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/Sym/Sym2.lean | Sym2.map_id' | [] | [
417,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.log_two_mul_two_le_sqrt_log_eight | [
{
"state_after": "α : Type ?u.611385\nβ : Type ?u.611388\nn d k N : ℕ\nx : Fin n → ℕ\nthis : 8 = 2 ^ ↑3\n⊢ log 2 * 2 ≤ Real.sqrt (log 8)",
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"tactic": "have : (8 : ℝ) = 2 ^ ((3 : ℕ) : ℝ) ... | [
300,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.neg_linear | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | Antitone.vecCons | [] | [
85,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Data/Pi/Algebra.lean | Pi.apply_mulSingle₂ | [
{
"state_after": "case pos\nI : Type u\nα : Type ?u.15668\nβ : Type ?u.15671\nγ : Type ?u.15674\nf : I → Type v₁\ng : I → Type v₂\nh✝ : I → Type v₃\nx✝ y✝ : (i : I) → f i\ni✝ : I\ninst✝³ : DecidableEq I\ninst✝² : (i : I) → One (f i)\ninst✝¹ : (i : I) → One (g i)\ninst✝ : (i : I) → One (h✝ i)\nf' : (i : I) → f i... | [
301,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
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Mathlib/Order/CompleteLattice.lean | iInf₂_mono' | [] | [
877,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
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Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_nsmul | [
{
"state_after": "no goals",
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"tactic": "contradiction"
},
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.448176\nγ : Type ?u.4481... | [
3167,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3162,
1
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Mathlib/Algebra/Algebra/Basic.lean | Algebra.linearMap_apply | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/Deprecated/Subgroup.lean | Group.conjugatesOfSet_subset_normalClosure | [] | [
704,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
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Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.inf_dom_right | [] | [
1392,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.subtype_coe | [] | [
1100,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.pos_add_zero_add_neg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.482840\nγ : Type ?u.482843\nδ : Type ?u.482846\ninst✝² : AddCommGroup α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalAddGroup α\nf✝ g✝ : β → α\na a₁ a₂ b : α\nf : ℤ → α\nhpos : HasSum (fun n => f (↑n + 1)) a\nhneg : HasSum (fun n => f (-↑(Nat.succ n))) b\ng : ℕ → ... | [
1028,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_lt | [
{
"state_after": "case zero\nR : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhgt : ¬map f p ≤ P ^ Nat.zero\n⊢ ramificationIdx f p P < Nat.zero\n\ncase succ\nR : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Idea... | [
109,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Matrix/DMatrix.lean | DMatrix.ext | [] | [
46,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/List/Zip.lean | List.get_zipWith | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.159788\nε : Type ?u.159791\nf : α → β → γ\nl : List α\nl' : List β\ni : Fin (length (zipWith f l l'))\n⊢ ∃ x y,\n get? l ↑i = some x ∧\n get? l' ↑i = some y ∧\n f x y =\n f (get l { val := ↑i, isLt := (_ : ↑i < length ... | [
407,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
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Mathlib/Computability/Primrec.lean | Nat.Primrec'.add | [
{
"state_after": "v : Vector ℕ (Nat.succ 0 + 1)\n⊢ Nat.rec (Vector.head (Vector.tail v)) (fun y IH => Nat.succ IH) (Vector.head v) =\n Vector.head v + Vector.head (Vector.tail v)",
"state_before": "v : Vector ℕ (Nat.succ 0 + 1)\n⊢ Nat.rec (Vector.head (Vector.tail v)) (fun y IH => Nat.succ (Vector.head (... | [
1456,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.toInductiveLimit_isometry | [
{
"state_after": "X : ℕ → Type u\ninst✝ : (n : ℕ) → MetricSpace (X n)\nf : (n : ℕ) → X n → X (n + 1)\nI : ∀ (n : ℕ), Isometry (f n)\nn : ℕ\nx y : X n\n⊢ inductiveLimitDist f { fst := n, snd := x } { fst := n, snd := y } = dist x y",
"state_before": "X : ℕ → Type u\ninst✝ : (n : ℕ) → MetricSpace (X n)\nf : (... | [
634,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_eq_top | [] | [
1408,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsEulerian.edgesFinset_eq | [
{
"state_after": "case a\nV : Type u_1\nG : SimpleGraph V\ninst✝¹ : DecidableEq V\ninst✝ : Fintype ↑(edgeSet G)\nu v : V\np : Walk G u v\nh : IsEulerian p\ne : Sym2 V\n⊢ e ∈ IsTrail.edgesFinset (_ : IsTrail p) ↔ e ∈ edgeFinset G",
"state_before": "V : Type u_1\nG : SimpleGraph V\ninst✝¹ : DecidableEq V\nins... | [
134,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Order/Basic.lean | Eq.ge | [] | [
235,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
11
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_vsub_right_image | [] | [
713,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_le | [] | [
337,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrFilter.congr | [
{
"state_after": "α✝ : Type u\nβ✝ : Type v\nγ : Type w\nδ : Type x\nα : Type u_1\nβ : Type u_2\ninst✝ : Preorder β\nf g : α → β\na : α\nl : Filter α\nh : IsMinFilter f l a ∨ IsMaxFilter f l a\nheq : f =ᶠ[l] g\nhfga : f a = g a\n⊢ IsMinFilter g l a ∨ IsMaxFilter g l a",
"state_before": "α✝ : Type u\nβ✝ : Typ... | [
674,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_comap | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Topology/MetricSpace/Polish.lean | TopologicalSpace.Opens.CompleteCopy.dist_eq | [] | [
274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x 0 = 0",
"tactic": "simp [eval₂_eq_sum]"
}
] | [
69,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.sum_biUnion_boxes | [
{
"state_after": "ι : Type u_2\nI J J₁✝ J₂✝ : Box ι\nπ✝ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi✝ πi₁ πi₂ : (J : Box ι) → Prepartition J\nM : Type u_1\ninst✝ : AddCommMonoid M\nπ : Prepartition I\nπi : (J : Box ι) → Prepartition J\nf : Box ι → M\nJ₁ : Box ι\nh₁ : J₁ ∈ ↑π.boxes\nJ₂ : Box ι\nh₂ : J₂ ∈ ↑π.boxes\nhne ... | [
354,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.ext_iff' | [] | [
235,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullback_snd_image_fst_preimage | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\nU : Set ↑X\nx : (forget TopCat).obj Y\n⊢ x ∈ (forget TopCat).map pullback.snd '' ((forget TopCat).map pullback.fst ⁻¹' U) ↔\n x ∈ (forget TopCat).map g ⁻¹' ((forget TopCat).map f '' U)",
"state_before": "... | [
382,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Real/Irrational.lean | Nat.not_irrational | [] | [
192,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_monotone_left | [
{
"state_after": "x✝ x y : ℝ\nh : x ≤ y\nn : ℕ\n⊢ sqrt (2 + sqrtTwoAddSeries x n) ≤ sqrt (2 + sqrtTwoAddSeries y n)",
"state_before": "x✝ x y : ℝ\nh : x ≤ y\nn : ℕ\n⊢ sqrtTwoAddSeries x (n + 1) ≤ sqrtTwoAddSeries y (n + 1)",
"tactic": "rw [sqrtTwoAddSeries, sqrtTwoAddSeries]"
},
{
"state_after":... | [
722,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_tail | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns : Heap α\nh : NoSibling s\n⊢ size (Option.getD (tail? le s) nil) = size s - 1",
"state_before": "α : Type u_1\nle : α → α → Bool\ns : Heap α\nh : NoSibling s\n⊢ size (tail le s) = size s - 1",
"tactic": "simp only [Heap.tail]"
},
{
"state_afte... | [
153,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
149,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.range_coe | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : PartialOrder α\na b : α\nx : WithTop α\n⊢ x ∈ range some ↔ x ∈ Iio ⊤",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ range some = Iio ⊤",
"tactic": "ext x"
},
{
"state_after": "case h\nα : Type u_1\ninst✝ : PartialOrder α\na b :... | [
36,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.succ_def | [] | [
805,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.iUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\nι : Type u_1\ns : ι → Set α\nt : Set ι\nht : Set.Finite t\nhs : ∀ (i : ι), i ∈ t → Set.Finite (s i)\nhe : ∀ (i : ι), ¬i ∈ t → s i = ∅\n⊢ (⋃ (i : ι), s i) ⊆ ⋃ (i : ι) (_ : i ∈ t), s i",
"state_before": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ ... | [
817,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_one | [] | [
258,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
11
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.tendsto_nhds_left | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.196937\ninst✝ : UniformSpace α\nf : Filter β\nu : β → α\na : α\n⊢ Tendsto ((fun y => (y, a)) ∘ u) f (𝓤 α) ↔ Tendsto (fun x => (u x, a)) f (𝓤 α)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ... | [
1920,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1918,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_lt | [] | [
453,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_inter_gt | [] | [
407,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Algebra/Parity.lean | Odd.add_odd | [
{
"state_after": "case intro.intro\nF : Type ?u.83706\nα : Type u_1\nβ : Type ?u.83712\nR : Type ?u.83715\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n : α\n⊢ Even (2 * m + 1 + (2 * n + 1))",
"state_before": "F : Type ?u.83706\nα : Type u_1\nβ : Type ?u.83712\nR : Type ?u.83715\ninst✝¹ : Semiring α\ninst✝ :... | [
344,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Option/Basic.lean | Option.casesOn'_some | [] | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_Ioi | [
{
"state_after": "case h\nF : Type ?u.72433\nα : Type u_1\nβ : Type ?u.72439\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn : ℕ\na : α\nha : 0 ≤ a\nx✝ : ℕ\n⊢ x✝ ∈ Nat.cast ⁻¹' Ioi a ↔ x✝ ∈ Ioi ⌊a⌋₊",
"state_before": "F : Type ?u.72433\nα : Type u_1\nβ : Type ?u.72439\ninst✝¹ : LinearO... | [
414,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_Iic_sub_Iic | [
{
"state_after": "case inr\nι : Type ?u.16200147\n𝕜 : Type ?u.16200150\nE : Type u_1\nF : Type ?u.16200156\nA : Type ?u.16200159\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nha : IntegrableOn f (Iic a)\nhb : Integrable... | [
967,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
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Mathlib/Logic/Basic.lean | cast_eq_iff_heq | [
{
"state_after": "case refl\na✝ : Sort u_1\na : a✝\ne : a✝ = a✝\n⊢ cast e a = a",
"state_before": "a✝¹ a✝ : Sort u_1\ne : a✝¹ = a✝\na : a✝¹\na' : a✝\nh : HEq a a'\n⊢ cast e a = a'",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "case refl\na✝ : Sort u_1\na : a✝\ne : a✝ ... | [
556,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumDiffSubset_symm_apply_of_not_mem | [
{
"state_after": "case a\nα✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u_1\ns t : Set α\nh : s ⊆ t\ninst✝ : DecidablePred fun x => x ∈ s\nx : ↑t\nhx : ¬↑x ∈ s\n⊢ ↑(Set.sumDiffSubset h) (↑(Set.sumDiffSubset h).symm x) =\n ↑(Set.sumDiffSubset h) (Sum.inr { val := ↑x, property := (_ : ↑x ∈ t ∧ ¬↑x ∈ s) })",
... | [
390,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.sum_nat_mod | [
{
"state_after": "no goals",
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"tactic": "induction s using Multiset.induction <;> simp [Nat.add_mod, *]"
}
] | [
528,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.cylinder_longestPrefix_eq_of_longestPrefix_lt_firstDiff | [
{
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593,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.coprod_inr | [
{
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230,
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229,
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Mathlib/RingTheory/TensorProduct.lean | TensorProduct.AlgebraTensorModule.ext | [] | [
113,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | linearIndependent_set_iff_affineIndependent_vadd_union_singleton | [
{
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"state_before": "k... | [
178,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/LinearAlgebra/DirectSum/TensorProduct.lean | TensorProduct.directSum_lof_tmul_lof | [
{
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158,
33
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155,
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_eq_top_iff | [
{
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461,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
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Mathlib/Order/MinMax.lean | le_of_max_le_right | [] | [
284,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/Algebra/MonoidAlgebra/Support.lean | AddMonoidAlgebra.support_mul_single | [] | [
131,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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src/lean/Init/Data/Nat/Div.lean | Nat.div_add_mod | [
{
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},
{
"state_after": "m n : Nat\nh : Decidable (0 < n ∧ n ≤ m)\n⊢ n * ite (0 < n ∧ n ≤ m) ... | [
175,
46
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166,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_neg_of_pi_div_two_lt_of_lt | [
{
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},
{
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] | [
479,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.card_eq_sum_ones | [
{
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}
] | [
1754,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1753,
1
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Mathlib/Data/Finset/Sups.lean | Finset.disjSups_right_comm | [
{
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}
] | [
550,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
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Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.isIso_toPlus_of_isSheaf | [
{
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296,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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Mathlib/Data/Sign.lean | SignType.nonpos_iff_ne_one | [
{
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}
] | [
180,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Order/Circular.lean | Set.left_mem_cIcc | [] | [
365,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Std/Data/List/Basic.lean | List.replace_eq_replaceTR | [
{
"state_after": "case h.h.h.h.h\nα : Type u_1\nx✝ : BEq α\nl : List α\nb c : α\n⊢ replace l b c = replaceTR l b c",
"state_before": "⊢ @replace = @replaceTR",
"tactic": "funext α _ l b c"
},
{
"state_after": "case h.h.h.h.h\nα : Type u_1\nx✝ : BEq α\nl : List α\nb c : α\n⊢ replace l b c = repla... | [
127,
44
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118,
10
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_le_iff_le_coe | [] | [
674,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
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Mathlib/CategoryTheory/Limits/MonoCoprod.lean | CategoryTheory.Limits.MonoCoprod.mk' | [
{
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"state_before": "C : Type u_1\ninst... | [
91,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Topology/Instances/EReal.lean | EReal.nhds_bot_basis | [
{
"state_after": "α : Type ?u.14563\ninst✝ : TopologicalSpace α\nx : EReal\nhx : ⊥ < x\n⊢ ∃ i', True ∧ Iio ↑i' ⊆ Iio x",
"state_before": "α : Type ?u.14563\ninst✝ : TopologicalSpace α\n⊢ HasBasis (𝓝 ⊥) (fun x => True) fun x => Iio ↑x",
"tactic": "refine nhds_bot_basis.to_hasBasis (fun x hx => ?_) fun _... | [
161,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.salient_positive | [] | [
593,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_iInter_cthickening | [
{
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"state_before": "ι : Sort ?u.141178\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t ... | [
1317,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1313,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_right_inj | [] | [
845,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.param_inv_mul | [] | [
279,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_mono_ae_restrict | [
{
"state_after": "ι : Type ?u.20977613\n𝕜 : Type ?u.20977616\nE : Type ?u.20977619\nF : Type ?u.20977622\nA : Type ?u.20977625\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → ℝ\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhab : a ≤ b\nhf : IntervalIntegrable f μ a b\nhg :... | [
1386,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
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Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_natCast | [] | [
203,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_pred_of_lt | [] | [
124,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.iSup_induction' | [
{
"state_after": "ι : Sort u_2\nM : Type u_1\nA : Type ?u.9929\nB : Type ?u.9932\ninst✝ : Mul M\nS : ι → Subsemigroup M\nC : (x : M) → (x ∈ ⨆ (i : ι), S i) → Prop\nhp : ∀ (i : ι) (x : M) (hxS : x ∈ S i), C x (_ : x ∈ ⨆ (i : ι), S i)\nhmul :\n ∀ (x y : M) (hx : x ∈ ⨆ (i : ι), S i) (hy : y ∈ ⨆ (i : ι), S i),\n ... | [
145,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.MulEtransform.card | [
{
"state_after": "no goals",
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181,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
11
] |
Mathlib/Data/Set/Basic.lean | Set.singleton_inter_eq_empty | [] | [
1346,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.prod.of | [] | [
914,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.cons_injective_right | [] | [
109,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.teichmuller_mul_aux₂ | [
{
"state_after": "p : ℕ\nR : Type u_1\nS : Type ?u.90078\nhp : Fact (Nat.Prime p)\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nx y : MvPolynomial R ℤ\n⊢ ↑(map (MvPolynomial.map (Int.castRingHom ℚ))) (teichmullerFun p (x * y)) =\n ↑(map (MvPolynomial.map (Int.castRingHom ℚ))) (teichmullerFun p x * teichmullerFun... | [
95,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
9
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.erase_aux | [
{
"state_after": "case nil\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\na₁ : WithBot α\na₂ : WithTop α\nh : Valid' a₁ nil a₂\n⊢ Valid' a₁ nil a₂",
"state_before": "case nil\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\na₁ : Wit... | [
1632,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/Data/Finsupp/BigOperators.lean | Multiset.support_sum_subset | [
{
"state_after": "case h\nι : Type u_2\nM : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : AddCommMonoid M\na✝ : List (ι →₀ M)\n⊢ (sum (Quot.mk Setoid.r a✝)).support ⊆ sup (map Finsupp.support (Quot.mk Setoid.r a✝))",
"state_before": "ι : Type u_2\nM : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : AddCommMonoid M\ns... | [
54,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.coeff_natTrailingDegree_pred_eq_zero | [] | [
283,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | nhds_mul_nhds_one | [] | [
162,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.hasBasis_symmetric | [] | [
546,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_add_sub_eq_zero_iff | [
{
"state_after": "𝕜 : Type ?u.3117342\nE : Type ?u.3117345\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\n⊢ inner (x + y) (x - y) = 0 ↔ ‖x‖ * ‖x‖ = ‖y‖ * ‖y‖",
"... | [
1522,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.trunc_C | [
{
"state_after": "R : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\na : R\nm : ℕ\n⊢ (if m < n + 1 then if m = 0 then a else 0 else 0) = if m = 0 then a else 0",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\na : R\nm : ℕ\n⊢ Polynomial.coeff (trunc (n + 1) (↑(C R) a)) m = Polynomial.coeff (↑Polynom... | [
1841,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1838,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | Path.continuous_delayReflRight | [] | [
252,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.abs_re_div_norm_le_one | [
{
"state_after": "K : Type u_1\nE : Type ?u.6892273\ninst✝ : IsROrC K\nz : K\n⊢ abs (↑re z) / ‖z‖ ≤ 1",
"state_before": "K : Type u_1\nE : Type ?u.6892273\ninst✝ : IsROrC K\nz : K\n⊢ abs (↑re z / ‖z‖) ≤ 1",
"tactic": "rw [abs_div, abs_norm]"
},
{
"state_after": "no goals",
"state_before": "K... | [
753,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Computability/Partrec.lean | Nat.rfindOpt_mono | [
{
"state_after": "α : Type u_1\nf : ℕ → Option α\nH : ∀ {a : α} {m n : ℕ}, m ≤ n → a ∈ f m → a ∈ f n\na : α\nx✝ : ∃ n, a ∈ f n\nn : ℕ\nh : a ∈ f n\nh' : (rfindOpt f).Dom\n⊢ a ∈ rfindOpt f",
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155,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.mul_right | [] | [
102,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.of_iso | [
{
"state_after": "case refine'_1\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\nX Y : C\nhY : IsZero Y\ne : X ≅ Y\nZ : C\nf : X ⟶ Z\n⊢ f = default\n\ncase refine'_2\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\nX Y : C\nhY : IsZero Y\ne : X ≅ Y\nZ : C\nf : Z ⟶ X\n⊢ f = d... | [
128,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Analysis/Convex/Hull.lean | AffineMap.image_convexHull | [
{
"state_after": "case h₁\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nf : E →ᵃ[𝕜] F\n⊢ ↑f '' ↑(convexHull 𝕜).toOrderHom s ⊆ ↑(convexHull 𝕜).toOrderHom (↑f '' s)\n\ncase h₂\n𝕜 : Ty... | [
214,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Std/Data/List/Lemmas.lean | List.length_iota | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ length (iota n) = n",
"tactic": "simp [iota_eq_reverse_range']"
}
] | [
1936,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1936,
9
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.cast_eq_iff_heq | [
{
"state_after": "α✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Sort u_1\na b : α\n⊢ ↑(Equiv.cast (_ : α = α)) a = b ↔ HEq a b",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα β : Sort u_1\nh : α = β\na : α\nb : β\n⊢ ↑(Equiv.cast h) a = b ↔ HEq a b",
"tactic": "subst h"
},
{
"state_after": ... | [
327,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_eq_C | [] | [
1395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1394,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.arrow_iso_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.16029\ninst✝ : Category D\nP : MorphismProperty C\nhP : RespectsIso P\nf g : Arrow C\ne : f ≅ g\n⊢ P f.hom ↔ P g.hom",
"tactic": "rw [← Arrow.inv_left_hom_right e.hom, hP.cancel_left_isIso, hP.cancel_right_isIso]"... | [
166,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Complex/ExponentialBounds.lean | Real.exp_neg_one_gt_d9 | [
{
"state_after": "⊢ exp 1 < 0.36787944116⁻¹\n\n\n⊢ 0 < 0.36787944116",
"state_before": "⊢ 0.36787944116 < exp (-1)",
"tactic": "rw [exp_neg, lt_inv _ (exp_pos _)]"
},
{
"state_after": "⊢ 1 / 10 ^ 10 + 2244083 / 825552 < 0.36787944116⁻¹\n\n\n⊢ 0 < 0.36787944116",
"state_before": "⊢ exp 1 < 0.... | [
50,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.cosh | [] | [
862,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_addSubmonoid_closure | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\ns : Set R\nx : R\n⊢ x ∈ closure ↑(AddSubmonoid.closure s) ↔ x ∈ closure s",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonAs... | [
913,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.getVert_length | [] | [
232,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "d : ℤ\nx : ℤ√d\nh : Int.natAbs (norm x) = 1\nhx : 0 ≤ norm x\n⊢ 1 = x * star x",
"tactic": "rwa [← Int.coe_nat_inj', Int.natAbs_of_nonneg hx, ← @Int.cast_inj (ℤ√d) _ _,\n norm_eq_mul_conj, eq_comm] at h"
},
{
"state_after": "no goals",
"state_be... | [
600,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
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