • a ↔ c • 0 < c ... | [
131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_sInter | [] | [
94,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_attach_biUnion | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Semiring B\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ns✝ t : Set A\ninst✝ : DecidableEq A\nα : Type u_1\ns : Finset α\nf : { x // x ∈ s } → Finset A\n⊢ adjoin R ↑(Finset... | [
79,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.pow_apply_eq_of_apply_apply_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h✝ : Perm α\nx : α\nhffx : ↑f (↑f x) = x\nn : ℕ\nh : ↑(f ^ n) x = x\n⊢ ↑(f ^ (n + 1)) x = ↑f x",
"tactic": "rw [pow_succ, mul_apply, h]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h✝ : Perm α\nx : α\nhffx... | [
167,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.realSize_deleteMin | [
{
"state_after": "case cons.refl\nα : Type u_1\nle : α → α → Bool\nr : Nat\na : α\nc : HeapNode α\ns : Heap α\n⊢ realSize (cons r a c s) =\n realSize\n (merge le (HeapNode.toHeap (findMin le (cons r a c) s { before := id, val := a, node := c, next := s }).node)\n (FindMin.before (findMin le (... | [
246,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
236,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.eq_of_not_disjoint | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.10571\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na b : G\nh : ¬Disjoint (doset b ↑H ↑K) (doset a ↑H ↑K)\n⊢ doset a ↑H ↑K = doset b ↑H ↑K",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.10571\ninst✝ : Mul α\nJ : Subgro... | [
74,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_sub_pi | [] | [
326,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | constantCoeff_wittPolynomial | [
{
"state_after": "p : ℕ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : DecidableEq R\nS : Type ?u.75140\ninst✝ : CommRing S\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ (∑ x in range (n + 1), if single x (p ^ (n - x)) = 0 then ↑p ^ x else 0) = 0",
"state_before": "p : ℕ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : Deci... | [
138,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_of_norm_le_const_ae | [
{
"state_after": "ι : Type ?u.12289686\n𝕜 : Type ?u.12289689\nE : Type u_1\nF : Type ?u.12289695\nA : Type ?u.12289698\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na✝ b✝ : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\na b C : ℝ\nf : ℝ → E\nh : ∀ᵐ (x : ℝ), x ∈ Ι a b → ‖f x‖... | [
571,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_exponent_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.528018\nF : Type u_2\nG : Type ?u.528024\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\n⊢ snorm f ⊤ μ = snormEssSup f μ... | [
106,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Order/Partition/Equipartition.lean | Finpartition.IsEquipartition.card_part_le_average_add_one | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nhP : IsEquipartition P\nht : t ∈ P.parts\n⊢ Finset.card t ≤ (Finset.sum P.parts fun i => Finset.card i) / Finset.card P.parts + 1",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartitio... | [
65,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.baseSet_at | [] | [
707,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Order/BoundedOrder.lean | eq_bot_or_bot_lt | [] | [
390,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Order/Interval.lean | Interval.forall | [] | [
359,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Data/Set/Function.lean | Set.surjective_mapsTo_image_restrict | [] | [
538,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.countable_cover_nhds | [
{
"state_after": "case intro.intro\nα : Type u\nt : TopologicalSpace α\ninst✝ : SecondCountableTopology α\nf : α → Set α\nhf : ∀ (x : α), f x ∈ 𝓝 x\ns : Set α\nhsc : Set.Countable s\nhsU : (⋃ (i : α) (_ : i ∈ s), interior (f i)) = ⋃ (i : α), interior (f i)\n⊢ ∃ s, Set.Countable s ∧ (⋃ (x : α) (_ : x ∈ s), f x)... | [
751,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.lt_div_iff' | [] | [
845,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensor_right_iff | [
{
"state_after": "no goals",
"state_before": "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 X Y : C\nf g : X ⟶ Y\n⊢ f ⊗ 𝟙 (𝟙_ C) = g ⊗ 𝟙 (𝟙_ C) ↔ f = g",
"tactic": "simp"
}
] | [
274,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iSup_inf_of_antitone | [] | [
169,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_subset_iff | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ns : Set ι\nf : Π₀ (i : ι), β i\n⊢ (∀ (x : ι), ¬↑f x = 0 → x ∈ s) ↔ ∀ (i : ι), ¬i ∈ s → ↑f i = 0",
"state_before":... | [
1158,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_C_index | [] | [
975,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.injective_of_isPartialInv | [] | [
319,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sInf_apply | [] | [
1023,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Init/CcLemmas.lean | if_eq_of_eq | [] | [
96,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
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