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/Combinatorics/Composition.lean | Composition.sizeUpTo_zero | [
{
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"state_before": "n : ℕ\nc : Composition n\n⊢ sizeUpTo c 0 = 0",
"tactic": "simp [sizeUpTo]"
}
] | [
218,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coordChange_coordChange | [
{
"state_after": "ι : Type ?u.55888\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.55899\nZ : Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\nproj : Z → B\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace (TotalSpace E)\ne : Trivialization F proj\nx✝ : Z\ne' : Trivialization F TotalSpace.... | [
695,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.42415\nγ : Type ?u.42418\nδ : Type ?u.42421\nι : Type u_2\nR : Type ?u.42427\nR' : Type ?u.42430\nm✝ : MeasurableSpace α\nμ✝ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ : Set α\nm : MeasurableSpace α\nμ : Measure α\ns : Finset ι\nt : ι → Set α\nh : ∀ (i : ι), i ∈ s → MeasurableSet... | [
423,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/Geometry/Manifold/ChartedSpace.lean | mem_achart_source | [] | [
577,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
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Mathlib/Order/Bounds/OrderIso.lean | OrderIso.lowerBounds_image | [] | [
31,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.top_coe | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.norm_toL1 | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1315289\nδ : Type ?u.1315292\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nhf : Integrable f\n⊢ ENNReal.toReal (∫⁻ (a : α), ↑‖f a‖₊ ∂μ) = ENNReal.toReal (∫⁻ (a... | [
1396,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_union_Ioc_eq_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.125811\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ a b c : α\nh₁ : a ≤ b\nh₂ : b ≤ c\n⊢ Ioc a b ∪ Ioc b c = Ioc a c",
"tactic": "rw [← coe_inj, coe_union, coe_Ioc, coe_Ioc, coe_Ioc, Set.Ioc_union_Ioc_eq_Ioc h₁ h₂]"
... | [
764,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap | [] | [
1794,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1792,
1
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.coe_inl | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_mul_mk'_one | [] | [
409,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
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Mathlib/Order/PartialSups.lean | partialSups_succ | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Topology/QuasiSeparated.lean | OpenEmbedding.isQuasiSeparated_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\nh : OpenEmbedding f\ns : Set α\n⊢ IsQuasiSeparated (f '' s) → IsQuasiSeparated s",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β... | [
101,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Deprecated/Group.lean | IsGroupHom.inv | [] | [
354,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
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Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wPathDestRight_wPathCasesOn | [] | [
108,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
1175,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
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Mathlib/GroupTheory/Finiteness.lean | Subgroup.fg_iff_add_fg | [
{
"state_after": "M : Type ?u.71766\nN : Type ?u.71769\ninst✝³ : Monoid M\ninst✝² : AddMonoid N\nG : Type u_1\nH : Type ?u.71781\ninst✝¹ : Group G\ninst✝ : AddGroup H\nP : Subgroup G\n⊢ Submonoid.FG P.toSubmonoid ↔ AddSubmonoid.FG (↑toAddSubgroup P).toAddSubmonoid",
"state_before": "M : Type ?u.71766\nN : T... | [
267,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/GroupTheory/SpecificGroups/Alternating.lean | Equiv.Perm.closure_three_cycles_eq_alternating | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : σ ∈ alternatingGroup α\nhind :\n ∀ (n : ℕ) (l : List (Perm α)),\n (∀ (g : Perm α), g ∈ l → IsSwap g) → List.length l = 2 * n → List.prod l ∈ closure {σ | IsThreeCycle σ}\n⊢ σ ∈ closure {σ | IsThreeCycle σ}\n\ncase hi... | [
173,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_trans | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.continuous_iteratedFDeriv | [] | [
1654,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1652,
1
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Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.leftUnitor_hom_apply | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
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Mathlib/Data/Num/Lemmas.lean | Num.cast_toZNum | [] | [
789,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Partial.lean | Filter.rcomap_rcomap | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nr : Rel α β\ns : Rel β γ\nl : Filter γ\nt : Set α\n⊢ t ∈ (rcomap r (rcomap s l)).sets ↔ t ∈ (rcomap (Rel.comp r s) l).sets",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nr : Rel α β\ns : Rel β γ\nl : Filter γ\n⊢ (rcomap r (rcomap s l)).se... | [
125,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.isIdempotentComplete_iff_opposite | [
{
"state_after": "case mp\nC : Type u_1\ninst✝ : Category C\n⊢ IsIdempotentComplete Cᵒᵖ → IsIdempotentComplete C\n\ncase mpr\nC : Type u_1\ninst✝ : Category C\n⊢ IsIdempotentComplete C → IsIdempotentComplete Cᵒᵖ",
"state_before": "C : Type u_1\ninst✝ : Category C\n⊢ IsIdempotentComplete Cᵒᵖ ↔ IsIdempotentCo... | [
206,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.isEquiv_iff_val_le_one | [
{
"state_after": "no goals",
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447,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.asIdeal_le_asIdeal | [] | [
921,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
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] |
Mathlib/Data/Seq/Computation.lean | Computation.tail_think | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\nf : Stream' (Option α)\nal : ∀ ⦃n : ℕ⦄ ⦃a : α⦄, f n = some a → f (n + 1) = some a\n⊢ tail (think { val := f, property := al }) = { val := f, property := al }",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\n⊢ tail (think... | [
181,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | inner_orthogonalProjection_eq_of_mem_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.979345\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nu : { x ... | [
1064,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.image_symm_eq_preimage | [
{
"state_after": "no goals",
"state_before": "R₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.1603076\ninst✝²⁴ : Semiring R₁\ninst✝²³ : Semiring R₂\ninst✝²² : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₁ : R₂ →+* R₁\ninst✝²¹ : RingHomInvPair σ₁₂ σ₂₁\ninst✝²⁰ : RingHomInvPair σ₂₁ σ₁₂\nσ₂₃ : R₂ →+* R₃\nσ₃₂ : R₃ →+* R₂\ninst✝... | [
2121,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2120,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryCofan.IsColimit.hom_ext | [] | [
289,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.InfHom.le_apply_bliminf | [] | [
971,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.id_apply | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.disjoint_out' | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.40758\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na b : Quotient ↑H.toSubmonoid ↑K\n⊢ ¬Disjoint (doset (Quotient.out' a) ↑H ↑K) (doset (Quotient.out' b) ↑H ↑K) → a = b",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.40... | [
160,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_const | [] | [
1074,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_div_of_lt_top | [] | [
1551,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1551,
1
] |
Mathlib/Data/Holor.lean | Holor.cprankMax_mul | [
{
"state_after": "no goals",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝ : Ring α\nx : Holor α [d]\n⊢ CPRankMax 0 (x ⊗ 0)",
"tactic": "simp [mul_zero x, CPRankMax.zero]"
},
{
"state_after": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝ : Ring α\nn : ℕ\nx : Holor α [d]\ny₁... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_span_singleton_eq_map | [
{
"state_after": "case h\nι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\nm : M\nx✝ : Submodule R N\n⊢ ... | [
176,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.exists_mem | [] | [
133,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/Data/Set/Function.lean | StrictMonoOn.mono | [] | [
308,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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] |
Mathlib/Topology/Category/Profinite/CofilteredLimit.lean | Profinite.exists_locallyConstant_fin_two | [
{
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"stat... | [
137,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.coeff_bdd_of_roots_le | [
{
"state_after": "case inl\nα : Type ?u.202389\nR : Type ?u.202392\ninst✝³ : NormedRing R\ninst✝² : IsAbsoluteValue norm\nF : Type u_1\nK : Type u_2\ninst✝¹ : CommRing F\ninst✝ : NormedField K\nB : ℝ\nd : ℕ\nf : F →+* K\np : F[X]\nh1 : Monic p\nh2 : Splits f p\nh3 : natDegree p ≤ d\nh4 : ∀ (z : K), z ∈ roots (m... | [
211,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
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] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_neg | [] | [
1059,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.add_lt_aleph0 | [
{
"state_after": "α β : Type u\na b : Cardinal\nm n : ℕ\nha : ↑m < ℵ₀\nhb : ↑n < ℵ₀\n⊢ ↑(m + n) < ℵ₀",
"state_before": "α β : Type u\na b : Cardinal\nm n : ℕ\nha : ↑m < ℵ₀\nhb : ↑n < ℵ₀\n⊢ ↑m + ↑n < ℵ₀",
"tactic": "rw [← Nat.cast_add]"
},
{
"state_after": "no goals",
"state_before": "α β : T... | [
1526,
76
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1524,
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Mathlib/Algebra/GroupPower/Lemmas.lean | one_lt_zpow' | [
{
"state_after": "case intro\nα : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : OrderedCommGroup α\nm n✝ : ℤ\na b : α\nha : 1 < a\nk : ℤ\nhk : 0 < k\nn : ℕ\nhn : k = ↑n\n⊢ 1 < a ^ k",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\... | [
325,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
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] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.comp_continuousOn | [] | [
326,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.appendFun_id_id | [] | [
303,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Ico | [] | [
448,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | analyticAt_const | [] | [
530,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Equiv.coe_toEmbedding | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Logic/IsEmpty.lean | Function.extend_of_isEmpty | [] | [
218,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_withConstants | [] | [
760,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
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Mathlib/Algebra/ModEq.lean | AddCommGroup.add_modEq_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\n⊢ a + b ≡ a [PMOD p] ↔ b ≡ 0 [PMOD p]",
"tactic": "simp [← modEq_sub_iff_add_modEq']"
}
] | [
285,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.isSpecial_iff | [
{
"state_after": "u : XgcdType\n⊢ u.wp + u.zp + u.wp * u.zp = u.x * u.y ↔ w u * z u = succPNat (u.x * u.y)",
"state_before": "u : XgcdType\n⊢ IsSpecial u ↔ IsSpecial' u",
"tactic": "dsimp [IsSpecial, IsSpecial']"
},
{
"state_after": "u : XgcdType\nwp x y zp ap bp : ℕ\n⊢ { wp := wp, x := x, y := ... | [
159,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_mul_swap_mul_swap | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nx y z : α\nhwz : x ≠ y\nhxz : x ≠ z\nn : α\n⊢ (if\n (if (if n = y then z else if n = z then y else n) = x then y\n else\n if (if n = y then z else if n = z then y else n) = y then x\n else if n = y then z else... | [
595,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
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Mathlib/GroupTheory/Congruence.lean | Con.liftOn_coe | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.separatingLeft_iff_det_ne_zero | [
{
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755,
74
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753,
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Mathlib/Algebra/Homology/Additive.lean | ChainComplex.single₀MapHomologicalComplex_hom_app_succ | [] | [
380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
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Mathlib/Topology/SubsetProperties.lean | Set.Finite.isCompact_sUnion | [
{
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"state_before": "α : Type u\nβ :... | [
428,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
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Std/Data/Int/DivMod.lean | Int.mul_ediv_cancel | [
{
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},
{
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187,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
185,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.exists_bound_of_continuous | [
{
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140,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
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Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.C_content_dvd | [] | [
232,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.noSibling_combine | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns : Heap α\n⊢ NoSibling\n (match s with\n | h₁@h_1:(node a child h₂@h:(node a_1 child_1 s)) => merge le (merge le h₁ h₂) (combine le s)\n | h => h)",
"state_before": "α : Type u_1\nle : α → α → Bool\ns : Heap α\n⊢ NoSibling (combine le s)",
"ta... | [
102,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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1
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Mathlib/Data/Matrix/DMatrix.lean | DMatrix.neg_apply | [] | [
131,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Data/List/Basic.lean | List.enumFrom_get? | [
{
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"state_before": "ι : Type ?u.430582\nα : Type u\nβ : Type v\nγ : Type w\nδ... | [
3827,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3823,
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Mathlib/Data/Fintype/Card.lean | fin_injective | [] | [
313,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_prodExtendRight | [
{
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745,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | dNext_comp_right | [] | [
71,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Data/Finset/NAry.lean | Finset.card_le_card_image₂_right | [
{
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286,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Analysis/Convex/Extreme.lean | isExtreme_sInter | [
{
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134,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_inter_self | [] | [
2082,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2081,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | AntitoneOn.integrableOn_of_measure_ne_top | [] | [
349,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.neg | [] | [
495,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | ContinuousWithinAt.log | [] | [
399,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
8
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.map_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R →+* S\n⊢ map f (T R 0) = T S 0",
"tactic": "simp only [T_zero, Polynomial.map_one]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : C... | [
169,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Std/Data/Int/Lemmas.lean | Int.min_le_right | [
{
"state_after": "a b : Int\n⊢ (if a ≤ b then a else b) ≤ b",
"state_before": "a b : Int\n⊢ min a b ≤ b",
"tactic": "rw [Int.min_def]"
},
{
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"state_before": "a b : Int\n⊢ (if a ≤ b then a else b) ≤ b",
"tactic": "split <;> simp [*]"
}
] | [
695,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
695,
11
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_iff_isSymmetric | [
{
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285,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_ball | [
{
"state_after": "ι : Type u_1\ninst✝ : Fintype ι\na : ι → ℝ\nr : ℝ\nhr : 0 < r\n⊢ ofReal (2 * r) ^ Finset.card Finset.univ = ofReal ((2 * r) ^ Fintype.card ι)",
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263,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
8
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.num_add | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Logic/Basic.lean | eq_mpr_eq_cast | [] | [
520,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
9
] |
src/lean/Init/Data/List/Basic.lean | List.filter_eq_filterTR | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\n⊢ ∀ (x : Type u_1), filter = filterTR",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\n⊢ @filter = @filterTR",
"tactic": "apply funext"
},
{
"state_after": "case h\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\n⊢ filter = f... | [
255,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
253,
10
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.map_one | [] | [
591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Algebra/Order/Group/WithTop.lean | WithTop.coe_neg | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inr_le_inr_iff | [] | [
352,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.not_mem_support_iff | [
{
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"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m✝ : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q p : MvPolynomial σ R\nm : σ →₀ ℕ\n⊢ ¬m ∈ support p ↔ coeff m p = 0",
"tactic": "simp"
}
] | [
588,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_subtype_eq_top | [
{
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1637,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_le_maxVar | [] | [
150,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
9
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.modByMonicHom_mk | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.exists_separable_of_irreducible | [
{
"state_after": "F : Type u\ninst✝¹ : Field F\nK : Type v\ninst✝ : Field K\np : ℕ\nHF : CharP F p\nf : F[X]\nhf : Irreducible f\nhp : Nat.Prime p\n⊢ ∃ n g, Separable g ∧ ↑(expand F (p ^ n)) g = f",
"state_before": "F : Type u\ninst✝¹ : Field F\nK : Type v\ninst✝ : Field K\np : ℕ\nHF : CharP F p\nf : F[X]\n... | [
358,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.exp_four_lt | [
{
"state_after": "α : Type ?u.837007\nβ : Type ?u.837010\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ 4 / ↑6 < log 2\n\nα : Type ?u.837007\nβ : Type ?u.837010\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ 0 < ↑6",
"state_before": "α : Type ?u.837007\nβ : Type ?u.837010\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ exp 4 < 64",
"tactic": "rw [show... | [
523,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.coe_castRingHom | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.types_ι_jointly_surjective | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ : Category C'\nD✝ : GlueData C\nD : GlueData (Type u_1)\nx : glued D\n⊢ ∃ i y, Multicoequalizer.π (diagram D) i y = x",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ : Category C'\nD✝ : GlueData C\nD : GlueData ... | [
250,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.coe_prodCongr | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.nat_ne_top | [] | [
689,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
9
] |
Mathlib/Data/Quot.lean | Quotient.mk''_eq_mk | [] | [
804,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
11
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.isNat.natElim | [] | [
58,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_abs | [] | [
179,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_pow_add_C | [
{
"state_after": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\na : R\nthis : degree (↑C a) < degree (X ^ n)\n⊢ degree (X ^ n + ↑C a) = ↑n",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semirin... | [
1382,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_generator_self_inv | [
{
"state_after": "R : Type ?u.65551\nA : Type ?u.65554\nK : Type u_2\ninst✝¹⁴ : CommRing R\ninst✝¹³ : CommRing A\ninst✝¹² : Field K\ninst✝¹¹ : IsDomain A\nR₁✝ : Type ?u.65752\ninst✝¹⁰ : CommRing R₁✝\ninst✝⁹ : IsDomain R₁✝\ninst✝⁸ : Algebra R₁✝ K\ninst✝⁷ : IsFractionRing R₁✝ K\nI✝ J : FractionalIdeal R₁✝⁰ K\nK' ... | [
205,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_preimage | [] | [
294,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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