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/Data/Polynomial/Module.lean | PolynomialModule.eval_map | [
{
"state_after": "case h0\nR : Type u_1\nM : Type u_2\ninst✝¹² : CommRing R\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : Module R M\nI : Ideal R\nS : Type ?u.548565\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Algebra S R\ninst✝⁷ : Module S M\ninst✝⁶ : IsScalarTower S R M\nR' : Type u_4\nM' : Type u_3\ninst✝⁵ : CommRing R'\ninst... | [
312,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset' | [] | [
194,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.nhds_coe | [] | [
80,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.281796\np : α → Prop\ninst✝ : DecidablePred p\nf : α → Option β\ns : Multiset α\nl : List α\n⊢ List.filterMap f (List.filter (fun b => decide (p b)) l) = List.filterMap (fun x => if p x then f x else none) l",
"tactic"... | [
2164,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2162,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.mono | [] | [
242,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.ext | [] | [
137,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.const_mul | [] | [
489,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.isSFiniteKernel_sum | [
{
"state_after": "case inl\nα : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\ninst✝ : Countable ι\nκs : ι → { x // x ∈ kernel α β }\nhκs : ∀ (n : ι), IsSFiniteKernel (κs n)\nval✝ : Fintype ι\n⊢ IsSFiniteKernel (kernel.sum κs)\n\ncase inr\nα : ... | [
338,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_empty | [] | [
315,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/Part.lean | Part.assert_defined | [] | [
659,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Algebra/Field/Defs.lean | not_isField_of_subsingleton | [] | [
218,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.comp_id | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_comm | [] | [
1140,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin_apply | [
{
"state_after": "R : Type ?u.1104806\nM✝ : Type ?u.1104809\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : AddCommMonoid M✝\ninst✝¹⁵ : Module R M✝\nR₁ : Type ?u.1104845\nM₁ : Type ?u.1104848\ninst✝¹⁴ : Ring R₁\ninst✝¹³ : AddCommGroup M₁\ninst✝¹² : Module R₁ M₁\nR₂ : Type u_2\nM₂ : Type u_3\ninst✝¹¹ : CommSemiring R₂\ninst✝¹⁰... | [
316,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_center_le_pow | [
{
"state_after": "case intro.intro\nG : Type u_1\ninst✝² : Group G\nH K L : Subgroup G\ninst✝¹ : Finite ↑(commutatorSet G)\ninst✝ : Group.FG G\nS : Finset G\nhS1 : Finset.card S = Group.rank G\nhS2 : closure ↑S = ⊤\n⊢ index (center G) ≤ Nat.card ↑(commutatorSet G) ^ Group.rank G",
"state_before": "G : Type ... | [
614,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Data/List/Permutation.lean | List.map_permutations' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\nts : List α\n⊢ map (map f) (permutations' ts) = permutations' (map f ts)",
"tactic": "induction' ts with t ts ih <;> [rfl; simp [← ih, map_bind, ← map_map_permutations'Aux, bind_map]]"
}
] | [
249,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.extract_gcd' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.40816\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf✝ f g : β → α\nhs : ∃ x, x ∈ s ∧ f x ≠ 0\nhg : ∀ (b : β), b ∈ s → f b = gcd s f * g b\n⊢ gcd s f * gcd s g = gcd s f",
"ta... | [
269,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_isPrincipal | [
{
"state_after": "case mp.mk.intro\nR : Type u_1\ninst✝⁷ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\nP : Type ?u.141600\ninst✝⁴ : CommRing P\ng : R →+* P\nT : Submonoid P\nhy : M ≤ Submonoid.comap g T\nQ : Type ?u.142432\ninst✝³ : CommRing Q\ninst✝² : Algebra P Q\nins... | [
138,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.rcomap'_sets | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | le_nhds_iff_adhp_of_cauchy | [] | [
137,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.piCongrRight_symm | [] | [
481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.zero_seq | [] | [
272,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.54421\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nμa : Measure α\nμb : Measure β\nμc : Measure γ\nμd : Measure δ\ng : β → γ\nf : α → β\nhg :... | [
102,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
11
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.induction_on | [
{
"state_after": "ι : Type u_1\nι₂ : Type ?u.230665\nι₃ : Type ?u.230668\nR : Type u_2\ninst✝⁷ : CommSemiring R\nR₁ : Type ?u.230677\nR₂ : Type ?u.230680\ns : ι → Type u_3\ninst✝⁶ : (i : ι) → AddCommMonoid (s i)\ninst✝⁵ : (i : ι) → Module R (s i)\nM : Type ?u.230870\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R ... | [
336,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.skewProd_apply | [] | [
2259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2257,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.isThreeCycle_cycleRange_two | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ IsThreeCycle (cycleRange 2)",
"tactic": "rw [IsThreeCycle, cycleType_cycleRange] <;> simp [Fin.eq_iff_veq]"
}
] | [
313,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1290163\nR₂ : Type ?u.1290166\nM : Type ?u.1290169\nM₁ : Type u_2\nM₂ : Type u_3\nM₁' : Type ?u.1290178\nM₂' : Type ?u.1290181\nn : Type u_4\nm : Type u_5\nn' : Type ?u.1290190\nm' : Type ?u.1290193\nι : Type ?u.1290196\ninst✝⁸ : CommR... | [
382,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_unit_right_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ne : C ≌ D\nW X X' Y : C\nf : W ⟶ X\ng : X ⟶ Y\nf' : W ⟶ X'\ng' : X' ⟶ Y\n⊢ f ≫ g ≫ (unit e).app Y = f' ≫ g' ≫ (unit e).app Y ↔ f ≫ g = f' ≫ g'",
"tactic": "s... | [
408,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_int_cast | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_eq_zero_iff | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ inner x y / (‖x‖ * ‖y‖) ≤ 1",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ angle x y = 0 ↔ x ≠ 0 ∧ ∃ r, 0 < r ∧ y = r • x",
"tac... | [
214,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.toOuterMeasure_trim_eq_trim_toOuterMeasure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3496438\nγ : Type ?u.3496441\nδ : Type ?u.3496444\nι : Type ?u.3496447\nR : Type ?u.3496450\nR' : Type ?u.3496453\nm m0 : MeasurableSpace α\nμ✝ : Measure α\ns : Set α\nμ : Measure α\nhm : m ≤ m0\n⊢ ↑(trim μ hm) = OuterMeasure.trim ↑μ",
... | [
4363,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4361,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.inter_ae_eq_right_of_ae_eq_univ | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type ?u.122594\nγ : Type ?u.122597\nδ : Type ?u.122600\nι : Type ?u.122603\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : s =ᵐ[μ] univ\n⊢ t = univ ∩ t",
"state_before": "α : Type u_1\nβ : Type ?u.122594\nγ : Type ?u.122597\nδ : Type ?... | [
533,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.exists_pow_eq'' | [
{
"state_after": "case intro.zero.intro\nι : Type ?u.239854\nα : Type u_1\nβ : Type ?u.239860\nf g : Perm α\np : α → Prop\nx z : α\ninst✝ : Finite α\nhi : Nat.zero < orderOf f\nh : SameCycle f x (↑(f ^ Nat.zero) x)\n⊢ ∃ i x_1 x_2, ↑(f ^ i) x = ↑(f ^ Nat.zero) x\n\ncase intro.succ.intro\nι : Type ?u.239854\nα : ... | [
260,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexRange_self | [
{
"state_after": "case pos\nι : Type u_2\nι' : Type ?u.373505\nR : Type u_3\nR₂ : Type ?u.373511\nK : Type ?u.373514\nM : Type u_1\nM' : Type ?u.373520\nM'' : Type ?u.373523\nV : Type u\nV' : Type ?u.373528\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\ninst✝ : M... | [
475,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s s' : Set α\n⊢ Set.ite univ s s' = s",
"tactic": "simp [Set.ite]"
}
] | [
2283,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2283,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.linearEquivFunOnFintype_lof | [
{
"state_after": "case h\nR : Type u\ninst✝⁶ : Semiring R\nι : Type v\ndec_ι : DecidableEq ι\nM : ι → Type w\ninst✝⁵ : (i : ι) → AddCommMonoid (M i)\ninst✝⁴ : (i : ι) → Module R (M i)\nN : Type u₁\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nφ : (i : ι) → M i →ₗ[R] N\nψ ψ' : (⨁ (i : ι), M i) →ₗ[R] N\ninst✝¹ ... | [
174,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | interior_smul | [] | [
286,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.reverse_inj | [
{
"state_after": "case mp\nU : Type ?u.753\nV : Type u_1\nW : Type ?u.759\ninst✝² : Quiver U\ninst✝¹ : Quiver V\ninst✝ : Quiver W\nh : HasInvolutiveReverse V\na b : V\nf g : a ⟶ b\n⊢ reverse f = reverse g → f = g\n\ncase mpr\nU : Type ?u.753\nV : Type u_1\nW : Type ?u.759\ninst✝² : Quiver U\ninst✝¹ : Quiver V\n... | [
77,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Zorn.lean | zorn_preorder | [] | [
110,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_subset_Ici | [] | [
420,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_iSup_iSup | [] | [
3037,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3035,
1
] |
Mathlib/Algebra/Parity.lean | isSquare_mul_self | [] | [
59,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_sub_cancel_right | [] | [
1146,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
11
] |
Mathlib/RingTheory/Polynomial/RationalRoot.lean | UniqueFactorizationMonoid.integer_of_integral | [] | [
132,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | three_add_one_eq_four | [
{
"state_after": "α : Type u_1\ninst✝ : AddMonoidWithOne α\n⊢ ↑(1 + 1 + 1 + 1) = 4",
"state_before": "α : Type u_1\ninst✝ : AddMonoidWithOne α\n⊢ 3 + 1 = 4",
"tactic": "rw [←two_add_one_eq_three, ←one_add_one_eq_two, ←Nat.cast_one,\n ←Nat.cast_add, ←Nat.cast_add, ←Nat.cast_add]"
},
{
"state_aft... | [
242,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.mono | [] | [
454,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_sq | [
{
"state_after": "x y : ℂ\n⊢ cosh x ^ 2 = sinh x ^ 2 + (cosh x ^ 2 - sinh x ^ 2)",
"state_before": "x y : ℂ\n⊢ cosh x ^ 2 = sinh x ^ 2 + 1",
"tactic": "rw [← cosh_sq_sub_sinh_sq x]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh x ^ 2 = sinh x ^ 2 + (cosh x ^ 2 - sinh x ^ 2... | [
761,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | AbsoluteValue.sum_le | [] | [
744,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.inj_on_of_surj_on_of_ncard_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ns t✝ : Set α\na b x y : α\nf✝ : α → β\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhsurj : ∀ (b : β), b ∈ t → ∃ a ha, b = f a ha\nhst : ncard s ≤ ncard t\na₁ a₂ : α\nha₁ : a₁ ∈ s\nha₂ : a₂ ∈ s\nha₁a₂ :... | [
453,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_X_pow | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\nn : ℕ\n⊢ eval₂ f x (↑(monomial n) 1) = x ^ n",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring... | [
89,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.Tendsto.prod_mk | [] | [
149,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_eq_intro | [
{
"state_after": "no goals",
"state_before": "n m k l : ℕ\nh : n + m = k + l\n⊢ dist n k = dist (n + m) (k + m)",
"tactic": "rw [dist_add_add_right]"
},
{
"state_after": "no goals",
"state_before": "n m k l : ℕ\nh : n + m = k + l\n⊢ dist (n + m) (k + m) = dist (k + l) (k + m)",
"tactic":... | [
93,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Basic.lean | gt_or_eq_of_le | [] | [
406,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.size_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\narr : Array α\n⊢ size (map f arr) = size arr",
"tactic": "simp [size]"
}
] | [
180,
14
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
179,
9
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_eq_iInter_innerDualCone_singleton | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.19025\nE : Type ?u.19028\nF : Type ?u.19031\nG : Type ?u.19034\nH : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℝ H\ns t : Set H\n⊢ ↑(innerDualCone s) = ⋂ (i : ↑s), ↑(innerDualCone {↑i})",
"tactic": "rw [← ConvexCone.coe_i... | [
123,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.sInf_apply | [] | [
358,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_inj | [] | [
125,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_eq_zero_of_dvd_aeval_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type ?u.1237620\nB' : Type ?u.1237623\na✝ b : R\nn : ℕ\ninst✝⁹ : CommSemiring A'\ninst✝⁸ : Semiring B'\ninst✝⁷ : CommSemiring R\np✝ q✝ : R[X]\ninst✝⁶ : Semiring A\ninst✝⁵ : Algebra R A\nB : Type ?u.1237836\ninst✝⁴ : Semiring B\ninst✝³ : Alge... | [
339,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.ofPiFork_π_app_right | [] | [
474,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.induction_on' | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nC : Set α → Prop\nS : Set α\nh : Set.Finite S\nH0 : C ∅\nH1 : ∀ {a : α} {s : Set α}, a ∈ S → s ⊆ S → ¬a ∈ s → C s → C (insert a s)\n⊢ ∀ {a : α} {s : Set α}, ¬a ∈ s → Set.Finite s → (fun s => s ⊆ S → C s) s → (fun s => s ⊆ S → C s) (insert a s)",
... | [
1152,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_sum_of_nonneg | [
{
"state_after": "α : Type u_1\ns : Finset α\nf : α → ℝ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ ∑ i in s, f i = ∑ a in s, ↑(Real.toNNReal (f a))",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℝ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ Real.toNNReal (∑ a in s, f a) = ∑ a in s, Real.toNNReal (f a)",
"tacti... | [
337,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange_multiset_sum | [] | [
239,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_prod | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nA : Type ?u.99397\nB : Type ?u.99400\nM : Type u_1\nN : Type ?u.99406\nP : Type ?u.99409\nR : Type ?u.99412\nS : Type ?u.99415\nG : Type ?u.99418\nM₀ : Type ?u.99421\nG₀ : Type ?u.99424\nι : Sort ?u.99427\ninst✝ : CommMonoid M\ns : Finset α\nf : α → β → M\n⊢ ∀ (x : ... | [
398,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | separate_convex_open_set | [
{
"state_after": "𝕜 : Type ?u.8\nE : Type u_1\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : TopologicalAddGroup E\ninst✝¹ : Module ℝ E\ninst✝ : ContinuousSMul ℝ E\ns : Set E\nhs₀ : 0 ∈ s\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nx₀ : E\nhx₀ : ¬x₀ ∈ s\nf : E →ₗ.[ℝ] ℝ := LinearPMap.mkSpanSingleton x₀ ... | [
79,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly.map | [
{
"state_after": "case mk'.intro\np : ℕ\nR S : Type u\nσ : Type ?u.696707\nidx : Type ?u.696710\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\nf : ⦃R : Type u⦄ → [inst : CommRing R] → 𝕎 R → 𝕎 R\ng : R →+* S\nx : 𝕎 R\nφ : ℕ → MvPolynomial ℕ ℤ\nhf : ∀ ⦃R : Type u⦄ [inst : CommRing R] (x... | [
564,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.eq | [] | [
51,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
11
] |
Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.map_swap_antidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ map Prod.swap (antidiagonal n) = antidiagonal n",
"tactic": "rw [antidiagonal, coe_map, List.Nat.map_swap_antidiagonal, coe_reverse]"
}
] | [
81,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Module/Basic.lean | Function.Injective.noZeroSMulDivisors | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.261935\nR✝ : Type ?u.261938\nk : Type ?u.261941\nS : Type ?u.261944\nM✝ : Type ?u.261947\nM₂ : Type ?u.261950\nM₃ : Type ?u.261953\nι : Type ?u.261956\nR : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁵ : Zero R\ninst✝⁴ : Zero M\ninst✝³ : Zero N\ninst✝... | [
597,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.closure | [] | [
383,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.wbtw_secondInter | [
{
"state_after": "case pos\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np p' : P\nhp : p ∈ s\nhp' : dist p' s.center ≤ s.radius\nh : p' = p\n⊢ Wbtw ℝ p p' (secondInter s p (p' -ᵥ p))\n\ncase neg\nV ... | [
172,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.eq_prime_pow_of_dvd_least_prime_pow | [
{
"state_after": "case intro.intro\np k : ℕ\npp : Prime p\nl : ℕ\nh : l ≤ k + 1\nh₁ : ¬p ^ l ∣ p ^ k\nh₂ : p ^ l ∣ p ^ (k + 1)\n⊢ p ^ l = p ^ (k + 1)",
"state_before": "a p k : ℕ\npp : Prime p\nh₁ : ¬a ∣ p ^ k\nh₂ : a ∣ p ^ (k + 1)\n⊢ a = p ^ (k + 1)",
"tactic": "obtain ⟨l, ⟨h, rfl⟩⟩ := (dvd_prime_pow p... | [
713,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_bracket | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/TietzeExtension.lean | ContinuousMap.exists_restrict_eq_of_closed | [] | [
419,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_fromBlocks_zero₁₂ | [
{
"state_after": "no goals",
"state_before": "m : Type u_1\nn : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix m m R\nC : Matrix n m R\nD : Matrix n n R\n⊢ det (fromBlocks A 0 C D) = det A * det D",
"tactic": "... | [
710,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_iff_infinitesimal_inv | [] | [
767,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_le_cancel | [
{
"state_after": "ctx : Context\nm₁ m₂ : Poly\nh : denote_le ctx (m₁, m₂)\n⊢ denote_le ctx (cancel m₁ m₂)",
"state_before": "ctx : Context\nm₁ m₂ : Poly\nh : denote_le ctx (m₁, m₂)\n⊢ denote_le ctx (cancel m₁ m₂)",
"tactic": "simp"
},
{
"state_after": "case h\nctx : Context\nm₁ m₂ : Poly\nh : de... | [
497,
44
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
496,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.chain_ne_nil | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\nl m : List α\na : α\n_H : ∀ (hl : m ≠ []), Chain r ↑m ↔ List.Chain r (getLast m hl) m\nhl✝ : m ++ [a] ≠ []\n⊢ Chain r ↑(m ++ [a]) ↔ List.Chain r (getLast (m ++ [a]) hl✝) (m ++ [a])",
"state_before": "α : Type u_1\nr : α → α → Prop\nl : List α\n⊢ ∀ (l : List ... | [
953,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.image2 | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nt : Set β\nhs : Set.Countable s\nht : Set.Countable t\nf : α → β → γ\n⊢ Set.Countable ((fun x => f x.fst x.snd) '' s ×ˢ t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nt : Set β\nhs : Set.Countable ... | [
288,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | Differentiable.add | [] | [
163,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_map | [] | [
3940,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3939,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_mul_negSucc | [] | [
377,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
377,
9
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | IsCompact.totallyBounded | [] | [
590,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
11
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | image_circleMap_Ioc | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.19235\ninst✝ : NormedAddCommGroup E\nc : ℂ\nR : ℝ\n⊢ circleMap c R '' Ioc 0 (2 * π) = sphere c (Abs.abs R)",
"tactic": "rw [← range_circleMap, ← (periodic_circleMap c R).image_Ioc Real.two_pi_pos 0, zero_add]"
}
] | [
158,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion₂_subset_iUnion | [] | [
424,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Algebra/Pi.lean | AlgEquiv.piCongrRight_symm | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/Normed/Group/ControlledClosure.lean | controlled_closure_range_of_complete | [
{
"state_after": "case hyp\nG : Type u_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : CompleteSpace G\nH : Type u_2\ninst✝¹ : NormedAddCommGroup H\nf : NormedAddGroupHom G H\nK : Type u_3\ninst✝ : SeminormedAddCommGroup K\nj : NormedAddGroupHom K H\nhj : ∀ (x : K), ‖↑j x‖ = ‖x‖\nC ε : ℝ\nhC : 0 < C\nhε : 0 < ε\nhyp... | [
133,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_upShadow_iff_exists_mem_card_add_one | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\n⊢ (∃ a, a ∈ s ∧ erase s a ∈ 𝒜) → ∃ t, t ∈ 𝒜 ∧ t ⊆ s ∧ card t + 1 = card s\n\ncase refine'_2\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (... | [
245,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftl'_sub | [
{
"state_after": "b : Bool\nm n k : ℕ\nh : k + 1 ≤ n + 1\n⊢ shiftl' b m (n - k) = shiftr (bit b (shiftl' b m n)) (k + 1)",
"state_before": "b : Bool\nm n k : ℕ\nh : k + 1 ≤ n + 1\n⊢ shiftl' b m (n + 1 - (k + 1)) = shiftr (shiftl' b m (n + 1)) (k + 1)",
"tactic": "simp [shiftl']"
},
{
"state_afte... | [
339,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.nhds_coe_coe | [] | [
85,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Ring/Units.lean | IsUnit.neg | [] | [
99,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.range_succ | [] | [
3004,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3003,
1
] |
Mathlib/Algebra/PUnitInstances.lean | PUnit.mul_eq | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/RingTheory/Polynomial/RationalRoot.lean | scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero | [
{
"state_after": "case h.e'_2.h.e\nA : Type u_1\nK : Type ?u.888\nR : Type ?u.891\nS : Type u_2\ninst✝⁷ : CommRing A\ninst✝⁶ : Field K\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing S\nM : Submonoid A\ninst✝³ : Algebra A S\ninst✝² : IsLocalization M S\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\np : A[X]\nr : A\... | [
48,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_obj_inl_inl | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.PointedMap.map_pt | [] | [
373,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.rightAdjointUniq_trans | [
{
"state_after": "case w.h\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG G' G'' : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F ⊣ G'\nadj3 : F ⊣ G''\nx✝ : D\n⊢ ((rightAdjointUniq adj1 adj2).hom ≫ (rightAdjointUniq adj2 adj3).hom).app x✝ = (rightAdjointUniq adj1 adj3).hom.app x✝",
"state_b... | [
310,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_eq_inter_iff_left | [] | [
1811,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1810,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.contDiff_cos | [] | [
85,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 p3 : P\nhp1p2 : p1 ≠ p2\nhp3p2 : p3 ≠ p2\n⊢ ‖p1 -ᵥ ?p3 - (p3 -ᵥ ?p3)‖ = abs (‖p1 -ᵥ p2‖ - ‖p3 -ᵥ p2‖) ↔ ∠ p1 p2 p3 = 0\n\ncase p3\nV : Type u_2\... | [
249,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.compactConvNhd_subset_compactOpen | [
{
"state_after": "case intro.intro.intro\nα : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV✝ : Set (β × β)\nf : C(α, β)\nhK : IsCompact K\nU : Set β\nhU : IsOpen U\nhf : f ∈ CompactOpen.gen K U\nV : Set (β × β)\nhV₁ : V ∈ 𝓤 β\nhV₂ : IsOpen V\nhV₃ : ∀ (x : β), x ∈ ↑f ''... | [
217,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.