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/Analysis/SpecialFunctions/Pow/Real.lean | Complex.abs_cpow_inv_nat | [
{
"state_after": "x : ℂ\nn : ℕ\n⊢ ↑abs (x ^ (↑n)⁻¹) = ↑abs (x ^ ↑(↑n)⁻¹)",
"state_before": "x : ℂ\nn : ℕ\n⊢ ↑abs (x ^ (↑n)⁻¹) = ↑abs x ^ (↑n)⁻¹",
"tactic": "rw [← abs_cpow_real]"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nn : ℕ\n⊢ ↑abs (x ^ (↑n)⁻¹) = ↑abs (x ^ ↑(↑n)⁻¹)",
"ta... | [
291,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_subtype_eq_of_support_subset | [] | [
606,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
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Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.coeq₃_condition₃ | [] | [
402,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLE_symm_mk | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_mem | [] | [
1680,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.add_right | [] | [
1232,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.forall_iff | [] | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Order/BooleanAlgebra.lean | sdiff_sdiff_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.28604\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ x \\ y ⊔ x ⊓ y ⊓ z = z ⊓ x ⊓ y ⊔ x \\ y",
"tactic": "ac_rfl"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.28604\nw x y z : α\ninst✝ : G... | [
372,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.mem_range_mulIndicator | [
{
"state_after": "α : Type u_1\nβ : Type ?u.36476\nι : Type ?u.36479\nM : Type u_2\nN : Type ?u.36485\ninst✝¹ : One M\ninst✝ : One N\ns✝ t : Set α\nf✝ g : α → M\na : α\nr : M\ns : Set α\nf : α → M\n⊢ (∃ y, (if y ∈ s then f y else 1) = r) ↔ r = 1 ∧ ¬s = univ ∨ ∃ x, x ∈ s ∧ f x = r",
"state_before": "α : Type... | [
351,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Ext.lean | CancelCommMonoid.toCommMonoid_injective | [
{
"state_after": "case mk.mk.mk.mk.mk.mk\nM : Type u\ntoOne✝¹ : One M\nnpow✝¹ : ℕ → M → M\nnpow_zero✝¹ : ∀ (x : M), npow✝¹ 0 x = 1\ntoSemigroup✝¹ : Semigroup M\nmul_left_cancel✝¹ : ∀ (a b c : M), a * b = a * c → b = c\none_mul✝¹ : ∀ (a : M), 1 * a = a\nmul_one✝¹ : ∀ (a : M), a * 1 = a\nnpow_succ✝¹ : ∀ (n : ℕ) (... | [
112,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.supSpanSingleton_apply_mk | [
{
"state_after": "case h\nR : Type ?u.359475\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.360556\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\nK : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : Module K E\nins... | [
563,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
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Mathlib/Topology/Order/Basic.lean | Antitone.map_sInf_of_continuousAt' | [] | [
2742,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2739,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.isBigO_sub_rev | [] | [
1338,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
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Mathlib/Order/Hom/Lattice.lean | InfHom.toFun_eq_coe | [] | [
538,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.convergenceR_cond | [
{
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453,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_antiperiodic | [
{
"state_after": "no goals",
"state_before": "⊢ Function.Antiperiodic sin π",
"tactic": "simp [sin_add]"
}
] | [
230,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.image2_smul | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.inv_comp | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝² : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\ninst✝¹ : IsIso f\ninst✝ : IsIso h\n⊢ (f ≫ h) ≫ inv h ≫ inv f = 𝟙 X",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\ninst✝¹ : IsIso f\ninst✝ : IsIso h\n⊢ inv (f ≫ h) =... | [
401,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_bool | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14\nγ : Type ?u.17\ninst✝ : CommMonoid α\nf : Bool → α\n⊢ ∏ b : Bool, f b = f true * f false",
"tactic": "simp"
}
] | [
42,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.toHomeomorph_symm | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
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Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.Γ_obj_op | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | one_div_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na✝ b a : α\nn : ℤ\n⊢ (1 / a) ^ n = 1 / a ^ n",
"tactic": "simp only [one_div, inv_zpow]"
}
] | [
368,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
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Std/Data/Rat/Lemmas.lean | Rat.sub_eq_add_neg | [
{
"state_after": "no goals",
"state_before": "a b : Rat\n⊢ a - b = a + -b",
"tactic": "simp [add_def, sub_def, Int.neg_mul, Int.sub_eq_add_neg]"
}
] | [
237,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
236,
11
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | Equiv.Perm.IsThreeCycle.alternating_normalClosure | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh5 : 5 ≤ card α\nf : Perm α\nhf : IsThreeCycle f\nhi : Function.Injective ↑(Subgroup.subtype (alternatingGroup α))\n⊢ ⊤ ≤ normalClosure {{ val := f, property := (_ : f ∈ alternatingGroup α) }}",
"state_before": "α : Type u_1\ninst✝¹ ... | [
191,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Data/List/BigOperators/Lemmas.lean | List.dvd_sum | [
{
"state_after": "case nil\nι : Type ?u.11902\nα : Type ?u.11905\nM : Type ?u.11908\nN : Type ?u.11911\nP : Type ?u.11914\nM₀ : Type ?u.11917\nG : Type ?u.11920\nR : Type u_1\ninst✝ : Semiring R\na : R\nl : List R\nh✝ : ∀ (x : R), x ∈ l → a ∣ x\nh : ∀ (x : R), x ∈ [] → a ∣ x\n⊢ a ∣ sum []\n\ncase cons\nι : Type... | [
94,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Matrix/Basic.lean | RingHom.mapMatrix_comp | [] | [
1543,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1541,
1
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Mathlib/Dynamics/PeriodicPts.lean | Function.is_periodic_id | [] | [
68,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.lowerBound?_le | [] | [
231,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
230,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_map | [
{
"state_after": "case a.h\nl : Type u_2\nm : Type u_4\nn : Type u_1\no : Type u_5\np : Type ?u.6743\nq : Type ?u.6746\nm' : o → Type ?u.6751\nn' : o → Type ?u.6756\np' : o → Type ?u.6761\nR : Type ?u.6764\nS : Type ?u.6767\nα : Type u_3\nβ : Type u_6\nA : Matrix n l α\nB : Matrix n m α\nC : Matrix o l α\nD : M... | [
149,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.fst_equivOfRightInverse | [] | [
2408,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2406,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.is_compressed_self | [] | [
150,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.map_bot | [] | [
319,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_union | [
{
"state_after": "x y z : ZFSet\n⊢ z ∈ toSet (x ∪ y) ↔ z ∈ x ∨ z ∈ y",
"state_before": "x y z : ZFSet\n⊢ z ∈ x ∪ y ↔ z ∈ x ∨ z ∈ y",
"tactic": "rw [← mem_toSet]"
},
{
"state_after": "no goals",
"state_before": "x y z : ZFSet\n⊢ z ∈ toSet (x ∪ y) ↔ z ∈ x ∨ z ∈ y",
"tactic": "simp"
}
] | [
1169,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_sum | [] | [
272,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
11
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_eq_empty_of_le | [] | [
109,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.of'_modOf | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\ng : G\n⊢ of' k G g %ᵒᶠ g = 0",
"tactic": "simpa only [one_mul] using mul_of'_modOf (1 : AddMonoidAlgebra k G) g"
}
] | [
175,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.op | [] | [
1338,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
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Mathlib/Algebra/Periodic.lean | Finset.periodic_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.39863\nf✝ g : α → β\nc c₁ c₂ x : α\ninst✝¹ : Add α\ninst✝ : CommMonoid β\nι : Type u_3\nf : ι → α → β\ns : Finset ι\nhs : ∀ (i : ι), i ∈ s → Periodic (f i) c\n⊢ ∀ (f_1 : α → β), f_1 ∈ List.map f (Finset.toList s) → Periodi... | [
101,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.right_mem_affineSpan_of_left_ne | [
{
"state_after": "case intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.489120\nP : Type u_3\nP' : Type ?u.489126\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y : P\nhne : x ≠ y\nr : R\nh : Wbtw R x y (↑(lineMap x y) r)\n⊢ ↑(lineMap x y) r ∈ affineS... | [
703,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_zero_zero | [
{
"state_after": "case h\nα : Type u\nm n o : ℕ\nm' : Type ?u.75560\nn' : Type ?u.75563\no' : Type ?u.75566\ninst✝ : Zero α\ni : Fin (Nat.succ n)\n⊢ vecCons 0 0 i = OfNat.ofNat 0 i",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.75560\nn' : Type ?u.75563\no' : Type ?u.75566\ninst✝ : Zero α\n⊢ vecCons... | [
541,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | continuous_thickenedIndicatorAux | [
{
"state_after": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nδ_pos : 0 < δ\nE : Set α\n⊢ Continuous fun x => 1 - infEdist x E / ENNReal.ofReal δ",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nδ_pos : 0 < δ\nE : Set α\n⊢ Continuous (thickenedIndicatorAux δ E)",
"tactic": "u... | [
69,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_comp_botHom | [] | [
671,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ sin (π / 2) = 1 ∨ sin (π / 2) = -1",
"tactic": "simpa [sq, mul_self_eq_one_iff] using sin_sq_add_cos_sq (π / 2)"
},
{
"state_after": "no goals",
"state_before": "this : sin (π / 2) = 1 ∨ sin (π / 2) = -1\nh : sin (π / 2) = -1\n⊢ ¬0 < -1",
"... | [
442,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | PUnit.norm_eq_zero | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_div_nat_cast | [
{
"state_after": "p : ℝ\nhp : Fact (0 < p)\nm n : ℕ\nthis : p⁻¹ * (↑m / ↑n * p) = ↑m / ↑n\n⊢ ‖↑(↑m / ↑n * p)‖ = p * (↑(min (m % n) (n - m % n)) / ↑n)",
"state_before": "p : ℝ\nhp : Fact (0 < p)\nm n : ℕ\n⊢ ‖↑(↑m / ↑n * p)‖ = p * (↑(min (m % n) (n - m % n)) / ↑n)",
"tactic": "have : p⁻¹ * (↑m / ↑n * p) =... | [
252,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.norm_eq_integral | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.218028\n𝕜 : Type ?u.218031\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nm : MeasurableSpace α\nμ : Measure α\nf : { x // x ∈ simpleFunc E 1 μ }\n⊢ ∑ x in SimpleFunc.range (toSimpleFunc f), ENNReal.toReal (↑↑μ (↑(toSimpleFunc f) ⁻¹' {x})... | [
475,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_wbtw_left_ne | [] | [
519,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_of_infinite | [] | [
108,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_two_iff | [
{
"state_after": "α β : Type u\n⊢ (∃ t, ↑t = univ ∧ ∃ x y, x ≠ y ∧ t = {x, y}) ↔ ∃ x y, x ≠ y ∧ {x, y} = univ",
"state_before": "α β : Type u\n⊢ (#α) = 2 ↔ ∃ x y, x ≠ y ∧ {x, y} = univ",
"tactic": "simp only [← @Nat.cast_two Cardinal, mk_eq_nat_iff_finset, Finset.card_eq_two]"
},
{
"state_after"... | [
2243,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2237,
1
] |
Mathlib/Topology/Order/Basic.lean | Continuous.min | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\nf g : β → α\ninst✝ : TopologicalSpace β\nhf : Continuous f\nhg : Continuous g\n⊢ Continuous fun b => if f b ≤ g b then f b else g b",
"state_before": "α : Type u\nβ : Ty... | [
682,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
11
] |
Mathlib/Data/Finmap.lean | Finmap.keys_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns✝ : Finmap β\ns : AList β\n⊢ keys (erase a ⟦s⟧) = Finset.erase (keys ⟦s⟧) a",
"tactic": "simp"
}
] | [
434,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_lt_add_iff_left | [] | [
783,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
782,
11
] |
Mathlib/Data/List/AList.lean | AList.union_erase | [] | [
452,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.mono_inr_of_isColimit | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : Abelian C\ninst✝¹ : HasPushouts C\nW X Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\ninst✝ : Mono f\ns : PushoutCocone f g\nhs : IsColimit s\nthis : Mono ((colimit.cocone (span f g)).ι.app WalkingCospan.right)\n⊢ Mono (PushoutCocone.inr s)",
"state_before": "C : ... | [
764,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.zero_lt_top | [] | [
408,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | isClosed_separationRel | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\n⊢ IsClosed (⋂₀ (closure '' (𝓤 α).sets))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\n⊢ IsClosed... | [
201,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/Basic.lean | not_le_of_lt | [] | [
354,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_empty | [] | [
593,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_one_iff_of_pos | [] | [
316,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.812591\nδ : Type ?u.812594\ninst✝¹ : MeasurableSpace α\nK : Type ?u.812600\ninst✝ : Zero β\nf : α →ₛ β\ns : Set α\nhs : MeasurableSet s\na : α\n⊢ ↑(restrict f s) a = indicator s (↑f) a",
"tactic": "simp only [f.coe_res... | [
784,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_mul_right | [] | [
348,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.le_closure | [] | [
157,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.zero_product | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.card_support_eq_three | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝ : Semiring R\nf : R[X]\nh : card (support f) = 3\n⊢ ∃ k m n hkm hmn x y z hx hy hz, f = ↑C x * X ^ k + ↑C y * X ^ m + ↑C z * X ^ n\n\ncase refine'_2\nR : Type u_1\ninst✝ : Semiring R\nf : R[X]\n⊢ (∃ k m n hkm hmn x y z hx hy hz, f = ↑C x * X ^ k + ↑C y * X ^... | [
387,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.cosh | [] | [
1078,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Topology/DenseEmbedding.lean | Filter.HasBasis.hasBasis_of_denseInducing | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.42701\nδ : Type ?u.42704\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T3Space β\nι : Type u_3\ns : ι → Set α\np : ι → Prop\nx : α\nh : ∀ (t : Set α), t ∈ 𝓝 x ↔ ∃ i, p i ∧ s i ⊆ t\nf : α → β\nhf : DenseInducing f\n⊢ ∀ (t : Set β), t... | [
388,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.one_lt_mul | [] | [
971,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.smul_apply | [] | [
250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_bit1 | [
{
"state_after": "R : Type u\ninst✝ : AddGroupWithOne R\nn : ℤ\n⊢ bit0 ↑n + 1 = bit1 ↑n",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\nn : ℤ\n⊢ ↑(bit1 n) = bit1 ↑n",
"tactic": "rw [bit1, Int.cast_add, Int.cast_one, cast_bit0]"
},
{
"state_after": "no goals",
"state_before": "R : T... | [
149,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_comp_val_Ici_atTop | [
{
"state_after": "ι : Type ?u.339440\nι' : Type ?u.339443\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.339452\ninst✝ : SemilatticeSup α\na : α\nf : α → β\nl : Filter β\n⊢ Tendsto (fun x => f ↑x) atTop l ↔ Tendsto (f ∘ Subtype.val) atTop l",
"state_before": "ι : Type ?u.339440\nι' : Type ?u.339443\nα : Type u_1\... | [
1624,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_re | [] | [
1158,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.asIdeal_lt_asIdeal | [] | [
926,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/RingTheory/Noetherian.lean | wellFounded_submodule_gt | [] | [
340,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_univ_pi | [
{
"state_after": "case h\nα : Type u_2\nβ : Type ?u.288374\nγ : Type ?u.288377\nι : Sort u_3\nι' : Sort ?u.288383\nι₂ : Sort ?u.288386\nκ : ι → Sort ?u.288391\nκ₁ : ι → Sort ?u.288396\nκ₂ : ι → Sort ?u.288401\nκ' : ι' → Sort ?u.288406\nπ : α → Type u_1\nt : (i : α) → ι → Set (π i)\nx✝ : (i : α) → π i\n⊢ (x✝ ∈ ⋃... | [
2039,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2036,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_atBot | [] | [
198,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_natCast | [] | [
506,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_left_injective | [
{
"state_after": "no goals",
"state_before": "n m m' : ℕ\nh : lxor' m n = lxor' m' n\n⊢ m = m'",
"tactic": "rw [← lxor_cancel_right n m, ← lxor_cancel_right n m', h]"
}
] | [
257,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_union_ball | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.37673\nι : Type ?u.37676\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ sphere x ε ∪ ball x ε = closedBall x ε",
"tactic": "rw [union_comm, ball_union_sphere]"
}
] | [
560,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Data/List/Card.lean | List.remove_eq_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.19160\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\na : α\nx✝ : ¬a ∈ []\n⊢ remove a [] = []",
"tactic": "simp [remove]"
},
{
"state_after": "α : Type u_1\nβ : Sort ?u.19160\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\na... | [
68,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | LinearEquiv.coeFn_toContinuousLinearEquivOfContinuous_symm | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Ico_iff_integrableOn_Ioo' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.3301315\nE : Type u_2\nF : Type ?u.3301321\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : PartialOrder α\ninst✝ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\nha : ↑↑μ {a} ≠ ⊤\nhab : a < b\n⊢ IntegrableOn... | [
647,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.toComposition_length | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nc : CompositionAsSet n\n⊢ Composition.length (toComposition c) = length c",
"tactic": "simp [CompositionAsSet.toComposition, Composition.length, Composition.blocks]"
}
] | [
1011,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | bot_eq_one | [] | [
226,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Finset.aemeasurable_prod' | [] | [
950,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.inv_tendsto_atTop | [] | [
150,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_zero | [] | [
158,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | lt_inv' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LT 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\na b c d : α\n⊢ a < b⁻¹ ↔ b < a⁻¹",
"tactic": "rw [← inv_lt_inv_... | [
399,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | subset_interior_div_left | [] | [
1350,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_aleph0_iff_subtype_countable | [] | [
1515,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.choose_le_centralBinom | [
{
"state_after": "no goals",
"state_before": "r n : ℕ\n⊢ choose (2 * n) (2 * n / 2) = choose (2 * n) n",
"tactic": "rw [Nat.mul_div_cancel_left n zero_lt_two]"
}
] | [
62,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mono | [] | [
135,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Filter.Tendsto.nndist | [] | [
1856,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1853,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mk'_mem_incidenceSet_right_iff | [] | [
843,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.mono | [] | [
894,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.bddAbove_l_image | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.8887\na a₁ a₂ : α\nb b₁ b₂ : β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nl : α → β\nu : β → α\ngc : GaloisConnection l u\ns : Set α\nx✝ : BddAbove (l '' s)\nx : β\nhx : x ∈ upperBounds (l '' s)\n⊢ u... | [
126,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | TensorProduct.LieModule.coe_liftLie_eq_lift_coe | [
{
"state_after": "R : Type u\ninst✝¹⁸ : CommRing R\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\nQ : Type w₃\ninst✝¹⁷ : LieRing L\ninst✝¹⁶ : LieAlgebra R L\ninst✝¹⁵ : AddCommGroup M\ninst✝¹⁴ : Module R M\ninst✝¹³ : LieRingModule L M\ninst✝¹² : LieModule R L M\ninst✝¹¹ : AddCommGroup N\ninst✝¹⁰ : Module R N... | [
128,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/List/Basic.lean | List.length_pos_iff_ne_nil | [] | [
188,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.eq_zero_of_dvd_of_lt | [] | [
215,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.prod_map | [] | [
1640,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearEquiv.nonempty_equiv_iff_lift_rank_eq | [] | [
975,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
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