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/Real/ENNReal.lean | ENNReal.le_inv_iff_le_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.269244\nβ : Type ?u.269247\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a ≤ b⁻¹ ↔ b ≤ a⁻¹",
"tactic": "simpa only [inv_inv] using @ENNReal.inv_le_inv a⁻¹ b"
}
] | [
1500,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1499,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.get_bind | [] | [
823,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_congr_right | [] | [
862,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.measurable_of_countable_ne | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44496\nδ : Type ?u.44499\nδ' : Type ?u.44502\nι : Sort uι\ns t✝ u : Set α\nf g : α → β\nm : MeasurableSpace α\nmβ : MeasurableSpace β\ninst✝ : MeasurableSingletonClass α\nhf : Measurable f\nh : Set.Countable {x | f x ≠ g x}\nt : Set β\nht : MeasurableSet... | [
365,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_map | [] | [
253,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_coe | [] | [
242,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.exists_mem_subset_iff | [] | [
212,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_symm_apply | [] | [
446,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.coprodᵢ_cocompact | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.140164\nπ : ι → Type ?u.140169\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ns t : Set α\ninst✝¹ : (i : ι) → TopologicalSpace (π i)\nδ : Type u_1\nκ : δ → Type u_2\ninst✝ : (d : δ) → TopologicalSpace (κ d)\n⊢ cocompact ((d : δ) → κ d) ≤ Filter.c... | [
1057,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_restrictFreeVar | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.135581\nP : Type ?u.135584\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn✝¹ l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝¹ : Fin l ... | [
474,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_le_one_div_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.82335\nα : Type u_1\nβ : Type ?u.82341\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nh : a ≤ b\n⊢ 1 / b ≤ 1 / a",
"tactic": "simpa using inv_le_inv_of_le ha h"
}
] | [
454,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.lift_unique | [
{
"state_after": "case a\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\ng : R →+* ℤ_[p]\nhg : ∀ (n : ℕ), RingHom.comp (toZ... | [
659,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.integral_cos_pow_eq | [
{
"state_after": "z : ℂ\nn✝ n : ℕ\n⊢ ((∫ (x : ℝ) in 0 ..π / 2, cos x ^ n) + ∫ (x : ℝ) in 0 ..π / 2, cos x ^ n) = ∫ (x : ℝ) in 0 ..π, sin x ^ n",
"state_before": "z : ℂ\nn✝ n : ℕ\n⊢ (∫ (x : ℝ) in 0 ..π / 2, cos x ^ n) = 1 / 2 * ∫ (x : ℝ) in 0 ..π, sin x ^ n",
"tactic": "rw [mul_comm (1 / 2 : ℝ), ← div_eq... | [
206,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_two_mul_add_two | [
{
"state_after": "n : ℕ\n⊢ fib n * (2 * fib (n + 1) - fib n) + (fib (n + 1) ^ 2 + fib n ^ 2) = fib (n + 1) * (2 * fib n + fib (n + 1))",
"state_before": "n : ℕ\n⊢ fib (2 * n + 2) = fib (n + 1) * (2 * fib n + fib (n + 1))",
"tactic": "rw [fib_add_two, fib_two_mul, fib_two_mul_add_one]"
},
{
"stat... | [
180,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.Tendsto.exists_forall_le | [] | [
178,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Category/Mon/FilteredColimits.lean | MonCat.FilteredColimits.colimitMulAux_eq_of_rel_left | [
{
"state_after": "case mk\nJ : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ MonCat\ninst✝ : IsFiltered J\nx' y : (j : J) × ↑(F.obj j)\nj₁ : J\nx : ↑(F.obj j₁)\nhxx' : Types.FilteredColimit.Rel (F ⋙ forget MonCat) { fst := j₁, snd := x } x'\n⊢ colimitMulAux F { fst := j₁, snd := x } y = colimitMulAux F x' y",
"... | [
153,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_eq_zero_iff | [
{
"state_after": "θ : Angle\n⊢ sin θ = sin 0 ↔ θ = 0 ∨ θ = ↑π",
"state_before": "θ : Angle\n⊢ sin θ = 0 ↔ θ = 0 ∨ θ = ↑π",
"tactic": "nth_rw 1 [← sin_zero]"
},
{
"state_after": "θ : Angle\n⊢ θ = 0 ∨ θ + 0 = ↑π ↔ θ = 0 ∨ θ = ↑π",
"state_before": "θ : Angle\n⊢ sin θ = sin 0 ↔ θ = 0 ∨ θ = ↑π",
... | [
368,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.snd_inv | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.sum_pow_mul_eq_add_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.35983\nβ : Type ?u.35986\nn : ℕ\nR : Type u_1\ninst✝ : CommSemiring R\na b : R\n⊢ ∑ s : Finset (Fin n), a ^ card s * b ^ (n - card s) = (a + b) ^ n",
"tactic": "simpa using Fintype.sum_pow_mul_eq_add_pow (Fin n) a b"
}
] | [
165,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.map_midpoint | [
{
"state_after": "E : Type u_3\nPE : Type u_1\nF : Type u_4\nPF : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : MetricSpace PE\ninst✝⁴ : NormedAddTorsor E PE\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : MetricSpace PF\ninst✝ : NormedAddTorsor F PF\nf : PE ≃ᵢ P... | [
101,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Box.measurableSet_Ioo | [] | [
70,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.trans_wSameSide | [] | [
579,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_add_div | [
{
"state_after": "m n : Nat\n⊢ ↑m % ↑(succ n) + -↑(succ n) * -↑(m / succ n) = ↑m",
"state_before": "m n : Nat\n⊢ mod (ofNat m) -[n+1] + -[n+1] * div (ofNat m) -[n+1] = ofNat m",
"tactic": "show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m"
},
{
"state_after": "m n : Nat\n⊢ ↑m % ↑(succ n)... | [
280,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
267,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_eq_measure_of_null_diff | [] | [
265,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.shearMulRight_symm_coe | [] | [
669,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | IsAssociatedPrime.annihilator_le | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝⁴ : CommRing R\nJ : Ideal R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nM' : Type ?u.70734\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nx : M\nhI : Ideal.IsPrime (Submodule.annihilator (Submodule.span R {x}))\n⊢ Submodule... | [
141,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.Symmetrify.lift_unique | [
{
"state_after": "U : Type ?u.8739\nV : Type u_2\nW : Type ?u.8745\ninst✝⁴ : Quiver U\ninst✝³ : Quiver V\ninst✝² : Quiver W\nV' : Type u_1\ninst✝¹ : Quiver V'\ninst✝ : HasReverse V'\nΦ : Symmetrify V ⥤q V'\nhΦinv : ∀ {X Y : Symmetrify V} (f : X ⟶ Y), Φ.map (reverse f) = reverse (Φ.map f)\n⊢ Φ = lift (of ⋙q Φ)",... | [
224,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_sub_of_gt | [
{
"state_after": "α : Type u_1\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p b < multiplicity p a\n⊢ multiplicity p b < multiplicity p a",
"state_before": "α : Type u_1\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p b <... | [
457,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.coe_dualDual | [] | [
956,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.toPlus_naturality | [
{
"state_after": "case w.h\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP✝ : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nx✝ : Cᵒᵖ... | [
234,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Hom.apply_mem_neighborSet | [] | [
1694,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1693,
1
] |
Std/Tactic/Ext.lean | PUnit.ext | [] | [
205,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
205,
18
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_le_of_one_lt | [] | [
672,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_def | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.mapFun.pow | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_2\nS : Type u_1\nT : Type ?u.460757\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.460772\nβ : Type ?u.460775\nf : R →+* S\nx y : 𝕎 R\nn : ℕ\n⊢ mapFun (↑f) (x ^ n) = mapFun (↑f) x ^ n",
... | [
133,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.subset_one_iff | [] | [
138,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.IsSubordinate.mono | [] | [
285,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Products.lean | CategoryTheory.Limits.PreservesProduct.iso_hom | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castLT_succAbove | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nx : Fin n\ny : Fin (n + 1)\nh : ↑castSucc x < y\nh' : optParam (↑(↑(succAbove y) x) < n) (_ : ↑(↑(succAbove y) x) < n)\n⊢ castLT (↑(succAbove y) x) h' = x",
"tactic": "simp only [succAbove_below _ _ h, castLT_castSucc]"
}
] | [
2147,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2145,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_top_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.818755\nβ : Type ?u.818758\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ ENNReal.toNNReal (⊤ * a) = 0",
"tactic": "simp"
}
] | [
2203,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2203,
1
] |
Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.imClm_norm | [
{
"state_after": "no goals",
"state_before": "⊢ 1 = ‖↑imClm I‖",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "⊢ ‖I‖ ≤ 1",
"tactic": "simp"
}
] | [
58,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftOn_div | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nP : Sort v\np q : K[X]\nf : K[X] → K[X] → P\nf0 : ∀ (p : K[X]), f p 0 = f 0 1\nH' : ∀ {p q p' q' : K[X]}, q ≠ 0 → q' ≠ 0 → q' * p = q * p' → f p q = f p' q'\nH :\n optParam (∀ {p q p' q' : K[X]}, q ∈ K[X]⁰ → ... | [
1013,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Analysis/Convex/Normed.lean | convexOn_norm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.38\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\nhs : Convex ℝ s\nx : E\nx✝² : x ∈ s\ny : E\nx✝¹ : y ∈ s\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nx✝ : a + b = 1\n⊢ ‖a • x‖ + ‖b • y‖ = a * ‖x‖ + b * ‖y‖",
"tactic... | [
47,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antitone.monovary | [] | [
329,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
11
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | exists_sum_eq_one_iff_pairwise_coprime' | [
{
"state_after": "case h.e'_2.a\nR : Type u\nI : Type v\ninst✝³ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\ninst✝² : Fintype I\ninst✝¹ : Nonempty I\ninst✝ : DecidableEq I\n⊢ Pairwise (IsCoprime on s) ↔ Pairwise (IsCoprime on fun i => s ↑i)",
"state_before": "R : Type u\nI : Type v\ninst✝³ : CommSe... | [
174,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.tendsto_iff_tendstoUniformly | [] | [
277,
34
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263,
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Mathlib/Algebra/Group/Basic.lean | mul_div_assoc' | [] | [
314,
29
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.braid_natural | [
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Mathlib/Algebra/CharP/Two.lean | CharTwo.add_sq | [] | [
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Mathlib/Data/Nat/Order/Basic.lean | Nat.eq_zero_of_le_half | [] | [
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Mathlib/Algebra/GroupWithZero/Basic.lean | inv_eq_of_mul | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackSymmetry_inv_comp_fst | [
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.mem_comap | [] | [
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Mathlib/Topology/Order/Basic.lean | Monotone.map_iInf_of_continuousAt | [] | [
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.tendsto_nhds_atTop | [
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Mathlib/Data/List/MinMax.lean | List.not_lt_of_mem_argmax | [] | [
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Mathlib/Order/Filter/Pointwise.lean | Filter.pure_div | [] | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Ici | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.X_pow_comp | [
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_isInternal | [
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Mathlib/Logic/Function/Iterate.lean | Function.Surjective.iterate | [] | [
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Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lowerCentralSeries_eq_lcs_comap | [
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Mathlib/Analysis/Calculus/ParametricIntegral.lean | hasDerivAt_integral_of_dominated_loc_of_deriv_le | [
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Mathlib/MeasureTheory/Function/SpecialFunctions/Arctan.lean | Measurable.arctan | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.div | [] | [
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Mathlib/Topology/PathConnected.lean | IsPathConnected.preimage_coe | [
{
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1008,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.le_toIdeal_homogeneousHull | [
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557,
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Mathlib/Data/Quot.lean | Trunc.out_eq | [] | [
580,
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Mathlib/Data/Finset/Prod.lean | Finset.product_eq_biUnion_right | [
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131,
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Mathlib/SetTheory/Game/PGame.lean | PGame.moveRight_neg_symm' | [
{
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Mathlib/Order/Hom/Set.lean | OrderIso.symm_image_image | [] | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.prod_single | [
{
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.lift_word_prod_nontrivial_of_other_i | [
{
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Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.isSymmetric_id | [] | [
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Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCore_zero_mem | [] | [
131,
81
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_restrict | [] | [
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.congr_apply | [] | [
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6
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Mathlib/Data/Prod/Basic.lean | Prod.Lex.refl_right | [] | [
253,
35
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_mul_left_unit | [
{
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Mathlib/Topology/Algebra/Group/Basic.lean | Subgroup.le_topologicalClosure | [] | [
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.funMap_eq_coe_constants | [] | [
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33
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376,
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.mk_coe | [] | [
405,
19
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Mathlib/Order/SupIndep.lean | Finset.supIndep_singleton | [
{
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.ne_zero | [] | [
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_add | [] | [
686,
42
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686,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.continuous_const_section | [
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_comp_self | [
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Mathlib/RingTheory/Noetherian.lean | isNoetherian_iff_wellFounded | [
{
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right | [] | [
906,
65
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901,
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Mathlib/Data/Real/NNReal.lean | NNReal.finset_sup_mul | [] | [
572,
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_le_map_iff_of_injective | [] | [
983,
30
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_eq_lsub' | [] | [
1782,
35
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1780,
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Mathlib/Data/List/Sublists.lean | List.mem_sublistsLen | [] | [
336,
50
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332,
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_le_multiplicity_of_dvd_left | [] | [
334,
84
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332,
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Mathlib/Computability/Primrec.lean | Nat.Primrec.swap' | [
{
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1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inf_subgroupOf_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.292171\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.292180\ninst✝² : AddGroup A\nH✝ K✝ : Subgroup G\nk : Set G\nN : Type ?u.292201\ninst✝¹ : Group N\nP : Type ?u.292207\ninst✝ : Group P\nH K : Subgroup G\n⊢ subgroupOf (K ⊓ H) K = ... | [
1682,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasDerivWithinAt_arcsin_Iic | [
{
"state_after": "case inl\nh : -1 ≠ 1\n⊢ HasDerivWithinAt arcsin (1 / sqrt (1 - (-1) ^ 2)) (Iic (-1)) (-1)\n\ncase inr\nx : ℝ\nh : x ≠ 1\nh' : ¬x = -1\n⊢ HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Iic x) x",
"state_before": "x : ℝ\nh : x ≠ 1\n⊢ HasDerivWithinAt arcsin (1 / sqrt (1 - x ^ 2)) (Iic x) x"... | [
82,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_reindex_right | [] | [
177,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.codisjoint_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.177622\nι : Sort ?u.177625\nκ : ι → Sort ?u.177630\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : UpperSet α\nt t₁ t₂ : UpperSet β\nx : α × β\n⊢ Codisjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Codisjoint s₁ s₂ ∨ Codisjoint t₁ t₂",... | [
1637,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | left_lt_toIocMod | [] | [
103,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
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