file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/Group/Conj.lean | isConj_one_left | [] | [
84,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Ioi b = Ioi (b - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
382,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/Analysis/Calculus/Deriv/Inverse.lean | not_differentiableWithinAt_of_local_left_inverse_hasDerivWithinAt_zero | [
{
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126,
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Std/Data/Int/Lemmas.lean | Int.neg_mul | [] | [
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36
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467,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.mono_iff_stalk_mono | [] | [
526,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Order/Hom/Lattice.lean | InfHom.comp_id | [] | [
607,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Constructions.lean | openEmbedding_inr | [] | [
914,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/WithTerminal.lean | CategoryTheory.WithInitial.liftStar_lift_map | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u_1\ninst✝ : Category D\nZ : D\nF : C ⥤ D\nM : (x : C) → Z ⟶ F.obj x\nhM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y\nx : C\n⊢ (lift F M hM).map (Limits.IsInitial.to starInitial (incl.obj x)) = M x",
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379,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ioo | [] | [
512,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsCodetector.def | [] | [
509,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_apply | [] | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_apply | [] | [
792,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
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Mathlib/Topology/LocalExtr.lean | IsLocalMin.congr | [] | [
615,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
8
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Mathlib/Topology/MetricSpace/Basic.lean | comap_dist_left_atTop_eq_cocompact | [] | [
2811,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2809,
1
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Mathlib/Order/LocallyFinite.lean | Finset.map_subtype_embedding_Iic | [
{
"state_after": "α : Type u_1\nβ : Type ?u.225442\ninst✝² : Preorder α\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : LocallyFiniteOrderBot α\na : Subtype p\nhp : ∀ ⦃a x : α⦄, x ≤ a → p a → p x\n⊢ map (Embedding.subtype p) (Finset.subtype p (Iic ↑a)) = Iic ↑a",
"state_before": "α : Type u_1\nβ : Type ?u.... | [
1357,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1355,
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Mathlib/Data/Complex/Exponential.lean | Real.cosh_sq_sub_sinh_sq | [
{
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"state_before": "x✝ y x : ℝ\n⊢ cosh x ^ 2 - sinh x ^ 2 = 1",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\n⊢ ↑(cosh x ^ 2 - sinh x ^ 2) = ↑1",
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}
] | [
1431,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
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Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_symm | [] | [
53,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Topology/Algebra/Monoid.lean | continuousOn_pow | [] | [
586,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
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Mathlib/Combinatorics/Additive/Energy.lean | Finset.multiplicativeEnergy_empty_left | [
{
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}
] | [
98,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.coe_map | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Computability/Reduce.lean | manyOneEquiv_up | [] | [
293,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_pi_univ_eq | [
{
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335,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.equivMapOfInjective_coe_mulEquiv | [
{
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1466,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
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Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.support_add | [
{
"state_after": "X : Type u_1\na b : FreeAbelianGroup X\n⊢ (↑toFinsupp a + ↑toFinsupp b).support ⊆ (↑toFinsupp a).support ∪ (↑toFinsupp b).support",
"state_before": "X : Type u_1\na b : FreeAbelianGroup X\n⊢ support (a + b) ⊆ support a ∪ support b",
"tactic": "simp only [support, AddMonoidHom.map_add]"... | [
200,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.neg_val' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ val (-a) = val (-a) % n",
"tactic": "rw [Nat.mod_eq_of_lt (-a).val_lt]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ val (-a) + ?m.539514 a ≡ n - val a + ?m.539514 ... | [
885,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Extension.lean | exists_dual_vector | [
{
"state_after": "𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nh : x ≠ 0\np : Submodule 𝕜 E := span 𝕜 {x}\n⊢ ∃ g, ‖g‖ = 1 ∧ ↑g x = ↑‖x‖",
"state_before": "𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : Nor... | [
136,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_self | [] | [
354,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.t0Space | [] | [
286,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.mul_refl | [] | [
924,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.support_ofMultiset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.178630\nγ : Type ?u.178633\ns : Multiset α\nhs : s ≠ 0\n⊢ ∀ (x : α), x ∈ support (ofMultiset s hs) ↔ x ∈ ↑(Multiset.toFinset s)",
"tactic": "simp [mem_support_iff, hs]"
}
] | [
186,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_eq_zero_of_not_mem | [] | [
2416,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2415,
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_mul | [] | [
229,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Init/Logic.lean | decide_True' | [
{
"state_after": "no goals",
"state_before": "a b c d : Prop\np : ?m.25343\nh : Decidable True\n⊢ decide True = true",
"tactic": "simp"
}
] | [
273,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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] |
Std/Data/String/Lemmas.lean | String.utf8Len_le_of_sublist | [] | [
68,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
65,
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Mathlib/Order/RelIso/Basic.lean | wellFounded_lift₂_iff | [
{
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477,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Algebra/Homology/Single.lean | CochainComplex.single₀_obj_X_succ | [] | [
352,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Topology/Sober.lean | IsGenericPoint.mem | [] | [
71,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.derivation_eq_zero_of_forall_mem_vars | [] | [
96,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_nat | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ aleph' (succ ↑n) = ↑(Nat.succ n)",
"tactic": "rw [aleph'_succ, aleph'_nat n, nat_succ]"
}
] | [
212,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | PiToModule.fromEnd_injective | [
{
"state_after": "ι : Type u_3\ninst✝³ : Fintype ι\nM : Type u_1\ninst✝² : AddCommGroup M\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Module R M\nI : Ideal R\nb : ι → M\nhb✝ hb : Submodule.span R (Set.range b) = ⊤\nx y : Module.End R M\ne : ↑(fromEnd R b) x = ↑(fromEnd R b) y\n⊢ x = y",
"state_before": "ι :... | [
80,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_fintype_fun_eq_card | [] | [
150,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearMap_comp | [] | [
837,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_assoc | [
{
"state_after": "no goals",
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"tactic": "simp [cast_heq, mul_assoc0, assocLeft]"
}
] | [
208,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableAt.comp_differentiableWithinAt | [] | [
137,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | lp.hasSum_inner | [] | [
171,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.apply_iterate | [] | [
91,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_four | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\n⊢ ↑↑4 = ↑4",
"tactic": "rw [cast_ofNat, Nat.cast_ofNat]"
}
] | [
163,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.submodule_independent | [] | [
337,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.Term.listDecode_encode_list | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.2133\nP : Type ?u.2136\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nl : List (Term L α)\nh : ∀ (t : Term L α) (l : List (α ⊕ (i : ℕ) × Functions L i)), listDecode (listEncode t ++ l) = some t :: listDeco... | [
103,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.mapsTo_smul_closure | [] | [
141,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | Measurable.map_prod_mk_right | [
{
"state_after": "case h\nα : Type u_1\nα' : Type ?u.2748751\nβ : Type u_2\nβ' : Type ?u.2748757\nγ : Type ?u.2748760\nE : Type ?u.2748763\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ✝ μ' : MeasureTheory.Measure ... | [
210,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | fderivWithin_exp | [] | [
314,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_natDiv | [
{
"state_after": "no goals",
"state_before": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ / ↑n✝ = ↑(Nat.div n✝¹ n✝)",
"tactic": "aesop"
}
] | [
992,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.leftLim_eq_sSup | [] | [
95,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lieIdeal_oper_eq_span | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | leibniz_cross | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nu v w : Fin 3 → R\n⊢ ![u 1 * vecCons (v 1 * w 2 - v 2 * w 1) ![v 2 * w 0 - v 0 * w 2, v 0 * w 1 - v 1 * w 0] 2 -\n u 2 * vecCons (v 1 * w 2 - v 2 * w 1) ![v 2 * w 0 - v 0 * w 2, v 0 * w 1 - v 1 * w 0] 1,\n u 2 * vecCons (v 1 * w 2 - v 2 * w 1) ![v ... | [
142,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_add | [
{
"state_after": "case inl\nα : Type ?u.99924\nr : α → α → Prop\na : Ordinal\nh : 0 ≠ 0\n⊢ cof (a + 0) = cof 0\n\ncase inr.inl.intro\nα : Type ?u.99924\nr : α → α → Prop\na c : Ordinal\nh : succ c ≠ 0\n⊢ cof (a + succ c) = cof (succ c)\n\ncase inr.inr\nα : Type ?u.99924\nr : α → α → Prop\na b : Ordinal\nh : b ≠... | [
703,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.zero_comp | [
{
"state_after": "case h\nR₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type u_6\ninst✝¹⁷ : Semiring R₁\ninst✝¹⁶ : Semiring R₂\ninst✝¹⁵ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_3\ninst✝¹⁴ : TopologicalSpace M₁\ninst✝¹³ : AddCommMonoid M₁\nM'₁ : Type ?u.517394\ninst✝¹² : TopologicalSpac... | [
814,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.dualMap_def | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_div | [] | [
784,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finiteDimensional_of_finrank | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nh : ¬FiniteDimensional K V\n⊢ ¬0 < finrank K V",
"state_before": "K : Type u\nV : Type v\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGro... | [
205,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_subset_one_on_sdiff | [
{
"state_after": "ι : Type ?u.331175\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\nh : s₁ ⊆ s₂\nhg : ∀ (x : α), x ∈ s₂ \\ s₁ → g x = 1\nhfg : ∀ (x : α), x ∈ s₁ → f x = g x\n⊢ ∏ i in s₁, f i = ∏ x in s₁, g x",
"state_before": "ι : T... | [
742,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_lt_sub_left | [
{
"state_after": "m n : Nat\nx✝¹ : 0 < m + 1\nx✝ : 0 < n + 1\n⊢ m - n < m + 1 - 0",
"state_before": "m n : Nat\nx✝¹ : 0 < m + 1\nx✝ : 0 < n + 1\n⊢ m + 1 - (n + 1) < m + 1 - 0",
"tactic": "rw [Nat.add_sub_add_right]"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nx✝¹ : 0 < m + 1\... | [
627,
86
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
623,
11
] |
Mathlib/Order/Lattice.lean | AntitoneOn.min | [] | [
1235,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
11
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.op_smul_set_smul_eq_smul_smul_set | [
{
"state_after": "case h\nF : Type ?u.52743\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝² : SMul αᵐᵒᵖ β\ninst✝¹ : SMul β γ\ninst✝ : SMul α γ\na : α\ns : Set β\nt : Set γ\nh : ∀ (a : α) (b : β) (c : γ), (op a • b) • c = b • a • c\nx✝ : γ\n⊢ x✝ ∈ (op a • s) • t ↔ x✝ ∈ s • a • t",
"state_before": "F : Type... | [
779,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.zero_descFactorial_succ | [
{
"state_after": "no goals",
"state_before": "k : ℕ\n⊢ descFactorial 0 (succ k) = 0",
"tactic": "rw [descFactorial_succ, zero_tsub, zero_mul]"
}
] | [
355,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.natDegree_taylor | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nr✝ : R\nf p : R[X]\nr : R\n⊢ ∀ (n : ℕ) (c : R), c ≠ 0 → natDegree (↑(taylor r) (↑(monomial n) c)) = n",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr✝ : R\nf p : R[X]\nr : R\n⊢ natDegree (↑(taylor r) p) = natDegree p",
"tactic": "refine' map_nat... | [
105,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sigma.completeSpace | [
{
"state_after": "ι : Type u_2\nE : ι → Type u_1\ninst✝¹ : (i : ι) → MetricSpace (E i)\ninst✝ : ∀ (i : ι), CompleteSpace (E i)\ns : ι → Set ((i : ι) × E i) := fun i => Sigma.fst ⁻¹' {i}\n⊢ CompleteSpace ((i : ι) × E i)",
"state_before": "ι : Type u_2\nE : ι → Type u_1\ninst✝¹ : (i : ι) → MetricSpace (E i)\n... | [
453,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
11
] |
Mathlib/GroupTheory/GroupAction/Option.lean | Option.smul_def | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Data/Matrix/Basic.lean | AddEquiv.mapMatrix_trans | [] | [
1451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_eq_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0\n⊢ 0 ^ 2 = x ↔ x = 0",
"tactic": "rw [eq_comm, sq, zero_mul]"
}
] | [
77,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.algebraMap_apply'' | [] | [
2698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2696,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodComm_apply | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | Commute.list_prod_left | [] | [
259,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/Constructions.lean | CofiniteTopology.isOpen_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.17451\nδ : Type ?u.17454\nε : Type ?u.17457\nζ : Type ?u.17460\ns : Set (CofiniteTopology α)\n⊢ IsOpen s ↔ s = ∅ ∨ Set.Finite (sᶜ)",
"tactic": "simp only [isOpen_iff, nonempty_iff_ne_empty, or_iff_not_imp_left]"
}
] | [
287,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_thickening_subset | [
{
"state_after": "case inl\nι : Sort ?u.157071\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns✝ t : Set α\nx : α\nhε : 0 ≤ ε\nδ : ℝ\ns : Set α\nhδ : δ ≤ 0\n⊢ cthickening ε (thickening δ s) ⊆ cthickening (ε + δ) s\n\ncase inr\nι : Sort ?u.157071\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSp... | [
1497,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_add_lt_add_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : a + b < c + b\n⊢ b + a < b + c",
"tactic": "rwa [Int.add_comm b a, Int.add_comm b c]"
}
] | [
777,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
776,
11
] |
Std/Data/Array/Lemmas.lean | Array.get?_push_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\nx : α\n⊢ (push a x)[size a]? = some x",
"tactic": "rw [getElem?_pos, get_push_eq]"
}
] | [
83,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
82,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.range_mk | [] | [
439,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.refl_apply | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.sublist | [
{
"state_after": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na b : α\ninst✝ : IsTrans α R\nhl : Pairwise R l₂\nh : l₁ <+ l₂\n⊢ Pairwise R l₁",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na b : α\ninst✝ : IsTrans α R\nhl : Chain' R l₂\nh : l₁ <+ l₂\n⊢ Cha... | [
254,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.mul_zero | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\nk : Fin n\n⊢ k * 0 = 0",
"tactic": "simp [eq_iff_veq, mul_def]"
}
] | [
2536,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2536,
11
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr'_symm | [] | [
564,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
9
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Differentiable.analyticAt | [] | [
611,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
11
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBounded.isCobounded_le | [] | [
213,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.replicate_mem_sym | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b✝ : α\nn✝ : ℕ\nm : Sym α n✝\nha : a ∈ s\nn : ℕ\nb : α\nhb : b ∈ Sym.replicate n a\n⊢ b ∈ s",
"tactic": "rwa [(Sym.mem_replicate.1 hb).2]"
}
] | [
171,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.extend_unique | [
{
"state_after": "α : Type u_1\ninst✝³ : UniformSpace α\npkg : AbstractCompletion α\nβ : Type u_2\ninst✝² : UniformSpace β\nf : α → β\ninst✝¹ : CompleteSpace β\ninst✝ : SeparatedSpace β\nhf : UniformContinuous f\ng : pkg.space → β\nhg : UniformContinuous g\nh : ∀ (a : α), f a = g (coe pkg a)\n⊢ ∀ (a : α), Abstr... | [
164,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/GDelta.lean | residual_of_dense_open | [] | [
210,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.continuous_id | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.11276\ninst✝² : OmegaCompletePartialOrder α\ninst✝¹ : OmegaCompletePartialOrder β\ninst✝ : OmegaCompletePartialOrder γ\nf : α →o β\ng : β →o γ\nc : Chain α\n⊢ ↑OrderHom.id (ωSup c) = ωSup (map c OrderHom.id)",
"state_before": "α : Type u\nβ : Type v\nγ :... | [
284,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/LocallyFinite.lean | Ioi_ofDual | [] | [
914,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_congr | [
{
"state_after": "α : Type u_1\nα' : Type ?u.45879\nβ : Type u_2\nβ' : Type ?u.45885\nγ : Type u_3\nγ' : Type ?u.45891\nδ : Type ?u.45894\nδ' : Type ?u.45897\nε : Type ?u.45900\nε' : Type ?u.45903\nζ : Type ?u.45906\nζ' : Type ?u.45909\nν : Type ?u.45912\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵... | [
229,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasStrictDerivAt.complexToReal_fderiv' | [
{
"state_after": "no goals",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nx : ℂ\nf' : E\nh : HasStrictDerivAt f f' x\n⊢ HasStrictFDerivAt f (ContinuousLinearMap.smulRight reClm f' + I • ContinuousLinearMap.smulRight imClm f') x",... | [
106,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.IsFiniteKernel.bound_ne_top | [] | [
142,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.flip_unflip | [] | [
448,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/List/Cycle.lean | List.nextOr_concat | [
{
"state_after": "case nil\nα : Type u_1\ninst✝ : DecidableEq α\nxs : List α\nx d : α\nh✝ : ¬x ∈ xs\nh : ¬x ∈ []\n⊢ nextOr ([] ++ [x]) x d = d\n\ncase cons\nα : Type u_1\ninst✝ : DecidableEq α\nxs : List α\nx d : α\nh✝ : ¬x ∈ xs\nz : α\nzs : List α\nIH : ¬x ∈ zs → nextOr (zs ++ [x]) x d = d\nh : ¬x ∈ z :: zs\n⊢... | [
95,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_zero | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\n⊢ logb b 0 = 0",
"tactic": "simp [logb]"
}
] | [
52,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_image_eq | [] | [
2031,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2030,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.ext | [
{
"state_after": "case mk\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC₂ : HomologicalComplex V c\nX₁ : ι → V\nd₁ : (i j : ι) → X₁ i ⟶ X₁ j\ns₁ : ∀ (i j : ι), ¬ComplexShape.Rel c i j → d₁ i j = 0\nh₁ : ∀ (i j k : ι), ComplexShape.Rel c i j → ComplexShape.Rel c... | [
95,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_curry | [] | [
107,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_finset_map_embedding_subtype | [
{
"state_after": "ι : Type ?u.490158\nι' : Type ?u.490161\nR : Type u_2\nK : Type ?u.490167\nA : Type u_1\nA' : Type ?u.490173\nA'' : Type ?u.490176\nV : Type u\nV' : Type ?u.490181\nx : ι → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra R A\ninst✝¹ : ... | [
242,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
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