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/PNat/Prime.lean | PNat.Coprime.gcd_mul_left_cancel_right | [
{
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"state_before": "m n k : ℕ+\n⊢ Coprime k m → gcd m (k * n) = gcd m n",
"tactic": "intro h"
},
{
"state_after": "m n k : ℕ+\nh : Coprime k m\n⊢ gcd (k * n) m = gcd n m",
"state_before": "m n k : ℕ+\nh : Coprime k m\n⊢ ... | [
220,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.image_sphere | [] | [
1055,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_mul_aux | [
{
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150,
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137,
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Mathlib/Order/UpperLower/Basic.lean | isUpperSet_univ | [] | [
79,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.isNClique_bot_iff | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\nn : ℕ\ns : Finset α\n⊢ Set.Subsingleton ↑s ∧ Finset.card s = n ↔ n ≤ 1 ∧ Finset.card s = n",
"state_before": "α : Type u_1\nG H : SimpleGraph α\nn : ℕ\ns : Finset α\n⊢ IsNClique ⊥ n s ↔ n ≤ 1 ∧ Finset.card s = n",
"tactic": "rw [isNClique_iff, isCliqu... | [
129,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | ContinuousWithinAt.vsub | [] | [
300,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_nat_mod | [
{
"state_after": "ι : Type ?u.876983\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ns : Finset α\nn : ℕ\nf : α → ℕ\n⊢ Multiset.prod (Multiset.map ((fun x => x % n) ∘ fun i => f i) s.val) % n =\n Multiset.prod (Multiset.map (fun i => f i % n) s.val) % n",
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1952,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1950,
1
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_image_continuousLinearMap | [] | [
310,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
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Mathlib/Algebra/Module/Torsion.lean | Submodule.supIndep_torsionBySet_ideal | [
{
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443,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_univ | [] | [
599,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.openEmbedding_coe | [] | [
275,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_cos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx₁ : 0 ≤ x\nhx₂ : x ≤ π\n⊢ arccos (cos x) = x",
"tactic": "rw [arccos, ← sin_pi_div_two_sub, arcsin_sin] <;> simp [sub_eq_add_neg] <;> linarith"
}
] | [
366,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.cancel_right | [] | [
331,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_injective_of_surjective | [] | [
471,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_id | [] | [
2913,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2912,
1
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coeFn_coe | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.int_cast_imK | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_filter | [
{
"state_after": "no goals",
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"tactic": "rw [inter_comm, filter_inter, inter_comm]"
}
] | [
2836,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2835,
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Mathlib/Computability/Primrec.lean | Primrec.option_map₁ | [] | [
639,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Continuous.stronglyMeasurable | [
{
"state_after": "α : Type u_1\nβ✝ : Type ?u.138812\nγ : Type ?u.138815\nι : Type ?u.138818\ninst✝⁵ : Countable ι\nf✝ g : α → β✝\ninst✝⁴ : MeasurableSpace α\ninst✝³ : TopologicalSpace α\ninst✝² : OpensMeasurableSpace α\nβ : Type u_2\ninst✝¹ : TopologicalSpace β\ninst✝ : PseudoMetrizableSpace β\nh : SecondCounta... | [
687,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
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Mathlib/Topology/LocalExtr.lean | IsLocalMin.bicomp_mono | [] | [
279,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
8
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_insert_self | [
{
"state_after": "no goals",
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"tactic": "simp [piece... | [
1364,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_image_of_injOn | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ns t : Set α\na b x y : α\nf : α → β\nH : InjOn f s\nh : Set.Finite s\n⊢ ncard (f '' s) = ncard s\n\ncase inr\nα : Type u_1\nβ : Type u_2\ns t : Set α\na b x y : α\nf : α → β\nH : InjOn f s\nh : Set.Infinite s\n⊢ ncard (f '' s) = ncard s",
"state_before... | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/List/Count.lean | List.countp_map | [
{
"state_after": "α : Type u_2\nl✝ : List α\np✝ q : α → Bool\nβ : Type u_1\np : β → Bool\nf : α → β\na : α\nl : List α\n⊢ (countp (p ∘ f) l + if p (f a) = true then 1 else 0) = countp (p ∘ f) l + if (p ∘ f) a = true then 1 else 0",
"state_before": "α : Type u_2\nl✝ : List α\np✝ q : α → Bool\nβ : Type u_1\np... | [
143,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.as_ideal_lt_as_ideal | [] | [
495,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
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Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_symm_eq | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_bit0_nonneg | [] | [
130,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | ContinuousLinearMap.continuous_det | [
{
"state_after": "𝕜 : Type u\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁵ : AddCommGroup F'\ninst✝⁴ : Module 𝕜 F'\ninst✝³ : TopologicalSpace F'\ninst✝² : To... | [
179,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Analysis/Convex/Segment.lean | segment_eq_image₂ | [
{
"state_after": "no goals",
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68,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/Units.lean | map_units_inv | [] | [
150,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.mem_sphere' | [] | [
103,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_congr | [
{
"state_after": "α : Type u\nm : ℕ\nf : Fin m → α\n⊢ ofFn f = ofFn fun i => f (↑(Fin.cast (_ : m = m)) i)",
"state_before": "α : Type u\nm n : ℕ\nh : m = n\nf : Fin m → α\n⊢ ofFn f = ofFn fun i => f (↑(Fin.cast (_ : n = m)) i)",
"tactic": "subst h"
},
{
"state_after": "no goals",
"state_bef... | [
107,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.le_measure_liminf_of_limsup_measure_compl_le | [] | [
135,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.ConeMorphism.ext | [
{
"state_after": "case mk\nJ : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u₃\ninst✝¹ : Category C\nD : Type u₄\ninst✝ : Category D\nF : J ⥤ C\nc c' : Cone F\ng : c ⟶ c'\nHom✝ : c.pt ⟶ c'.pt\nw✝ : ∀ (j : J), Hom✝ ≫ c'.π.app j = c.π.app j\nw : (mk Hom✝).Hom = g.Hom\n⊢ mk Hom✝ = g",
... | [
306,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.comp_apply | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.preimage_iUnion₂ | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1721,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.mul_apply | [] | [
1240,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
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Mathlib/Data/Fintype/Card.lean | Fintype.card_range_le | [
{
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"tactic": "simp"
},
{
"state_... | [
491,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_le_cancelAux | [
{
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"tactic": "assumption"
},
{
"state_after": "case succ\nctx : Context\nfuel : Nat\nih :\n ∀... | [
461,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
429,
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Mathlib/Analysis/Convex/Function.lean | LinearMap.convexOn | [
{
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361,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measurePreserving_mul_left | [] | [
131,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Data/Sum/Order.lean | OrderIso.sumLexDualAntidistrib_symm_inr | [] | [
730,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
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] |
Mathlib/Order/Chain.lean | IsChain.mono | [] | [
76,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
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Mathlib/Topology/Basic.lean | monotone_closure | [] | [
464,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/List/Lattice.lean | List.mem_inter | [
{
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"tactic": "erw [mem_filter]"
... | [
167,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Data/Finset/Card.lean | Finset.card_erase_le | [] | [
150,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.ennreal_toReal | [] | [
1923,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1921,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.ne_infty_iff_exists | [
{
"state_after": "no goals",
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"tactic": "induction x using OnePoint.rec <;> simp"
}
] | [
148,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/LinearAlgebra/Finrank.lean | linearIndependent_of_top_le_span_of_card_eq_finrank | [
{
"state_after": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\nι : Type u_1\ninst✝ : Fintype ι\nb : ι → V\nspans : ⊤ ≤ span K (Set.range b)\ncard_eq : Fintype.card ι = finrank K V\ns : Finset ι\ng : ι → K\ndependent : (Finset.sum s fun i => g i • b i) = 0\ni : ι... | [
418,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.snd_mem_support_of_mem_edges | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nt u v w : V\np : Walk G v w\nhe : Quotient.mk (Sym2.Rel.setoid V) (u, t) ∈ edges p\n⊢ u ∈ support p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : Simple... | [
810,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_zero | [] | [
535,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.sbtw_secondInter | [
{
"state_after": "case refine'_1\nV : 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\nhp : p ∈ s\nhp' : dist p' s.center < s.radius\n⊢ p' ≠ p\n\ncase refine'_2\nV : Type u_2\nP : Type u_1\ninst✝³ ... | [
186,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_inv | [] | [
259,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.conj_eqToHom_iff_hEq | [
{
"state_after": "case refl\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nW X Z : C\nf : W ⟶ X\nh' : X = Z\ng : W ⟶ Z\n⊢ f = eqToHom (_ : W = W) ≫ g ≫ eqToHom (_ : Z = X) ↔ HEq f g",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nW X Y Z : C\nf : W ... | [
196,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.smul_monomial | [] | [
286,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_eq_card_fintype | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ (Fintype.card ↑fun x => x < n ∧ p x) = Fintype.card { k // k < n ∧ p k }",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p n = Fintype.card { k // k < n ∧ p k }",
"tactic": "rw [count_eq_card_filter_range, ← Finty... | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Regular/Pow.lean | IsRegular.pow | [] | [
45,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_le_iff_mul_self_le | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a ≤ abs b ↔ abs a * abs a ≤ abs b * abs b",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a ≤ abs b ↔ a * a ≤ b * b",
"tactic": "rw [← abs_mul_abs_self, ← abs_mul_abs_self b]"
},
{
"state... | [
98,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_one | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_congr | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.17877\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ : Finset β\nf✝ f g : β → α\nhfg : ∀ (a : β), a ∈ s₁ → f a = g a\n⊢ gcd s₁ f = gcd s₁ g",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.17877\ninst✝¹ : CancelCo... | [
195,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.range_coe | [] | [
829,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Data/Part.lean | Part.div_get_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.65716\nγ : Type ?u.65719\ninst✝ : Div α\na b : Part α\nhab : (a / b).Dom\n⊢ get (Part.bind a fun y => map (fun x => y / x) b) (_ : (Part.bind a fun y => map (fun x => y / x) b).Dom) =\n get a (_ : a.Dom) / get b (_ : b.Dom)",
"state_before": "α : Type u_1\nβ : ... | [
775,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Order/Filter/Archimedean.lean | tendsto_rat_cast_atBot_iff | [
{
"state_after": "α : Type u_2\nR : Type u_1\ninst✝¹ : LinearOrderedField R\ninst✝ : Archimedean R\nf : α → ℚ\nl : Filter α\n⊢ Tendsto (fun n => ↑(f n)) l atBot ↔ Tendsto (Rat.cast ∘ f) l atBot",
"state_before": "α : Type u_2\nR : Type u_1\ninst✝¹ : LinearOrderedField R\ninst✝ : Archimedean R\nf : α → ℚ\nl ... | [
95,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/List/Basic.lean | List.monotone_filter_right | [
{
"state_after": "case nil\nι : Type ?u.380416\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np✝ p q : α → Bool\nh : ∀ (a : α), p a = true → q a = true\n⊢ filter p [] <+ filter q []\n\ncase cons\nι : Type ?u.380416\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np✝ p q : α → B... | [
3582,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3570,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | tendsto_zpow_atTop_atTop | [
{
"state_after": "case intro\n𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\nn : ℕ\nhn : 0 < ↑n\n⊢ Tendsto (fun x => x ^ ↑n) atTop atTop",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\nn : ℤ\nhn : 0 < n\n⊢ Tendsto (fun x => x ^ n) atTop atTop",
"tactic": "lift n to ℕ using hn.le"
},
... | [
62,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_inter_Ici | [] | [
639,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_iUnion | [] | [
440,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_mk' | [] | [
503,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/Filter/Archimedean.lean | tendsto_int_cast_atBot_iff | [
{
"state_after": "α : Type u_2\nR : Type u_1\ninst✝¹ : StrictOrderedRing R\ninst✝ : Archimedean R\nf : α → ℤ\nl : Filter α\n⊢ Tendsto (fun n => ↑(f n)) l atBot ↔ Tendsto (Int.cast ∘ f) l atBot",
"state_before": "α : Type u_2\nR : Type u_1\ninst✝¹ : StrictOrderedRing R\ninst✝ : Archimedean R\nf : α → ℤ\nl : ... | [
66,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_one | [] | [
60,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/Basic.lean | continuous_iff_ultrafilter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.171379\nδ : Type ?u.171382\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\n⊢ Continuous f ↔ ∀ (x : α) (g : Ultrafilter α), ↑g ≤ 𝓝 x → Tendsto f (↑g) (𝓝 (f x))",
"tact... | [
1733,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_comap | [] | [
262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_iSup_map_of_injective | [] | [
420,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.ext_iff | [] | [
1334,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
] |
Mathlib/Combinatorics/Hindman.lean | Hindman.FP.mul | [
{
"state_after": "case head\nM : Type u_1\ninst✝ : Semigroup M\na✝ : Stream' M\nm : M\na : Stream' M\n⊢ ∃ n, ∀ (m' : M), m' ∈ FP (Stream'.drop n a) → Stream'.head a * m' ∈ FP a\n\ncase tail\nM : Type u_1\ninst✝ : Semigroup M\na✝ : Stream' M\nm✝ : M\na : Stream' M\nm : M\nhm : FP (Stream'.tail a) m\nih : ∃ n, ∀ ... | [
134,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_eq | [] | [
70,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_monic_ne_zero | [] | [
868,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.toNFA_correct | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Finset/Lattice.lean | Multiset.map_finset_sup | [] | [
1742,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1740,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_quotientMap | [] | [
125,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.coinduced_eq | [] | [
242,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.gcd_map_mul | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\na : α\ns : Multiset α\n⊢ gcd (map ((fun x x_1 => x * x_1) a) 0) = ↑normalize a * gcd 0\n\ncase refine'_2\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\na : α\ns... | [
193,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.one | [
{
"state_after": "R : Type u_1\nS : Type ?u.8602\nM : Type u_2\na✝ b✝ : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\na b : M\nab : 1 • a = 1 • b\n⊢ a = b",
"state_before": "R : Type u_1\nS : Type ?u.8602\nM : Type u_2\na✝ b✝ : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\na b : M\nab : (fun x =... | [
141,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.univ_mul_univ | [] | [
948,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Topology/Algebra/Module/LocallyConvex.lean | Disjoint.exists_open_convexes | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁶ : LinearOrderedField 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : TopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : LocallyConvexSpace 𝕜 E\ns t : Set E\ndisj : Disjoint s t\nhs₁ : Convex 𝕜 s\nhs₂ ... | [
145,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.natDegree_multiset_sum_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\nS : Type u_1\ninst✝ : Semiring S\nl : Multiset S[X]\n⊢ ∀ (a : List S[X]),\n natDegree (Multiset.sum (Quotient.mk (List.isSetoid S[X]) a)) ≤\n foldr max (_ : ∀ (a b c : ℕ), max a (max b c) = max b (max a c)) 0\n ... | [
57,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_quadratic_lt | [] | [
1180,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_le_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.23021\nι : Type ?u.23024\ninst✝ : PseudoMetricSpace α\nx y : α\nr : ℝ\nhr : 0 ≤ r\n⊢ edist x y ≤ ENNReal.ofReal r ↔ dist x y ≤ r",
"tactic": "rw [edist_dist, ENNReal.ofReal_le_ofReal_iff hr]"
}
] | [
377,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.range_fst | [] | [
1246,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.centroid_eq_iff | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : CharZero k\nn : ℕ\ns : Simplex k P n\nfs₁ fs₂ : Finset (Fin (n + 1))\nm₁ m₂ : ℕ\nh₁ : Finset.card fs₁ = m₁ + 1\nh₂ : Finset.card fs₂ = m₂ + 1\nh : ... | [
952,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.comp_update | [] | [
663,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_smul_smul_comm | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.11403\nN : Type ?u.11406\nG : Type ?u.11409\nA : Type ?u.11412\nB : Type ?u.11415\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\ninst✝⁷ : SMul α β\ninst✝⁶ : SMul α γ\ninst✝⁵ : SMul β δ\ninst✝⁴ : SMul α δ\ninst✝³ : SMul γ δ\ninst✝² : IsScala... | [
428,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Multiset.Nat.antidiagonalTuple_zero_succ | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_sdiff_sub | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_2\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.117278\ns₂✝ : Finset ι₂\ninst✝ : DecidableEq ι\ns₂ : Finset ι\nh : s₂ ⊆ s\nw : ι → k\np : ι → P... | [
221,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.toContinuousLinearMap_inj | [] | [
353,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.evalList_sort_cons | [
{
"state_after": "α : Sort u_1\nctx : Context α\nh : IsCommutative ctx.op\nx : Nat\nxs : List Nat\n⊢ evalList α ctx (sort.loop (insert x []) xs) = evalList α ctx (x :: sort.loop [] xs)",
"state_before": "α : Sort u_1\nctx : Context α\nh : IsCommutative ctx.op\nx : Nat\nxs : List Nat\n⊢ evalList α ctx (sort ... | [
247,
37
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
225,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Subsemigroup.centralizer_univ | [] | [
214,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.uncurry_curry | [] | [
158,
26
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map.isMaximal | [
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Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.upper_two_blockTriangular | [
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147,
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144,
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