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/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.withBotCoe_subset_iff | [
{
"state_after": "case bot\nι : Type u_1\nI J✝ : Box ι\nx y : ι → ℝ\nJ : WithBot (Box ι)\n⊢ ↑⊥ ⊆ ↑J ↔ ⊥ ≤ J\n\ncase coe\nι : Type u_1\nI J✝ : Box ι\nx y : ι → ℝ\nJ : WithBot (Box ι)\na✝ : Box ι\n⊢ ↑↑a✝ ⊆ ↑J ↔ ↑a✝ ≤ J",
"state_before": "ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ ↑I ⊆ ... | [
303,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_add | [] | [
1939,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1938,
1
] |
Mathlib/Order/CompleteLattice.lean | IsLUB.iSup_eq | [] | [
783,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.toEquiv_mulLeft₀ | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.range_natCast | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nx : Cardinal\n⊢ x ∈ range Nat.cast ↔ x ∈ Iio ℵ₀",
"tactic": "simp only [mem_Iio, mem_range, eq_comm, lt_aleph0]"
}
] | [
1461,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_zero' | [] | [
1922,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1918,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.uncurry_id_eq_ev | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nA B X X' Y Y' Z : C\ninst✝ : Closed A\n⊢ uncurry (𝟙 ((ihom A).obj X)) = (ihom.ev A).app X",
"tactic": "rw [uncurry_eq, tensor_id, id_comp]"
}
] | [
239,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\na : Fin n\n⊢ ↑a = ↑0 ↔ ↑(↑castSucc a) = ↑0",
"tactic": "simp"
}
] | [
1291,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/CategoryTheory/Linear/FunctorCategory.lean | CategoryTheory.NatTrans.app_smul | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.add_apply | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_preimage | [] | [
200,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Nat/Cast/Field.lean | Nat.one_div_le_one_div | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : LinearOrderedSemifield α\nn m : ℕ\nh : n ≤ m\n⊢ 0 < ↑n + 1\n\ncase refine'_2\nα : Type u_1\ninst✝ : LinearOrderedSemifield α\nn m : ℕ\nh : n ≤ m\n⊢ ↑n + 1 ≤ ↑m + 1",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedSemifield α\nn m : ℕ\nh : n ≤ m\n⊢... | [
75,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_false | [] | [
670,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Finset.measurableSet | [] | [
315,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
11
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.post_post | [
{
"state_after": "J : Type u₁\ninst✝⁶ : Category J\nK : Type u₂\ninst✝⁵ : Category K\nC : Type u\ninst✝⁴ : Category C\nF : J ⥤ C\nD : Type u'\ninst✝³ : Category D\ninst✝² : HasLimit F\nG : C ⥤ D\ninst✝¹ : HasLimit (F ⋙ G)\nE : Type u''\ninst✝ : Category E\nH : D ⥤ E\nh : HasLimit ((F ⋙ G) ⋙ H)\nthis : HasLimit ... | [
484,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.pre_map | [
{
"state_after": "case w\nJ : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF : J ⥤ C\ninst✝¹ : HasColimitsOfShape J C\nG : J ⥤ C\nα : F ⟶ G\ninst✝ : HasColimitsOfShape K C\nE : K ⥤ J\nj✝ : K\n⊢ ι (E ⋙ F) j✝ ≫ pre F E ≫ colim.map α = ι (E ⋙ F) j✝ ≫ colim.map (w... | [
1119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_ne_zero | [] | [
1257,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | ContinuousOn.surjOn_Icc | [] | [
605,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.ext | [
{
"state_after": "case mk\nC : Type u\ninst✝ : Category C\nX Y Z : C\nβ : X ≅ Y\nhom✝ : X ⟶ Y\ninv✝ : Y ⟶ X\nhom_inv_id✝ : hom✝ ≫ inv✝ = 𝟙 X\ninv_hom_id✝ : inv✝ ≫ hom✝ = 𝟙 Y\nw : (mk hom✝ inv✝).hom = β.hom\nthis : (mk hom✝ inv✝).inv = β.inv\n⊢ mk hom✝ inv✝ = β",
"state_before": "C : Type u\ninst✝ : Catego... | [
97,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.inv_symm_left | [] | [
225,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toAlgHom_toLinearMap | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/RingTheory/Localization/Away/AdjoinRoot.lean | IsLocalization.adjoin_inv | [] | [
46,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.nontrivial_reverse_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Cycle α\n⊢ Nontrivial (reverse s) ↔ Nontrivial s",
"tactic": "simp [Nontrivial]"
}
] | [
638,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.exists_right_complement'_of_coprime_of_fintype | [] | [
289,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toFinset_toMultiset | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.51824\nι : Type ?u.51827\ninst✝ : DecidableEq α\nf : α →₀ ℕ\n⊢ Multiset.toFinset (↑toMultiset 0) = 0.support\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.51824\nι : Type ?u.51827\ninst✝ : DecidableEq α\nf : α →₀ ℕ\n⊢ ∀ (a : α) (b : ℕ) (f : α →₀ ℕ),\n ... | [
118,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_zero | [] | [
345,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_one' | [] | [
915,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_right_cancel_iff | [] | [
447,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Analysis/Normed/Group/ControlledClosure.lean | controlled_closure_of_complete | [
{
"state_after": "G : Type u_1\ninst✝² : NormedAddCommGroup G\ninst✝¹ : CompleteSpace G\nH : Type u_2\ninst✝ : NormedAddCommGroup H\nf : NormedAddGroupHom G H\nK : AddSubgroup H\nC ε : ℝ\nhC : 0 < C\nhε : 0 < ε\nhyp : NormedAddGroupHom.SurjectiveOnWith f K C\nh : H\nh_in : h ∈ AddSubgroup.topologicalClosure K\n... | [
114,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.top_toSubalgebra | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Order/WithBot.lean | WithBot.unbot'_bot_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.39753\nγ : Type ?u.39756\nδ : Type ?u.39759\na✝ b✝ : α\ninst✝¹ : LE α\ninst✝ : OrderBot α\na : WithBot α\nb : α\n⊢ unbot' ⊥ a ≤ b ↔ a ≤ ↑b",
"tactic": "cases a <;> simp [none_eq_bot, some_eq_coe]"
}
] | [
390,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.srange_top_of_surjective | [] | [
793,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.eq_pure_of_finite | [] | [
326,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_biUnion_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.558165\nγ : Type ?u.558168\nδ : Type ?u.558171\nι : Type u_2\nR : Type ?u.558177\nR' : Type ?u.558180\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ : Set α\ns : ι → Set α\nt : Set ι\nht : Se... | [
2743,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2740,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.self_lt_sinh_iff | [] | [
777,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/RingTheory/RingInvo.lean | RingInvo.involution | [] | [
100,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_succ_ne_one | [] | [
185,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.186829\nι : Type ?u.186832\nG : Type ?u.186835\nM : Type u_2\nN : Type ?u.186841\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\nhf : Set.Finite (mulSupport f)\n⊢ (∏ᶠ (i : α), f i) = ∏ i in Finite.toFinset hf, f i",
"tactic... | [
431,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Order/Synonym.lean | ofLex_inj | [] | [
205,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_add | [
{
"state_after": "no goals",
"state_before": "r s : ℝ\n⊢ (↑(r + s)).re = (↑r + ↑s).re ∧ (↑(r + s)).im = (↑r + ↑s).im",
"tactic": "simp [ofReal']"
}
] | [
227,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_diff_left | [] | [
1843,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1842,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean | CategoryTheory.IsKernelPair.isIso_of_mono | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nR X Y Z : C\nf : X ⟶ Y\na b : R ⟶ X\nh : IsKernelPair f a b\ninst✝ : Mono f\n⊢ IsIso\n (IsLimit.conePointUniqueUpToIso (IsPullback.isLimit (_ : IsKernelPair f (𝟙 X) (𝟙 X))) (IsPullback.isLimit h)).inv",
"state_before": "C : Type u\ninst✝¹ : Category C\... | [
214,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_empty | [] | [
575,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.csin | [] | [
395,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_le_sqrt | [] | [
108,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.comp_antitone | [] | [
273,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
8
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.iSup_eq_closure | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.22167\nA : Type ?u.22170\ninst✝¹ : Mul M\ns : Set M\ninst✝ : Add A\nt : Set A\nS : Subsemigroup M\nι : Sort u_1\np : ι → Subsemigroup M\n⊢ (⨆ (i : ι), p i) = closure (⋃ (i : ι), ↑(p i))",
"tactic": "simp_rw [Subsemigroup.closure_iUn... | [
461,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Std/Data/String/Lemmas.lean | String.offsetOfPos_of_valid | [
{
"state_after": "no goals",
"state_before": "l r : List Char\n⊢ offsetOfPos { data := l ++ r } { byteIdx := utf8Len l } = List.length l",
"tactic": "simpa using offsetOfPosAux_of_valid [] l r 0"
}
] | [
677,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
676,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.mk_eq_top_of_isIso | [] | [
275,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_comap_eq_of_surjective | [] | [
453,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_toNonUnitalRingHom_comp_toNonUnitalRingHom | [
{
"state_after": "case a\nF : Type ?u.86962\nα : Type ?u.86965\nβ : Type ?u.86968\nR : Type u_1\nS : Type u_2\nS' : Type ?u.86977\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring S'\ne : R ≃+* S\nx✝ : R\n⊢ ↑(NonUnitalRingHom.comp (toNonUnitalRingHom ... | [
662,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.of_eq_of_gradedMonoid_eq | [] | [
152,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Independence.lean | Projectivization.independent_iff_not_dependent | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nK : Type u_2\nV : Type u_3\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : ι → ℙ K V\n⊢ Independent f ↔ ¬Dependent f",
"tactic": "rw [dependent_iff_not_independent, Classical.not_not]"
}
] | [
106,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Associated.lean | Associated.dvd_dvd | [] | [
543,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
11
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.image_of_equiv | [
{
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172,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_prod | [
{
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348,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.hasSum_iff | [
{
"state_after": "α : Type u_2\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → 𝕜\nc : 𝕜\n⊢ HasSum (fun x => ↑re (f x)) (↑re c) ∧ HasSum (fun x => ↑im (f x)) (↑im c) → HasSum f c",
"state_before": "α : Type u_2\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → 𝕜\nc : 𝕜\n⊢ HasSum f c ↔ HasSum (fun x => ↑re (f x)) (↑r... | [
549,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_def | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Std/Logic.lean | ne_of_mem_of_not_mem' | [] | [
679,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
679,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_cases | [
{
"state_after": "R : Type ?u.616312\ninst✝¹⁰ : CommRing R\nM : Type u_1\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nM' : Type ?u.616903\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nι : Type ?u.617445\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Fintype ι\ne : Basis ι R M\nA : Type u_2\ninst✝³ : CommRing A\ninst✝² ... | [
246,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.rightMoves_add_cases | [
{
"state_after": "x y : PGame\nk : RightMoves (x + y)\nP : RightMoves (x + y) → Prop\nhl : ∀ (j : RightMoves x), P (↑toRightMovesAdd (Sum.inl j))\nhr : ∀ (j : RightMoves y), P (↑toRightMovesAdd (Sum.inr j))\n⊢ P (↑toRightMovesAdd (↑toRightMovesAdd.symm k))",
"state_before": "x y : PGame\nk : RightMoves (x +... | [
1574,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1568,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.orderedSMul | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.89486\nS : Type ?u.89489\na b : ℂ\nr : ℝ\nhab : a < b\nhr : 0 < r\n⊢ (r • a).re ≤ (r • b).re",
"tactic": "simp [hr, hab.1.le]"
},
{
"state_after": "no goals",
"state_before": "R : Type ?u.89486\nS : Type ?u.89489\na b : ℂ\nr : ℝ\nhab ... | [
140,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.mul_nat_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nhn : n ≠ 0\n⊢ LiouvilleWith p (x * ↑n) ↔ LiouvilleWith p x",
"tactic": "rw [← Rat.cast_coe_nat, mul_rat_iff (Nat.cast_ne_zero.2 hn)]"
}
] | [
169,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_setOf | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.65383\nγ : Type ?u.65386\nι : Sort u_2\nι' : Sort ?u.65392\nι₂ : Sort ?u.65395\nκ : ι → Sort ?u.65400\nκ₁ : ι → Sort ?u.65405\nκ₂ : ι → Sort ?u.65410\nκ' : ι' → Sort ?u.65415\nP : ι → α → Prop\nx✝ : α\n⊢ (x✝ ∈ ⋂ (i : ι), {x | P i x}) ↔ x✝ ∈ {x | ∀ (i : ι), P i... | [
439,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.ext | [] | [
71,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.ofSet.inj | [
{
"state_after": "x y : ZFSet\nh : ↑x = ↑y\nz : ZFSet\n⊢ ↑x z ↔ ↑y z",
"state_before": "x y : ZFSet\nh : ↑x = ↑y\nz : ZFSet\n⊢ z ∈ x ↔ z ∈ y",
"tactic": "change (x : Class.{u}) z ↔ (y : Class.{u}) z"
},
{
"state_after": "no goals",
"state_before": "x y : ZFSet\nh : ↑x = ↑y\nz : ZFSet\n⊢ ↑x z... | [
1613,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsSymm.eq | [] | [
227,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
11
] |
Mathlib/Order/CompleteLattice.lean | le_sInf | [] | [
212,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Rel.lean | Rel.image_inter | [] | [
147,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.eq_of_le_of_card_le | [] | [
770,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_comp_mul_left_Ioi | [
{
"state_after": "E : Type u_1\nf : ℝ → E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\ng : ℝ → E\na b : ℝ\nhb : 0 < b\nthis : ∀ (c : ℝ), MeasurableSet (Ioi c)\n⊢ (∫ (x : ℝ) in Ioi a, g (b * x)) = abs b⁻¹ • ∫ (x : ℝ) in Ioi (b * a), g x",
"state_before": "E : Type u_1\nf... | [
886,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_singleton_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.35142\nγ : Type ?u.35145\ns✝ : Finset α\na✝ b : α\ns : Finset α\na : α\n⊢ s ⊆ {a} ↔ s = ∅ ∨ s = {a}",
"tactic": "rw [← coe_subset, coe_singleton, Set.subset_singleton_iff_eq, coe_eq_empty, coe_eq_singleton]"
}
] | [
781,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Algebra/Lie/Basic.lean | sub_lie | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\n... | [
184,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_eq_toReal | [
{
"state_after": "case intro\nα : Type ?u.827878\nβ : Type ?u.827881\nb c d : ℝ≥0∞\nr p q : ℝ≥0\nhb : b ≠ ⊤\na : ℝ≥0\n⊢ ENNReal.toReal ↑a = ENNReal.toReal b ↔ ↑a = b",
"state_before": "α : Type ?u.827878\nβ : Type ?u.827881\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ ⊤\nhb : b ≠ ⊤\n⊢ ENNReal.toReal a = ENNReal.t... | [
2270,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2267,
1
] |
Mathlib/Algebra/Star/Module.lean | star_int_cast_smul | [] | [
49,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_mul | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 ≤ x\ny : ℝ\n⊢ sqrt (x * y) = sqrt x * sqrt y",
"tactic": "simp_rw [sqrt, ← NNReal.coe_mul, NNReal.coe_eq, Real.toNNReal_mul hx, NNReal.sqrt_mul]"
}
] | [
396,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Order/BoundedOrder.lean | min_top_left | [] | [
843,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Combinatorics/Derangements/Finite.lean | numDerangements_sum | [
{
"state_after": "case zero\nα : Type ?u.22310\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n⊢ ↑(numDerangements Nat.zero) = ∑ k in Finset.range (Nat.zero + 1), (-1) ^ k * ↑(Nat.ascFactorial k (Nat.zero - k))\n\ncase succ\nα : Type ?u.22310\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nhn : ↑(numDerangements... | [
130,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_add | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₁ b₂ : R\n⊢ a * (b₁ + b₂) = a * b₁ + 0 + a * b₂",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₁ c₁ b₂ c₂ d : R\nx✝² : a... | [
413,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivAt.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 : HasDerivAt f f' x\n⊢ HasFDerivAt f (ContinuousLinearMap.smulRight reClm f' + I • ContinuousLinearMap.smulRight imClm f') x",
"tactic... | [
111,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.coe_eq_coe | [] | [
468,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Data/Nat/Parity.lean | Function.Involutive.iterate_two_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α\nn✝ : ℕ\nhf : Involutive f\nn : ℕ\n⊢ f^[2 * n] = id",
"tactic": "rw [iterate_mul, involutive_iff_iter_2_eq_id.1 hf, iterate_id]"
}
] | [
312,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Finsupp.basis_repr | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.exists_mem_range_of_norm_rat_le_one | [] | [
141,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/Int/Lemmas.lean | Int.min_eq_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : a ≤ b\n⊢ min a b = a",
"tactic": "simp [Int.min_def, h]"
}
] | [
703,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
703,
11
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | Submodule.subtypeₗᵢ_toLinearMap | [] | [
471,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.coe_injective | [] | [
97,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.singleMapHomologicalComplex_inv_app_ne | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁶ : Category V\ninst✝⁵ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh✝ k : D ⟶ E\ni✝ : ι\ninst✝⁴ : HasZeroObject V\nW : Type u_3\ninst✝³ : Category W\ninst✝² : Preadditive W\ninst✝¹ : HasZeroObj... | [
336,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.truncate_approx | [] | [
288,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Hom.comp_apply | [] | [
580,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.mul_transvection_apply_of_ne | [
{
"state_after": "no goals",
"state_before": "n : Type u_1\np : Type ?u.18322\nR : Type u₂\n𝕜 : Type ?u.18327\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ni j : n\ninst✝ : Fintype n\na b : n\nhb : b ≠ j\nc : R\nM : Matrix n n R\n⊢ (M ⬝ transvection i j c) a b = M... | [
141,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Logic/Basic.lean | eq_mp_eq_cast | [] | [
517,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
9
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ext_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.28742\nδ : Type ?u.28745\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne✝ : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ne : LocalHomeomorph α β\n⊢ (∀ (x : α), ↑e x = ↑e x) ∧\n (∀... | [
332,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
11
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_le_nadd_right | [
{
"state_after": "case inl\na✝ b c : Ordinal\nh✝ : b ≤ c\na : Ordinal\nh : b < c\n⊢ b ♯ a ≤ c ♯ a\n\ncase inr\na✝ b a : Ordinal\nh : b ≤ b\n⊢ b ♯ a ≤ b ♯ a",
"state_before": "a✝ b c : Ordinal\nh : b ≤ c\na : Ordinal\n⊢ b ♯ a ≤ c ♯ a",
"tactic": "rcases lt_or_eq_of_le h with (h | rfl)"
},
{
"stat... | [
243,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.coe_subtypeL | [] | [
1035,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.isSubterminal_of_isTerminal | [] | [
89,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_insert_eq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.40151\nι : Sort ?u.40154\nι' : Sort ?u.40157\nf✝ : α → β\ns✝ t : Set α\nf : α → β\na : α\ns : Set α\nx✝ : β\n⊢ x✝ ∈ f '' insert a s ↔ x✝ ∈ insert (f a) (f '' s)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.40151\nι : Sort ?u.401... | [
391,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Lattice.lean | inf_left_right_swap | [] | [
510,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Icc_iff | [] | [
555,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_compTendsto | [] | [
255,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
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