file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.le_map_comap | [] | [
184,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycleOn_support_cycleOf | [
{
"state_after": "case refine_1\nι : Type ?u.2583510\nα : Type u_1\nβ : Type ?u.2583516\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝¹ y : α\nf : Perm α\nx x✝ : α\nh : ↑f x✝ ∈ ↑(support (cycleOf f x))\n⊢ SameCycle f x x✝ ∧ x ∈ support f\n\ncase refine_2\nι : Type ?u.2583510\nα : Type u_1\nβ : Ty... | [
1193,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Lattice.lean | Finset.iInf_singleton | [
{
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"tactic": "simp"
}
] | [
1935,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1935,
1
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Mathlib/Data/Stream/Init.lean | Stream'.interchange | [] | [
752,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
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src/lean/Init/SimpLemmas.lean | ite_congr | [
{
"state_after": "no goals",
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"tactic": "cases Decidable.em c with\n| inl h => rw [if_pos h]; subst b; rw [if_pos h]; exact h₂ h\n| inr h =>... | [
60,
63
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Algebra/Order/Field/Basic.lean | add_halves | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.89441\nα : Type u_1\nβ : Type ?u.89447\ninst✝ : LinearOrderedSemifield α\na✝ b c d e : α\nm n : ℤ\na : α\n⊢ a / 2 + a / 2 = a",
"tactic": "rw [div_add_div_same, ← two_mul, mul_div_cancel_left a two_ne_zero]"
}
] | [
498,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Mathlib/Data/Finset/Basic.lean | Finset.subset_insert_iff_of_not_mem | [
{
"state_after": "no goals",
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"tactic": "rw [subset_insert_iff, erase_eq_of_not_mem h]"
}
] | [
2003,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2002,
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Mathlib/Deprecated/Subfield.lean | Field.ring_closure_subset | [] | [
92,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.extendDomain_eq_one_iff | [] | [
341,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
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Mathlib/Order/Lattice.lean | inf_lt_of_left_lt | [] | [
420,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
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Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_pos_of_inter_ne_zero | [
{
"state_after": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\ninst✝ : IsFiniteMeasure μ\nhms : MeasurableSet s\nhci : ↑↑μ (s ∩ t) ≠ 0\n⊢ 0 < (↑↑μ s)⁻¹ * ↑↑μ (s ∩ t)",
"state_before": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\ninst✝ : Is... | [
124,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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] |
Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Ici_of_monotone_surjective | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Monotone f\nh_surj : Surjective f\na : α\n⊢ SurjOn f (Ioi a ∪ {a}) (Ioi (f a) ∪ {f a})",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh... | [
84,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_of_nonpos_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.34618\ninst✝ : OrderedRing α\na b c d : α\nh : b ≤ a\nhc : c ≤ 0\n⊢ a * c ≤ b * c",
"tactic": "simpa only [mul_neg, neg_le_neg_iff] using mul_le_mul_of_nonneg_right h (neg_nonneg.2 hc)"
}
] | [
356,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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Mathlib/Data/Fin/Basic.lean | Fin.castAdd_lt | [
{
"state_after": "no goals",
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}
] | [
1142,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
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Mathlib/Order/Filter/Lift.lean | Filter.principal_le_lift' | [] | [
337,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.Disjoint.isConj_mul | [
{
"state_after": "case intro\nι : Type ?u.3042712\nα✝ : Type ?u.3042715\nβ : Type ?u.3042718\ninst✝² : DecidableEq α✝\ninst✝¹ : Fintype α✝\nσ✝ τ✝ : Perm α✝\nα : Type u_1\ninst✝ : Finite α\nσ τ π ρ : Perm α\nhc1 : IsConj σ π\nhc2 : IsConj τ ρ\nhd1 : Disjoint σ τ\nhd2 : Disjoint π ρ\nval✝ : Fintype α\n⊢ IsConj (σ... | [
1815,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
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Mathlib/MeasureTheory/Group/Pointwise.lean | MeasurableSet.const_smul₀ | [
{
"state_after": "case inl\nG₀ : Type u_1\nα : Type u_2\ninst✝⁶ : GroupWithZero G₀\ninst✝⁵ : Zero α\ninst✝⁴ : MulActionWithZero G₀ α\ninst✝³ : MeasurableSpace G₀\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSMul G₀ α\ninst✝ : MeasurableSingletonClass α\ns : Set α\nhs : MeasurableSet s\n⊢ MeasurableSet (0 • s... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_single | [] | [
524,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.range_arcsin | [
{
"state_after": "⊢ Subtype.val '' range (IccExtend arcsin.proof_2 ↑(OrderIso.symm sinOrderIso)) = Icc (-(π / 2)) (π / 2)",
"state_before": "⊢ range arcsin = Icc (-(π / 2)) (π / 2)",
"tactic": "rw [arcsin, range_comp Subtype.val]"
},
{
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48,
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46,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_Iio_atBot | [
{
"state_after": "ι : Type ?u.334826\nι' : Type ?u.334829\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.334838\ninst✝ : SemilatticeInf α\na : α\nf : β → ↑(Iio a)\nl : Filter β\n⊢ Tendsto (Subtype.val ∘ f) l atBot ↔ Tendsto (fun x => ↑(f x)) l atBot",
"state_before": "ι : Type ?u.334826\nι' : Type ?u.334829\nα : ... | [
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44
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1600,
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Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_add | [
{
"state_after": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : Rˣ\n✝ : Nontrivial R\n⊢ ∀ᶠ (t : R) in 𝓝 0, inverse (↑x + t) = inverse (1 + ↑x⁻¹ * t) * ↑x⁻¹",
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129,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basis.lean | Basis.ext | [
{
"state_after": "case h\nι : Type u_5\nι' : Type ?u.181637\nR : Type u_1\nR₂ : Type ?u.181643\nK : Type ?u.181646\nM : Type u_3\nM' : Type ?u.181652\nM'' : Type ?u.181655\nV : Type u\nV' : Type ?u.181660\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\ninst✝⁶ : AddCommMonoid M'\ninst✝⁵ : Mo... | [
281,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Rat/Lemmas.lean | Rat.divInt_add_divInt | [
{
"state_after": "no goals",
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"tactic": "rcases Int.eq_nat_or_neg d₁ with ⟨_, rfl | rfl⟩ <;>\nrcases Int.eq_nat_or_neg d₂ with ⟨_, rfl | rfl⟩ <;>\nsimp_all [Int.ofNat_eq_zero, Int.neg_... | [
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Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.IsLocal.mem_jacobson_or_exists_inv | [
{
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"state_before": "R : Type u\nS : Type v\ninst✝ : CommRing R\nI : Ideal R\nhi : IsLocal I\nx... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
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Mathlib/Algebra/BigOperators/Pi.lean | Pi.list_prod_apply | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Connected.lean | IsPreconnected.union' | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nι : Type ?u.4171\nπ : ι → Type ?u.4176\ninst✝ : TopologicalSpace α\ns✝ t✝ u v s t : Set α\nhs : IsPreconnected s\nht : IsPreconnected t\nx : α\nhxs : x ∈ s\nhxt : x ∈ t\n⊢ IsPreconnected (s ∪ t)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?... | [
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148,
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.hasSum_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_3\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\nγ : Type u_1\ninst✝² : LocallyCompactSpace α\ninst✝¹ : AddCommMonoid β\ninst✝ : ContinuousAdd β\nf : γ → C(α, β)\ng : C(α, β)\nhf : HasSum f g\nx : α\nevₓ : C(α, β) →+ β := AddMonoidHom.comp (Pi.evalAddMonoid... | [
431,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofRealLi_apply | [] | [
1000,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/CategoryTheory/Category/TwoP.lean | TwoP_swap_comp_forget_to_Bipointed | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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] |
Mathlib/Algebra/Field/ULift.lean | ULift.down_ratCast | [] | [
36,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
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Mathlib/Order/Monotone/Basic.lean | StrictMono.comp_strictAnti | [] | [
679,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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Mathlib/Data/Pi/Lex.lean | Pi.lex_desc | [
{
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242,
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Mathlib/Order/Filter/Bases.lean | Filter.HasAntitoneBasis.hasBasis_ge | [] | [
1063,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.gcd_mul_addOrderOf_div_eq | [
{
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392,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
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Mathlib/LinearAlgebra/Dimension.lean | cardinal_lift_le_rank_of_linearIndependent | [
{
"state_after": "case a\nK : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.100046\nR : Type u\ninst✝⁷ : Ring R\nM : Type v\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM' : Type v'\ninst✝⁴ : AddCommGroup M'\ninst✝³ : Module R M'\nM₁ : ... | [
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Mathlib/Data/List/Basic.lean | List.get_enumFrom | [
{
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},
{
"state_after": "ι : Type ?u.450946\nα : Type u\nβ : Typ... | [
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Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.continuants_stable_of_terminated | [
{
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"tactic": "simp only [nth_cont_eq_succ_nth_cont_aux,\n continuantsAux_stable_of_term... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.sub_imK | [] | [
279,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_mono | [
{
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224,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Order/Heyting/Basic.lean | le_sdiff_sup | [
{
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"tactic": "rw [sup_comm, ← sdiff_le_iff]"
}
] | [
537,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_tendsto_closure_iSup | [
{
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908,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.comp_smul | [
{
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352,
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349,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | sum_add_tsum_nat_add' | [] | [
966,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.single_neg | [
{
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1021,
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1016,
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Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.rankGT.le_trans | [] | [
355,
40
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352,
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Mathlib/Data/Stream/Init.lean | Stream'.even_tail | [] | [
481,
6
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480,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.div | [] | [
1728,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_eq_one | [
{
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"tactic": "refine' ⟨fun h ↦ _, by rintro ⟨a, rfl⟩; rw [ncard_s... | [
644,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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Mathlib/Data/Real/NNReal.lean | Real.le_toNNReal_iff_coe_le | [
{
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] | [
678,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.toFractionRing_smul | [
{
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455,
29
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452,
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.map_smul | [] | [
506,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
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Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.reflectsEpimorphisms_of_preserves_of_reflects | [] | [
116,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.sumMap_comp_inr | [] | [
221,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Data/Polynomial/Div.lean | Polynomial.modByMonic_eq_self_iff | [
{
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217,
91
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214,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_top | [
{
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1291,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
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Mathlib/GroupTheory/Exponent.lean | Monoid.exponentExists_iff_ne_zero | [
{
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},
{
"state_after": "case inl\nG : Type u\ninst✝ : Monoid G\n... | [
86,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Order/Filter/Basic.lean | Filter.NeBot.comap_of_image_mem | [] | [
2442,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2440,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.top_caratheodory | [
{
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},
{
"state_after": "no goals",
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1106,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | Measurable.ennreal_induction | [
{
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1351,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPushouts_of_hasColimit_span | [] | [
2680,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2678,
1
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Mathlib/Data/Nat/Bitwise.lean | Nat.lt_of_testBit | [
{
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138,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.liftAux_inrHom | [] | [
833,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_iSup | [
{
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454,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.isoProd_inv | [
{
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"tactic": "apply biprod.hom_ext <;> simp [Iso.inv_comp_eq]"
}
] | [
1448,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.lift_mem_embed | [] | [
527,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.add_lt_aleph0_iff | [] | [
1531,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/RingTheory/Algebraic.lean | AlgHom.bijective | [] | [
278,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.ext | [] | [
357,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Set/Prod.lean | Set.image_prod_mk_subset_prod | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.83491\ns✝ s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nf : α → β\ng : α → γ\ns : Set α\nx : α\nhx : x ∈ s\n⊢ (fun x => (f x, g x)) x ∈ (f '' s) ×ˢ (g '' s)",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\n... | [
335,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.sum_mem_biSup | [] | [
314,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_nonneg | [
{
"state_after": "ι : Type ?u.134844\nα : Type u_1\nβ : Type ?u.134850\nγ : Type ?u.134853\ninst✝ : OrderedCommSemiring α\nm : Multiset α\n⊢ (∀ (a : α), a ∈ m → 0 ≤ a) → 0 ≤ prod m",
"state_before": "ι : Type ?u.134844\nα : Type u_1\nβ : Type ?u.134850\nγ : Type ?u.134853\ninst✝ : OrderedCommSemiring α\nm :... | [
441,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.continuousOn | [] | [
1889,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1888,
11
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_le | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nhK : IsPGroup p { x // x ∈ K }\nhHK : H ≤ K\na b : { x // x ∈ H }\nh : ↑(Subgroup.inclusion hHK) a = ↑(Subgroup.inclusion hHK) b\n⊢ ↑(↑(Subgroup.inclusion hHK) a) = ↑(↑(Subgroup.inclusion hHK) b)",
"state_before": "p : ℕ\nG : Type u_1... | [
273,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_nat_mul_iff | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nm : ℤ\nn : ℕ\nx : ℝ\n⊢ Irrational (↑n * x) ↔ n ≠ 0 ∧ Irrational x",
"tactic": "rw [← cast_coe_nat, irrational_rat_mul_iff, Nat.cast_ne_zero]"
}
] | [
624,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Topology/Paracompact.lean | normal_of_paracompact_t2 | [
{
"state_after": "ι : Type u\nX : Type v\nY : Type w\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space X\ninst✝ : ParacompactSpace X\nthis :\n ∀ (s t : Set X),\n IsClosed s →\n IsClosed t →\n (∀ (x : X), x ∈ s → ∃ u v, IsOpen u ∧ IsOpen v ∧ x ∈ u ∧ t ⊆ v ∧ Disjoint u v)... | [
323,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | isPrimePow_of_minFac_pow_factorization_eq | [
{
"state_after": "case inl\nR : Type ?u.706\ninst✝ : CommMonoidWithZero R\nn p : R\nk : ℕ\nh : Nat.minFac 0 ^ ↑(Nat.factorization 0) (Nat.minFac 0) = 0\nhn : 0 ≠ 1\n⊢ IsPrimePow 0\n\ncase inr\nR : Type ?u.706\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n : ℕ\nh : Nat.minFac n ^ ↑(Nat.factorization n) (Nat.minFac... | [
37,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.extendDomainHom_injective | [] | [
336,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.smulRight_one_pow | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹⁵ : Ring R\nR₂ : Type ?u.888280\ninst✝¹⁴ : Ring R₂\nR₃ : Type ?u.888286\ninst✝¹³ : Ring R₃\nM : Type ?u.888292\ninst✝¹² : TopologicalSpace M\ninst✝¹¹ : AddCommGroup M\nM₂ : Type ?u.888301\ninst✝¹⁰ : TopologicalSpace M₂\ninst✝⁹ : AddCommGroup M₂\nM₃ : Type ?u.8883... | [
1437,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_univ | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\ninst✝ : IsProbabilityMeasure μ\n⊢ μ[|Set.univ] = μ",
"tactic": "simp [cond, measure_univ, Measure.restrict_univ]"
}
] | [
101,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.div' | [
{
"state_after": "no goals",
"state_before": "p a b✝ : ℕ\nhp : Fact (Nat.Prime p)\nm : ℕ\ncpm : coprime p m\nb : ℕ\ndvd : m ∣ b\n⊢ padicValNat p (b / m) = padicValNat p b",
"tactic": "rw [padicValNat.div_of_dvd dvd, eq_zero_of_not_dvd (hp.out.coprime_iff_not_dvd.mp cpm),\n Nat.sub_zero]"
}
] | [
442,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
11
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.iff_addMonoid_fg | [] | [
546,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_of_mem | [] | [
1465,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_diff_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.197269\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ico a b \\ Iio c = Ico (max a c) b",
"tactic": "rw [diff_eq, compl_Iio, Ico_inter_Ici, sup_eq_max]"
}
] | [
1816,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1815,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_top | [] | [
539,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.74361\nγ : Type ?u.74364\nδ : Type ?u.74367\nm : MeasurableSpace α\nμ ν : Measure α\n⊢ (∫⁻ (x : α), 0 ∂μ) = 0",
"tactic": "simp"
}
] | [
171,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_pow | [
{
"state_after": "case zero\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\n⊢ adjugate (A ^ Nat.zero) = adjugate A ^ Nat.zero\n\ncase succ\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq ... | [
514,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.flip_separatingLeft | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type u_1\nR₂ : Type u_5\nR₃ : Type ?u.540765\nM : Type ?u.540768\nM₁ : Type u_3\nM₂ : Type u_4\nMₗ₁ : Type ?u.540777\nMₗ₁' : Type ?u.540780\nMₗ₂ : Type ?u.540783\nMₗ₂' : Type ?u.540786\nK : Type ?u.540789\nK₁ : Type ?u.540792\nK₂ : Type ?u.540... | [
692,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion₂_vsub | [] | [
726,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Topology/Constructions.lean | Inducing.of_codRestrict | [] | [
999,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equivalence.lean | CategoryTheory.hasTerminal_of_equivalence | [] | [
40,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.toGroupSeminorm_eq_coe | [] | [
768,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.haarContent_outerMeasure_self_pos | [
{
"state_after": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : T2Space G\nK₀ : PositiveCompacts G\n⊢ 1 ≤ ↑(Content.outerMeasure (haarContent K₀)) ↑K₀",
"state_before": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup... | [
586,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_omega | [
{
"state_after": "c : Cardinal\n⊢ (∀ (o' : Ordinal) (x : ℕ), o' = ↑x → aleph' o' ≤ c) ↔ ∀ (n : ℕ), ↑n ≤ c",
"state_before": "c : Cardinal\n⊢ aleph' ω ≤ c ↔ ℵ₀ ≤ c",
"tactic": "simp only [aleph'_le_of_limit omega_isLimit, lt_omega, exists_imp, aleph0_le]"
},
{
"state_after": "no goals",
"stat... | [
234,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.addOrderOf_one | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.43695\nR : Type u_1\ninst✝ : Semiring R\nn : ℕ\n⊢ ↑n = 0 ↔ addOrderOf 1 ∣ n",
"tactic": "rw [← Nat.smul_one_eq_coe, addOrderOf_dvd_iff_nsmul_eq_zero]"
}
] | [
130,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | mul_eq_one_iff | [] | [
234,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_le_iff | [
{
"state_after": "case h.e'_2.h.a\nα : Type ?u.349869\nβ : Type ?u.349872\nγ : Type ?u.349875\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\na : Ordinal\na✝ : Ordinal\n⊢ (∀ (h : a✝ < o), f a✝ h < a) ↔ ∀ (h : a✝ < o), succ (f a✝ h) ≤ a",
"state_before... | [
1808,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1805,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_dirac | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.329647\nδ : Type ?u.329650\nι : Type ?u.329653\nR : Type ?u.329656\nR' : Type ?u.329659\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ni... | [
2005,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2004,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_mem_eq_self_iff | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.813892\ninst✝ : DecidableEq α\nl : List α\nx : α\nhl : Nodup l\nk : ℕ\nhk : k < length l\nhx : nthLe l k hk ∈ l\n⊢ ↑(formPerm l) (nthLe l k hk) = nthLe l k hk ↔ length l ≤ 1",
"state_before": "α : Type u_1\nβ : Type ?u.813892\ninst✝ : DecidableEq... | [
394,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isLittleO_exp_comp_exp_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx y z : ℝ\nl : Filter α\nf g : α → ℝ\n⊢ ((fun x => exp (f x)) =o[l] fun x => exp (g x)) ↔ Tendsto (fun x => g x - f x) l atTop",
"tactic": "simp only [isLittleO_iff_tendsto, exp_ne_zero, ← exp_sub, ← tendsto_neg_atTop_iff, false_imp_iff,\n imp... | [
386,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.integral_image_eq_integral_abs_deriv_smul | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.1055778\nF : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : FiniteDimensional ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ns✝ : Set E\nf✝ : E → E\nf'✝ : E → E →L[ℝ] E\ninst✝³ : MeasurableSpace E\ninst✝² :... | [
1256,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
1
] |
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