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/Algebra/Order/Ring/Defs.lean | mul_nonneg_iff | [] | [
1063,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_mul_dvd_mul_gcd | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nk m n m' n' : α\nhm' : m' ∣ m\nhn' : n' ∣ n\nh : gcd k (m * n) = m' * n'\n⊢ gcd k (m * n) ∣ gcd k m * gcd k n",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : ... | [
561,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_succ | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\ni : Fin n\ny : α (succ i)\nz : α 0\n⊢ cons x p (succ i) = p i",
"tactic": "simp [cons]"
}
] | [
78,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_inter_of_monotone | [] | [
591,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.dvd_of_factorization_pos | [] | [
187,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.unpair₂ | [
{
"state_after": "n : ℕ\nf : Vector ℕ n → ℕ\nhf : Primrec' f\ns : Primrec' fun v => Nat.sqrt (f v)\n⊢ Primrec' fun v => (unpair (f v)).snd",
"state_before": "n : ℕ\nf : Vector ℕ n → ℕ\nhf : Primrec' f\n⊢ Primrec' fun v => (unpair (f v)).snd",
"tactic": "have s := sqrt.comp₁ _ hf"
},
{
"state_aft... | [
1521,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Continuous.bounded_above_of_compact_support | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1232898\n𝕜 : Type ?u.1232901\nα : Type u_1\nι : Type ?u.1232907\nκ : Type ?u.1232910\nE : Type u_2\nF : Type ?u.1232916\nG : Type ?u.1232919\ninst✝¹ : NormedAddGroup E\ninst✝ : TopologicalSpace α\nf : α → E\nhf : Continuous f\nh : HasCompactSupport... | [
2069,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2067,
1
] |
Mathlib/Data/Real/Basic.lean | Real.sSup_of_not_bddAbove | [] | [
817,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.eq_iff_div_mem | [
{
"state_after": "G : Type u\ninst✝¹ : Group G\nN✝ : Subgroup G\nnN✝ : Subgroup.Normal N✝\nH : Type v\ninst✝ : Group H\nN : Subgroup G\nnN : Subgroup.Normal N\nx y : G\n⊢ y⁻¹ * x ∈ N ↔ x / y ∈ N",
"state_before": "G : Type u\ninst✝¹ : Group G\nN✝ : Subgroup G\nnN✝ : Subgroup.Normal N✝\nH : Type v\ninst✝ : G... | [
139,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | Pairwise.aedisjoint | [] | [
74,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_neg_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ 2 • ↑(-π / 2) = ↑π",
"tactic": "rw [two_zsmul, ← two_nsmul, two_nsmul_neg_pi_div_two]"
}
] | [
157,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.add_def | [
{
"state_after": "a b : Rat\n⊢ Rat.add a b = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den)",
"state_before": "a b : Rat\n⊢ a + b = normalize (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den)",
"tactic": "show Rat.add .. = _"
},
{
"state_after": "a b : Rat\n⊢ (let g := Nat.gcd a.den... | [
181,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrOn.comp_antitone | [] | [
368,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.fun_prop_of_mem_aeSeqSet | [
{
"state_after": "ι : Sort u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.363672\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nf : ι → α → β\nμ : MeasureTheory.Measure α\np : α → (ι → β) → Prop\nhf : ∀ (i : ι), AEMeasurable (f i)\nx : α\nhx : x ∈ aeSeqSet hf p\nh_eq : (fun n => f n x) = fun n => aeSeq h... | [
89,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | neg_one_pow_eq_pow_mod_two | [
{
"state_after": "α : Type ?u.287126\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Ring R\nn : ℕ\n⊢ (-1) ^ (n % 2) * ((-1) ^ 2) ^ (n / 2) = (-1) ^ ((n % 2 + 2 * (n / 2)) % 2)",
"state_before": "α : Type ?u.287126\nM : Type u\nN : Type v\nG : Type ... | [
633,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyRel.symm_symm | [] | [
628,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.Monic.ne_zero_of_polynomial_ne | [] | [
871,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_eq_zero | [] | [
188,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/WithBot.lean | WithBot.map_toDual | [] | [
954,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | sum_add_tsum_compl | [] | [
917,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) ⁻¹' Ioc b c = Ioc (b + a) (c + a)",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
207,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.seq_subset | [] | [
1963,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1960,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.lfp_le_map | [] | [
92,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.203251\nγ : Type ?u.203254\np✝ : α → Prop\ninst✝² : DecidablePred p✝\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Multiset α\n_l : List α\nh : ∀ (x : α), x ∈ Quot.mk Setoid.r _l → (p x ↔ q x)\n⊢ ∀ (x : α), x ∈... | [
1934,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1932,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_preimage_eq | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_congr_ae' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.16560177\n𝕜 : Type ?u.16560180\nE : Type u_1\nF : Type ?u.16560186\nA : Type ?u.16560189\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nh : ∀ᵐ (x : ℝ) ∂μ, x ∈... | [
989,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.π_eq_app_right | [] | [
542,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_eq_top_of_mclosure_eq_top | [] | [
1312,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.empty_toList | [] | [
468,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_of_locally_liftPropOn | [
{
"state_after": "H : Type u_2\nM : Type u_1\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.38312\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : StructureGr... | [
392,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/RingTheory/Nilpotent.lean | isReduced_of_injective | [
{
"state_after": "case eq_zero\nR S : Type u\nx y : R\ninst✝³ : MonoidWithZero R\ninst✝² : MonoidWithZero S\nF : Type u_1\ninst✝¹ : MonoidWithZeroHomClass F R S\nf : F\nhf : Function.Injective ↑f\ninst✝ : IsReduced S\n⊢ ∀ (x : R), IsNilpotent x → x = 0",
"state_before": "R S : Type u\nx y : R\ninst✝³ : Mono... | [
100,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Connected.lean | isConnected_iff_sUnion_disjoint_open | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.76010\nπ : ι → Type ?u.76015\ninst✝ : TopologicalSpace α\ns✝ t u v s : Set α\n⊢ (Set.Nonempty s ∧ ∀ (u v : Set α), IsOpen u → IsOpen v → s ⊆ u ∪ v → s ∩ (u ∩ v) = ∅ → s ⊆ u ∨ s ⊆ v) ↔\n ∀ (U : Finset (Set α)),\n (∀ (u v : Set α), u ∈ U → v ∈ U → Set.... | [
930,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Algebra/Star/Module.lean | algebraMap_star_comm | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.168559\nA✝ : Type ?u.168562\ninst✝¹³ : Semiring R✝\ninst✝¹² : StarSemigroup R✝\ninst✝¹¹ : TrivialStar R✝\ninst✝¹⁰ : AddCommGroup A✝\ninst✝⁹ : Module R✝ A✝\ninst✝⁸ : StarAddMonoid A✝\ninst✝⁷ : StarModule R✝ A✝\ninst✝⁶ : Invertible 2\nR : Type u_1\nA ... | [
196,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_mono | [] | [
52,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Set/Countable.lean | Set.exists_seq_cover_iff_countable | [] | [
177,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_irrefl' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.100319\nE : Type ?u.100322\nF : Type ?u.100325\nG : Type ?u.100328\nE' : Type u_2\nF' : Type ?u.100334\nG' : Type ?u.100337\nE'' : Type ?u.100340\nF'' : Type ?u.100343\nG'' : Type ?u.100346\nR : Type ?u.100349\nR' : Type ?u.100352\n𝕜 : Type ?u.100355\n𝕜' : Type ?u.1... | [
588,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_symm | [
{
"state_after": "case h.h\nR₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.1591553\ninst✝²⁴ : Semiring R₁\ninst✝²³ : Semiring R₂\ninst✝²² : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₁ : R₂ →+* R₁\ninst✝²¹ : RingHomInvPair σ₁₂ σ₂₁\ninst✝²⁰ : RingHomInvPair σ₂₁ σ₁₂\nσ₂₃ : R₂ →+* R₃\nσ₃₂ : R₃ →+* R₂\ninst✝¹⁹ : RingHomInvPair σ₂... | [
2096,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2094,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutationsAux2_snd_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nt : α\nts : List α\nr : List β\ny : α\nys : List α\nf : List α → β\n⊢ (permutationsAux2 t ts r (y :: ys) f).snd =\n f (t :: y :: ys ++ ts) :: (permutationsAux2 t ts r ys fun x => f (y :: x)).snd",
"tactic": "simp [permutationsA... | [
74,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.sup_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.458131\nδ : Type ?u.458134\ninst✝⁵ : MeasurableSpace α\nμ ν : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : SemilatticeSup β\ninst✝ : ContinuousSup β\nf g f' : α →ₘ[μ] β\nhf : ↑f ≤ᵐ[μ] ↑f'\nhg ... | [
488,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasInitial_of_hasTerminal_op | [] | [
441,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Set/Basic.lean | Set.compl_union_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\n⊢ sᶜ ∪ s = univ",
"tactic": "rw [union_comm, union_compl_self]"
}
] | [
1722,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_two | [
{
"state_after": "x✝ y z x : ℝ\n⊢ x ^ 2 = x ^ ↑2",
"state_before": "x✝ y z x : ℝ\n⊢ x ^ 2 = x ^ 2",
"tactic": "rw [← rpow_nat_cast]"
},
{
"state_after": "no goals",
"state_before": "x✝ y z x : ℝ\n⊢ x ^ 2 = x ^ ↑2",
"tactic": "simp only [Nat.cast_ofNat]"
}
] | [
367,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_union | [
{
"state_after": "x y : ZFSet\n⊢ toSet (⋃₀ {x, y}) = toSet x ∪ toSet y",
"state_before": "x y : ZFSet\n⊢ toSet (x ∪ y) = toSet x ∪ toSet y",
"tactic": "change (⋃₀ {x, y}).toSet = _"
},
{
"state_after": "no goals",
"state_before": "x y : ZFSet\n⊢ toSet (⋃₀ {x, y}) = toSet x ∪ toSet y",
"t... | [
1149,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein.principalSeg_coe | [] | [
596,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv_symm | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_zero | [
{
"state_after": "case h\nl : Type ?u.843153\nm : Type u_2\nn : Type u_1\no : Type ?u.843162\nm' : o → Type ?u.843167\nn' : o → Type ?u.843172\nR : Type ?u.843175\nS : Type ?u.843178\nα : Type v\nβ : Type w\nγ : Type ?u.843185\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype n\nA : Matrix m n α\nx✝ : m\n⊢... | [
1721,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1719,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.norm_star_mul_self' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.35174\nE : Type u_1\nα : Type ?u.35180\ninst✝² : NonUnitalNormedRing E\ninst✝¹ : StarRing E\ninst✝ : CstarRing E\nx : E\n⊢ ‖x⋆ * x‖ = ‖x⋆‖ * ‖x‖",
"tactic": "rw [norm_star_mul_self, norm_star]"
}
] | [
126,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.homCongr_trans | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX₁ Y₁ X₂ Y₂ X₃ Y₃ : C\nα₁ : X₁ ≅ X₂\nβ₁ : Y₁ ≅ Y₂\nα₂ : X₂ ≅ X₃\nβ₂ : Y₂ ≅ Y₃\nf : X₁ ⟶ Y₁\n⊢ ↑(homCongr (α₁ ≪≫ α₂) (β₁ ≪≫ β₂)) f = ↑((homCongr α₁ β₁).trans (homCongr α₂ β₂)) f",
"tactic": "simp"
}
] | [
68,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ringEquivOfRingEquiv_eq_map | [] | [
698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_of_dominated_convergence | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.737955\nδ : Type ?u.737958\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nF✝ : ℕ → α → β\nf✝ : α → β\nbound✝ : α → ℝ\nF : ℕ → α → β\nf : α → β\nbound : α → ℝ\nbound_hasFin... | [
319,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.c_eq_algebraMap | [] | [
646,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMaxOn.hasFDerivWithinAt_nonpos | [
{
"state_after": "case intro.intro.intro.intro\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMaxOn f s a\nhf : HasFDerivWithinAt f f' s a\ny : E\nc : ℕ → ℝ\nd : ℕ → E\nhd : ∀ᶠ (n : ℕ) in atTop, a + d n ∈ s\nhc : Tendsto c atTop atTop... | [
126,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_sum_of_disjoint | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.195288\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\nι : Type u_2\nt : Finset ι\nφ : ι → MvPolynomial σ R\ninst✝ : DecidableEq σ\nh : Pairwise (Disjoint on fun i => vars (φ ... | [
445,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.low_scores | [] | [
571,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.pure_mul_pure | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.cosh | [] | [
163,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Order/Basic.lean | closure_Icc | [] | [
159,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_mem_set | [] | [
1075,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | Commute.zpow_zpow | [] | [
494,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.unique | [
{
"state_after": "A : Type u_1\nB : Type u_2\ninst✝² : Field A\ninst✝¹ : Ring B\ninst✝ : Algebra A B\nx : B\np : A[X]\npmonic : Monic p\nhp : ↑(Polynomial.aeval x) p = 0\npmin : ∀ (q : A[X]), Monic q → ↑(Polynomial.aeval x) q = 0 → degree p ≤ degree q\nhx : IsIntegral A x\n⊢ p = minpoly A x",
"state_before"... | [
66,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.eq_bot_of_comap_eq_bot | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\nS : Type u_2\ninst✝³ : CommRing S\nf : R →+* S\nI J : Ideal S\ninst✝² : Algebra R S\ninst✝¹ : Nontrivial R\ninst✝ : IsDomain S\nhRS : Algebra.IsIntegral R S\nhI : comap (algebraMap R S) I = ⊥\nx : S\nhx : x ∈ I\n⊢ x ∈ ⊥",
"state_before": "R : Type u_1\nin... | [
290,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nn : ℕ\n⊢ eraseLead (X ^ n) = 0",
"tactic": "rw [X_pow_eq_monomial, eraseLead_monomial]"
}
] | [
151,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_eq_self | [] | [
84,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_iInf_eq_top | [] | [
714,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_nonneg_of_nonpos_of_nonpos | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.35871\ninst✝ : OrderedRing α\na b c d : α\nha : a ≤ 0\nhb : b ≤ 0\n⊢ 0 ≤ a * b",
"tactic": "simpa only [zero_mul] using mul_le_mul_of_nonpos_right ha hb"
}
] | [
360,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_restrictScalars | [] | [
1243,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_rat_mul | [] | [
348,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.copy_eq | [] | [
228,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.smul_apply | [] | [
391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion₂_subset_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.59765\nγ : Type ?u.59768\nι : Sort u_2\nι' : Sort ?u.59774\nι₂ : Sort ?u.59777\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.59787\nκ₂ : ι → Sort ?u.59792\nκ' : ι' → Sort ?u.59797\ns : (i : ι) → κ i → Set α\nt : Set α\n⊢ (⋃ (i : ι) (j : κ i), s i... | [
311,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.preimage_Iic | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\nb : β\nx : α\n⊢ x ∈ ↑e ⁻¹' Iic b ↔ x ∈ Iic (↑(symm e) b)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\nb : β\n⊢ ↑e ⁻¹' Iic b = Iic (↑(symm e) b)",
... | [
28,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.span_repr_eq | [
{
"state_after": "ι : Type u'\nι' : Type ?u.460868\nR : Type u_1\nK : Type ?u.460874\nM : Type u_2\nM' : Type ?u.460880\nM'' : Type ?u.460883\nV : Type u\nV' : Type ?u.460888\nv : ι → M\ninst✝⁷ : Ring R\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : AddCommGroup M''\ninst✝³ : Module R M\ninst✝² : ... | [
829,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_eq_tsum' | [] | [
294,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.const | [] | [
128,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Data/Int/Units.lean | Int.mul_eq_neg_one_iff_eq_one_or_neg_one | [
{
"state_after": "no goals",
"state_before": "z w : ℤ\n⊢ z * w = -1 ↔ z = 1 ∧ w = -1 ∨ z = -1 ∧ w = 1",
"tactic": "refine' ⟨eq_one_or_neg_one_of_mul_eq_neg_one', fun h => Or.elim h (fun H => _) fun H => _⟩ <;>\n rcases H with ⟨rfl, rfl⟩ <;>\n rfl"
}
] | [
87,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Connected.lean | IsConnected.union | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι : Type ?u.4449\nπ : ι → Type ?u.4454\ninst✝ : TopologicalSpace α\ns✝ t✝ u v s t : Set α\nHs : IsConnected s\nHt : IsConnected t\nx : α\nhx : x ∈ s ∩ t\n⊢ IsConnected (s ∪ t)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.4449\nπ : ι → Type ?u.4... | [
159,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | zero_le_mul_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.101539\ninst✝ : LinearOrderedSemiring α\na b c d : α\nh : 0 < c\n⊢ 0 ≤ c * b ↔ 0 ≤ b",
"tactic": "simpa using (mul_le_mul_left h : c * 0 ≤ c * b ↔ 0 ≤ b)"
}
] | [
842,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image_image2_right_comm | [] | [
376,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_inter_subset | [] | [
214,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.natDegree_prod_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R\nf : ι → R[X]\nt : Multiset R[X]\n⊢ natDegree (∏ i in s, f i) ≤ ∑ i in s, natDegree (f i)",
"tactic": "simpa using natDegree_multiset_prod_le (s.1.map f)"
}
] | [
124,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | DifferentiableAt.of_dslope | [] | [
138,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.pure_injective | [] | [
310,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Finset/Card.lean | List.card_toFinset | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.forall | [] | [
112,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
11
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_union | [] | [
368,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_eq_zero_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3400\nγ : Type ?u.3403\ninst✝ : Finite α\nthis : Fintype α\n⊢ Nat.card α = 0 ↔ IsEmpty α",
"state_before": "α : Type u_1\nβ : Type ?u.3400\nγ : Type ?u.3403\ninst✝ : Finite α\n⊢ Nat.card α = 0 ↔ IsEmpty α",
"tactic": "haveI := Fintype.ofFinite α"
},
{
... | [
121,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.ind | [
{
"state_after": "case h\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nβ : ComponentCompl G K → Prop\nf : ∀ ⦃v : V⦄ (hv : ¬v ∈ K), β (componentComplMk G hv)\n⊢ ∀ (v : ↑(Kᶜ)), β (connectedComponentMk (induce (Kᶜ) G) v)",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nβ : ComponentCompl... | [
102,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
11
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.exists_adj_boundary_pair | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : Preconnected G\nhK : Set.Nonempty K\nv : V\nvnK : ¬v ∈ K\n⊢ ∃ ck, ck.fst ∈ componentComplMk G vnK ∧ ck.snd ∈ K ∧ Adj G ck.fst ck.snd",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : Preconnected G\nhK : Set.Nonem... | [
170,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.exists_fixedPoint | [] | [
113,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_inj | [
{
"state_after": "no goals",
"state_before": "z w : ℝ\n⊢ z = w → ↑z = ↑w",
"tactic": "apply congrArg"
}
] | [
109,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_induction | [] | [
934,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | split_by_characteristic_domain | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\nP : Prop\ninst✝ : IsDomain R\nh_pos : ∀ (p : ℕ), Nat.Prime p → CharP R p → P\nh_equal : Algebra ℚ R → P\nh_mixed : ∀ (p : ℕ), Nat.Prime p → MixedCharZero R p → P\n⊢ ∀ (p : ℕ), p ≠ 0 → CharP R p → P",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\nP :... | [
371,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.bit1_right | [] | [
63,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "⊢ φ 0 = 1 ↔ 0 = 1 ∨ 0 = 2",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "⊢ φ 1 = 1 ↔ 1 = 1 ∨ 1 = 2",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "⊢ φ 2 = 1 ↔ 2 = 1 ∨ 2 = 2",
"tactic": ... | [
277,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Logic/Basic.lean | not_iff_not | [] | [
430,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.expand_card | [
{
"state_after": "K : Type ?u.1088147\nR : Type ?u.1088150\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : (ZMod p)[X]\nh : ↑(expand (ZMod p) (Fintype.card (ZMod p))) f = f ^ Fintype.card (ZMod p)\n⊢ ↑(expand (ZMod p) p) f = f ^ p",
"state_before": "K : Type ?u.1088147\nR : Type ?u.1088150\np : ℕ\ninst✝ : Fact (Nat... | [
451,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_mul | [
{
"state_after": "no goals",
"state_before": "x y : EReal\n⊢ EReal.abs (x * y) = EReal.abs x * EReal.abs y",
"tactic": "induction x, y using induction₂_symm_neg with\n| top_zero => simp only [zero_mul, mul_zero, abs_zero]\n| top_top => rfl\n| symm h => rwa [mul_comm, EReal.mul_comm]\n| coe_coe => simp o... | [
1103,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Data/Int/Units.lean | Int.mul_eq_one_iff_eq_one_or_neg_one | [
{
"state_after": "no goals",
"state_before": "z w : ℤ\n⊢ z * w = 1 ↔ z = 1 ∧ w = 1 ∨ z = -1 ∧ w = -1",
"tactic": "refine' ⟨eq_one_or_neg_one_of_mul_eq_one', fun h => Or.elim h (fun H => _) fun H => _⟩ <;>\n rcases H with ⟨rfl, rfl⟩ <;>\n rfl"
}
] | [
73,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.toMatrix_lmul' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : Ring S\ninst✝² : Algebra R S\nm : Type u_3\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nb : Basis m R S\nx : S\ni j : m\n⊢ ↑(toMatrix b b) (↑(lmul R S) x) i j = ↑(↑b.repr (x * ↑b j)) i",
"tactic": "sim... | [
851,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.autCongr_trans | [] | [
709,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
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