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/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GLPos.coe_neg | [] | [
230,
6
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229,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_add | [] | [
542,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
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Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.differentiableAt_log_iff | [] | [
67,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_map_of_injective | [
{
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"tactic": "simp [vars, degree... | [
462,
45
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461,
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src/lean/Init/Core.lean | Subsingleton.helim | [
{
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},
{
"state_after": "case h\na✝ b✝ c d : Prop\nα : Sort u\nh₁ : Subsingleton ... | [
879,
26
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876,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.self_comp_symm | [] | [
843,
24
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842,
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Mathlib/Analysis/SpecificLimits/Basic.lean | edist_le_of_edist_le_geometric_of_tendsto | [
{
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... | [
325,
96
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322,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_def_of_mem | [
{
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"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np q : K[X]\nhq : q ∈ K[X]⁰\n⊢ RatFunc.mk p q = { toFractionRing := IsLocalization.mk' (FractionRing K[X]) p { val := q, property := hq } }",
"tactic": "simp only [← mk_coe_def]"
}
] | [
216,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.dartOfNeighborSet_injective | [
{
"state_after": "ι : Sort ?u.99591\n𝕜 : Type ?u.99594\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w : V\ne : Sym2 V\nv : V\ne₁ e₂ : ↑(neighborSet G v)\nh' : (v, ↑e₁) = (v, ↑e₂)\n⊢ ↑e₁ = ↑e₂",
"state_before": "ι : Sort ?u.99591\n𝕜 : Type ?u.99594\nV : Type u\nW :... | [
813,
34
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809,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.ofIsEmpty_top | [] | [
422,
6
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420,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.disjoint_closedBall_of_lt_infDist | [] | [
551,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
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Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.derivation_eq_of_forall_mem_vars | [] | [
91,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_eq_nil_iff_not_periodic_pt | [
{
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"tactic": "si... | [
509,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprodComparison_natural | [
{
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1359,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_id | [
{
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436,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_boxes | [] | [
70,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/Data/List/Count.lean | List.count_concat | [
{
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"tactic": "simp"
}
] | [
240,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.ext_iff | [] | [
186,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/GroupTheory/Submonoid/Basic.lean | MonoidHom.eqLocusM_same | [] | [
594,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
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Mathlib/Data/List/Perm.lean | List.Perm.bind_left | [
{
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"tactic": "rwa [List.forall₂_map_right_iff, List.forall₂_map_left_iff, List.forall₂_same]"
}
] | [
1090,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measureUnivNNReal_zero | [] | [
3102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3101,
1
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.monad_seq_eq_seq | [] | [
122,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_nat_floor_mul_div_atTop | [
{
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592,
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Mathlib/Algebra/Order/Pointwise.lean | csSup_inv | [
{
"state_after": "α : Type u_1\ninst✝³ : ConditionallyCompleteLattice α\ninst✝² : Group α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ns t : Set α\nhs₀ : Set.Nonempty s\nhs₁ : BddBelow s\n⊢ sSup (Inv.inv ''... | [
135,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_lt_card_fiber_of_mul_lt_card | [] | [
393,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanExt_inv_app_left | [
{
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431,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Basic.lean | Real.ciSup_empty | [
{
"state_after": "x y : ℝ\nα : Sort u_1\ninst✝ : IsEmpty α\nf : α → ℝ\n⊢ sSup (Set.range fun i => f i) = 0",
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"tactic": "dsimp [iSup]"
},
{
"state_after": "case h.e'_2.h.e'_3\nx y : ℝ\nα : Sort u_1\nins... | [
806,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.IsLimit.homIso_natural | [] | [
566,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_of_not_one_lt_left | [
{
"state_after": "no goals",
"state_before": "b : Ordinal\nh : ¬1 < b\nx : Ordinal\n⊢ log b x = 0",
"tactic": "simp only [log, dif_neg h]"
}
] | [
271,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Order/PropInstances.lean | Prop.isCompl_iff | [
{
"state_after": "P Q : Prop\n⊢ ¬(P ∧ Q) ∧ (P ∨ Q) ↔ (¬P ↔ Q)",
"state_before": "P Q : Prop\n⊢ IsCompl P Q ↔ ¬(P ↔ Q)",
"tactic": "rw [_root_.isCompl_iff, Prop.disjoint_iff, Prop.codisjoint_iff, not_iff]"
},
{
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113,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/Data/Sym/Card.lean | Sym2.card_subtype_diag | [
{
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182,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/Analysis/Calculus/ContDiff.lean | hasFTaylorSeriesUpToOn_pi | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁷ : No... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
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Mathlib/Computability/Partrec.lean | Nat.Partrec.ppred | [
{
"state_after": "case zero\nthis : Primrec₂ fun n m => if n = Nat.succ m then 0 else 1\n⊢ (Nat.rfind fun n => Part.some false) = Part.none\n\ncase succ\nthis : Primrec₂ fun n m => if n = Nat.succ m then 0 else 1\nn✝ : ℕ\n⊢ (Nat.rfind fun n => Part.some (decide (¬n✝ = n → False))) = Part.some n✝",
"state_be... | [
232,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.support_rename_of_injective | [
{
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347,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.sum_type | [] | [
686,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.merge_nil_right | [] | [
645,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.preimage_mul_right_singleton | [
{
"state_after": "no goals",
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"tactic": "classical rw [← image_mu... | [
1221,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.fst_app_right | [
{
"state_after": "C : Type u\ninst✝ : Category C\nI : MultispanIndex C\nK : Multicofork I\na : I.L\n⊢ (MultispanIndex.multispan I).map (WalkingMultispan.Hom.fst a) ≫\n K.ι.app (WalkingMultispan.right (MultispanIndex.fstFrom I a)) =\n MultispanIndex.fst I a ≫ π K (MultispanIndex.fstFrom I a)",
"state... | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_union_of_symmetric | [
{
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151,
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149,
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Mathlib/Algebra/BigOperators/Fin.lean | finFunctionFinEquiv_single | [
{
"state_after": "α : Type ?u.147970\nβ : Type ?u.147973\nm n : ℕ\ninst✝ : NeZero m\ni : Fin n\nj : Fin m\n⊢ ∀ (x : Fin n), x ≠ i → ↑(Pi.single i j x) * m ^ ↑x = 0",
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358,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.isLimit_aleph0 | [] | [
1448,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_mul_of_lt_order | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\nn : ℕ\nh : ↑n < order ψ\nthis : ↑(coeff R n) (φ * ψ) = ∑ p in Finset.Nat.antidiagonal n, 0\n⊢ ↑(coeff R n) (φ * ψ) = 0\n\ncase this\nR : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\nn : ℕ\nh : ↑n < order ψ\n⊢ ↑(coeff R n) (φ * ... | [
2421,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2411,
1
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Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_neg_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝³ : CommRing R\nx : R\nB : Type u_1\ninst✝² : CommRing B\ninst✝¹ : Algebra R B\ninst✝ : IsLocalization.Away x B\nd : ℤ\n⊢ selfZpow x B (-d) * selfZpow x B d = 1",
"tactic": "rw [mul_comm, selfZpow_mul_neg x B d]"
}
] | [
291,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Set/Prod.lean | Set.union_pi | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.144565\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\n⊢ pi (s₁ ∪ s₂) t = pi s₁ t ∩ pi s₂ t",
"tactic": "simp [pi, or_imp, forall_and, setOf_and]"
}
] | [
762,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.isIso_of_mono_of_nonzero | [] | [
61,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.prod | [] | [
657,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.comap_coe_nhds_infty | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ comap some (𝓝 ∞) = coclosedCompact X",
"tactic": "simp [nhds_infty_eq, comap_sup, comap_map coe_injective]"
}
] | [
346,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.addLsb_eq_twice_add_one | [
{
"state_after": "no goals",
"state_before": "x : ℕ\nb : Bool\n⊢ addLsb x b = 2 * x + bif b then 1 else 0",
"tactic": "simp [addLsb, two_mul]"
}
] | [
86,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_lt_sin_of_lt_of_le_pi_div_two | [
{
"state_after": "x y : ℝ\nhx₁ : -(π / 2) ≤ x\nhy₂ : y ≤ π / 2\nhxy : x < y\n⊢ cos (-(x - π / 2)) < cos (-(y - π / 2))",
"state_before": "x y : ℝ\nhx₁ : -(π / 2) ≤ x\nhy₂ : y ≤ π / 2\nhxy : x < y\n⊢ sin x < sin y",
"tactic": "rw [← cos_sub_pi_div_two, ← cos_sub_pi_div_two, ← cos_neg (x - _), ← cos_neg (... | [
598,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.one_le_rpow | [
{
"state_after": "case none\nz : ℝ\nhz : 0 < z\nhx : 1 ≤ none\n⊢ 1 ≤ none ^ z\n\ncase some\nz : ℝ\nhz : 0 < z\nval✝ : ℝ≥0\nhx : 1 ≤ Option.some val✝\n⊢ 1 ≤ Option.some val✝ ^ z",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx : 1 ≤ x\nhz : 0 < z\n⊢ 1 ≤ x ^ z",
"tactic": "cases x"
},
{
"state_after": "no g... | [
704,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsCoseparating.isCodetecting | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : Balanced C\n𝒢 : Set C\n⊢ IsCoseparating 𝒢 → IsCodetecting 𝒢",
"tactic": "simpa only [← isDetecting_op_iff, ← isSeparating_op_iff] using IsSeparating.isDetecting"
}
] | [
186,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.cons_eval | [
{
"state_after": "no goals",
"state_before": "f fs : Code\n⊢ eval (cons f fs) = fun v => do\n let n ← eval f v\n let ns ← eval fs v\n pure (List.headI n :: ns)",
"tactic": "simp [eval]"
}
] | [
155,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.symm_dual_comp | [] | [
1546,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tmul_neg | [] | [
1248,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_Lp_add_le | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\nhg : AEMeasurable g\nhp1 : 1 ≤ p\nhp_pos : 0 < p\n⊢ (∫⁻ (a : α), (f + g) a ^ p ∂μ) ^ (1 / p) ≤ (∫⁻ (a : α), f a ^ p ∂μ) ^ (1 / p) + (∫⁻ (a : α), g a ^ p ∂μ) ^ (1 / p)",
"state_... | [
374,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.nil_comp | [
{
"state_after": "no goals",
"state_before": "V : Type u\ninst✝ : Quiver V\na✝¹ b c d a x✝ b✝ : V\np : Path a b✝\na✝ : b✝ ⟶ x✝\n⊢ comp nil (cons p a✝) = cons p a✝",
"tactic": "rw [comp_cons, nil_comp p]"
}
] | [
111,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.nontrivial_of_finrank_eq_succ | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁶ : Ring K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nV₂ : Type v'\ninst✝³ : AddCommGroup V₂\ninst✝² : Module K V₂\ninst✝¹ : Nontrivial K\ninst✝ : NoZeroSMulDivisors K V\nn : ℕ\nhn : finrank K V = Nat.succ n\n⊢ 0 < Nat.succ n",
"state_before": "K : Type u\n... | [
109,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_top | [] | [
332,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
9
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.ext | [] | [
79,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.liftRel_pure | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\na : α\nb : β\n⊢ (∃ b_1, b_1 ∈ pure b ∧ R a b_1) ↔ R a b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\na : α\nb : β\n⊢ LiftRel R (pure a) (pure b) ↔ R a b",
"tactic": "rw [liftRel_pure_left]"
},
{
"... | [
1197,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.inf_eq_inter | [] | [
1814,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.24509\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\n⊢ ‖iteratedFDerivWithin... | [
114,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.coe_smul | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.inv_eq_symplectic_inv | [
{
"state_after": "no goals",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA✝ A : Matrix (l ⊕ l) (l ⊕ l) R\nhA : A ∈ symplecticGroup l R\n⊢ (-J l R) ⬝ Aᵀ ⬝ J l R ⬝ A = 1",
"tactic": "simp only [Matrix.neg_mul, inv_left_mul_aux hA]"
}
] | [
211,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/List/Basic.lean | List.doubleton_eq | [
{
"state_after": "ι : Type ?u.7883\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx y : α\nh : x ≠ y\n⊢ ¬x ∈ {y}",
"state_before": "ι : Type ?u.7883\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nx y : α\nh : x ≠ y\n⊢ {x, y} =... | [
264,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.add_apply | [] | [
290,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_iInf_comap_of_surjective | [] | [
485,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.inv_mul_integral_comp_div_sub | [] | [
303,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMap₂'_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nR₁ : Type ?u.1177421\nR₂ : Type ?u.1177424\nM✝ : Type ?u.1177427\nM₁ : Type ?u.1177430\nM₂ : Type ?u.1177433\nM₁' : Type ?u.1177436\nM₂' : Type ?u.1177439\nn : Type u_1\nm : Type u_2\nn' : Type u_4\nm' : Type u_5\nι : Type ?u.1177454\ninst✝¹⁰ : Com... | [
337,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Analysis/Convex/Independent.lean | ConvexIndependent.mono | [] | [
112,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_add_int_mul_two_pi | [] | [
284,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.homogeneousIdeal_le_vanishingIdeal_zeroLocus | [] | [
172,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.slice_union_shadow_falling_succ | [
{
"state_after": "case a\n𝕜 : Type ?u.21156\nα : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\ninst✝ : DecidableEq α\nk : ℕ\n𝒜 : Finset (Finset α)\ns✝ s : Finset α\n⊢ s ∈ 𝒜 # k ∪ (∂ ) (falling (k + 1) 𝒜) ↔ s ∈ falling k 𝒜",
"state_before": "𝕜 : Type ?u.21156\nα : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\n... | [
166,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | BoundedSMul.of_norm_smul_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : SeminormedRing α\ninst✝¹ : SeminormedAddCommGroup β\ninst✝ : Module α β\nh : ∀ (r : α) (x : β), ‖r • x‖ ≤ ‖r‖ * ‖x‖\na : α\nb₁ b₂ : β\n⊢ dist (a • b₁) (a • b₂) ≤ dist a 0 * dist b₁ b₂",
"tactic": "simpa [smul_sub, dist_eq... | [
81,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.lt_right_of_left_lt' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.592639\nα : Type ?u.592642\nβ : Type u_3\nι : Type ?u.592648\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : LinearOrderedCancelAddCommMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul �... | [
794,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_injective | [] | [
105,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_singleton | [
{
"state_after": "α : Type u\nβ : α → Type v\nx y : α\nb : β y\n⊢ x ∈ ⟦AList.singleton y b⟧ ↔ x = y",
"state_before": "α : Type u\nβ : α → Type v\nx y : α\nb : β y\n⊢ x ∈ singleton y b ↔ x = y",
"tactic": "simp only [singleton]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ ... | [
251,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Inducing.withSeminorms | [
{
"state_after": "𝕜 : Type u_5\n𝕜₂ : Type u_2\n𝕝 : Type ?u.841276\n𝕝₂ : Type ?u.841279\nE : Type u_4\nF : Type u_3\nG : Type ?u.841288\nι : Type u_1\nι' : Type ?u.841294\ninst✝⁹ : NormedField 𝕜\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module 𝕜 E\ninst✝⁶ : NormedField 𝕜₂\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Modul... | [
749,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | ENNReal.rpow_add_le_mul_rpow_add_rpow | [
{
"state_after": "case inl\nι : Type u\ns : Finset ι\nz₁ z₂ : ℝ≥0∞\nhp : 1 ≤ 1\n⊢ (z₁ + z₂) ^ 1 ≤ 2 ^ (1 - 1) * (z₁ ^ 1 + z₂ ^ 1)\n\ncase inr\nι : Type u\ns : Finset ι\nz₁ z₂ : ℝ≥0∞\np : ℝ\nhp : 1 ≤ p\nh'p : 1 < p\n⊢ (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p)",
"state_before": "ι : Type u\ns : Finset ι... | [
305,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_sum_measure | [] | [
1469,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1467,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set_inter | [] | [
503,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_eq_zero_iff_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : Group α\ninst✝¹ : AddMonoid β\ninst✝ : DistribMulAction α β\na : α\nx : β\nh : a • x = 0\n⊢ x = 0",
"tactic": "rw [← inv_smul_smul a x, h, smul_zero]"
}
] | [
274,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.image_preimage | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : DecidableEq β\nf : α → β\ns : Finset β\ninst✝ : (x : β) → Decidable (x ∈ Set.range f)\nhf : InjOn f (f ⁻¹' ↑s)\n⊢ {x | x ∈ ↑s ∧ x ∈ Set.range f} = {x | x ∈ s ∧ x ∈ Set.range f}",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ... | [
101,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | NNReal.tendsto_pow_atTop_nhds_0_of_lt_1 | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.41397\nβ : Type ?u.41400\nι : Type ?u.41403\nr : ℝ≥0\nhr : r < 1\n⊢ Tendsto (fun a => ↑(r ^ a)) atTop (𝓝 ↑0)",
"tactic": "simp only [NNReal.coe_pow, NNReal.coe_zero,\n _root_.tendsto_pow_atTop_nhds_0_of_lt_1 r.coe_nonneg hr]"
}
] | [
166,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_sub | [
{
"state_after": "no goals",
"state_before": "r₁ r₂ : ℝ≥0\nh : r₂ ≤ r₁\n⊢ ↑r₂ ≤ ↑r₁ - 0",
"tactic": "simp [show (r₂ : ℝ) ≤ r₁ from h]"
}
] | [
211,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
11
] |
Mathlib/GroupTheory/Transfer.lean | MonoidHom.transfer_eq_pow | [
{
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189,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_eq_iff_eq_mul | [
{
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"tactic": "rw... | [
760,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.rightInvOn | [] | [
244,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lift_is_succ | [
{
"state_after": "no goals",
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"tactic": "rw [h,... | [
227,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_union_compl | [] | [
1877,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1876,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_sUnion | [
{
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"state_before": "x y : Class\n⊢ y ∈ ⋃₀ x ↔ ∃ z, z ∈ x ∧ y ∈ z",
"tactic": "constructor"
},
{
"state_after": "case mp.intro.intro.intro.intro\nx : Class\nw : ZFSet... | [
1697,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1692,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.append_append | [] | [
288,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.zero_coeff | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_submatrix | [] | [
2468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2467,
1
] |
Mathlib/Data/Set/Basic.lean | SetCoe.exists' | [] | [
198,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | AffineSubspace.closed_of_finiteDimensional | [] | [
390,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.MonoidalOpposite.op_injective | [] | [
51,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_add | [] | [
669,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Icc_iff_left | [] | [
104,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.congr | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nF' : ι → α → β\nhf : TendstoUniformlyOnFilter F f p (𝓟 s)\nhff' : ∀ᶠ (n : ι) in p, EqOn (F n) (F' n) s\n⊢ TendstoUniformlyOnFilter F' ... | [
221,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
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