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/Data/Nat/Factors.lean | Nat.le_of_mem_factors | [
{
"state_after": "case inl\np : ℕ\nh : p ∈ factors 0\n⊢ p ≤ 0\n\ncase inr\nn p : ℕ\nh : p ∈ factors n\nhn : n > 0\n⊢ p ≤ n",
"state_before": "n p : ℕ\nh : p ∈ factors n\n⊢ p ≤ n",
"tactic": "rcases n.eq_zero_or_pos with (rfl | hn)"
},
{
"state_after": "case inl\np : ℕ\nh : p ∈ []\n⊢ p ≤ 0",
... | [
166,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.comap_top | [] | [
1034,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | derivWithin_arctan | [] | [
151,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.bddAbove_iff | [
{
"state_after": "R : Type ?u.762821\nR' : Type ?u.762824\n𝕜 : Type u_2\n𝕜₂ : Type ?u.762830\n𝕜₃ : Type ?u.762833\n𝕝 : Type ?u.762836\nE : Type u_1\nE₂ : Type ?u.762842\nE₃ : Type ?u.762845\nF : Type ?u.762848\nG : Type ?u.762851\nι : Type ?u.762854\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ :... | [
580,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
11
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearMap.finrank_range_add_finrank_ker | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\nf : V →ₗ[K] V₂\n⊢ finrank K (V ⧸ ker f) + finrank K { x // x ∈ ker f } = finrank K V",
"state_before":... | [
958,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.centralizer_eq_top_iff_subset | [] | [
879,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.IsVonNBounded.subset | [] | [
93,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_id | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nS R✝ : Sieve X\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nR : Sieve X\nY✝ : C\nf✝ : Y✝ ⟶ X\n⊢ (functorPullback (𝟭 C) R).arrows f✝ ↔ R.arrows f✝",
"state_before": "C : Type u₁\nin... | [
606,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongEpi.of_arrow_iso | [
{
"state_after": "C : Type u\ninst✝ : Category C\nP Q R : C\nf✝ : P ⟶ Q\ng✝ : Q ⟶ R\nA B A' B' : C\nf : A ⟶ B\ng : A' ⟶ B'\ne : Arrow.mk f ≅ Arrow.mk g\nh : StrongEpi f\n⊢ Epi (e.inv.left ≫ f ≫ e.hom.right)",
"state_before": "C : Type u\ninst✝ : Category C\nP Q R : C\nf✝ : P ⟶ Q\ng✝ : Q ⟶ R\nA B A' B' : C\n... | [
162,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.map | [] | [
378,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal | [
{
"state_after": "case inl\nx : ℝ\nh : 0 ≤ x\n⊢ ↑x = ↑↑(Real.toNNReal x) - ↑↑(Real.toNNReal (-x))\n\ncase inr\nx : ℝ\nh : x ≤ 0\n⊢ ↑x = ↑↑(Real.toNNReal x) - ↑↑(Real.toNNReal (-x))",
"state_before": "x : ℝ\n⊢ ↑x = ↑↑(Real.toNNReal x) - ↑↑(Real.toNNReal (-x))",
"tactic": "rcases le_total 0 x with (h | h)... | [
882,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.comp_X_sub_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nhp : Monic p\nr : R\n⊢ Monic (Polynomial.comp p (X - ↑C r))",
"tactic": "simpa using hp.comp_X_add_C (-r)"
}
] | [
840,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimitRecOn_limit | [] | [
380,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_iInter | [] | [
295,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.attach_affineCombination_coe | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type ?u.279611\ns✝ : Finset ι\nι₂ : Type ?u.279617\ns₂ : Finset ι₂\ns : Finset P\nw : P → k\n⊢ ↑(affineCombination k (attach s) Subty... | [
460,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.mem_map_of_mem | [] | [
244,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | constantCoeff_wittStructureInt_zero | [
{
"state_after": "p : ℕ\nR : Type ?u.1978909\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℤ\ninj : Function.Injective ↑(Int.castRingHom ℚ)\n⊢ ↑constantCoeff (wittStructureInt p Φ 0) = ↑constantCoeff Φ",
"state_before": "p : ℕ\nR : Type ?u.1978909\nidx : Type u_1\ninst✝ ... | [
379,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_mul_eq_sum_mul_comp_perm_iff | [] | [
511,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_mul | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.449883\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q a b : MvPolynomial σ R\nn : σ →₀ ℕ\nhn : n ∈ support (a * b)\nthis : n ∈ Finset.biUnion a.support fun a₁ => Finset.biUnion b.support fun a₂ => {a₁ + a₂}\n⊢ (sum n fun x e =... | [
696,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootSet_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\np q : R[X]\ninst✝³ : CommRing T\nS : Type u_1\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra T S\n⊢ rootSet 0 S = ∅",
"tactic": "rw [← C_0, rootSet_C]"... | [
905,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | sq_dvd_add_pow_sub_sub | [
{
"state_after": "case zero\nR : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x✝ y p x : R\n⊢ p ^ 2 ∣ (x + p) ^ Nat.zero - x ^ (Nat.zero - 1) * p * ↑Nat.zero - x ^ Nat.zero\n\ncase succ\nR : Type u_1\nn✝ : ℕ\ninst✝ : CommRing R\na b x✝ y p x : R\nn : ℕ\n⊢ p ^ 2 ∣ (x + p) ^ Nat.succ n - x ^ (Nat.succ n - 1) * p * ↑(... | [
77,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.IsTerminal.subsingleton_to | [] | [
202,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.hom_ext | [
{
"state_after": "case h\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X ⟶ Y\nh : ∀ (n : ℕ), φ s f n = φ s g n\nΔ : SimplexCategoryᵒᵖ\n⊢ f.app Δ = g.app Δ",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C... | [
316,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_div | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.mapsTo_sin_Ioo | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : x ∈ Ioo (-(π / 2)) (π / 2)\n⊢ sin x ∈ Ioo (-1) 1",
"tactic": "rwa [mem_Ioo, ← arcsin_lt_pi_div_two, ← neg_pi_div_two_lt_arcsin, arcsin_sin h.1.le h.2.le]"
}
] | [
281,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.tendsto_nhds_infty | [
{
"state_after": "no goals",
"state_before": "X : Type u_2\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nα : Type u_1\nf : OnePoint X → α\nl : Filter α\n⊢ Tendsto f (pure ∞) l ∧ Tendsto (f ∘ some) (coclosedCompact X) l ↔\n ∀ (s : Set α), s ∈ l → f ∞ ∈ s ∧ ∃ t, IsClosed t ∧ IsCompact t ∧ M... | [
370,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_simple_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\n⊢ F⟮α⟯ = ⊥ ↔ α ∈ ⊥",
"tactic": "simp"
}
] | [
682,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.sub_mem | [] | [
195,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
11
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.liftAux_comp_inrHom | [] | [
827,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinearMapRight'_mul | [] | [
152,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_eq_lsub | [] | [
1794,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1792,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Associates.prod_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33213\nγ : Type ?u.33216\nδ : Type ?u.33219\ninst✝ : CommMonoid α\np : Multiset α\n⊢ Multiset.prod (Multiset.map Associates.mk 0) = Associates.mk (Multiset.prod 0)",
"tactic": "simp"
},
{
"state_after": "no goals",
"stat... | [
113,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/NormedSpace/Extend.lean | ContinuousLinearMap.norm_extendTo𝕜'_bound | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nF : Type u_1\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : IsScalarTower ℝ 𝕜 F\nfr : F →L[ℝ] ℝ\nx : F\nlm : F →ₗ[𝕜] 𝕜 := LinearMap.extendTo𝕜' ↑fr\n⊢ ‖↑lm x‖ ≤ ‖fr‖ * ‖x‖",
"state_before": "𝕜 : Type u... | [
123,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coeSubtype | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.think_congr | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns t : WSeq α\nh : s ~ʷ t\n⊢ LiftRel (fun x x_1 => x = x_1) (think s) (think t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns t : WSeq α\nh : s ~ʷ t\n⊢ think s ~ʷ think t",
"tactic": "unfold Equiv"
},
{
"state_after": "α : Type u\nβ... | [
1124,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.finsuppTotal_apply | [
{
"state_after": "ι : Type u_1\nM : Type u_3\ninst✝² : AddCommGroup M\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Module R M\nI : Ideal R\nv : ι → M\nhv : Submodule.span R (Set.range v) = ⊤\nf : ι →₀ { x // x ∈ I }\n⊢ ↑(Finsupp.total ι M R v) (Finsupp.mapRange Subtype.val (_ : ↑(Submodule.subtype I) 0 = 0) f) =... | [
1903,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1899,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_inf_neg_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na : α\n⊢ a⁺ ⊓ a⁻ = 1",
"tactic": "rw [← mul_right_inj (a⁻)⁻¹, mul_inf, mul_one, mul_left_inv, mul_comm, ← div_eq_mul_inv,\n pos_div... | [
300,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.aleph0_le_cof | [
{
"state_after": "case inl\nα : Type ?u.100268\nr : α → α → Prop\n⊢ ℵ₀ ≤ cof 0 ↔ IsLimit 0\n\ncase inr.inl.intro\nα : Type ?u.100268\nr : α → α → Prop\no : Ordinal\n⊢ ℵ₀ ≤ cof (succ o) ↔ IsLimit (succ o)\n\ncase inr.inr\nα : Type ?u.100268\nr : α → α → Prop\no : Ordinal\nl : IsLimit o\n⊢ ℵ₀ ≤ cof o ↔ IsLimit o"... | [
721,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.meas_snormEssSup_lt | [] | [
895,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_zero | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ ‖0‖ = 0\n\ncase inr.inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ ‖0‖ = 0\n\ncase inr.inr\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α... | [
453,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_three_mul | [
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ cos (3 * x) = 4 * cos x ^ 3 - 3 * cos x",
"state_before": "x y : ℂ\n⊢ cos (3 * x) = 4 * cos x ^ 3 - 3 * cos x",
"tactic": "have h1 : x + 2 * x = 3 * x := by ring"
},
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ cos x * cos (2 * x) - si... | [
1068,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/Data/Prod/TProd.lean | List.TProd.elim_of_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nα : ι → Type v\ni j : ι\nl : List ι\nf : (i : ι) → α i\ninst✝ : DecidableEq ι\nhj : j ∈ i :: l\nhji : j ≠ i\nv : TProd α (i :: l)\n⊢ TProd.elim v hj = TProd.elim v.snd (_ : j ∈ l)",
"tactic": "simp [TProd.elim, hji]"
}
] | [
98,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_inter_distrib | [] | [
536,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.coe_toPNat' | [] | [
173,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | nndist_smul_le | [] | [
46,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.coe_algebraMap | [] | [
825,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero | [
{
"state_after": "case refine'_1\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁶ : Fintype ι\ninst✝¹⁵ : Fintype ι'\ninst✝¹⁴ : NontriviallyNormedField 𝕜\ninst✝¹³ : (i : ι) → NormedAddComm... | [
865,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | pow_dvd_pow_of_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommMonoid α\na✝ b✝ a b : α\nh : a ∣ b\n⊢ a ^ 0 ∣ b ^ 0",
"tactic": "rw [pow_zero, pow_zero]"
},
{
"state_after": "α : Type u_1\ninst✝ : CommMonoid α\na✝ b✝ a b : α\nh : a ∣ b\nn : ℕ\n⊢ a * a ^ n ∣ b * b ^ n",
"state_before"... | [
205,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_lift_le_max | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : IsDomain A\ninst✝¹ : Algebra R A\ninst✝ : NoZeroSMulDivisors R A\n⊢ lift (max (#R) ℵ₀) * ℵ₀ ≤ max (lift (#R)) ℵ₀",
"tactic": "simp"
}
] | [
63,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.limit_ext | [
{
"state_after": "case a\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nx y : limit F\nw : ∀ (j : J), limit.π F j x = limit.π F j y\n⊢ ↑(limitEquivSections F) x = ↑(limitEquivSections F) y",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nx y : limit F\nw : ∀ (j : J), limit.π ... | [
165,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Any_def | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\nt : RBNode α\n⊢ Any p t ↔ ∃ x, x ∈ t ∧ p x",
"tactic": "induction t <;> simp [or_and_right, exists_or, *]"
}
] | [
104,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
103,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_eq_of_dvd_sub_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CommRing α\ninst✝¹ : IsDomain α\ninst✝ : NormalizedGCDMonoid α\na b c : α\nh : a ∣ b - c\n⊢ gcd b a = gcd c a",
"tactic": "rw [gcd_comm _ a, gcd_comm _ a, gcd_eq_of_dvd_sub_right h]"
}
] | [
998,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiff.rpow_const_of_ne | [] | [
536,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumCompl_symm_apply_of_mem | [
{
"state_after": "α✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\nx : α\nhx : x ∈ s\nthis : ↑{ val := x, property := (_ : x ∈ s ∨ x ∈ sᶜ) } ∈ s\n⊢ ↑(Set.sumCompl s).symm x = Sum.inl { val := x, property := hx }",
"state_before": "α✝ : Sort u\nβ : Sort v\nγ :... | [
335,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_sq | [
{
"state_after": "x y : ℂ\n⊢ sinh x ^ 2 = cosh x ^ 2 - (cosh x ^ 2 - sinh x ^ 2)",
"state_before": "x y : ℂ\n⊢ sinh x ^ 2 = cosh x ^ 2 - 1",
"tactic": "rw [← cosh_sq_sub_sinh_sq x]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sinh x ^ 2 = cosh x ^ 2 - (cosh x ^ 2 - sinh x ^ 2... | [
766,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_sum_type | [] | [
297,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_spec | [
{
"state_after": "F : Type ?u.131282\nα : Type u_1\nβ : Type ?u.131288\n𝕜 : Type ?u.131291\nE : Type ?u.131294\ninst✝³ : DecidableEq α\ninst✝² : Monoid α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid β\ns t : Finset α\n⊢ MulSalemSpencer ∅",
"state_before": "F : Type ?u.131282\nα : Type u_1\nβ : Type ?u.131288\n�... | [
346,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Std/Classes/Order.lean | Std.TransCmp.gt_asymm | [] | [
62,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
61,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_id' | [] | [
1862,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1861,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_top | [] | [
584,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.sin | [] | [
1044,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.zero_im | [] | [
182,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
9
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.const | [] | [
99,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/Grade.lean | IsMin.grade | [] | [
133,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_neg | [
{
"state_after": "x✝ y✝ z x : ℝ\nhx : 0 ≤ x\ny : ℝ\n⊢ (if x = 0 then if -y = 0 then 1 else 0 else exp (log x * -y)) =\n (if x = 0 then if y = 0 then 1 else 0 else exp (log x * y))⁻¹",
"state_before": "x✝ y✝ z x : ℝ\nhx : 0 ≤ x\ny : ℝ\n⊢ x ^ (-y) = (x ^ y)⁻¹",
"tactic": "simp only [rpow_def_of_nonneg ... | [
225,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | Int.two_pow_sub_pow | [
{
"state_after": "R : Type ?u.865616\nn✝ : ℕ\nx y : ℤ\nn : ℕ\nhxy : 2 ∣ x - y\nhx : ¬2 ∣ x\nhn : Even n\nhy : Odd y\n⊢ multiplicity 2 (x ^ n - y ^ n) + 1 = multiplicity 2 (x + y) + multiplicity 2 (x - y) + multiplicity 2 ↑n",
"state_before": "R : Type ?u.865616\nn✝ : ℕ\nx y : ℤ\nn : ℕ\nhxy : 2 ∣ x - y\nhx :... | [
360,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Set.IsPwo.submonoid_closure | [
{
"state_after": "α : Type u_1\nG : Type ?u.364481\nM : Type ?u.364484\nR : Type ?u.364487\nA : Type ?u.364490\ninst✝² : Monoid M\ninst✝¹ : AddMonoid A\ninst✝ : OrderedCancelCommMonoid α\ns : Set α\nhpos : ∀ (x : α), x ∈ s → 1 ≤ x\nh : IsPwo s\n⊢ IsPwo (List.prod '' {l | ∀ (x : α), x ∈ l → x ∈ s})",
"state_... | [
708,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_zero | [] | [
2897,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2897,
9
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_subset | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.43836\nι : Type ?u.43839\ninst✝ : PseudoMetricSpace α\nx y z✝ : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nh : dist x y ≤ ε₂ - ε₁\nz : α\nzx : z ∈ ball x ε₁\n⊢ z ∈ ball y (ε₁ + (ε₂ - ε₁))",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.43836\nι : Type ?u.43839\... | [
662,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_eq_zero | [
{
"state_after": "α : Type ?u.9836\nι : Type u_1\nβ : ι → Type u_2\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.9868\ninst✝ : (i : ι) → DecidableEq (γ i)\nx y : (i : ι) → β i\nH : x = y\n⊢ hammingDist y y = 0",
"state_before": "α : Type ?u.9836\nι : Type u_1\nβ : ι → Type u_2\n... | [
105,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | one_add_mul_self_le_rpow_one_add | [
{
"state_after": "case inl\ns : ℝ\nhs : -1 ≤ s\nhp : 1 ≤ 1\n⊢ 1 + 1 * s ≤ (1 + s) ^ 1\n\ncase inr\ns : ℝ\nhs : -1 ≤ s\np : ℝ\nhp✝ : 1 ≤ p\nhp : 1 < p\n⊢ 1 + p * s ≤ (1 + s) ^ p",
"state_before": "s : ℝ\nhs : -1 ≤ s\np : ℝ\nhp : 1 ≤ p\n⊢ 1 + p * s ≤ (1 + s) ^ p",
"tactic": "rcases eq_or_lt_of_le hp with ... | [
231,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_pos_of_lt | [] | [
357,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_inter_nonempty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.52785\nι : Sort ?u.52788\nι' : Sort ?u.52791\nf✝ : α → β\ns✝ t✝ : Set α\nf : α → β\ns : Set α\nt : Set β\n⊢ Set.Nonempty (f '' s ∩ t) ↔ Set.Nonempty (s ∩ f ⁻¹' t)",
"tactic": "rw [← image_inter_preimage, nonempty_image... | [
522,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Set/MulAntidiagonal.lean | Set.swap_mem_mulAntidiagonal_aux | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommSemigroup α\ns t : Set α\na : α\nx : α × α\n⊢ x.snd ∈ s ∧ x.fst ∈ t ∧ x.snd * x.fst = a ↔ x ∈ mulAntidiagonal t s a",
"tactic": "simp [mul_comm, and_left_comm]"
}
] | [
66,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | IsHilbertSum.mk | [
{
"state_after": "ι : Type u_4\n𝕜 : Type u_2\ninst✝⁵ : IsROrC 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type u_1\ninst✝² : (i : ι) → NormedAddCommGroup (G i)\ninst✝¹ : (i : ι) → InnerProductSpace 𝕜 (G i)\nV : (i : ι) → G i →ₗᵢ[𝕜] E\nF : ... | [
313,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.measurableSet_bliminf | [
{
"state_after": "α : Type u_1\nβ : Type ?u.910929\nγ : Type ?u.910932\nδ : Type ?u.910935\nδ' : Type ?u.910938\nι : Sort uι\ns✝ t u : Set α\ninst✝ : MeasurableSpace α\ns : ℕ → Set α\np : ℕ → Prop\nh : ∀ (n : ℕ), p n → MeasurableSet (s n)\n⊢ MeasurableSet (⋃ (i : ℕ), ⋂ (j : ℕ) (_ : p j ∧ i ≤ j), s j)",
"sta... | [
1901,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1898,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.image_Ioi | [] | [
86,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_top | [] | [
262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Icc_mem_nhds' | [] | [
1481,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nhp0 : p ≠ 0\n⊢ ↑(↑Multiset.card\n (if h : p = 0 then ∅\n else\n Classical.choose (_ : ∃ s, ↑(↑Multiset.card s) ≤ degree p ∧ ∀ (a : R), count a s = rootMultiplicity a ... | [
541,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_dirac' | [] | [
3022,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3020,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_ofNat_zero | [] | [
39,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
39,
15
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.exp_log_of_neg | [
{
"state_after": "x y : ℝ\nhx : x < 0\n⊢ abs x = -x",
"state_before": "x y : ℝ\nhx : x < 0\n⊢ exp (log x) = -x",
"tactic": "rw [exp_log_eq_abs (ne_of_lt hx)]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : x < 0\n⊢ abs x = -x",
"tactic": "exact abs_of_neg hx"
}
] | [
69,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherian_of_linearEquiv | [] | [
136,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/Calculus/Series.lean | contDiff_tsum | [
{
"state_after": "α : Type u_4\nβ : Type ?u.121726\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nf' : α → E → E →L[𝕜] F\nv : ℕ... | [
252,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | isExtreme_biInter | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF✝ : Type ?u.3511\nι : Type ?u.3514\nπ : ι → Type ?u.3519\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\nA B C : Set E\nx : E\nF : Set (Set E)\nhF : Set.Nonempty F\nhA : ∀ (B : Set E), B ∈ F → IsExtreme 𝕜 A B\nthis : Nonempty ↑F\n⊢ IsEx... | [
125,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactConvNhd_filter_isBasis | [
{
"state_after": "case mk.mk.intro.intro\nα : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nK₁ : Set α\nV₁ : Set (β × β)\nK₂ : Set α\nV₂ : Set (β × β)\nhK₁ : IsCompact (K₁, V₁).fst\nhV₁ : (K₁, V₁).snd ∈ 𝓤 β\nhK₂ : IsCompact (K₂, V₂).fst\nhV₂... | [
150,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Set/Sups.lean | Set.iUnion_image_inf_right | [] | [
338,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.append | [] | [
298,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
src/lean/Init/SimpLemmas.lean | not_false_eq_true | [] | [
100,
75
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
100,
9
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.neg_left | [] | [
104,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.of_mul | [
{
"state_after": "R : Type u_1\nS : Type ?u.5473\nM : Type u_2\na b : R\ns : S\ninst✝⁵ : SMul R M\ninst✝⁴ : SMul R S\ninst✝³ : SMul S M\ninst✝² : IsScalarTower R S M\ninst✝¹ : Mul R\ninst✝ : IsScalarTower R R M\nab : IsSMulRegular M (a • b)\n⊢ IsSMulRegular M b",
"state_before": "R : Type u_1\nS : Type ?u.5... | [
108,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.eq_of_associated_of_nonneg | [] | [
133,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.of_vector_cons | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.13471\nn n' m : ℕ\ns : Sym α n\na✝ b a : α\nval✝ : List α\nproperty✝ : List.length val✝ = n\n⊢ ofVector (a ::ᵥ { val := val✝, property := property✝ }) = a ::ₛ ofVector { val := val✝, property := property✝ }",
"state_before": "α : Type u_1\nβ : Type ?u.134... | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | Part.ωSup_eq_some | [] | [
337,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_smul | [] | [
812,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.segment_subset | [] | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.leadingCoeff_prod | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : ι → R[X]\nt : Multiset R[X]\n⊢ leadingCoeff (∏ i in s, f i) = ∏ i in s, leadingCoeff (f i)",
"tactic": "simpa using leadingCoeff_multiset_prod (s.1.map f)"
}
] | [
365,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.mem_univ | [] | [
265,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.not_mem_commonNeighbors_right | [] | [
1029,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.