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/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.trans_sSameSide | [] | [
611,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
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Mathlib/Topology/Constructions.lean | set_pi_mem_nhds_iff | [
{
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1351,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
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Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideCoequalizer.cotrident_ι_app_one | [] | [
708,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
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Mathlib/Data/Set/Lattice.lean | Set.biUnion_pair | [
{
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1002,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.smul_isLittleO | [
{
"state_after": "case refine'_2\nα : Type u_1\nβ : Type ?u.572622\nE : Type ?u.572625\nF : Type ?u.572628\nG : Type ?u.572631\nE' : Type u_4\nF' : Type u_5\nG' : Type ?u.572640\nE'' : Type ?u.572643\nF'' : Type ?u.572646\nG'' : Type ?u.572649\nR : Type ?u.572652\nR' : Type ?u.572655\n𝕜 : Type u_2\n𝕜' : Type ... | [
1765,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1762,
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Mathlib/Data/List/Basic.lean | List.nthLe_reverse | [] | [
1463,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
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Mathlib/Data/Stream/Init.lean | Stream'.iterate_eq | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nf : α → α\na : α\n⊢ head (iterate f a) :: tail (iterate f a) = a :: iterate f (f a)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → α\na : α\n⊢ iterate f a = a :: iterate f (f a)",
"tactic": "rw [← Stream'.eta (iterate f a)]"
},
{
... | [
286,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/Data/Real/EReal.lean | EReal.coe_ne_bot | [] | [
292,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/Order/CompleteLattice.lean | sSup_le | [] | [
144,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Computability/Encoding.lean | Computability.decode_encodePosNum | [
{
"state_after": "n : PosNum\n⊢ decodePosNum (encodePosNum n) = n",
"state_before": "⊢ ∀ (n : PosNum), decodePosNum (encodePosNum n) = n",
"tactic": "intro n"
},
{
"state_after": "case one\n\n⊢ (if [] = [] then PosNum.one else PosNum.bit1 (decodePosNum [])) = PosNum.one\n\ncase bit1\nm : PosNum\... | [
142,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_apply | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Topology/Algebra/Order/Filter.lean | Filter.Tendsto.nhds_atTop | [] | [
38,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Analysis/SumIntegralComparisons.lean | MonotoneOn.integral_le_sum | [
{
"state_after": "x₀ : ℝ\na b : ℕ\nf : ℝ → ℝ\nhf : MonotoneOn f (Icc x₀ (x₀ + ↑a))\n⊢ ∑ x in Finset.range a, -f (x₀ + ↑(x + 1)) ≤ ∫ (x : ℝ) in x₀..x₀ + ↑a, -f x",
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171,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/Data/Semiquot.lean | Semiquot.univ_unique | [] | [
270,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.bot_apply | [] | [
510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | separatedSpace_iff | [] | [
133,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Order/WithBot.lean | WithBot.strictMono_iff | [] | [
360,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.AddValuation.map_mul | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\n⊢ (if x * y = 0 then ⊤ else ↑(valuation (x * y))) =\n (if x = 0 then ⊤ else ↑(valuation x)) + if y = 0 then ⊤ else ↑(valuation y)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\n⊢ addValuationDef (x * y) = addValuationDef x + ... | [
1128,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.inv_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : LinearOrderedField α\nβ : Type u_2\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : CauSeq β abv\nhf : ¬LimZero f\n⊢ (if h : LimZero f then 0 else inv f h) = inv f hf",
"tactic": "rw [dif_neg]"
}
] | [
242,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
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Mathlib/Order/Lattice.lean | sup_eq_left | [
{
"state_after": "no goals",
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"tactic": "simp [le_rfl]"
}
] | [
180,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_toAdd | [] | [
3196,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3196,
9
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.star_moveLeft | [] | [
1849,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1848,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isVonNBounded_singleton | [] | [
206,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Ring/Units.lean | Units.divp_sub_divp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : CommRing α\na b : α\nu₁ u₂ : αˣ\n⊢ a /ₚ u₁ - b /ₚ u₂ = (a * ↑u₂ - ↑u₁ * b) /ₚ (u₁ * u₂)",
"tactic": "simp only [sub_eq_add_neg, neg_divp, divp_add_divp, mul_neg]"
}
] | [
126,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_add_mul_left_left | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ gcd (m + n * k) n = gcd m n",
"tactic": "rw [gcd_comm, gcd_add_mul_left_right, gcd_comm]"
}
] | [
61,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Part.lean | Part.mem_map_iff | [] | [
450,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Topology/QuasiSeparated.lean | QuasiSeparatedSpace.of_openEmbedding | [] | [
134,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.mapIso_inv_app | [
{
"state_after": "no goals",
"state_before": "X Y Z : TopCat\nf g : X ⟶ Y\nh : f = g\nU : Opens ↑Y\n⊢ (map g).obj U = (map f).obj U",
"tactic": "rw [h]"
}
] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_apply_prime_pow | [
{
"state_after": "case inl\nR : Type ?u.590526\np k : ℕ\nhp : Prime p\nhk : k ≠ 0\nh : k = 1\n⊢ ↑μ (p ^ k) = -1\n\ncase inr\nR : Type ?u.590526\np k : ℕ\nhp : Prime p\nhk : k ≠ 0\nh : ¬k = 1\n⊢ ↑μ (p ^ k) = 0",
"state_before": "R : Type ?u.590526\np k : ℕ\nhp : Prime p\nhk : k ≠ 0\n⊢ ↑μ (p ^ k) = if k = 1 t... | [
992,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13308\nγ : Type ?u.13311\nδ : Type ?u.13314\ninst✝ : TopologicalSpace α\na : α\n⊢ 𝓝[∅] a = ⊥",
"tactic": "rw [nhdsWithin, principal_empty, inf_bot_eq]"
}
] | [
237,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousWithinAt.inv | [] | [
262,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.conj_apply | [] | [
2370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2368,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Set.Finite.isBounded | [] | [
308,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.ext₁ | [
{
"state_after": "no goals",
"state_before": "R₁ : Type u_1\nR₂ : Type ?u.1520303\nR₃ : Type ?u.1520306\ninst✝²⁵ : Semiring R₁\ninst✝²⁴ : Semiring R₂\ninst✝²³ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₁ : R₂ →+* R₁\ninst✝²² : RingHomInvPair σ₁₂ σ₂₁\ninst✝²¹ : RingHomInvPair σ₂₁ σ₁₂\nσ₂₃ : R₂ →+* R₃\nσ₃₂ : R₃ →+* R₂... | [
1913,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1912,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.prod_map | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s'✝ : Set α\nx : α\np : Filter ι\np'✝ : Filter α\ng : ι → α\nι' : Type u_1\nα' : Type u_2\nβ' : Type u_3\ninst✝ : UniformSpace β'\nF' : ι' → α' → β'\nf' : α' → β'\np' : Filter ι'\ns' : Set α'\n... | [
291,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_rfl | [] | [
67,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.SeparationQuotient.lift_mk | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : SeparatedSpace β\nf : α → β\nh : UniformContinuous f\na : α\n⊢ Quotient.lift f (_ : ∀ (x x_1 : α), x ≈ x_1 → f x = f x_1) (Quotient.mk (separationSetoid α) a) = f a",
"sta... | [
380,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.image_to_eq_image | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝³ : Category V\ninst✝² : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝¹ : HasImages V\ninst✝ : HasEqualizers V\ni j : ι\nr : ComplexShape.Rel c i j\n⊢ imageSubobject ((xPrevIso C r).hom ≫ d C i j) = imageSubobject (d C i j)",
"stat... | [
468,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_lt_false | [] | [
712,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.comp₂ | [] | [
1513,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1511,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_pow_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.173585\nα : Type u_1\nβ : Type ?u.173591\nf g : Perm α\np : α → Prop\nx y z : α\nn : ℕ\n⊢ SameCycle f x (↑(f ^ n) y) ↔ SameCycle f x y",
"tactic": "rw [← zpow_ofNat, sameCycle_zpow_right]"
}
] | [
180,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.add_imJ | [] | [
221,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
9
] |
Mathlib/Data/Finset/Image.lean | Equiv.finsetCongr_apply | [] | [
785,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.append_overlap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁✝ l₂✝ : List α\na b : α\nl₁ l₂ l₃ : List α\nh₁ : Chain' R (l₁ ++ l₂)\nh₂ : Chain' R (l₂ ++ l₃)\nhn : l₂ ≠ []\n⊢ ∀ (x : α), x ∈ getLast? (l₁ ++ l₂) → ∀ (y : α), y ∈ head? l₃ → R x y",
"tactic": "simpa only [getL... | [
376,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.trans_apply | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Finset/PImage.lean | Finset.coe_pimage | [] | [
75,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.apply_coe_mem_map | [] | [
250,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_eq_zero | [
{
"state_after": "case inl\nb : Ordinal\nhbo : 0 < b\n⊢ log b 0 = 0\n\ncase inr\nb o : Ordinal\nhbo : o < b\nho : o ≠ 0\n⊢ log b o = 0",
"state_before": "b o : Ordinal\nhbo : o < b\n⊢ log b o = 0",
"tactic": "rcases eq_or_ne o 0 with (rfl | ho)"
},
{
"state_after": "case inr.inl\nb o : Ordinal\n... | [
354,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.toDual_ofDual | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.support_cycleOf_eq_nil_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2512943\nα : Type u_1\nβ : Type ?u.2512949\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\n⊢ support (cycleOf f x) = ∅ ↔ ¬x ∈ support f",
"tactic": "simp"
}
] | [
1135,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null | [
{
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"state_before": "α : Type u_2\nβ : Type ... | [
332,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Std/Data/List/Lemmas.lean | List.isSuffix.length_le | [] | [
1638,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1637,
1
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.app_bijective_of_stalkFunctor_map_bijective | [] | [
593,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.K'.elim_aux | [] | [
1274,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
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Mathlib/Data/List/Perm.lean | List.Perm.eq_nil | [] | [
160,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DifferentiableOn.diffContOnCl_ball | [] | [
152,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_neg | [] | [
108,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.lift_snd | [] | [
1371,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1369,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.seq_is_cauchySeq | [] | [
692,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.subsingleton | [] | [
210,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
11
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Mathlib/LinearAlgebra/GeneralLinearGroup.lean | LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap | [
{
"state_after": "case h\nR : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf : GeneralLinearGroup R M\nx✝ : M\n⊢ ↑↑(↑(generalLinearEquiv R M) f) x✝ = ↑↑f x✝",
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76,
62
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75,
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src/lean/Init/SimpLemmas.lean | decide_True | [] | [
158,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
158,
9
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.eval_unique | [
{
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278,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.mk_eq | [] | [
51,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/Algebra/Order/Field/Basic.lean | le_one_div_of_neg | [
{
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"state_before": "ι : Type ?u.158424\nα : Type u_1\nβ : Type ?u.158430\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nha : a < 0\nhb : b < 0\n⊢ a ≤ 1 / b ↔ b ≤ 1 / a",
"tactic": "simpa using le_inv_of_neg ha hb"
}
] | [
828,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
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src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Poly.denote_insertSorted | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nk : Nat\nm : Mon\np : Poly\n⊢ denote ctx (insertSorted k m p) = denote ctx p + k * Mon.denote ctx m",
"tactic": "match p with\n| [] => simp!\n| (k', m') :: p =>\n by_cases h : m < m' <;> simp! [h, denote_insertSorted ctx k m p, Nat.add_assoc,... | [
149,
117
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
145,
1
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasFDerivAt.prodMap | [] | [
347,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
11
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.forget_obj | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Asymptotics.isLittleO_pow_pow_atTop_of_lt | [
{
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88,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Data/Nat/Basic.lean | Nat.decreasingInduction_succ' | [
{
"state_after": "m✝ n k : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → P (n + 1) → P n\nm : ℕ\nmsm : m ≤ m + 1\nhP : P (m + 1)\n⊢ leRecOn msm (fun {k} ih hsk => ih (h k hsk)) (fun h => h) hP = h m hP",
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519,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_apply_prime | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.590184\np : ℕ\nhp : Prime p\n⊢ ↑μ p = -1",
"tactic": "rw [moebius_apply_of_squarefree hp.squarefree, cardFactors_apply_prime hp, pow_one]"
}
] | [
983,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_inv | [
{
"state_after": "no goals",
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1688,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pushforward_union | [] | [
533,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
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Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.split_imp_of_iso | [
{
"state_after": "case intro.intro.intro.intro\nC : Type u_2\ninst✝ : Category C\nX X' : C\nφ : X ≅ X'\np : X ⟶ X\np' : X' ⟶ X'\nhpp' : p ≫ φ.hom = φ.hom ≫ p'\nY : C\ni : Y ⟶ X\ne : X ⟶ Y\nh₁ : i ≫ e = 𝟙 Y\nh₂ : e ≫ i = p\n⊢ ∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p'",
"state_before": "C : Type u_2\ninst✝ ... | [
142,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_left | [] | [
368,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_eq_zero_of_eq | [] | [
216,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.support_scaleRoots_eq | [
{
"state_after": "A : Type ?u.32461\nK : Type ?u.32464\nR : Type u_1\nS : Type ?u.32470\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\ns : R\nhs : s ∈ nonZeroDivisors R\ni : ℕ\n⊢ i ∈ support p → i ∈ support (scaleRoots p s)",
... | [
73,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.right_mem_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.4890\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ b ∈ Ioc a b ↔ a < b",
"tactic": "simp only [mem_Ioc, and_true_iff, le_rfl]"
}
] | [
139,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Calculus/Deriv/Prod.lean | HasDerivAtFilter.prod | [] | [
61,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
8
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.binaryProductIso_hom_comp_snd | [] | [
163,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.sum_single_index | [] | [
1200,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_map_mem_range | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.551485\nδ : Type ?u.551488\nι : Type ?u.551491\nR : Type ?u.551494\nR' : Type ?u.551497\nm0✝ : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nm0 : MeasurableSpace α\... | [
2724,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2717,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.exact | [] | [
1260,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_collinear | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np p' : P\n⊢ Collinear ℝ {secondInter s p (p' -ᵥ p), p, p'}",
"state_before": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGrou... | [
157,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_comap_eq_self_of_surjective | [] | [
3032,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3030,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_erase_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.365585\nγ : Type ?u.365588\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nl : List α\n⊢ count a (erase (Quotient.mk (isSetoid α) l) a) = count a (Quotient.mk (isSetoid α) l) - 1",
"tactic": "convert List.count_erase_self a l <;> rw ... | [
2446,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2444,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.det | [
{
"state_after": "α : Type u_1\nβ : Type ?u.100450\nm : Type u_2\nn : Type ?u.100456\no : Type ?u.100459\nm' : α → Type ?u.100464\nn' : α → Type ?u.100469\nR : Type v\ninst✝⁶ : CommRing R\nM : Matrix m m R\nb : m → α\ninst✝⁵ : DecidableEq m\ninst✝⁴ : Fintype m\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\ninst✝¹... | [
229,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
11
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.erase_mem_lifts | [
{
"state_after": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\nn : ℕ\nh : ∀ (n : ℕ), coeff p n ∈ RingHom.rangeS f\n⊢ ∀ (n_1 : ℕ), coeff (erase n p) n_1 ∈ RingHom.rangeS f",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* ... | [
139,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_nonneg | [
{
"state_after": "x : ℝ\n⊢ 0 ≤ π / 2 - arcsin x",
"state_before": "x : ℝ\n⊢ 0 ≤ arccos x",
"tactic": "unfold arccos"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ 0 ≤ π / 2 - arcsin x",
"tactic": "linarith [arcsin_le_pi_div_two x]"
}
] | [
354,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.Iso.inv_inv | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝ : Category C\nX Y Z : C\nf✝ g : X ⟶ Y\nh : Y ⟶ Z\nf : X ≅ Y\n⊢ f.inv ≫ f.hom = 𝟙 Y",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nf✝ g : X ⟶ Y\nh : Y ⟶ Z\nf : X ≅ Y\n⊢ inv f.inv = f.hom",
"tactic": "apply inv_eq_of_hom_inv_id"
},
{... | [
413,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | LaurentSeries.ofPowerSeries_powerSeriesPart | [
{
"state_after": "R : Type u\ninst✝ : Semiring R\nx : LaurentSeries R\n⊢ ↑(ofPowerSeries ℤ R) (powerSeriesPart x) =\n ↑(single (-order x)) 1 * (↑(single (order x)) 1 * ↑(ofPowerSeries ℤ R) (powerSeriesPart x))",
"state_before": "R : Type u\ninst✝ : Semiring R\nx : LaurentSeries R\n⊢ ↑(ofPowerSeries ℤ R) ... | [
116,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/BoxIntegral/Box/SubboxInduction.lean | BoxIntegral.Box.iUnion_coe_splitCenterBox | [
{
"state_after": "case h\nι : Type u_1\nI✝ J I : Box ι\nx : ι → ℝ\n⊢ (x ∈ ⋃ (s : Set ι), ↑(splitCenterBox I s)) ↔ x ∈ ↑I",
"state_before": "ι : Type u_1\nI✝ J I : Box ι\n⊢ (⋃ (s : Set ι), ↑(splitCenterBox I s)) = ↑I",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case h\... | [
100,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/NumberTheory/LSeries.lean | Nat.ArithmeticFunction.LSeriesSummable_of_bounded_of_one_lt_real | [
{
"state_after": "case pos\nf : ArithmeticFunction ℂ\nm : ℝ\nh : ∀ (n : ℕ), ↑Complex.abs (↑f n) ≤ m\nz : ℝ\nhz : 1 < z\nh0 : m = 0\n⊢ LSeriesSummable f ↑z\n\ncase neg\nf : ArithmeticFunction ℂ\nm : ℝ\nh : ∀ (n : ℕ), ↑Complex.abs (↑f n) ≤ m\nz : ℝ\nhz : 1 < z\nh0 : ¬m = 0\n⊢ LSeriesSummable f ↑z",
"state_bef... | [
80,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_pow | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz : ℤ_[p]\n⊢ ‖z ^ 0‖ = ‖z‖ ^ 0",
"tactic": "simp"
},
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz : ℤ_[p]\nk : ℕ\n⊢ ‖z‖ * ‖z ^ k‖ = ‖z‖ * ‖z‖ ^ k",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz... | [
280,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_inter_Ico | [
{
"state_after": "α : Type u_1\nβ : Type ?u.185024\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ici a₁ ∩ Iio b₁ ∩ (Ici a₂ ∩ Iio b₂) = Ici a₁ ∩ Ici a₂ ∩ (Iio b₁ ∩ Iio b₂)",
"state_before": "α : Type u_1\nβ : Type ?u.185024\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder ... | [
1784,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1783,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.not_mem_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nx✝ : a ∈ nil\nw✝ : ℕ\nh : some a = none\n⊢ False",
"tactic": "injection h"
}
] | [
187,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_prod | [] | [
778,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ici | [] | [
151,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.comap | [] | [
156,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
8
] |
Mathlib/Init/Data/Int/Order.lean | Int.mul_neg_eq_neg_mul_symm | [] | [
67,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
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