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/Set/Pairwise/Basic.lean | Set.Subsingleton.pairwise | [] | [
83,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
11
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.inter | [] | [
440,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
11
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Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.finrank_pi_fintype | [
{
"state_after": "R : Type u\nM✝ : Type v\nN : Type w\ninst✝¹⁴ : Ring R\ninst✝¹³ : StrongRankCondition R\ninst✝¹² : AddCommGroup M✝\ninst✝¹¹ : Module R M✝\ninst✝¹⁰ : Module.Free R M✝\ninst✝⁹ : Module.Finite R M✝\ninst✝⁸ : AddCommGroup N\ninst✝⁷ : Module R N\ninst✝⁶ : Module.Free R N\ninst✝⁵ : Module.Finite R N\... | [
130,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.Exact.comp_desc | [
{
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"tactic":... | [
306,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/RingTheory/Coprime/Lemmas.lean | Int.isCoprime_iff_gcd_eq_one | [
{
"state_after": "case mp\nR : Type u\nI : Type v\ninst✝ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\nm n : ℤ\n⊢ IsCoprime m n → gcd m n = 1\n\ncase mpr\nR : Type u\nI : Type v\ninst✝ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\nm n : ℤ\n⊢ gcd m n = 1 → IsCoprime m n",
"state_before": "R :... | [
43,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_sup | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.le_def | [] | [
232,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Algebra/Invertible.lean | invOf_inj | [] | [
285,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_mul | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5102758\ninst✝ : IsROrC K\nx : K\n⊢ ↑(starRingEnd K) x * x = ↑(↑normSq x)",
"tactic": "rw [mul_comm, mul_conj]"
}
] | [
528,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
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Mathlib/Data/Set/Finite.lean | Equiv.set_finite_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nhst : ↑s ≃ ↑t\n⊢ Set.Finite s ↔ Set.Finite t",
"tactic": "simp_rw [← Set.finite_coe_iff, hst.finite_iff]"
}
] | [
523,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_eq_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.52773\nα : Type u_1\nβ : Type ?u.52779\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢ ⌈a⌉₊ = 0 ↔ a ≤ 0",
"tactic": "rw [← le_zero_iff, ceil_le, Nat.cast_zero]"
}
] | [
332,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.finset_sum_iSup_nat | [
{
"state_after": "case refine'_1\nα✝ : Type ?u.147988\nβ : Type ?u.147991\nγ : Type ?u.147994\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns✝ : Set ℝ≥0∞\nα : Type u_1\nι : Type u_2\ninst✝ : SemilatticeSup ι\ns : Finset α\nf : α → ι → ℝ≥0∞\nhf : ∀ (a : α), Monotone (f a)\n⊢ ∑ a in ∅, iSup (f a) = ⨆ (n : ι... | [
638,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.Infinitesimal.mul | [
{
"state_after": "no goals",
"state_before": "x y : ℝ*\nhx : Infinitesimal x\nhy : Infinitesimal y\n⊢ Infinitesimal (x * y)",
"tactic": "simpa only [mul_zero] using hx.mul hy"
}
] | [
710,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
8
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_isNormal | [] | [
340,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
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Mathlib/Data/Sym/Sym2.lean | Sym2.ball | [
{
"state_after": "α : Type u_1\nβ : Type ?u.34632\nγ : Type ?u.34635\np : α → Prop\na b : α\nh : p a ∧ p b\nc : α\nhc : c ∈ Quotient.mk (Rel.setoid α) (a, b)\n⊢ p c",
"state_before": "α : Type u_1\nβ : Type ?u.34632\nγ : Type ?u.34635\np : α → Prop\na b : α\n⊢ (∀ (c : α), c ∈ Quotient.mk (Rel.setoid α) (a, ... | [
354,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Over/Products.lean | CategoryTheory.Over.ConstructProducts.has_over_limit_discrete_of_widePullback_limit | [] | [
140,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | cpow_eq_nhds' | [
{
"state_after": "α : Type ?u.99046\np : ℂ × ℂ\nhp_fst : p.fst ≠ 0\nthis : ∀ᶠ (x : ℂ × ℂ) in 𝓝 p, x.fst ≠ 0\n⊢ (fun x => x.fst ^ x.snd) =ᶠ[𝓝 p] fun x => Complex.exp (Complex.log x.fst * x.snd)\n\ncase this\nα : Type ?u.99046\np : ℂ × ℂ\nhp_fst : p.fst ≠ 0\n⊢ ∀ᶠ (x : ℂ × ℂ) in 𝓝 p, x.fst ≠ 0",
"state_befo... | [
69,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHom_trans | [] | [
648,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.nextFixed_le_iff | [] | [
230,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/NhdsSet.lean | mem_nhdsSet_interior | [] | [
107,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Real/Basic.lean | Real.sInf_nonneg | [
{
"state_after": "case inl\nx y : ℝ\nhS : ∀ (x : ℝ), x ∈ ∅ → 0 ≤ x\n⊢ 0 ≤ sInf ∅\n\ncase inr\nx y : ℝ\nS : Set ℝ\nhS : ∀ (x : ℝ), x ∈ S → 0 ≤ x\nhS₂ : Set.Nonempty S\n⊢ 0 ≤ sInf S",
"state_before": "x y : ℝ\nS : Set ℝ\nhS : ∀ (x : ℝ), x ∈ S → 0 ≤ x\n⊢ 0 ≤ sInf S",
"tactic": "rcases S.eq_empty_or_nonempt... | [
898,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inrCokernelCofork_π | [] | [
1731,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1730,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_dist_to_a | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\n_h : 0 < 1\n⊢ ‖newton_seq 1 - a‖ = ‖Polynomial.eval a F‖ / ‖Polynomial.eval a... | [
347,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
9
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableAt.cpow | [] | [
118,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.rank_eq_four | [
{
"state_after": "S : Type ?u.258028\nT : Type ?u.258031\nR : Type u_1\ninst✝¹ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\ninst✝ : StrongRankCondition R\n⊢ ↑4 = 4",
"state_before": "S : Type ?u.258028\nT : Type ?u.258031\nR : Type u_1\ninst✝¹ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\nins... | [
571,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | boundedSpace_induced_iff | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.106997\nβ✝ : Type ?u.107000\nι : Type ?u.107003\nπ : ι → Type ?u.107008\ninst✝⁴ : Fintype ι\ninst✝³ : Bornology α✝\ninst✝² : Bornology β✝\ninst✝¹ : (i : ι) → Bornology (π i)\nα : Type u_1\nβ : Type u_2\ninst✝ : Bornology β\nf : α → β\n⊢ BoundedSpace... | [
161,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.div_zero_nonneg | [] | [
926,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_cancel_left | [] | [
2138,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2137,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.mem_map | [
{
"state_after": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\ns✝ t : Subfield K\nf✝ f : K →+* L\ns : Subfield K\ny : L\n⊢ (y ∈\n let src := Subring.map f s.toSubring;\n {\n toSubring :=\n { toSubsemiring := src.toSubsemiring,\n ne... | [
523,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Analysis/Convex/Segment.lean | mem_segment_add_sub | [
{
"state_after": "case h.e'_4\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.167100\nG : Type ?u.167103\nι : Type ?u.167106\nπ : ι → Type ?u.167111\ninst✝³ : LinearOrderedRing 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\nx✝ y✝ : E\ninst✝ : Invertible 2\nx y : E\n⊢ x = midpoint 𝕜 (x + y) (x - y)",
"state_b... | [
318,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.forget_obj | [] | [
215,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.eq_prod_range_div' | [
{
"state_after": "ι : Type ?u.621749\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\nM : Type u_1\ninst✝ : CommGroup M\nf : ℕ → M\nn : ℕ\n⊢ f 0 * ∏ i in range n, f (i + 1) / f i = ∏ i in range (n + 1), if i = 0 then f 0 else f i / f (i - 1)",
"state_befor... | [
1419,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.toOrdinal_symm_eq | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.node4L | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\nhl : Sized l\nhm : Sized m\nhr : Sized r\n⊢ Sized (Ordnode.node4L l x m y r)",
"tactic": "cases m <;> [exact (hl.node' hm).node' hr; exact (hl.node' hm.2.1).node' (hm.2.2.node' hr)]"
... | [
386,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.lipschitz | [] | [
492,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.of_image | [] | [
128,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.smul_tmul' | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_lt | [] | [
73,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_sup' | [
{
"state_after": "F : Type ?u.248430\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.248439\nι : Type ?u.248442\nκ : Type ?u.248445\ninst✝ : SemilatticeSup α\ns : Finset β\nH : Finset.Nonempty s\nf : β → α\nb : β\nh : b ∈ s\n⊢ ↑(f b) ≤ sup s (WithBot.some ∘ f)",
"state_before": "F : Type ?u.248430\nα : Type u_2\nβ... | [
812,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.Odd.sub_even | [] | [
201,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Part.lean | Part.inv_def | [] | [
701,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_mul_self_left | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.57650\n𝕜 : Type ?u.57653\nα : Type ?u.57656\nι : Type ?u.57659\nκ : Type ?u.57662\nE : Type u_1\nF : Type ?u.57668\nG : Type ?u.57671\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na✝ a₁ a₂ b✝ b₁ b₂ :... | [
441,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
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Mathlib/Topology/Order.lean | generateFrom_iUnion | [] | [
950,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
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Mathlib/Data/List/BigOperators/Basic.lean | List.Sublist.prod_le_prod' | [
{
"state_after": "case slnil\nι : Type ?u.76473\nα : Type ?u.76476\nM : Type u_1\nN : Type ?u.76482\nP : Type ?u.76485\nM₀ : Type ?u.76488\nG : Type ?u.76491\nR : Type ?u.76494\ninst✝⁵ : Monoid M\ninst✝⁴ : Monoid N\ninst✝³ : Monoid P\nl l₁✝ l₂✝ : List M\na : M\ninst✝² : Preorder M\ninst✝¹ : CovariantClass M M (... | [
290,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.continuous_posPart | [] | [
1133,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.iUnion_right_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ns t✝ u v : Set α\ninst✝ : Countable ι\nt : ι → Set α\n⊢ AEDisjoint μ s (⋃ (i : ι), t i) ↔ ∀ (i : ι), AEDisjoint μ s (t i)",
"tactic": "simp only [AEDisjoint, inter_iUnion, measure_iUnion_null_... | [
104,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.convex | [] | [
111,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
11
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.id | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.23732\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.23822\ninst✝¹ : NormedAddCommGroup G\ninst✝ : Nor... | [
112,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_mul_cancel' | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nf g₁ g₂ : R\nU : Opens ↑(PrimeSpectrum.Top R)\nhu₁ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₁ ∈ Ideal.primeCompl x.asIdeal\nhu₂ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₂ ∈ Ideal.primeCompl x.asIdeal\n⊢ const R g₁ g₂ U hu₂ * c... | [
407,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_of_right_le | [] | [
125,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.box_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1778\nβ : Type ?u.1781\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ box (n + 1) 0 = ∅",
"tactic": "simp [box]"
}
] | [
85,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.id_apply | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Std/Data/Option/Lemmas.lean | Option.get_mem | [] | [
25,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_nat_cast | [
{
"state_after": "case zero\na : ℕ\n⊢ val ↑a = a % Nat.zero\n\ncase succ\na n✝ : ℕ\n⊢ val ↑a = a % Nat.succ n✝",
"state_before": "n a : ℕ\n⊢ val ↑a = a % n",
"tactic": "cases n"
},
{
"state_after": "case succ\na n✝ : ℕ\n⊢ val (Fin.ofNat'' a) = a % Nat.succ n✝",
"state_before": "case succ\na ... | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToTop_obj | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_mk_of_ne_zero | [
{
"state_after": "F : Type ?u.4202\nι : Type ?u.4205\nα : Type u_1\nβ : Type ?u.4211\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\nb0' : b ≠ 0\n⊢ ↑(a /. b) = ↑a / ↑b",
"state_before": "F : Type ?u.4202\nι : Type ?u.4205\nα : Type u_1\nβ : Type ?u.4211\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\n⊢ ↑(a /.... | [
101,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/Normed/Field/InfiniteSum.lean | tsum_mul_tsum_eq_tsum_sum_range_of_summable_norm | [
{
"state_after": "R : Type u_1\nι : Type ?u.12044\nι' : Type ?u.12047\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nf g : ℕ → R\nhf : Summable fun x => ‖f x‖\nhg : Summable fun x => ‖g x‖\n⊢ ((∑' (n : ℕ), f n) * ∑' (n : ℕ), g n) = ∑' (n : ℕ), ∑ ij in antidiagonal n, f ij.fst * g ij.snd",
"state_before": ... | [
116,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.traverse_pure | [] | [
243,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.disjoint_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.189730\nι : Sort ?u.189733\nκ : ι → Sort ?u.189738\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : LowerSet α\nt t₁ t₂ : LowerSet β\nx : α × β\n⊢ Disjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Disjoint s₁ s₂ ∨ Disjoint t₁ t₂",
"... | [
1743,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1742,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.subset | [] | [
451,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_smul | [] | [
607,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.nodup_of_separable_prod | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\ns : Multiset R\nhs : Separable (Multiset.prod (Multiset.map (fun a => X - ↑C a) s))\n⊢ ∀ (a : R) (t : Multiset R), s ≠ a ::ₘ a ::ₘ t",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\ns : Multiset R\nhs : Separab... | [
223,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_1\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.106184\ns₂ : Finset ι₂\nw : ι → k\np₂ : ι → P\np₁ b : P\n⊢ ∑ i in s, w i • (p₁ -ᵥ p₂ i) = (∑ i i... | [
205,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_nat | [
{
"state_after": "case zero\na b c : Ordinal\n⊢ a ♯ ↑Nat.zero = a + ↑Nat.zero\n\ncase succ\na b c : Ordinal\nn : ℕ\nhn : a ♯ ↑n = a + ↑n\n⊢ a ♯ ↑(Nat.succ n) = a + ↑(Nat.succ n)",
"state_before": "a b c : Ordinal\nn : ℕ\n⊢ a ♯ ↑n = a + ↑n",
"tactic": "induction' n with n hn"
},
{
"state_after": ... | [
319,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_subset_erase | [] | [
1938,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearIsometry.coe_toSpanSingleton | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.mem_lift'_sets | [] | [
265,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_max | [] | [
703,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_le | [] | [
232,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.monotone | [] | [
232,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
11
] |
Mathlib/Analysis/Complex/Circle.lean | coe_inv_circle | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | isOfFinOrder_ofAdd_iff | [] | [
73,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_iff_nhds_basis | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns✝ s₁ s₂ t✝ : Set α\np✝ p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\na : α\np : ι → Prop\ns : ι → Set α\nh : HasBasis (𝓝 a) p s\nt : Set α\n⊢ (∀ (i : ι), p i → Set.Nonempty (s i ∩ t)) ↔ ∀ (i : ι), p i → ∃ y, y ∈ t ∧ ... | [
1355,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.of_fst | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_max_left | [
{
"state_after": "a b : Nat\n⊢ a ≤ if a ≤ b then b else a",
"state_before": "a b : Nat\n⊢ a ≤ max a b",
"tactic": "rw [Nat.max_def]"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ a ≤ if a ≤ b then b else a",
"tactic": "split <;> simp [*]"
}
] | [
202,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
202,
11
] |
Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean | CategoryTheory.Pretriangulated.inv_rot_of_dist_triangle | [] | [
118,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_reindex_left | [] | [
170,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.top_apply | [] | [
510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.independent_pempty | [] | [
277,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.apply_symm_apply | [] | [
378,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Topology/ContinuousOn.lean | mem_closure_ne_iff_frequently_within | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1018\nγ : Type ?u.1021\nδ : Type ?u.1024\ninst✝ : TopologicalSpace α\nz : α\ns : Set α\n⊢ z ∈ closure (s \\ {z}) ↔ ∃ᶠ (x : α) in 𝓝[{z}ᶜ] z, x ∈ s",
"tactic": "simp [mem_closure_iff_frequently, frequently_nhdsWithin_iff]"
}
] | [
64,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.one_def | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Lie/DirectSum.lean | DirectSum.lie_of_of_eq | [
{
"state_after": "R : Type u\nι : Type v\ninst✝³ : CommRing R\nL : ι → Type w\ninst✝² : (i : ι) → LieRing (L i)\ninst✝¹ : (i : ι) → LieAlgebra R (L i)\ninst✝ : DecidableEq ι\ni j : ι\nhij : j = i\nx : L i\ny : L j\nthis : ↑(of L j) y = ↑(of L i) (Eq.recOn hij y)\n⊢ ⁅↑(of L i) x, ↑(of L j) y⁆ = ↑(of L i) ⁅x, Eq.... | [
178,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_neg | [] | [
635,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
11
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | continuousOn_extChartAt | [] | [
1086,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMinOn.hasFDerivWithinAt_nonneg | [
{
"state_after": "no goals",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMinOn f s a\nhf : HasFDerivWithinAt f f' s a\ny : E\nhy : y ∈ posTangentConeAt s a\n⊢ 0 ≤ ↑f' y",
"tactic": "simpa using h.neg.hasFDer... | [
159,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_zero | [] | [
265,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
263,
9
] |
Mathlib/Order/Filter/Lift.lean | Filter.tendsto_lift | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Sort ?u.12537\nf f₁ f₂ : Filter α\ng g₁ g₂ : Set α → Filter β\nm : γ → β\nl : Filter γ\n⊢ Tendsto m l (Filter.lift f g) ↔ ∀ (s : Set α), s ∈ f → Tendsto m l (g s)",
"tactic": "simp only [Filter.lift, tendsto_iInf... | [
109,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuousAt_const_mul | [] | [
403,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
11
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_single | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\n⊢ { toFinsupp := Finsupp.single n r } = ↑(monomial n) r",
"tactic": "simp [monomial]"
}
] | [
428,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasDerivAt.clog_real | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.37754\ninst✝² : TopologicalSpace α\nE : Type ?u.37760\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → ℂ\nx : ℝ\nf' : ℂ\nh₁ : HasDerivAt f f' x\nh₂ : 0 < (f x).re ∨ (f x).im ≠ 0\n⊢ HasDerivAt (fun t => log (f t)) (f' / f x) x",
"t... | [
110,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.beq_eq_true_eq | [
{
"state_after": "a : Nat\n⊢ (a == a) = true",
"state_before": "a b : Nat\nh : a = b\n⊢ (a == b) = true",
"tactic": "subst h"
},
{
"state_after": "no goals",
"state_before": "a : Nat\n⊢ (a == a) = true",
"tactic": "apply LawfulBEq.rfl"
}
] | [
104,
150
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
104,
9
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_top | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.mul_integral_comp_mul_sub | [] | [
291,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.lt_two_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 1 < 2",
"tactic": "decide"
}
] | [
56,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | DifferentiableWithinAt.div_const | [] | [
310,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableAt.iterate | [] | [
258,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
11
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubmonoid_le | [] | [
144,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineEquiv.wSameSide_map_iff | [] | [
96,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_cauchy | [
{
"state_after": "𝕜 : Type ?u.331396\nE : Type ?u.331399\nF : Type ?u.331402\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → ℝ\nx x₀ : ℝ\nn : ℕ\nhx : x₀ < x\nhf : ContDiffOn ℝ (↑n) f (Icc x₀ x)\nhf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc x₀ x)) (Ioo x₀ x)\ngcont : ContinuousOn id (... | [
326,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
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