file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.mul | [] | [
334,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | le_add_tsub' | [] | [
233,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/Lattice.lean | Prod.fst_sup | [] | [
1269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.mono_iff_ker_eq_bot | [] | [
90,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_strictMono_right | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.226813\nA : Type ?u.226816\nG : Type ?u.226819\nM : Type ?u.226822\nR : Type u_1\ninst✝ : StrictOrderedSemiring R\na x y : R\nn✝ m : ℕ\nh : 1 < a\nthis : 0 < a\nn : ℕ\n⊢ a ^ n < a ^ (n + 1)",
"tactic": "simpa only [one_mul, pow_succ] using mul_lt... | [
498,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.cos | [] | [
153,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_orthogonal_left | [] | [
316,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Polynomial/Cardinal.lean | Polynomial.cardinal_mk_le_max | [
{
"state_after": "case inl\nR : Type u\ninst✝ : Semiring R\nh✝ : Subsingleton R\n⊢ (#R[X]) ≤ max (#R) ℵ₀\n\ncase inr\nR : Type u\ninst✝ : Semiring R\nh✝ : Nontrivial R\n⊢ (#R[X]) ≤ max (#R) ℵ₀",
"state_before": "R : Type u\ninst✝ : Semiring R\n⊢ (#R[X]) ≤ max (#R) ℵ₀",
"tactic": "cases subsingleton_or_n... | [
40,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | exists_maximal_independent' | [
{
"state_after": "ι : Type u'\nι' : Type ?u.501528\nR : Type u_1\nK : Type ?u.501534\nM : Type u_2\nM' : Type ?u.501540\nM'' : Type ?u.501543\nV : Type u\nV' : Type ?u.501548\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : Module R M\ninst✝¹ : ... | [
894,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.comp_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✝ : Semiring R\np q r : R[X]\n⊢ comp p 0 = ↑C (eval 0 p)",
"tactic": "rw [← C_0, comp_C]"
}
] | [
564,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_inf_of_mem | [
{
"state_after": "case h\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns₁ s₂ : AffineSubspace k P\np : P\nh₁ : p ∈ s₁\nh₂ : p ∈ s₂\nv : V\n⊢ v ∈ direction (s₁ ⊓ s₂) ↔ v ∈ direction s₁ ⊓ direction s₂",
"state_before": ... | [
913,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Topology/Order/Basic.lean | disjoint_nhds_atTop | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : NoMaxOrder α\nx y : α\nhy : x < y\n⊢ Disjoint (𝓝 x) atTop",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : Lin... | [
1535,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.forall_iff | [] | [
252,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_transpose | [] | [
520,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.lt_sup_principal_of_not_mem | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\ninst✝¹ : SemilatticeSup P\ninst✝ : IsDirected P fun x x_1 => x ≥ x_1\nx : P\nI J K s t : Ideal P\nhx : ¬x ∈ I\nh : I = I ⊔ principal x\n⊢ x ∈ I",
"tactic": "simpa only [left_eq_sup, principal_le_iff] using h"
}
] | [
427,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.natCoe_one | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : AddMonoidWithOne R\nn : ℕ\n⊢ ↑↑1 n = ↑1 n",
"state_before": "R : Type u_1\ninst✝ : AddMonoidWithOne R\n⊢ ↑1 = 1",
"tactic": "ext n"
},
{
"state_after": "no goals",
"state_before": "case h\nR : Type u_1\ninst✝ : AddMonoidWithOne R\nn : ℕ\n⊢ ↑↑1 ... | [
198,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.lintegral_deterministic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.398136\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nf : β → ℝ≥0∞\ng : α → β\na : α\nhg : Measurable g\ninst✝ : MeasurableSingletonClass β\n⊢ (∫⁻ (x : β), f x ∂↑(deterministic g hg) a) = f (... | [
379,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_spec | [] | [
961,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_inter | [] | [
2070,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2063,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | mul_inf | [] | [
88,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.X_pow_card_sub_X_natDegree_eq | [
{
"state_after": "K : Type ?u.726863\nR : Type ?u.726866\ninst✝² : Field K\ninst✝¹ : Fintype K\nK' : Type u_1\ninst✝ : Field K'\np n : ℕ\nhp : 1 < p\nh1 : degree X < degree (X ^ p)\n⊢ natDegree (X ^ p - X) = p",
"state_before": "K : Type ?u.726863\nR : Type ?u.726866\ninst✝² : Field K\ninst✝¹ : Fintype K\nK... | [
238,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.sInter_apply | [
{
"state_after": "x : Class\ny : ZFSet\n⊢ (∀ (z : ZFSet), x z → y ∈ z) → (⋂₀ x) y",
"state_before": "x : Class\ny : ZFSet\n⊢ (⋂₀ x) y ↔ ∀ (z : ZFSet), x z → y ∈ z",
"tactic": "refine' ⟨fun hxy z hxz => hxy _ ⟨z, rfl, hxz⟩, _⟩"
},
{
"state_after": "case intro.intro\nx : Class\ny : ZFSet\nH : ∀ (z... | [
1703,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1700,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.lt_four | [
{
"state_after": "q r : ℕ+\nhqr : q ≤ r\nH : 1 < sumInv {2, q, r}\nh4 : 0 < 4\n⊢ q < 4",
"state_before": "q r : ℕ+\nhqr : q ≤ r\nH : 1 < sumInv {2, q, r}\n⊢ q < 4",
"tactic": "have h4 : (0 : ℚ) < 4 := by norm_num"
},
{
"state_after": "q r : ℕ+\nhqr : q ≤ r\nh4 : 0 < 4\nH : ¬q < 4\n⊢ sumInv {2, q... | [
216,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.diagramNatTrans_comp | [
{
"state_after": "case w.h\nC : Type u\ninst✝² : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝¹ : Category D\ninst✝ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP✝ P Q R : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nγ : Q ⟶ R\nX : C\nx✝ : (Cover J X)ᵒᵖ\n⊢ (diagramNatTrans J (η ≫ γ) X).app... | [
100,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_range_le | [] | [
2008,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2007,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.inl_snd' | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nb : BinaryBicone X Y\nh : BinaryBicone.IsBilimit b\n⊢ IsPullback (b.inl ≫ b.fst) 0 0 (0 ≫ 0)",
"state_before": "C : Type u₁\ninst✝² : Categor... | [
574,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.quotientQuotientEquivQuotientAux_mk_mk | [] | [
640,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_one_nat_atTop_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.689842\nβ : Type ?u.689845\nE : Type ?u.689848\nF : Type ?u.689851\nG : Type ?u.689854\nE' : Type ?u.689857\nF' : Type ?u.689860\nG' : Type ?u.689863\nE'' : Type u_1\nF'' : Type ?u.689869\nG'' : Type ?u.689872\nR : Type ?u.689875\nR' : Type ?u.689878... | [
2131,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2128,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.isCycle | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : IsThreeCycle σ\n⊢ IsCycle σ",
"tactic": "rw [← card_cycleType_eq_one, h.cycleType, card_singleton]"
}
] | [
594,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.mkNormedAddGroupHom_norm_le' | [
{
"state_after": "case h\nV : Type ?u.279839\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.279848\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf✝ g : NormedAddGroupHom V₁ V₂\nf : V₁ →+ V₂\nC : ℝ\nh : ∀ (x : V₁), ‖↑f ... | [
318,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Topology/Algebra/Order/Group.lean | Filter.Tendsto.abs | [] | [
68,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.map_isLeast | [] | [
1197,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Algebra/Order/WithZero.lean | ne_zero_of_lt | [] | [
111,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.smul | [] | [
122,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.map_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\nx✝ : α\n⊢ ↑(AddMonoidHom.comp (map g) (map f)) (of x✝) = ↑(map (g ∘ f)) (of x✝)",
"tactic": "simp [map]"
}
] | [
385,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/Multiset/Range.lean | Multiset.range_zero | [] | [
34,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Algebra/Invertible.lean | mul_mul_invOf_self_cancel' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b : α\nx✝ : Invertible b\n⊢ a * b * ⅟b = a",
"tactic": "simp [mul_assoc]"
}
] | [
144,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | piiUnionInter_singleton | [
{
"state_after": "case h\nα : Type u_1\nι : Type u_2\nπ : ι → Set (Set α)\ni : ι\ns : Set α\n⊢ s ∈ piiUnionInter π {i} ↔ s ∈ π i ∪ {univ}",
"state_before": "α : Type u_1\nι : Type u_2\nπ : ι → Set (Set α)\ni : ι\n⊢ piiUnionInter π {i} = π i ∪ {univ}",
"tactic": "ext1 s"
},
{
"state_after": "case... | [
396,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.Eventually.prod_inl | [] | [
159,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_sup_sdiff | [] | [
534,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.inj | [] | [
1611,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1609,
11
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_iff | [] | [
79,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infEdist_ne_top | [
{
"state_after": "case intro\nι : Sort ?u.57852\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y✝ : α\nΦ : α → β\ny : α\nhy : y ∈ s\n⊢ infEdist x s ≠ ⊤",
"state_before": "ι : Sort ?u.57852\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : Ps... | [
491,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.smul_subset | [] | [
31,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Topology/Sober.lean | quasiSober_of_open_cover | [
{
"state_after": "α : Type u_1\nβ : Type ?u.12585\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nS : Set (Set α)\nhS : ∀ (s : ↑S), IsOpen ↑s\nhS' : ∀ (s : ↑S), QuasiSober ↑↑s\nhS'' : ⋃₀ S = ⊤\n⊢ ∀ {S : Set α}, IsIrreducible S → IsClosed S → ∃ x, IsGenericPoint x S",
"state_before": "α : Type u_1\... | [
242,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.toOuterMeasure_ofMultiset_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.184861\nγ : Type ?u.184864\ns : Multiset α\nhs : s ≠ 0\nt : Set α\n⊢ (∑' (x : α), Set.indicator t (↑(ofMultiset s hs)) x) =\n ∑' (i : α), ↑(Multiset.count i (Multiset.filter (fun x => x ∈ t) s)) * (↑(↑Multiset.card s))⁻¹",
"state_before": "α : Type u_1\nβ : Typ... | [
208,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.image_closedBall | [] | [
1060,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1059,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_eq_span_single | [
{
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Mathlib/Algebra/Homology/QuasiIso.lean | HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq | [
{
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175,
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164,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_inj | [
{
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Mathlib/FieldTheory/Subfield.lean | Subfield.coe_toSubring | [] | [
227,
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226,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.X_pow_eq | [] | [
1452,
29
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1451,
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.mul_const_inv | [] | [
500,
61
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498,
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Mathlib/RingTheory/Ideal/Prod.lean | Ideal.map_snd_prod | [
{
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81,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_pi | [] | [
126,
81
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124,
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_mk | [] | [
159,
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158,
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Mathlib/Data/Finset/Prod.lean | Finset.nonempty_product | [] | [
207,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
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Mathlib/Combinatorics/Configuration.lean | Configuration.HasLines.lineCount_eq_pointCount | [
{
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312,
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285,
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Mathlib/Data/Fin/VecNotation.lean | Matrix.head_sub | [] | [
517,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.pow_succ_lt_pow | [] | [
772,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
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Mathlib/Data/Bool/Basic.lean | Bool.and_intro | [
{
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}
] | [
176,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
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Mathlib/Order/Filter/NAry.lean | Filter.map₂_left_identity | [
{
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414,
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413,
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | IsClosed.diffContOnCl_iff | [] | [
48,
83
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47,
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Mathlib/Algebra/Squarefree.lean | UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree | [
{
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"tactic": "classical\n haveI := UniqueFactorizationMonoid.toGCDMonoid R\n exact ⟨hsq.isRadical n y... | [
264,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
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Mathlib/NumberTheory/Fermat4.lean | Fermat42.minimal_comm | [] | [
114,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Algebra/GroupPower/Basic.lean | ofMul_pow | [] | [
458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
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Mathlib/Order/Filter/Bases.lean | Filter.disjoint_principal_principal | [
{
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"tac... | [
709,
80
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708,
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Mathlib/Algebra/GCDMonoid/Basic.lean | dvd_gcd_mul_of_dvd_mul | [] | [
512,
67
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511,
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Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.Pi.reindex_inv_π | [
{
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] | [
416,
25
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415,
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_add_mul_right_left | [
{
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}
] | [
174,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix'_toLin' | [] | [
330,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
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Mathlib/Data/Finset/Preimage.lean | Finset.preimage_empty | [
{
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},
{
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50,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.diagonal | [
{
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555,
46
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549,
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_iInf | [
{
"state_after": "no goals",
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256,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.not_dvd_of_between_consec_multiples | [
{
"state_after": "case intro\nn k l d : ℕ\nh1 : n * k < n * d\nh2 : n * d < n * (k + 1)\n⊢ False",
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},
{
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564,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
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Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_mul | [
{
"state_after": "case zero\nS : Type u\ninst✝ : Semiring S\nn : ℕ\n⊢ pochhammer S n * comp (pochhammer S Nat.zero) (X + ↑n) = pochhammer S (n + Nat.zero)\n\ncase succ\nS : Type u\ninst✝ : Semiring S\nn m : ℕ\nih : pochhammer S n * comp (pochhammer S m) (X + ↑n) = pochhammer S (n + m)\n⊢ pochhammer S n * comp (... | [
143,
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138,
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Mathlib/Data/Real/Basic.lean | Real.sSup_le | [
{
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878,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
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Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_nhds_iff | [] | [
165,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Data/Nat/Size.lean | Nat.size_le_size | [] | [
175,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.inv_unique | [
{
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674,
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671,
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Mathlib/Algebra/Hom/Group.lean | MulHom.comp_mul | [
{
"state_after": "case h\nα : Type ?u.204587\nβ : Type ?u.204590\nM : Type u_1\nN : Type u_2\nP : Type u_3\nG : Type ?u.204602\nH : Type ?u.204605\nF : Type ?u.204608\ninst✝² : Mul M\ninst✝¹ : CommSemigroup N\ninst✝ : CommSemigroup P\ng : N →ₙ* P\nf₁ f₂ : M →ₙ* N\nx✝ : M\n⊢ ↑(comp g (f₁ * f₂)) x✝ = ↑(comp g f₁ ... | [
1475,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1472,
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Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_congr | [
{
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586,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
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] |
Std/Data/Nat/Lemmas.lean | Nat.shiftLeft_eq | [
{
"state_after": "no goals",
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] | [
803,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOnFilter.mono_left | [
{
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481,
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477,
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Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.inter | [
{
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105,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_eq_iff | [] | [
288,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.coe_mul | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : α\nha : a = 0\n⊢ ↑(a * b) = ↑a * ↑b\n\ncase neg\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : MulZeroClass α\na b : α\nha : ¬a = 0\n⊢ ↑(a * b) = ↑a * ↑b",
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98,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.some_eq_coe' | [] | [
155,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Data/Matrix/Basic.lean | Matrix.neg_mulVec | [
{
"state_after": "case h\nl : Type ?u.908864\nm : Type u_2\nn : Type u_1\no : Type ?u.908873\nm' : o → Type ?u.908878\nn' : o → Type ?u.908883\nR : Type ?u.908886\nS : Type ?u.908889\nα : Type v\nβ : Type w\nγ : Type ?u.908896\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype n\nv : n → α\nA : Matrix m n α\nx✝... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Basic.lean | nhds_basis_Ioo | [] | [
1335,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_map' | [
{
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1279,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.smul_imJ | [] | [
1041,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
9
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.mono_iff_injective | [
{
"state_after": "n m : SimplexCategory\nf : n ⟶ m\n⊢ Mono (skeletalEquivalence.functor.map f) ↔ Function.Injective ↑(Hom.toOrderHom f)",
"state_before": "n m : SimplexCategory\nf : n ⟶ m\n⊢ Mono f ↔ Function.Injective ↑(Hom.toOrderHom f)",
"tactic": "rw [← Functor.mono_map_iff_mono skeletalEquivalence.... | [
483,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/Connected.lean | isConnected_singleton | [] | [
89,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_tsub_tsub_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nh : c ≤ b\n⊢ a - c - (b - c) = a - b",
"... | [
71,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/RingTheory/QuotientNilpotent.lean | Ideal.isRadical_iff_quotient_reduced | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ IsRadical (RingHom.ker (Quotient.mk I)) ↔ IsReduced (R ⧸ I)",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ IsRadical I ↔ IsReduced (R ⧸ I)",
"tactic": "conv_lhs => rw [← @Ideal.mk_ker R _ I]"
},
{
"state_afte... | [
21,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
18,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.out_dvd_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\na : α\nb : Associates α\n⊢ ∀ (a_1 : α),\n Associates.out (Quotient.mk (Associated.setoid α) a_1) ∣ a ↔ Quotient.mk (Associated.setoid α) a_1 ≤ Associates.mk a",
"tactic": "s... | [
243,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.ascFactorial_le_pow_add | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ascFactorial n 0 ≤ (n + 0) ^ 0",
"tactic": "rw [ascFactorial_zero, pow_zero]"
},
{
"state_after": "n k : ℕ\n⊢ succ (n + k) * ascFactorial n k ≤ succ (n + k) * succ (n + k) ^ k",
"state_before": "n k : ℕ\n⊢ ascFactorial n (k + 1) ≤ (n + (... | [
312,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_zero | [] | [
258,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Std/Data/List/Init/Lemmas.lean | List.append_bind | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type u_2\nys : List α\nf : α → List β\n⊢ List.bind ([] ++ ys) f = List.bind [] f ++ List.bind ys f\n\ncase cons\nα : Type u_1\nβ : Type u_2\nys : List α\nf : α → List β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : List.bind (tail✝ ++ ys) f = List.bind tail✝ f ++ List.bind... | [
107,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
105,
9
] |
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