file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.generalizedEigenspace_le_maximal | [] | [
306,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.170280\nβ : Type ?u.170283\nM : Type u_1\nN : Type u_2\nP : Type u_3\nG : Type ?u.170295\nH : Type ?u.170298\nF : Type ?u.170301\ninst✝² : MulZeroOneClass M\ninst✝¹ : MulZeroOneClass N\ninst✝ : MulZeroOneClass P\ng : N →*₀ P\nf₁ f₂ : M →*₀ N\nhg : Fu... | [
1216,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
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Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.finset_prod_mem_finset_prod | [] | [
159,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.preimage_sphere | [] | [
252,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.projIcc | [
{
"state_after": "case refine'_1\nx✝ x : ℝ\nhx : x < 0\n⊢ smoothTransition x = smoothTransition 0\n\ncase refine'_2\nx✝ x : ℝ\nhx : 1 < x\n⊢ smoothTransition x = smoothTransition 1",
"state_before": "x : ℝ\n⊢ smoothTransition ↑(projIcc 0 1 (_ : 0 ≤ 1) x) = smoothTransition x",
"tactic": "refine' congr_f... | [
212,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.negPart_map_norm | [
{
"state_after": "α : Type u_1\nE : Type ?u.93564\nF : Type ?u.93567\n𝕜 : Type ?u.93570\ninst✝² : LinearOrder E\ninst✝¹ : Zero E\ninst✝ : MeasurableSpace α\nf : α →ₛ ℝ\n⊢ map norm (posPart (-f)) = posPart (-f)",
"state_before": "α : Type u_1\nE : Type ?u.93564\nF : Type ?u.93567\n𝕜 : Type ?u.93570\ninst✝²... | [
282,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_zero | [] | [
136,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_indicator_subset | [] | [
302,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_sum_single | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type ?u.897658\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), BoundedSMul 𝕜 (E i)\ninst✝ : DecidableEq α\nhp : 0 < ENNReal.toReal p\nf : (i : α) → E i\ns : Finset α\... | [
1046,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Prod.lean | Finset.card_product | [] | [
143,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_nat_eq_sum_factorization | [
{
"state_after": "case inl\nx y : ℝ\n⊢ log ↑0 = Finsupp.sum (Nat.factorization 0) fun p t => ↑t * log ↑p\n\ncase inr\nx y : ℝ\nn : ℕ\nhn : n ≠ 0\n⊢ log ↑n = Finsupp.sum (Nat.factorization n) fun p t => ↑t * log ↑p",
"state_before": "x y : ℝ\nn : ℕ\n⊢ log ↑n = Finsupp.sum (Nat.factorization n) fun p t => ↑t ... | [
354,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.symm | [] | [
1135,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_emetric_ball | [
{
"state_after": "case inl\nι : Type ?u.131283\ninst✝ : Fintype ι\na : ℝ\n⊢ ↑↑volume (EMetric.ball a ⊤) = 2 * ⊤\n\ncase inr\nι : Type ?u.131283\ninst✝ : Fintype ι\na : ℝ\nr : ℝ≥0∞\nhr : r ≠ ⊤\n⊢ ↑↑volume (EMetric.ball a r) = 2 * r",
"state_before": "ι : Type ?u.131283\ninst✝ : Fintype ι\na : ℝ\nr : ℝ≥0∞\n⊢ ... | [
126,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_le_one_of_one_le | [] | [
1268,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_bit0 | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ fib (bit0 n) = fib n * (2 * fib (n + 1) - fib n)",
"tactic": "rw [bit0_eq_two_mul, fib_two_mul]"
}
] | [
187,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.prod_sum | [
{
"state_after": "case empty\nι✝ : Type ?u.943028\nβ : Type u\nα✝ : Type v\nγ : Type w\ns s₁ s₂ : Finset α✝\na : α✝\nf✝ g : α✝ → β\ninst✝¹ : DecidableEq α✝\nα : Type u_1\nι : Type u_2\ninst✝ : CommMonoid α\nf : ι → Multiset α\n⊢ prod (∑ x in ∅, f x) = ∏ x in ∅, prod (f x)\n\ncase insert\nι✝ : Type ?u.943028\nβ ... | [
2180,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2175,
1
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Mathlib/RingTheory/Int/Basic.lean | gcd_eq_nat_gcd | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | StrictMono.pow_right' | [
{
"state_after": "no goals",
"state_before": "β : Type u_1\nA : Type ?u.67813\nG : Type ?u.67816\nM : Type u_2\nR : Type ?u.67822\ninst✝⁴ : Monoid M\ninst✝³ : Preorder M\ninst✝² : Preorder β\ninst✝¹ : CovariantClass M M (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : CovariantClass M M (swap fun x x_1 ... | [
169,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_cons_cons | [] | [
38,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_sep | [] | [
2161,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2160,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_of_subsingleton | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁰ : NormedAddCommGroup D\ninst✝⁹ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁴ : Norme... | [
111,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/UpperLower/Basic.lean | lowerClosure_image | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.137425\nι : Sort ?u.137428\nκ : ι → Sort ?u.137433\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\nx : α\nf : α ≃o β\n⊢ lowerClosure (↑f '' s) = ↑(OrderIso.symm (LowerSet.map (OrderIso.symm f))) (lowerClosure s)",
"state_before": "α : Type u_1... | [
1338,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | tsum_of_norm_bounded | [
{
"state_after": "case pos\nι : Type u_1\nα : Type ?u.16948\nE : Type u_2\nF : Type ?u.16954\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : SeminormedAddCommGroup F\nf : ι → E\ng : ι → ℝ\na : ℝ\nhg : HasSum g a\nh : ∀ (i : ι), ‖f i‖ ≤ g i\nhf : Summable f\n⊢ ‖∑' (i : ι), f i‖ ≤ a\n\ncase neg\nι : Type u_1\nα : Typ... | [
134,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.coeFn_neg | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.reApplyInnerSelf_apply | [] | [
2297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2295,
1
] |
Mathlib/Data/Part.lean | Part.eq_get_iff_mem | [] | [
244,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.coinduced_continuous | [
{
"state_after": "α✝ : Type u\nβ✝ : Type v\nG : Type w\nH : Type x\ninst✝¹ : Group α✝\nα : Type u_1\nβ : Type u_2\nt : TopologicalSpace α\ninst✝ : Group β\nf : α → β\n⊢ ∀ (t_1 : TopologicalSpace β),\n t_1 ∈ toTopologicalSpace '' {b | TopologicalSpace.coinduced f t ≤ b.toTopologicalSpace} → Continuous f",
... | [
2026,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2022,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_comp_ofList | [] | [
73,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_tProd_elim' | [] | [
966,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.tr_respects_aux₁ | [
{
"state_after": "case zero\nK : Type u_1\ninst✝² : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_4\ninst✝¹ : Inhabited Λ\nσ : Type u_3\ninst✝ : Inhabited σ\nM : Λ → Stmt₂\nk : K\no : StAct k\nq : Stmt₂\nv : σ\nS : List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ListBlank.map (proj k) L = ListBlank.mk (L... | [
2667,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2658,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | Conformal.comp | [] | [
145,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.nhds_left_eq_nhds | [
{
"state_after": "no goals",
"state_before": "s : Set Ordinal\na✝ : Ordinal\na : Ordinal\n⊢ 𝓝[Set.Iic a] a = 𝓝 a",
"tactic": "rw [← nhds_left_sup_nhds_right', nhds_right', sup_bot_eq]"
}
] | [
68,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.iInf_empty | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.2629\nβ : Type ?u.2632\nγ : Type ?u.2635\nι : Sort u_2\nα : Type u_1\ninst✝¹ : IsEmpty ι\ninst✝ : InfSet α\nf : ι → WithTop α\n⊢ (⨅ (i : ι), f i) = ⊤",
"tactic": "rw [iInf, range_eq_empty, WithTop.sInf_empty]"
}
] | [
91,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_near_of_forall_near | [] | [
643,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.not_unit_of_finite | [] | [
92,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Fintype/Powerset.lean | Finset.powerset_eq_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Fintype α\ns : Finset α\n⊢ powerset s = univ ↔ s = univ",
"tactic": "rw [← Finset.powerset_univ, powerset_inj]"
}
] | [
39,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.other_ne | [
{
"state_after": "α : Type u_1\nβ : Type ?u.41545\nγ : Type ?u.41548\na : α\nz : Sym2 α\nh : a ∈ z\nhd : Mem.other h = a\n⊢ IsDiag z",
"state_before": "α : Type u_1\nβ : Type ?u.41545\nγ : Type ?u.41548\na : α\nz : Sym2 α\nhd : ¬IsDiag z\nh : a ∈ z\n⊢ Mem.other h ≠ a",
"tactic": "contrapose! hd"
},
... | [
475,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.add_smul_mem | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.179651\nE : Type u_2\nF : Type ?u.179657\nβ : Type ?u.179660\ninst✝⁶ : OrderedRing 𝕜\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalSpace F\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns t✝ : Set E\nx y : E\nhs : ... | [
351,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
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] |
Mathlib/Algebra/Hom/Group.lean | OneHom.coe_coe | [] | [
264,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff_right | [] | [
1967,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1966,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | conformalAt_id | [] | [
66,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/ULift.lean | PLift.down_surjective | [] | [
62,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.cast_cast | [] | [
138,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_list_map_count | [
{
"state_after": "case nil\nι : Type ?u.450788\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝² : CommMonoid β\ninst✝¹ : DecidableEq α\nM : Type u_1\ninst✝ : CommMonoid M\nf : α → M\n⊢ prod (List.map f []) = ∏ m in toFinset [], f m ^ count m []\n\ncase cons\nι : Type ?u.45078... | [
1290,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1275,
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] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.ringHom_ext | [] | [
600,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_ofDual | [] | [
3246,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3246,
9
] |
Mathlib/Order/SuccPred/Limit.lean | Order.IsPredLimit.pred_ne | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : PredOrder α\ninst✝ : NoMinOrder α\nb : α\nh : IsPredLimit (pred b)\n⊢ False",
"state_before": "α : Type u_1\ninst✝² : Preorder α\na : α\ninst✝¹ : PredOrder α\ninst✝ : NoMinOrder α\nh : IsPredLimit a\nb : α\n⊢ pred b ≠ a",
"tactic": "rintro rf... | [
306,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | deriv_cosh | [] | [
878,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nf : α → Set (Set α)\ns : Set α\nh : FineSubfamilyOn v f s\ninst✝ : SecondCountableTopology α\nρ : MeasureTheory.Measure α\nhρ : ρ ≪ μ\n⊢ s ⊆\n (s \\... | [
177,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.lt_size | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ m < size n ↔ 2 ^ m ≤ n",
"tactic": "rw [← not_lt, Decidable.iff_not_comm, not_lt, size_le]"
}
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_zero | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.norm | [
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Mathlib/Data/Set/NAry.lean | Set.image2_right_comm | [
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Mathlib/GroupTheory/IsFreeGroup.lean | IsFreeGroup.ext_hom | [] | [
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Mathlib/GroupTheory/Divisible.lean | pow_left_surj_of_rootableBy | [] | [
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Mathlib/Data/Sum/Order.lean | Sum.Lex.toLex_le_toLex | [] | [
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Mathlib/LinearAlgebra/Basis.lean | Basis.mem_span_repr_support | [
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Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.mem_support_uniformOfFintype | [
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Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_div | [] | [
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Mathlib/Data/PNat/Prime.lean | PNat.Coprime.factor_eq_gcd_right | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_apply | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.eq_adjoin_of_eq_algebra_adjoin | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.bot_or_exists_ne_one | [
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Mathlib/Algebra/Algebra/Basic.lean | algebraMap.lift_map_eq_zero_iff | [] | [
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Mathlib/Analysis/Normed/Group/Pointwise.lean | singleton_mul_ball_one | [
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Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_add_one_pow_atTop_atTop_of_pos | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_empty | [
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Mathlib/Order/Heyting/Basic.lean | sup_sdiff_right | [] | [
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_fin_one | [] | [
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_Ici | [] | [
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Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_iterate_succ_of_not_isMax | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_succ_iff_hasFDerivWithinAt' | [
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Mathlib/Data/Countable/Defs.lean | Function.Surjective.countable | [] | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_add_right | [
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.realize_iff_of_model_completeTheory | [
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Mathlib/Order/Hom/Basic.lean | OrderEmbedding.wellFounded | [] | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.sub | [
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Mathlib/Topology/Basic.lean | Dense.nonempty_iff | [] | [
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Mathlib/Topology/Order/Basic.lean | exists_Icc_mem_subset_of_mem_nhdsWithin_Ici | [
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Mathlib/Order/Monotone/Basic.lean | Nat.rel_of_forall_rel_succ_of_le_of_le | [] | [
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.replaceHead_head | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_le_div_right_of_neg | [] | [
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Mathlib/Analysis/Calculus/ContDiff.lean | HasFTaylorSeriesUpToOn.exists_lipschitzOnWith | [] | [
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.MeasurePreserving.mul_right | [] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_apply_ite_of_false | [
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.add_apply | [] | [
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Mathlib/Topology/DenseEmbedding.lean | DenseRange.induction_on₃ | [] | [
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_sup_right | [] | [
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_invOf | [
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Mathlib/Data/Int/Log.lean | Int.zpow_log_le_self | [
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Mathlib/Data/Seq/Computation.lean | Computation.terminates_map_iff | [] | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleFactorsFinset_mem_commute | [] | [
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.continuousWithinAt | [] | [
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Mathlib/Topology/MetricSpace/Baire.lean | dense_iInter_of_open | [
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Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.gcd_ndunion | [
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Mathlib/Topology/ContinuousOn.lean | preimage_nhdsWithin_coinduced' | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.8061\nδ : Type ?u.8064\ninst✝ : TopologicalSpace α\nπ : α → β\ns : Set β\nt : Set α\na : { x // x ∈ t }\nhs : s ∈ 𝓝 (π ↑a)\n⊢ π ⁻¹' s ∈ 𝓝[t] ↑a",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.8061\nδ : Type ?u.8064\ninst✝ : T... | [
145,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.coe_sSup_eq' | [] | [
569,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
11
] |
Mathlib/Topology/Constructions.lean | continuous_uncurry_of_discreteTopology | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type u_1\nδ : Type ?u.34136\nε : Type ?u.34139\nζ : Type ?u.34142\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : TopologicalSpace γ\ninst✝³ : TopologicalSpace δ\ninst✝² : TopologicalSpace ε\ninst✝¹ : TopologicalSpace ζ\ninst✝ : DiscreteTopology ... | [
531,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/NumberTheory/Primorial.lean | primorial_le_4_pow | [
{
"state_after": "case h\nn : ℕ\nihn : ∀ (m : ℕ), m < n → m# ≤ 4 ^ m\n⊢ n# ≤ 4 ^ n",
"state_before": "n : ℕ\n⊢ n# ≤ 4 ^ n",
"tactic": "induction' n using Nat.strong_induction_on with n ihn"
},
{
"state_after": "case h.zero\nihn : ∀ (m : ℕ), m < zero → m# ≤ 4 ^ m\n⊢ zero# ≤ 4 ^ zero\n\ncase h.suc... | [
95,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | coprime_sq_sub_mul_of_odd_even | [
{
"state_after": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 1\nhn : n % 2 = 0\n⊢ Nat.gcd (Int.natAbs (-(m ^ 2 - n ^ 2))) (Int.natAbs (2 * m * n)) = 1",
"state_before": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 1\nhn : n % 2 = 0\n⊢ Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1",
"tactic": "rw [Int.gcd, ← In... | [
396,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
9
] |
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