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/Instances/ENNReal.lean | ENNReal.nhds_of_ne_top | [] | [
261,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.toProd_pf | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na a' : R\np : a = a'\n⊢ a = a' ^ Nat.rawCast 1 * Nat.rawCast 1",
"tactic": "simp [*]"
}
] | [
864,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closure_sphere | [] | [
1878,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1877,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.Measure.toSignedMeasure_zero | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.135956\nm : MeasurableSpace α\ni : Set α\n⊢ MeasurableSet i → ↑(toSignedMeasure 0) i = ↑0 i",
"state_before": "α : Type u_1\nβ : Type ?u.135956\nm : MeasurableSpace α\n⊢ toSignedMeasure 0 = 0",
"tactic": "ext i"
},
{
"state_after": "no goals",
... | [
464,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Module.End.ker_pow_constant | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End K V\nk : ℕ\nh : LinearMap.ker (f ^ k) = LinearMap.ker (f ^ Nat.succ k)\n⊢ LinearMap.ker (f ^ k) = LinearMap.ker (f ^ (k + 0))",
"tactic": "simp"
},
{
... | [
1505,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_ne_top | [] | [
292,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
9
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_rpow_iff | [] | [
157,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.unit_naturality | [] | [
214,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_def | [] | [
890,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.toFun_as_coe_apply | [] | [
195,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
9
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.refl_localEquiv | [] | [
742,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.trans | [] | [
281,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.map_eq_traverse_id | [] | [
78,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.ext | [
{
"state_after": "C : Type u\ninst✝² : Category C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : HasImage f\nW : C\ng h : image f ⟶ W\ninst✝ : HasLimit (parallelPair g h)\nw : factorThruImage f ≫ g = factorThruImage f ≫ h\nq : equalizer g h ⟶ image f := equalizer.ι g h\n⊢ g = h",
"state_before": "C : Type u\ninst✝² : Catego... | [
463,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_mul_inr | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Module Rᵐᵒᵖ M\nm₁ m₂ : M\n⊢ 0 • m₂ + 0 • m₁ = 0",
"tactic": "rw [zero_smul, zero_add, zero_smul]"
}
] | [
488,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.inv_one_add_tan_sq | [
{
"state_after": "x✝ y x : ℂ\nhx : cos x ≠ 0\nthis : cos x ^ 2 ≠ 0\n⊢ (1 + tan x ^ 2)⁻¹ = cos x ^ 2",
"state_before": "x✝ y x : ℂ\nhx : cos x ≠ 0\n⊢ (1 + tan x ^ 2)⁻¹ = cos x ^ 2",
"tactic": "have : cos x ^ 2 ≠ 0 := pow_ne_zero 2 hx"
},
{
"state_after": "x✝ y x : ℂ\nhx : cos x ≠ 0\nthis : cos x ... | [
1054,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.trans | [] | [
371,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanExt_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 ⟶ Y\ng : X ⟶ Z\nf' : X' ⟶ Y'\ng' : X' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iY.hom\nwg : iX.hom ≫ g' = g ≫ iZ.hom\n⊢ (spanExt iX iY iZ wf wg... | [
466,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.openSegment_closure_interior_subset_interior | [
{
"state_after": "case intro.intro.intro.intro.intro\nι : Type ?u.106301\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nx y : ... | [
196,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.lipschitzWith_equiv_aux | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.49389\n𝕜' : Type ?u.49392\nι : Type u_1\nα : ι → Type ?u.49400\nβ : ι → Type u_2\ninst✝³ : Fact (1 ≤ p)\ninst✝² : (i : ι) → PseudoMetricSpace (α i)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nx y : PiLp p β\n⊢ edist (↑(PiLp.equiv p β) x) (↑(PiLp.equ... | [
391,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.arzela_ascoli | [] | [
616,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.degree_compl | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.269926\n𝕜 : Type ?u.269929\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\ninst✝² : Fintype ↑(neighborSet G v)\ninst✝¹ : Fintype ↑(neighborSet (Gᶜ) v)\ninst✝ : Fintype V\n⊢ degree (Gᶜ) v = Fin... | [
1394,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.toSubtype'_of_subtype' | [
{
"state_after": "case a.h\nn : ℕ\nα : TypeVec n\nr : α ⊗ α ⟹ repeat n Prop\ni : Fin2 n\nx : Subtype_ r i\n⊢ (toSubtype' r ⊚ ofSubtype' r) i x = id i x",
"state_before": "n : ℕ\nα : TypeVec n\nr : α ⊗ α ⟹ repeat n Prop\n⊢ toSubtype' r ⊚ ofSubtype' r = id",
"tactic": "ext (i x)"
},
{
"state_after... | [
823,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_eq_bot | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nι : Type ?u.297281\ninst✝² : CommSemiring R✝\nI✝ J✝ K L : Ideal R✝\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nI J : Ideal R\nh : I = ⊥ ∨ J = ⊥\n⊢ I * J = ⊥",
"tactic": "cases' h with h h <;> rw [← Ideal.mul_bot, h, Ideal.m... | [
813,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | AlgEquiv.coe_restrictScalars | [] | [
226,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | int_cast_memℓp_infty | [] | [
896,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma0_is_congruence | [] | [
232,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.singleton_vsub | [] | [
1509,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.monoidHom_ext | [] | [
117,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_strictMono | [] | [
1322,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.scaleRoots_eval₂_mul | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.37521\nK : Type ?u.37524\nR : Type u_2\nS : Type u_1\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : S[X]\nf : S →+* R\nr : R\ns : S\n⊢ eval₂ f (↑f s * r) (scaleRoots p s) =\n... | [
115,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.sub_concaveOn | [] | [
917,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_graph_iff' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.457298\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nx : E × F\n⊢ x ∈ graph f ↔ ∃ y... | [
726,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.mem_of_pi_mem_pi | [
{
"state_after": "case intro.intro.intro.intro\nι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\ninst✝ : ∀ (i : ι), NeBot (f i)\nI : Set ι\nh : Set.pi I s ∈ pi f\ni : ι\nhi : i ∈ I\nI' : Set ι\nt : (i : ι) → Set (α i)\nhtf : ∀ (i : ι), t i ∈ f i\nhts : Set.pi I' t ⊆ Set... | [
100,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/List/Func.lean | List.Func.length_pointwise | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\nf : α → β → γ\nhead✝ : β\nbs : List β\n⊢ length (pointwise f [] (head✝ :: bs)) = max (length []) (length (head✝ :: bs))",
"tactic": "simp only [pointwise, length, length_map, max_... | [
312,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Std/Data/List/Lemmas.lean | List.mem_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b : α\n⊢ b ∈ replicate 0 a ↔ 0 ≠ 0 ∧ b = a",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b : α\nn : Nat\n⊢ b ∈ replicate (n + 1) a ↔ n + 1 ≠ 0 ∧ b = a",
"tactic": "simp [mem_replicate, Nat... | [
280,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
278,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_assoc | [] | [
272,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseEmbedding.to_embedding | [] | [
260,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semiring α\nm n : Num\n⊢ ↑(m + n) = ↑m + ↑n",
"tactic": "rw [← cast_to_nat, add_to_nat, Nat.cast_add, cast_to_nat, cast_to_nat]"
}
] | [
731,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.coe_mk | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan | [] | [
147,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate_singleton | [] | [
217,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/RingTheory/Localization/Cardinality.lean | IsLocalization.card | [] | [
58,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/Basic.lean | Dense.interior_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nh : Dense s\n⊢ Dense (sᶜᶜ)",
"tactic": "rwa [compl_compl]"
}
] | [
616,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.tot | [] | [
88,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.toOuterMeasure_map_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.41419\nf : α → β\np : Pmf α\nb : β\ns : Set β\n⊢ ↑(toOuterMeasure (map f p)) s = ↑(toOuterMeasure p) (f ⁻¹' s)",
"tactic": "simp [map, Set.indicator, toOuterMeasure_apply p (f ⁻¹' s)]"
}
] | [
98,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_subset_mul_right | [] | [
428,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_comp | [] | [
789,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.Path.reverse_toPath | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.coe_comp | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAsLocalEquiv_apply | [] | [
547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Combinatorics/Composition.lean | List.length_pos_of_mem_splitWrtComposition | [
{
"state_after": "n : ℕ\nα : Type u_1\nl l' : List α\nc : Composition (length l)\nh : l' ∈ splitWrtComposition l c\nthis : length l' ∈ map length (splitWrtComposition l c)\n⊢ 0 < length l'",
"state_before": "n : ℕ\nα : Type u_1\nl l' : List α\nc : Composition (length l)\nh : l' ∈ splitWrtComposition l c\n⊢ ... | [
716,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
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Mathlib/Data/Complex/Exponential.lean | Real.tan_zero | [
{
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}
] | [
1234,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
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Mathlib/Topology/MetricSpace/Basic.lean | dist_ofMul | [] | [
3187,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3187,
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Mathlib/Algebra/Order/Floor.lean | round_intCast | [
{
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}
] | [
1351,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1351,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.trans_sub | [
{
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"tactic": "s... | [
830,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
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Mathlib/Logic/Hydra.lean | Relation.cutExpand_add_left | [
{
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] | [
89,
97
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet | [
{
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498,
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_mem_ne_self_iff | [
{
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400,
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397,
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Mathlib/Order/SupIndep.lean | CompleteLattice.setIndependent_empty | [] | [
199,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.int_coeff_of_cyclotomic' | [
{
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235,
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.coe_bot | [] | [
211,
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210,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integrableOn_deriv_right_of_nonneg | [
{
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1285,
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Mathlib/Computability/Language.lean | Language.add_iSup | [] | [
234,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_strict_mono | [] | [
2008,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2007,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.findGreatest_spec | [
{
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636,
44
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Mathlib/Topology/Algebra/Module/LocallyConvex.lean | LocallyConvexSpace.convex_open_basis_zero | [] | [
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Mathlib/Data/Set/Basic.lean | Set.nmem_singleton_empty | [] | [
1355,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_nhdsWithin_eq_image' | [
{
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1162,
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1159,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_one_of_le | [] | [
782,
17
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776,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_comm | [] | [
509,
58
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507,
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_mul | [] | [
127,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.char_rmatch_iff | [
{
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238,
65
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227,
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Std/Data/List/Init/Lemmas.lean | List.foldl_append | [
{
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}
] | [
197,
80
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196,
9
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src/lean/Init/Data/Nat/Basic.lean | Nat.sub_add_eq | [
{
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"tactic": "induction c with\n| zero => simp\n| succ c ih => simp [Nat.add_succ, Nat.sub_succ, ih]"
},
{
"state_after": "no goals",
"state_before": "case zero\na b : Nat\n⊢ a - (b + zero) = a - b - zero",
... | [
257,
55
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
254,
1
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Mathlib/Data/Stream/Init.lean | Stream'.nth_succ_iterate | [
{
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}
] | [
295,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/Topology/Homeomorph.lean | Homeomorph.symm_comp_self | [] | [
196,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.mul_sum | [] | [
1083,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
11
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_comp_exp_atTop | [
{
"state_after": "no goals",
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"tactic": "simp_rw [←comp_apply (g := exp), ← tendsto_map'_iff, map_exp_atTop]"
}
] | [
318,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/Data/Set/Prod.lean | Set.pi_univ | [] | [
659,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
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Mathlib/Analysis/Convex/Normed.lean | convexHull_exists_dist_ge | [] | [
90,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_smul | [] | [
2435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2433,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.X_pow_dvd_iff | [
{
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"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ : PowerSeries R\n⊢ X ^ n ∣ φ ↔ ∀ (m : ℕ), m <... | [
1715,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1708,
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Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.iff_quotient_mvPolynomial' | [
{
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180,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsMaximal.exists_inv | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝ : Sem... | [
399,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
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Mathlib/Data/List/Indexes.lean | List.nthLe_mapIdx | [
{
"state_after": "no goals",
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"tactic": "simp [mapIdx_eq_enum_m... | [
201,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.IsCut.lt_trans | [] | [
124,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
122,
1
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Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.fderiv | [] | [
109,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.natTransExtension_hcomp | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝¹ : Category C\nW : MorphismProperty C\nD : Type u_4\ninst✝ : Category D\nG✝ : C ⥤ D\nhG : MorphismProperty.IsInvertedBy W G✝\nF G : MorphismProperty.Localization W ⥤ D\nτ : MorphismProperty.Q W ⋙ F ⟶ MorphismProperty.Q W ⋙ G\n⊢ 𝟙 (MorphismPr... | [
312,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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src/lean/Init/Data/List/Control.lean | List.forIn_cons | [] | [
158,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
156,
9
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Mathlib/Data/Multiset/Basic.lean | Multiset.filter_le_filter | [] | [
1953,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1952,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.ofEq_rfl | [
{
"state_after": "R : Type ?u.1945728\nR₂ : Type ?u.1945731\nR₃ : Type ?u.1945734\nR₄ : Type ?u.1945737\nE : Type u_1\nE₂ : Type ?u.1945743\nE₃ : Type ?u.1945746\nE₄ : Type ?u.1945749\nF : Type ?u.1945752\n𝓕 : Type ?u.1945755\ninst✝³⁶ : Semiring R\ninst✝³⁵ : Semiring R₂\ninst✝³⁴ : Semiring R₃\ninst✝³³ : Semiri... | [
1188,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
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Mathlib/Data/Finset/Basic.lean | Finset.filter_singleton | [
{
"state_after": "no goals",
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"tactic": "classical\n ext x\n simp\n split_ifs with h <;> by_cases h' : x = a <;> si... | [
2753,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2749,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_toPrenexImpRight | [
{
"state_after": "case of_isQF\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.166214\nP : Type ?u.166217\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ✝² ψ✝ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝¹ : Fin l... | [
531,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | MulHom.coe_ofDense | [] | [
535,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.mk_eq_rank'' | [
{
"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.378764\nR : Type u\ninst✝³ : Ring R\ninst✝² : StrongRankCondition R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nι : Type v\nv : Basis ι R M\nthis : Nontrivi... | [
795,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_indicator_one | [] | [
460,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/Data/Finset/Basic.lean | Finset.union_eq_empty_iff | [] | [
1781,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1780,
1
] |
Mathlib/Logic/Basic.lean | Decidable.not_exists_not | [
{
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"tactic": "simp only [not_exists, Decidable.not_not]"
}
] | [
701,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
11
] |
Mathlib/Data/List/Rotate.lean | List.IsRotated.perm | [] | [
479,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
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