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/Topology/ContinuousFunction/Basic.lean | ContinuousMap.congr_fun | [] | [
154,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
11
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.star_mem_resolventSet_iff | [
{
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"tactic": "refine' ⟨fun ... | [
261,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.refl_apply | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
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Mathlib/Data/Finset/Basic.lean | Finset.union_eq_right_iff_subset | [] | [
1476,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.right_le_sub_of_lt_1 | [
{
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.unit_leftAdjointUniq_hom | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\... | [
149,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ ∑ x in Nat.antidiagonal (natTrailingDegree p + natTrailingDegree q), coeff p x.fst * coeff q x.snd =\n trailingCoeff p * trailingCoeff q",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Sem... | [
397,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
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src/lean/Init/Data/List/Basic.lean | List.nil_append | [] | [
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64
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
92,
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Mathlib/Algebra/ContinuedFractions/Basic.lean | GeneralizedContinuedFraction.coe_toGeneralizedContinuedFraction | [] | [
183,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_comap_eq_of_surjective | [] | [
619,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Analysis/Complex/Circle.lean | expMapCircle_neg | [] | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | le_hasSum | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.15436\nα : Type u_1\ninst✝² : OrderedAddCommMonoid α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nf g : ι → α\na a₁ a₂ : α\nhf : HasSum f a\ni : ι\nhb : ∀ (j : ι), j ≠ i → 0 ≤ f j\n⊢ ∀ (i_1 : ι), ¬i_1 ∈ {i} → 0 ≤ f i_1",... | [
95,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sigmaFinite_trim_bot_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3500690\nγ : Type ?u.3500693\nδ : Type ?u.3500696\nι : Type ?u.3500699\nR : Type ?u.3500702\nR' : Type ?u.3500705\nm m0 : MeasurableSpace α\nμ : Measure α\ns : Set α\n⊢ IsFiniteMeasure (trim μ (_ : ⊥ ≤ m0)) ↔ IsFiniteMeasure μ",
"state_before": "α : Type u_1\nβ : ... | [
4448,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4444,
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Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.localTriv_continuousLinearMapAt | [
{
"state_after": "case h\nR : Type u_2\nB : Type u_1\nF : Type u_3\nE : B → Type ?u.436783\ninst✝⁸ : NontriviallyNormedField R\ninst✝⁷ : (x : B) → AddCommMonoid (E x)\ninst✝⁶ : (x : B) → Module R (E x)\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace R F\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpa... | [
800,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
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Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.insert | [] | [
317,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
312,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_add_left | [] | [
107,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_top_iff | [
{
"state_after": "case mp\nα : Type ?u.92811\nβ : Type ?u.92814\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\n⊢ a * b < ⊤ → a < ⊤ ∧ b < ⊤ ∨ a = 0 ∨ b = 0\n\ncase mpr\nα : Type ?u.92811\nβ : Type ?u.92814\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\n⊢ a < ⊤ ∧ b < ⊤ ∨ a = 0 ∨ b = 0 → a * b < ⊤",
"state_before": ... | [
604,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_1_ne_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nn ν : ℕ\nh : ν ≤ n\n⊢ ¬eval (Nat.succ ν) (pochhammer ℕ (n - ν)) = 0",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nn ν : ℕ\nh : ν ≤ n\n⊢ eval 1 ((↑derivative^[n - ν]) (bernsteinPolynomial R n ν)) ≠ 0",
"t... | [
245,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_orderHom | [] | [
350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Order/Lattice.lean | ofDual_min | [] | [
977,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.neg_f_apply | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.zero_min | [] | [
192,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
192,
11
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteEdges_le_of_le | [
{
"state_after": "case right\nι : Sort ?u.250888\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns✝ s s' : Set (Sym2 V)\nh : s ⊆ s'\n⊢ ∀ ⦃v w : V⦄, Adj G' v w → ¬Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ s' → ¬Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ s",
"state_before": "ι : Sort ?u.250888\nV : ... | [
1095,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
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Mathlib/Algebra/AddTorsor.lean | vsub_right_cancel_iff | [] | [
237,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanExt_inv_app_right | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Z\ng : Y ⟶ Z\nf' : X' ⟶ Z'\ng' : Y' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iZ.hom\nwg : iY.hom ≫ g' = g ≫ iZ.hom\n⊢ (cospanExt iX iY iZ wf ... | [
436,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
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] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.norm_set_integral_le_of_norm_le_const' | [] | [
554,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.liftp_iff_of_isUniform | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nh : IsUniform\nα : Type u\nx : F α\np : α → Prop\n⊢ (∃ a f, abs (repr x) = abs { fst := a, snd := f } ∧ ∀ (i : PFunctor.B (P F) a), p (f i)) ↔\n ∀ (u : α), u ∈ supp (abs (repr x)) → p u",
"state_before": "F : Type u → Type u\ninst✝ : Fu... | [
696,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
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Mathlib/Logic/Embedding/Basic.lean | Equiv.refl_toEmbedding | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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] |
Mathlib/Topology/Constructions.lean | continuous_sum_elim | [] | [
865,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.DualBases.dual_lc | [
{
"state_after": "R : Type u_2\nM : Type u_3\nι : Type u_1\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ne : ι → M\nε : ι → Dual R M\ninst✝ : DecidableEq ι\nh : DualBases e ε\nl : ι →₀ R\ni : ι\n⊢ (Finset.sum l.support fun i_1 => ↑(ε i) ((fun i a => a • e i) i_1 (↑l i_1))) = ↑l i",
"st... | [
708,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
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] |
Mathlib/Data/Tree.lean | Tree.numLeaves_eq_numNodes_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nx : Tree α\n⊢ numLeaves x = numNodes x + 1",
"tactic": "induction x <;> simp [*, Nat.add_comm, Nat.add_assoc, Nat.add_left_comm]"
}
] | [
121,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_self | [
{
"state_after": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ c * c ≤ c",
"state_before": "c : Cardinal\nh : ℵ₀ ≤ c\n⊢ c * c = c",
"tactic": "refine' le_antisymm _ (by simpa only [mul_one] using mul_le_mul_left' (one_le_aleph0.trans h) c)"
},
{
"state_after": "c✝ : Cardinal\nh : ℵ₀ ≤ c✝\nc : Cardinal\nx✝ : ∀ (y... | [
544,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | hasDerivAt_inv | [] | [
74,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | measurableSet_regionBetween | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\nhg : Measurable g\nhs : MeasurableSet s\n⊢ MeasurableSet ({a | a.fst ∈ s} ∩ {a | a.snd ∈ {a_1 | f a.fst < a_1} ∩ {a_1 | a_1 < g a.fst}})",
"state_before": "α : Type u_1\ninst✝ :... | [
487,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.weak_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Preorder α\no₁ : WithBot α\no₂ : WithTop α\nh : Bounded nil o₁ o₂\n⊢ Bounded nil o₁ ⊤",
"tactic": "cases o₁ <;> trivial"
}
] | [
923,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.abs_sum_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type ?u.93086\nβ : Type ?u.93089\nM : Type ?u.93092\nN : Type ?u.93095\nG✝ : Type ?u.93098\nk : Type ?u.93101\nR : Type ?u.93104\nG : Type u_1\ninst✝ : LinearOrderedAddCommGroup G\nf : ι → G\ns : Finset ι\nhf : ∀ (i : ι), i ∈ s → 0 ≤ f i\n⊢ abs... | [
268,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.26865\ninst✝ : CompleteBooleanAlgebra α\na b : α\ns : Set α\nf : ι → α\n⊢ sInf sᶜ = ⨆ (i : α) (_ : i ∈ s), iᶜ",
"tactic": "simp only [sInf_eq_iInf, compl_iInf]"
}
] | [
307,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.sin_arcsin' | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ Icc (-1) 1\n⊢ sin (arcsin x) = x",
"tactic": "simpa [arcsin, IccExtend_of_mem _ _ hx, -OrderIso.apply_symm_apply] using\n Subtype.ext_iff.1 (sinOrderIso.apply_symm_apply ⟨x, hx⟩)"
}
] | [
66,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
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] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_subset_verts | [] | [
218,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_le_of_mem | [
{
"state_after": "case inl\n𝕜 : Type ?u.46236\nE : Type u_1\nF : Type ?u.46242\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\nx : E\nha : 0 ≤ 0\nhx : x ∈ 0 • s\n⊢ gauge s x ≤ 0\n\ncase inr\n𝕜 : Type ?u.46236\nE : Type u_1\nF : Type ?u.46242\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E... | [
152,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.isRightRegular | [] | [
97,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.liftAux.smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.537847\ninst✝¹³ : Monoid R'\nR'' : Type ?u.537853\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type u_4\nQ : Type ?u.537868\nS : Type ?u.537871\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N... | [
465,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Ioc_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ (⋃ (n : ℤ), Ioc (↑n) (↑n + 1)) = univ",
"tactic": "simpa only [zero_add] using iUnion_Ioc_add_int_cast (0 : α)"
}
] | [
1110,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1109,
1
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Mathlib/Algebra/Regular/Basic.lean | not_isLeftRegular_zero_iff | [
{
"state_after": "R : Type u_1\ninst✝ : MulZeroClass R\na b : R\n⊢ (¬∃ x y, x ≠ y) ↔ ∀ (x y : R), x = y",
"state_before": "R : Type u_1\ninst✝ : MulZeroClass R\na b : R\n⊢ ¬IsLeftRegular 0 ↔ Nontrivial R",
"tactic": "rw [nontrivial_iff, not_iff_comm, isLeftRegular_zero_iff_subsingleton, subsingleton_iff... | [
216,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Finsupp.coe_basis | [
{
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124,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivAt.ccos | [] | [
311,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_mk | [
{
"state_after": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.3280447\ninst✝ : CommMonoid P\nf : Submonoid.LocalizationMap S N\nx : M\ny : { x // x ∈ S }\n⊢ ↑(mulEquivOfQuotient f) (Submonoid.LocalizationMap.mk' (monoidOf S) x y) = Submonoid.Localizatio... | [
1703,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_eq_arccos | [
{
"state_after": "x : ℝ\nh : 0 ≤ x\n⊢ arccos (cos (arcsin x)) = arcsin x",
"state_before": "x : ℝ\nh : 0 ≤ x\n⊢ arcsin x = arccos (sqrt (1 - x ^ 2))",
"tactic": "rw [eq_comm, ← cos_arcsin]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : 0 ≤ x\n⊢ arccos (cos (arcsin x)) = arcsin ... | [
470,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
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Mathlib/LinearAlgebra/Dimension.lean | rank_top | [
{
"state_after": "K : 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.78476\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nM₁ : Type v\nin... | [
220,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Analysis/Convex/Quasiconvex.lean | Monotone.quasilinearOn | [] | [
217,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.mem_fieldRange | [] | [
560,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_reindex | [
{
"state_after": "case h\nι : Type u_5\nι' : Type u_4\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j : ι\ne : ι ≃ ι'\ni : ι'\np✝ : P\n⊢ ↑(coord (reindex b e) i) p✝ = ↑(coord b (↑e.symm i... | [
167,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Std/Data/Int/Lemmas.lean | Int.le_trans | [
{
"state_after": "no goals",
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"tactic": "rw [← hm, ← hn, Int.add_assoc, ofNat_add]"
}
] | [
613,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
611,
11
] |
Mathlib/Order/SymmDiff.lean | compl_symmDiff_compl | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.88691\nα : Type u_1\nβ : Type ?u.88697\nπ : ι → Type ?u.88702\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ bᶜ \\ aᶜ ⊔ aᶜ \\ bᶜ = a ∆ b",
"tactic": "simp_rw [compl_sdiff_compl, sdiff_eq, symmDiff_eq]"
}
] | [
748,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
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Mathlib/Analysis/Complex/Isometry.lean | linear_isometry_complex_aux | [
{
"state_after": "f : ℂ ≃ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\n⊢ (↑f I).re = 0 ∧ ((↑f I).im = I.im ∨ (↑f I).im = -I.im)",
"state_before": "f : ℂ ≃ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\n⊢ ↑f I = I ∨ ↑f I = -I",
"tactic": "simp only [ext_iff, ← and_or_left, neg_re, I_re, neg_im, neg_zero]"
},
{
"state_after": "case left\nf : ℂ ... | [
142,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearMap.surjective_of_injective | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\nf : V →ₗ[K] V\nhinj : Injective ↑f\nh : Module.rank K V = Module.rank K { x // x ∈ range f }\n⊢ Surjective... | [
899,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.nullHomotopicMap_f_of_not_rel_left | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni k₁ k₀ : ι\nr₁₀ : ComplexShape.Rel c k₁ k₀\nhk₀ : ∀ (l : ι), ¬ComplexShape.Rel c k₀ l\nhom : (i j : ι) → X C i ⟶ X D j\n⊢ ↑(dNext k₀) hom + ↑(pre... | [
392,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_surjective | [] | [
519,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_singleton | [] | [
1347,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.hasSum_log_sub_log_of_abs_lt_1 | [
{
"state_after": "x : ℝ\nh : abs x < 1\nterm : ℕ → ℝ := fun n => -1 * ((-x) ^ (n + 1) / (↑n + 1)) + x ^ (n + 1) / (↑n + 1)\n⊢ HasSum (fun k => 2 * (1 / (2 * ↑k + 1)) * x ^ (2 * k + 1)) (log (1 + x) - log (1 - x))",
"state_before": "x : ℝ\nh : abs x < 1\n⊢ HasSum (fun k => 2 * (1 / (2 * ↑k + 1)) * x ^ (2 * k... | [
316,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.lt_one_of_lt_one | [] | [
224,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | MeasureTheory.Measure.withDensity_rnDeriv_eq | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.14\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : HaveLebesgueDecomposition μ ν\nh : μ ≪ ν\nleft✝ : Measurable (rnDeriv μ ν)\nhadd : μ = singularPart μ ν + withDensity ν (rnDeriv μ ν)\nE : Set α\nhE₁ : MeasurableSet E\nhE₂ : ↑↑(si... | [
62,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.log_rpow | [
{
"state_after": "case a\nx✝ y✝ z x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ exp (log (x ^ y)) = exp (y * log x)",
"state_before": "x✝ y✝ z x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ log (x ^ y) = y * log x",
"tactic": "apply exp_injective"
},
{
"state_after": "no goals",
"state_before": "case a\nx✝ y✝ z x : ℝ\nhx : 0 < ... | [
406,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_eq_gcd_image | [] | [
211,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableAt.fderiv_prod | [] | [
122,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.length_of | [] | [
502,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.xa_mul_xa | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/Hom/Order.lean | OrderHom.iterate_sup_le_sup_iff | [
{
"state_after": "case mp\nα✝ : Type ?u.11841\nβ : Type ?u.11844\ninst✝¹ : Preorder α✝\nα : Type u_1\ninst✝ : SemilatticeSup α\nf : α →o α\nh : ∀ (n₁ n₂ : ℕ) (a₁ a₂ : α), (↑f^[n₁ + n₂]) (a₁ ⊔ a₂) ≤ (↑f^[n₁]) a₁ ⊔ (↑f^[n₂]) a₂\n⊢ ∀ (a₁ a₂ : α), ↑f (a₁ ⊔ a₂) ≤ ↑f a₁ ⊔ a₂\n\ncase mpr\nα✝ : Type ?u.11841\nβ : Type ... | [
157,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_sup | [
{
"state_after": "no goals",
"state_before": "K : Type u_2\nV : Type u_1\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nS : Set (ℙ K V)\nW : Subspace K V\n⊢ span S ⊔ W = span (S ∪ ↑W)",
"tactic": "rw [span_union, span_coe]"
}
] | [
199,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | det_rotation | [
{
"state_after": "a : { x // x ∈ circle }\n⊢ ↑(Matrix.planeConformalMatrix (↑a).re (↑a).im (_ : (↑a).re ^ 2 + (↑a).im ^ 2 ≠ 0)) 0 0 *\n ↑(Matrix.planeConformalMatrix (↑a).re (↑a).im (_ : (↑a).re ^ 2 + (↑a).im ^ 2 ≠ 0)) 1 1 -\n ↑(Matrix.planeConformalMatrix (↑a).re (↑a).im (_ : (↑a).re ^ 2 + (↑a).im ... | [
169,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.exists_cons_eq_concat | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\nh : Adj G u v\np : Walk G v w\n⊢ ∃ x q h', cons h p = concat q h'",
"tactic": "induction p generalizing u with\n| nil => exact ⟨_, nil, h, rfl⟩\n... | [
309,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.pmap_congr | [] | [
1519,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.le_pointwise_smul_iff | [] | [
517,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_eq_iInf | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\ns : Set α\n⊢ ↑(trim m) s = ⨅ (t : Set α) (_ : MeasurableSet t) (_ : s ⊆ t), ↑m t",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\ns : Set α\n⊢ ↑(trim m) s = ⨅ (t : Set α) (_ : s ⊆ t) (_ : Measurable... | [
1659,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1655,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | fderiv.comp | [] | [
172,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Finset/Basic.lean | DirectedOn.exists_mem_subset_of_finset_subset_biUnion | [
{
"state_after": "α✝ : Type ?u.171200\nβ : Type ?u.171203\nγ : Type ?u.171206\ninst✝ : DecidableEq α✝\ns✝ s₁ s₂ t t₁ t₂ u v : Finset α✝\na b : α✝\nα : Type u_1\nι : Type u_2\nf : ι → Set α\nc : Set ι\nhn : Set.Nonempty c\nhc : DirectedOn (fun i j => f i ⊆ f j) c\ns : Finset α\nhs : ↑s ⊆ ⋃ (x : ↑c), f ↑x\n⊢ ∃ i,... | [
1553,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_subset_left | [] | [
1362,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1361,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.isOpen_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.63524\nδ : Type ?u.63527\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\ns : Set α\n⊢ IsOpen (↑h '' s) ↔ IsOpen s",
"tactic": "rw [← preim... | [
312,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.rat_rawCast_2 | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.79693\ninst✝¹ : CommSemiring R✝\nn : ℤ\nd : ℕ\nR : Type u_1\ninst✝ : DivisionRing R\n⊢ Rat.rawCast n d = ↑n / ↑d",
"tactic": "simp"
}
] | [
122,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.empty_product | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.differentiableOn | [] | [
124,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.charP_to_charZero | [] | [
469,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_iSup₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.90446\nγ : Type ?u.90449\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\ns t : LowerSet α\na : α\nf : (i : ι) → κ i → LowerSet α\n⊢ compl (⨆ (i : ι) (j : κ i), f i j) = ⨆ (i : ι) (j : κ i), compl (f i j)",
"tactic": "simp_rw [LowerSe... | [
926,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_comap | [] | [
1619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1618,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_tsub_left_of_le | [] | [
274,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_C | [
{
"state_after": "K F : Type u\ninst✝ : Field F\np q : F[X]\nf g : RatFunc F\nr : F\n⊢ ↑(ofPowerSeries ℤ F) (↑(PowerSeries.C F) r) = ↑HahnSeries.C r",
"state_before": "K F : Type u\ninst✝ : Field F\np q : F[X]\nf g : RatFunc F\nr : F\n⊢ ↑(↑C r) = ↑HahnSeries.C r",
"tactic": "rw [coe_num_denom, num_C, de... | [
1745,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsRegular.subsingleton | [] | [
204,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_eval_one_add | [
{
"state_after": "n : ℕ\nx : ℚ\nd : ℕ\nhd : ∀ (m : ℕ), m < d → eval (1 + x) (bernoulli m) = eval x (bernoulli m) + ↑m * x ^ (m - 1)\n⊢ eval (1 + x) (bernoulli d) = eval x (bernoulli d) + ↑d * x ^ (d - 1)",
"state_before": "n : ℕ\nx : ℚ\n⊢ eval (1 + x) (bernoulli n) = eval x (bernoulli n) + ↑n * x ^ (n - 1)"... | [
212,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.add_eq | [] | [
99,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
99,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.inv_inv | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝¹ : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\ninst✝ : IsIso f\n⊢ inv f ≫ f = 𝟙 Y",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\ninst✝ : IsIso f\n⊢ inv (inv f) = f",
"tactic": "apply inv_eq_of_hom_inv_id"
... | [
407,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Order/Interval.lean | Interval.subset_coe_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.28103\nδ : Type ?u.28106\nι : Sort ?u.28109\nκ : ι → Sort ?u.28114\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\ns t : Interval α\na b : α\nf : α →o β\n⊢ ↑f '' ↑⊥ ⊆ ↑(map f ⊥)",
"tactic": "simp"
}
] | [
515,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_eq_if | [] | [
255,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | continuous_neg' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\n⊢ Continuous NegPart.neg",
"tactic": "refine continuous_pos.comp <| @continuous_neg _ _ _ TopologicalAddGroup.toContinuousNeg"
}
] | [
213,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iInter_Ici_coe_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.136805\nβ : Type ?u.136808\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ (⋂ (n : ℕ), Ici ↑n) = {⊤}",
"tactic": "simp only [← compl_Iio, ← compl_iUnion, iUnion_Iio_coe_nat, compl_compl]"
}
] | [
894,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_isLeast | [] | [
189,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.not_mem_support_iff | [
{
"state_after": "X : Type u_1\nx : X\na : FreeAbelianGroup X\n⊢ ↑(↑toFinsupp a) x = 0 ↔ ↑(coeff x) a = 0",
"state_before": "X : Type u_1\nx : X\na : FreeAbelianGroup X\n⊢ ¬x ∈ support a ↔ ↑(coeff x) a = 0",
"tactic": "rw [support, Finsupp.not_mem_support_iff]"
},
{
"state_after": "no goals",
... | [
163,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOn.prod' | [] | [
543,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_iff_image_ball_subset_compact | [] | [
173,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_disjUnion | [] | [
275,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_iInf_comap_of_surjective | [] | [
477,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
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