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/Order/Filter/Basic.lean | Set.PairwiseDisjoint.exists_mem_filter | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.89945\nι✝ : Sort x\nf g : Filter α\ns t✝ : Set α\nι : Type u_1\nl : ι → Filter α\nt : Set ι\nhd : PairwiseDisjoint t l\nht : Set.Finite t\nthis : Finite ↑t\n⊢ ∃ s, (∀ (i : ι), s i ∈ l i) ∧ PairwiseDisjoint t s",
"state_before": "α : Type u\nβ... | [
749,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_one_sub_of_lt | [
{
"state_after": "K : Type ?u.2424657\nF : Type ?u.2424660\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.2424672\nΓ''₀ : Type ?u.2424675\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx y z : R\nh : ↑v (-x) <... | [
348,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_eq_multiplicity_X | [
{
"state_after": "case inl\nR✝ : Type ?u.4264976\ninst✝¹ : Semiring R✝\nφ : PowerSeries R✝\nR : Type u_1\ninst✝ : Semiring R\n⊢ order 0 = multiplicity X 0\n\ncase inr\nR✝ : Type ?u.4264976\ninst✝¹ : Semiring R✝\nφ✝ : PowerSeries R✝\nR : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nhφ : φ ≠ 0\n⊢ order φ = mu... | [
2473,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2454,
1
] |
Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.coe_top | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_vecMul_equiv | [] | [
2515,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2512,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_eq_foldl | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3031\nα : Type ?u.3034\nβ : Type ?u.3037\nγ : Type ?u.3040\ninst✝ : CommMonoid α\ns✝ t : Multiset α\na : α\nm : Multiset ι\nf g : ι → α\ns : Multiset α\nx y z : α\n⊢ (fun x x_1 => x * x_1) ((fun x x_1 => x * x_1) x y) z = (fun x x_1 => x * x_1) ((fun... | [
62,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_ulift | [] | [
108,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.pair_inj | [] | [
1335,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_Ioo_of_ae_eq | [] | [
153,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.size_eq_natSize | [] | [
759,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.self_sub_floor | [] | [
807,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.smul_tprod_one_asModule | [
{
"state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\ninst✝¹ : AddCommMonoid W\ninst✝ : Module k W\nρV : Representation k G V\nρW : Representation k G W\nr : MonoidAlgebra k G\nx : V\ny : W\n⊢ ↑(↑(asAl... | [
384,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Topology/Separation.lean | isOpen_iff_ultrafilter' | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : T2Space α\nf : Filter α\ninst✝ : CompactSpace α\nU : Set α\n⊢ (∀ (x : α), x ∈ U → ∀ (l : Ultrafilter α), ↑l ≤ 𝓝 x → U ∈ l) ↔ ∀ (F : Ultrafilter α), Ultrafilter.lim F ∈ U → U ∈ ↑F",
"state_before": "α : Type u\nβ : Type v\ninst✝... | [
1052,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.dist_reflection | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np₁ p₂ : P\n⊢ dist (↑(reflection s) (↑(refle... | [
621,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.Equivalent.pi | [] | [
149,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBounded.isBoundedUnder | [] | [
123,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/Category/FinPartOrd.lean | FinPartOrd.coe_of | [] | [
59,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | normUnit_one | [] | [
97,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_surjective | [] | [
121,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_congr | [] | [
2123,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2122,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.injective_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.84683\ninst✝¹ : CommSemigroup α\ninst✝ : PartialOrder α\na : α\nha : MulLECancellable a\nb c : α\nh : (fun x => x * a) b = (fun x => x * a) c\n⊢ a * b = a * c",
"state_before": "α : Type u_1\nβ : Type ?u.84683\ninst✝¹ : CommSemigroup α\ninst✝ : PartialOrder α\na :... | [
1618,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
11
] |
Mathlib/Data/Vector/Mem.lean | Vector.mem_succ_iff | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.1743\nn : ℕ\na a'✝ : α\nv : Vector α (n + 1)\na' : α\nv' : Vector α n\nh : v = a' ::ᵥ v'\n⊢ a ∈ toList v ↔ a = head v ∨ a ∈ toList (tail v)",
"state_before": "α : Type u_1\nβ : Type ?u.1743\nn : ℕ\na a' : α\nv : Vector α (n + 1)\n⊢ a ∈ toList v ↔... | [
57,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.Commute.left_bijOn_fixedPoints_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nf fa g : α → α\nx y : α\nfb : β → β\nm n k : ℕ\ne : Perm α\nh : Commute f g\n⊢ Set.BijOn f (fixedPoints (f ∘ g)) (fixedPoints (f ∘ g))",
"tactic": "simpa only [h.comp_eq] using bijOn_fixedPoints_comp g f"
}
] | [
193,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/LinearAlgebra/Pi.lean | Submodule.coe_pi | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq_zero | [
{
"state_after": "no goals",
"state_before": "⊢ stirlingSeq 0 = 0",
"tactic": "rw [stirlingSeq, cast_zero, MulZeroClass.mul_zero, Real.sqrt_zero, MulZeroClass.zero_mul,\n div_zero]"
}
] | [
62,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_le | [] | [
261,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.addHom_ext | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.423906\ninst✝ : AddZeroClass β\nf g : Multiset α →+ β\nh : ∀ (x : α), ↑f {x} = ↑g {x}\ns : Multiset α\n⊢ ↑f s = ↑g s",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.423906\ninst✝ : AddZeroClass β\nf g : Multiset α →+ β\nh : ∀ (x : ... | [
2604,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2600,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.contDiff_comp_iff | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
501,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/List/Zip.lean | List.unzip_cons | [] | [
209,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_eq_iff_covby | [
{
"state_after": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\na : α\ninst✝ : NoMaxOrder α\n⊢ a ⋖ succ a",
"state_before": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : NoMaxOrder α\n⊢ succ a = b → a ⋖ b",
"tactic": "rintro rfl"
},
{
"state_after"... | [
500,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arccos_eq_arctan | [
{
"state_after": "x : ℝ\nh : 0 < x\n⊢ arctan (sqrt (↑1 - x ^ 2) / x) = π / 2 - arcsin x",
"state_before": "x : ℝ\nh : 0 < x\n⊢ arccos x = arctan (sqrt (↑1 - x ^ 2) / x)",
"tactic": "rw [arccos, eq_comm]"
},
{
"state_after": "case refine'_1\nx : ℝ\nh : 0 < x\n⊢ tan (π / 2 - arcsin x) = sqrt (↑1 -... | [
205,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | zero_eq_mul_self | [
{
"state_after": "no goals",
"state_before": "G₀ : Type u\nM₀ : Type u_1\nM₀' : Type ?u.12644\nG₀' : Type ?u.12647\ninst✝¹ : MulZeroClass M₀\ninst✝ : NoZeroDivisors M₀\na b : M₀\n⊢ 0 = a * a ↔ a = 0",
"tactic": "simp"
}
] | [
279,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_empty | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_1\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.158854\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\n⊢ ↑(weightedVSub ∅ p) w = 0",
"tactic": "simp ... | [
288,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.measurable_rangeSplitting | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.381096\nδ : Type ?u.381099\nδ' : Type ?u.381102\nι : Sort uι\ns✝ t u : Set α\nmα : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nf : α → β\ng : β → γ\nhf : MeasurableEmbedding f\ns : Set α\nhs :... | [
1117,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.trNormal_respects | [
{
"state_after": "case zero'\nk : Cont\nv : List ℕ\ns : Option Γ'\n⊢ ∃ b₂,\n TrCfg (stepNormal Code.zero' k v) b₂ ∧\n Reaches₁ (TM2.step tr)\n { l := some (trNormal Code.zero' (trCont k)), var := s, stk := elim (trList v) [] [] (trContStack k) } b₂\n\ncase succ\nk : Cont\nv : List ℕ\ns : Option Γ... | [
1634,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1603,
1
] |
Mathlib/Init/Logic.lean | false_iff_iff | [] | [
201,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.zpow_lt_top | [
{
"state_after": "case ofNat\nα : Type ?u.434875\nβ : Type ?u.434878\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nh'a : a ≠ ⊤\na✝ : ℕ\n⊢ a ^ Int.ofNat a✝ < ⊤\n\ncase negSucc\nα : Type ?u.434875\nβ : Type ?u.434878\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nh'a : a ≠ ⊤\na✝ : ℕ\n⊢ a ^ Int.negSucc a✝ < ⊤",
"state_... | [
1871,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1868,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_of_injective_of_countable_image | [] | [
182,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.pow_length_le_mul_ofDigits | [
{
"state_after": "n b : ℕ\nl : List ℕ\nhl : l ≠ []\nhl2 : List.getLast l hl ≠ 0\n⊢ (b + 2) ^ List.length (List.dropLast l ++ [List.getLast l hl]) ≤\n (b + 2) * ofDigits (b + 2) (List.dropLast l ++ [List.getLast l hl])",
"state_before": "n b : ℕ\nl : List ℕ\nhl : l ≠ []\nhl2 : List.getLast l hl ≠ 0\n⊢ (b ... | [
454,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_sub | [] | [
190,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.trans_refl | [] | [
361,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_range_le_lift | [] | [
2013,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2011,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin'_apply | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.congr_arg | [] | [
124,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.dist | [] | [
819,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
11
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_type | [] | [
610,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackAssoc_hom_snd_snd | [
{
"state_after": "C : Type u\ninst✝⁷ : Category C\nD : Type u₂\ninst✝⁶ : Category D\nW X Y Z X₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝⁵ : HasPullback f₁ f₂\ninst✝⁴ : HasPullback f₃ f₄\ninst✝³ : HasPullback (pullback.snd ≫ sorryAx (sorryAx C true ⟶ Y₂) true) f₄\ninst✝² : H... | [
2434,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2427,
1
] |
Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.enoughInjectives_of_enoughProjectives_op | [] | [
278,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Polynomial/Basic.lean | IsSMulRegular.polynomial | [] | [
252,
76
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Mathlib/Analysis/Convex/Basic.lean | DirectedOn.convex_sUnion | [
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_lt | [
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Mathlib/Algebra/Module/Basic.lean | smul_ne_zero | [] | [
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | hasSum_mul_right_iff | [
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Mathlib/Data/List/Permutation.lean | List.length_foldr_permutationsAux2 | [] | [
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Mathlib/Algebra/Order/Floor.lean | Int.fract_int_nat | [
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Mathlib/Data/Nat/Prime.lean | Nat.Prime.mod_two_eq_one_iff_ne_two | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_self_le_one | [
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Mathlib/Order/SymmDiff.lean | bihimp_right_surjective | [] | [
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Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_sInf | [
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_coeMulHom | [] | [
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_hom | [
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Mathlib/Order/WellFoundedSet.lean | Finset.partiallyWellOrderedOn_sup | [
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_mul_pow_of_radius_pos | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.sub_left | [
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.compLinearMap_assoc | [] | [
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Mathlib/GroupTheory/Transfer.lean | MonoidHom.ker_transferSylow_disjoint | [] | [
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src/lean/Init/SimpLemmas.lean | Bool.and_assoc | [
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Mathlib/Data/Finite/Defs.lean | finite_or_infinite | [] | [
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Mathlib/Topology/Algebra/Group/Basic.lean | continuousInv_sInf | [] | [
386,
80
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Mathlib/Data/PNat/Basic.lean | Nat.succPNat_strictMono | [] | [
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_zero | [
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Mathlib/Topology/MetricSpace/Basic.lean | dist_triangle4_right | [
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineBasis.finite_set | [] | [
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src/lean/Init/SimpLemmas.lean | Bool.not_true | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.inv_congr | [
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_sub | [
{
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_eq_one_iff_mem | [
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Mathlib/RingTheory/FiniteType.lean | AlgHom.FiniteType.id | [] | [
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_eq_zero_of_differentiableOn | [] | [
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97
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeights_eq_one_of_card_ne_zero | [
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_inj | [] | [
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Mathlib/Order/Filter/Prod.lean | Filter.prod_sup | [
{
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_δ_self | [
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualEquivDual_def | [] | [
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Mathlib/Deprecated/Subgroup.lean | IsGroupHom.isNormalSubgroup_ker | [] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.sum_filter_count_eq_countp | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.coequalizer_ext | [
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Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMinOn.hasFDerivWithinAt_eq_zero | [
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Mathlib/Data/Set/UnionLift.lean | Set.liftCover_coe | [] | [
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Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_one_sub_ordered | [
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_top_eq_zero_of_infinite | [
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.ysq_dvd_yy | [
{
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},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ yn a1 n * yn a1 n ∣ yn a1 n * xn a1 n ^ (yn a1 n - 1) * yn a1 n",
"t... | [
493,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.mul_meas_ge_le_integral_of_nonneg | [
{
"state_after": "case inl\nα : Type u_1\nE : Type ?u.1501155\nF : Type ?u.1501158\n𝕜 : Type ?u.1501161\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGrou... | [
1646,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.coprime_of_coprime | [
{
"state_after": "x y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nH : ¬Int.gcd y z = 1\n⊢ False",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\n⊢ Int.gcd y z = 1",
"tactic": "by_contra H"
},
{
"state_after": "case intro.intro.intro\nx y z : ℤ\nh : P... | [
263,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isRegular_iff_ne_zero | [] | [
378,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.dual_id | [] | [
767,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.mk_one | [] | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27512\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Icc a b = ∅ ↔ ¬a ≤ b",
"tactic": "rw [← not_nonempty_iff_eq_empty, not_iff_not, nonempty_Icc]"
}
] | [
683,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_eq_zero_of_right | [] | [
241,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Topology/Separation.lean | t0Space_iff_inseparable | [] | [
183,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
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