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/FieldTheory/Tower.lean | rank_mul_rank | [
{
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Mathlib/Algebra/Lie/Submodule.lean | LieHom.range_subset_idealRange | [] | [
938,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_map | [] | [
469,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.const_smul | [] | [
1900,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1897,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_zero | [
{
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"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nx : OreLocalization R S\n⊢ x * 0 = 0",
"tactic": "induction' x using OreLoc... | [
700,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
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Mathlib/Data/Real/EReal.lean | EReal.mul_top_of_pos | [] | [
925,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GroupPower/Lemmas.lean | zsmul_int_int | [
{
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"tactic": "simp"
}
] | [
618,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.linearEquivAt_symm_apply | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
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Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.coe_id | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
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Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | span_gramSchmidtNormed | [
{
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329,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_refl | [] | [
860,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.map_post | [
{
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1141,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
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Mathlib/Order/WithBot.lean | WithTop.recTopCoe_coe | [] | [
630,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_eq_zero_iff | [] | [
883,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
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Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.yonedaEquiv_apply | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.algHom_ext' | [] | [
92,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.map_comp | [
{
"state_after": "case e_self\nC : Type u\ninst✝⁶ : Category C\nf g : Arrow C\ninst✝⁵ : HasImage f.hom\ninst✝⁴ : HasImage g.hom\nsq : f ⟶ g\ninst✝³ : HasImageMap sq\nh : Arrow C\ninst✝² : HasImage h.hom\nsq' : g ⟶ h\ninst✝¹ : HasImageMap sq'\ninst✝ : HasImageMap (sq ≫ sq')\n⊢ HasImageMap.imageMap (sq ≫ sq') = i... | [
826,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
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Mathlib/GroupTheory/IsFreeGroup.lean | IsFreeGroup.of_eq_freeGroup_of | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Ioc | [
{
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"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Ioc a b) = Ioc ↑a ↑b",
"tactic": "simp [Ioc_eq_finset_subtype, Finset.fin, Finset.map_map, Ioc_filter_lt_of_lt_right]"
}
] | [
70,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_centralizer_iff | [] | [
2281,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2280,
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Mathlib/Algebra/BigOperators/Basic.lean | ofMul_list_prod | [
{
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Mathlib/GroupTheory/Nilpotent.lean | upperCentralSeriesStep_eq_comap_center | [
{
"state_after": "case h\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nx✝ : G\n⊢ x✝ ∈ upperCentralSeriesStep H ↔ x✝ ∈ comap (mk' H) (center (G ⧸ H))",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ upperCentralSeriesStep H = comap (mk' H) (center (G... | [
122,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.mono_inl_of_factor_thru_epi_mono_factorization | [
{
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780,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.nat_trans_from_is_connected | [
{
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365,
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Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_eq_neg_one_pow | [
{
"state_after": "n : ℕ\nhn : n % 2 = 1\n⊢ (if n % 2 = 0 then 0 else if n % 4 = 1 then 1 else -1) = (-1) ^ (n / 2)",
"state_before": "n : ℕ\nhn : n % 2 = 1\n⊢ ↑χ₄ ↑n = (-1) ^ (n / 2)",
"tactic": "rw [χ₄_nat_eq_if_mod_four]"
},
{
"state_after": "n : ℕ\nhn : n % 2 = 1\n⊢ (if n % 4 = 1 then 1 else ... | [
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Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_dotProduct | [
{
"state_after": "no goals",
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"tactic": "simp [neighborFinset_e... | [
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Mathlib/CategoryTheory/Category/TwoP.lean | pointedToTwoPSnd_comp_swap | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.prod_mono_right | [] | [
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793,
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Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mod_add_div | [] | [
129,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | HasFDerivAt.inner | [] | [
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74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Interval.lean | Fin.card_Ici | [
{
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"state_before": "n : ℕ\na b : Fin n\n⊢ card (Ici a) = n - ↑a",
"tactic": "cases n with\n| zero => exact Fin.elim0 a\n| succ =>\n rw [← card_map, map_valEmbedding_Ici, Nat.card_Icc, Nat.succ_sub_one]\n assumption"
},
{
"state_after": "no goals",
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15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Basic.lean | isOpen_Iio | [] | [
298,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/Data/Fintype/Perm.lean | card_perms_of_finset | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.52511\nγ : Type ?u.52514\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nval✝ : Multiset α\nl : List α\nhs : Multiset.Nodup (Quot.mk Setoid.r l)\n⊢ card (permsOfFinset { val := Quot.mk Setoid.r l, nodup := hs }) = (card { val := Quot.mk Setoid.r l, nodup :... | [
149,
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148,
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.iff_pid_with_one_nonzero_prime | [
{
"state_after": "case mp\nR✝ : Type u\ninst✝⁴ : CommRing R✝\ninst✝³ : IsDomain R✝\ninst✝² : DiscreteValuationRing R✝\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ DiscreteValuationRing R → IsPrincipalIdealRing R ∧ ∃! P, P ≠ ⊥ ∧ IsPrime P\n\ncase mpr\nR✝ : Type u\ninst✝⁴ : CommRing R✝\ninst✝³ : IsDoma... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivWithinAt.csin | [] | [
219,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_isProbabilityMeasure | [
{
"state_after": "case h0\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns : Set Ω\nhs : Set.Finite s\nhs' : Set.Nonempty s\n⊢ ↑↑Measure.count s ≠ 0\n\ncase ht\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns : Set Ω\nhs : Set.Finite s\nhs' : Set.N... | [
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Mathlib/Data/Complex/Exponential.lean | sum_range_diag_flip | [
{
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Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_ofLE | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Categ... | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_mul_apply_of_not_exists_add | [] | [
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87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1650,
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Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_toReal | [
{
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179,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_iff | [] | [
57,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_symm_sub | [] | [
225,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.IsEquiv.trans | [] | [
383,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiffOn_of_continuousOn_differentiableOn_deriv | [
{
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99
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133,
1
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Mathlib/Data/Set/Image.lean | Set.powerset_insert | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.61243\nγ : Type ?u.61246\nι : Sort ?u.61249\nι' : Sort ?u.61252\ns : Set α\na : α\nt : Set α\n⊢ t ∈ 𝒫 insert a s ↔ t ∈ 𝒫 s ∪ insert a '' 𝒫 s",
"state_before": "α : Type u_1\nβ : Type ?u.61243\nγ : Type ?u.61246\nι : Sort ?u.61249\nι' : Sort ?u.61252\ns ... | [
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616,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_inf | [] | [
344,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushout.mapLift_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nW X✝ Y✝ Z X Y S T S' : C\nf : T ⟶ X\ng : T ⟶ Y\ni : S ⟶ T\ni' : S' ⟶ S\ninst✝³ : HasPushout f g\ninst✝² : HasPushout (i ≫ f) (i ≫ g)\ninst✝¹ : HasPushout (i' ≫ i ≫ f) (i' ≫ i ≫ g)\ninst✝ : HasPus... | [
1429,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_dvd_lcm_mul_left | [] | [
849,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
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Mathlib/LinearAlgebra/Ray.lean | sameRay_neg_swap | [
{
"state_after": "no goals",
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"tactic": "rw [← sameRay_neg_iff, ne... | [
406,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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Mathlib/Analysis/Convex/Gauge.lean | gauge_nonneg | [] | [
133,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.init_iff | [] | [
285,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.mem_closed_iff_bsup | [
{
"state_after": "no goals",
"state_before": "s : Set Ordinal\na : Ordinal\nhs : IsClosed s\n⊢ a ∈ s ↔ ∃ o _ho f, (∀ (i : Ordinal) (hi : i < o), f i hi ∈ s) ∧ bsup o f = a",
"tactic": "rw [← mem_closure_iff_bsup, hs.closure_eq]"
}
] | [
152,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/Data/Set/Basic.lean | Set.sep_eq_of_subset | [] | [
1425,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1424,
1
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_le_diam | [
{
"state_after": "case pos\nι : Type ?u.374130\ninst✝ : Fintype ι\ns : Set ℝ\nhs : Metric.Bounded s\n⊢ ↑↑volume s ≤ EMetric.diam s\n\ncase neg\nι : Type ?u.374130\ninst✝ : Fintype ι\ns : Set ℝ\nhs : ¬Metric.Bounded s\n⊢ ↑↑volume s ≤ EMetric.diam s",
"state_before": "ι : Type ?u.374130\ninst✝ : Fintype ι\ns ... | [
200,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/GroupTheory/IsFreeGroup.lean | IsFreeGroup.unique_lift | [
{
"state_after": "no goals",
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"tactic": "simpa only [Function.funext_iff] using lift.symm.bijective.existsUnique f"
}
] | [
130,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/Order/OrderIsoNat.lean | RelEmbedding.coe_natLt | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Data/Nat/Dist.lean | Nat.dist_comm | [
{
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}
] | [
31,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.one_im | [] | [
205,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
9
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_assoc | [
{
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"state_before": "i j k : ℤ\n⊢ lcm (↑(lcm i j)) k = lcm i ↑(lcm j k)",
"tactic": "rw [Int.lcm, Int.lcm, Int.lcm, Int.lcm, natAbs_ofNat, natAbs_ofNat]"
},
{
"sta... | [
450,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.prod_divisors_prime_pow | [
{
"state_after": "no goals",
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}
] | [
464,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.57096\ninst✝¹ : Preorder α\ninst✝ : OrderBot α\na : α\n⊢ Ico ⊥ a = Iio a",
"tactic": "simp [← Ici_inter_Iio]"
}
] | [
1031,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.findMin'_dual | [] | [
582,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_le_mk₃_iff | [] | [
146,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.open_eq_sUnion | [] | [
197,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_append | [
{
"state_after": "no goals",
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"tactic": "induction p with\n| nil => simp\n| cons _ _ ih => simp [... | [
405,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ioo_toReal | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ ENNReal.toReal (↑↑volume (Set.pi univ fun i => Ioo (a i) (b i))) = ∏ i : ι, (b i - a i)",
"tactic": "simp only [volume_pi_Ioo, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))]"
}
] | [
234,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | map_lt_lineMap_iff_slope_lt_slope_right | [] | [
266,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.ite_le_natDegree_coeff | [
{
"state_after": "case inl\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nI : Decidable (n < 1 + natDegree p)\nh : n < 1 + natDegree p\n⊢ coeff p n = coeff p n\n\ncase inr\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nI :... | [
383,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.eq_generateFrom_countableBasis | [] | [
644,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackSymmetry_hom_of_mono_eq | [
{
"state_after": "case h₀\nC : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶ Y\ninst✝ : Mono f\n⊢ (pullbackSymmetry f f).hom ≫ pullback.fst = 𝟙 (pullback f f) ≫ pullback.fst\n\ncase h₁\nC : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶... | [
1938,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | Commute.sq_eq_sq_iff_eq_or_eq_neg | [
{
"state_after": "no goals",
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"tactic": "rw [← sub_eq_zero, h.sq_sub_sq, mul_eq_zero, add_eq_zero_iff_eq_neg, sub_eq_zero, or_comm... | [
258,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
11
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Mathlib/Data/Finset/Image.lean | Finset.image_const | [
{
"state_after": "no goals",
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"tactic": "simp only [mem_image, exists_... | [
617,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.toSheafification_app | [] | [
530,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Logic/Basic.lean | apply_ite₂ | [] | [
1234,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.right | [] | [
516,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.removeNone_optionCongr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.8105\ne✝ : Option α ≃ Option β\ne : α ≃ β\nx : α\n⊢ ↑(optionCongr e) (some x) = some (↑e x)",
"tactic": "simp [EquivFunctor.map]"
}
] | [
163,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.toProdMulOpposite_injective | [] | [
340,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.memℒp_re_im_iff | [
{
"state_after": "α : Type u_1\nE : Type ?u.5158781\nF : Type ?u.5158784\nG : Type ?u.5158787\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\n𝕜 : Type ?u.5387273\ninst✝³ :... | [
981,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/LinearAlgebra/Multilinear/FiniteDimensional.lean | MultilinearMap.free_and_finite | [
{
"state_after": "case intro\nι : Type u_2\nR : Type u_1\nM₂ : Type u_3\nM₁ : ι → Type u_4\ninst✝⁹ : Finite ι\ninst✝⁸ : CommRing R\ninst✝⁷ : AddCommGroup M₂\ninst✝⁶ : Module R M₂\ninst✝⁵ : Module.Finite R M₂\ninst✝⁴ : Module.Free R M₂\ninst✝³ : (i : ι) → AddCommGroup (M₁ i)\ninst✝² : (i : ι) → Module R (M₁ i)\n... | [
68,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
9
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Down.erase_mem_compression_of_mem_compression | [
{
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"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Fins... | [
187,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_congr | [
{
"state_after": "no goals",
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"tactic": "simpa only [Iff.comm] using h"
}
] | [
1153,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousWithinAt_right_of_monotoneOn_of_closure_image_mem_nhdsWithin | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝⁶ : LinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : LinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology β\ninst✝ : DenselyOrdered β\nf : α → β\ns : Set α\na : α\nh_mono : MonotoneOn f s\nhs : s ∈ 𝓝[Ici a] a\nhfs : ... | [
93,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_singleton | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.247366\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : P\n⊢ Module.rank k { x // x ∈ ⊥ } ≤ 1",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.247366\ninst✝³ : ... | [
373,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.im_idem | [] | [
817,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
9
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.natTrailingDegree_mul_mirror | [
{
"state_after": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\np q : R[X]\ninst✝ : NoZeroDivisors R\nhp : p = 0\n⊢ natTrailingDegree (p * mirror p) = 2 * natTrailingDegree p\n\ncase neg\nR : Type u_1\ninst✝¹ : Semiring R\np q : R[X]\ninst✝ : NoZeroDivisors R\nhp : ¬p = 0\n⊢ natTrailingDegree (p * mirror p) = 2 ... | [
187,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_sInf | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_neighborFinset | [] | [
1355,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_map_symm | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.569528\ninst✝¹ : CommRing... | [
791,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Logic/Hydra.lean | Relation.not_cutExpand_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\ns : Multiset α\n⊢ ¬CutExpand r s 0",
"tactic": "classical\nrw [cutExpand_iff]\nrintro ⟨_, _, _, ⟨⟩, _⟩"
},
{
"state_after": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\ns : Multiset α\n⊢... | [
107,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.bot_lt_of_maximal | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nM : Ideal R\nhm : IsMaximal M\nnon_field : ¬IsField R\nI : Ideal R\nIbot : ⊥ < I\nItop : I < ⊤\n⊢ ⊥ < M",
"state_before": "α : Type u\nβ : Type v\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontr... | [
816,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Option/Basic.lean | Option.none_orElse' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15823\nγ : Type ?u.15826\nδ : Type ?u.15829\nx : Option α\n⊢ (Option.orElse none fun x_1 => x) = x",
"tactic": "cases x <;> rfl"
}
] | [
277,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.const_inv_smul₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf g : α → β\nc c₁ c₂ x : α\ninst✝³ : AddCommMonoid α\ninst✝² : Neg β\ninst✝¹ : DivisionSemiring γ\ninst✝ : Module γ α\nh : Antiperiodic f c\na : γ\nha : a ≠ 0\n⊢ Antiperiodic (fun x => f (a⁻¹ • x)) (a • c)",
"tactic"... | [
480,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.compl_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.18666\nγ : Type ?u.18669\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : DecidableEq α\na✝ a : α\n⊢ {a}ᶜ = erase univ a",
"tactic": "rw [compl_eq_univ_sdiff, sdiff_singleton_eq_erase]"
}
] | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/LocallyFinite.lean | Set.finite_Ico | [] | [
653,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.diff_left | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nl t₁ t₂ : List α\nh : t₁ ~ t₂\n⊢ List.diff l t₁ = List.diff l t₂",
"tactic": "induction h generalizing l <;>\n first |simp [*, Perm.erase, erase_comm]"
},
{
"state_after": "no goals",
... | [
802,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.image_univ_of_surjective | [] | [
259,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.antitone_principal | [] | [
132,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Set/Pairwise/Lattice.lean | Set.pairwiseDisjoint_sUnion | [] | [
65,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_map | [
{
"state_after": "case bisim\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : WSeq α\n⊢ Computation.IsBisimulation fun c1 c2 =>\n ∃ s, c1 = destruct (map f s) ∧ c2 = Computation.map (Option.map (Prod.map f (map f))) (destruct s)\n\ncase r\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : WSeq α\n⊢ ∃ s_1... | [
1492,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofMul_div | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
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