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/Order/BooleanAlgebra.lean | le_iff_disjoint_sdiff | [] | [
259,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.const_boundedAtFilter | [] | [
91,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.lt_sqrt_of_sq_lt | [] | [
445,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousOn.add | [] | [
503,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Algebra/Order/WithZero.lean | le_mul_inv_of_mul_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nh : c ≠ 0\nhab : a * c ≤ b\n⊢ a * c ≤ b * c⁻¹ * c",
"tactic": "simpa [h] using hab"
}
] | [
141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | LinearIsometry.map_orthogonalProjection | [
{
"state_after": "case refine'_1\n𝕜 : Type u_3\nE✝ : Type ?u.522362\nF : Type ?u.522365\ninst✝¹⁰ : IsROrC 𝕜\ninst✝⁹ : NormedAddCommGroup E✝\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : InnerProductSpace 𝕜 E✝\ninst✝⁶ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E✝\ninst✝⁵ : CompleteSpace { x // x ∈ K }\nE : Type u_1... | [
537,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_sphere_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.38896\nι : Type ?u.38899\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ x ∈ sphere y ε ↔ y ∈ sphere x ε",
"tactic": "rw [mem_sphere', mem_sphere]"
}
] | [
580,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.IsProper.not_mem_or_compl_not_mem | [
{
"state_after": "P : Type u_1\ninst✝ : BooleanAlgebra P\nx : P\nI : Ideal P\nhI : IsProper I\nh : xᶜ ∈ I → ¬x ∈ I\n⊢ ¬x ∈ I ∨ ¬xᶜ ∈ I",
"state_before": "P : Type u_1\ninst✝ : BooleanAlgebra P\nx : P\nI : Ideal P\nhI : IsProper I\n⊢ ¬x ∈ I ∨ ¬xᶜ ∈ I",
"tactic": "have h : xᶜ ∈ I → x ∉ I := hI.not_mem_of_... | [
505,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_min_le_max_abs_abs | [] | [
348,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.le_pure_iff' | [] | [
426,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.mem_of_le | [] | [
96,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.swap_induction_on | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Finite α\nP : Perm α → Prop\nf : Perm α\nval✝ : Fintype α\n⊢ P 1 → (∀ (f : Perm α) (x y : α), x ≠ y → P f → P (swap x y * f)) → P f",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Finite α\nP : P... | [
267,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\ninst✝ : IsIso f\n⊢ (pushoutCoconeOfLeftIso f g).ι.app none = g",
"tactic": "simp"
}
] | [
1795,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1794,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.snd_comp_mk | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Polynomial.eq_of_degree_sub_lt_of_eval_finset_eq | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : R[X]\ns : Finset R\ndegree_fg_lt : degree (f - g) < ↑(Finset.card s)\neval_fg : ∀ (x : R), x ∈ s → eval x f = eval x g\n⊢ f - g = 0",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : R[X]\ns : Finset ... | [
63,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.mul_iInf_of_nonneg | [] | [
119,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/ContinuousOn.lean | tendsto_nhdsWithin_iff_subtype | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.305005\nδ : Type ?u.305008\ninst✝ : TopologicalSpace α\ns : Set α\na : α\nh : a ∈ s\nf : α → β\nl : Filter β\n⊢ Tendsto (f ∘ Subtype.val) (𝓝 { val := a, property := h }) l ↔ Tendsto (restrict s f) (𝓝 { val := a, property := h }) l",
"state_before":... | [
512,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_append | [] | [
1423,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Set.Finite.toFinset_smul_set | [] | [
2253,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2251,
1
] |
Std/Data/List/Lemmas.lean | List.get?_mem | [] | [
530,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
529,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPullback | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nD : Type u₂\ninst✝ : Category D\nF : D ⥤ C\nZ : D\nT : Presieve (F.obj Z)\nx : FamilyOfElements P T\nh : Compatible x\nZ₁ Z₂ W : D\ng₁ : W ⟶ Z₁\ng₂ : W ⟶ Z₂\nf₁ : Z₁ ⟶ Z... | [
308,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.dvd_content_iff_C_dvd | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nr : R\n⊢ r ∣ content p ↔ ∀ (i : ℕ), r ∣ coeff p i",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nr : R\n⊢ r ∣ content p ↔ ↑C... | [
227,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_choose_eq_zero_of_lt | [
{
"state_after": "case pos\np n k : ℕ\nh : n < p\nhnk : n < k\n⊢ ↑(factorization (choose n k)) p = 0\n\ncase neg\np n k : ℕ\nh : n < p\nhnk : ¬n < k\n⊢ ↑(factorization (choose n k)) p = 0",
"state_before": "p n k : ℕ\nh : n < p\n⊢ ↑(factorization (choose n k)) p = 0",
"tactic": "by_cases hnk : n < k"
... | [
116,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.hasFiniteBiproducts | [] | [
278,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsMatching.support_eq_verts | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nh : IsMatching M\nv : V\nhv : v ∈ M.verts\n⊢ v ∈ support M",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nh : IsMatching M\n⊢ support M = M.verts",
"tactic": "refine M.support_subset_verts.antisymm fun v hv => ?_"
... | [
96,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/List/Sigma.lean | List.perm_nodupKeys | [] | [
145,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_left_strictMono | [
{
"state_after": "case intro\nα : Type ?u.160126\nβ : Type ?u.160129\nb c d : ℝ≥0∞\nr p q a : ℝ≥0\nh0 : ↑a ≠ 0\n⊢ StrictMono fun x => ↑a * x",
"state_before": "α : Type ?u.160126\nβ : Type ?u.160129\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh0 : a ≠ 0\nhinf : a ≠ ⊤\n⊢ StrictMono fun x => a * x",
"tactic": "lift a t... | [
1006,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Algebra/MonoidAlgebra/Ideal.lean | AddMonoidAlgebra.mem_ideal_span_of'_image | [] | [
72,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/GroupTheory/Torsion.lean | CommMonoid.torsion.isTorsion | [
{
"state_after": "G : Type u_1\nH : Type ?u.178531\ninst✝ : CommMonoid G\nx✝ : { x // x ∈ torsion G }\nx : G\nn : ℕ\nnpos : n > 0\nhn : Function.IsPeriodicPt ((fun x x_1 => x * x_1) x) n 1\n⊢ ↑(((fun x_1 => { val := x, property := (_ : ∃ n, n > 0 ∧ Function.IsPeriodicPt (fun x_2 => x * x_2) n 1) } * x_1)^[n])\n... | [
213,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_isClosed_basic | [
{
"state_after": "α : Type u\ns : Set α\n⊢ IsOpen ({u | s ∈ u}ᶜ)",
"state_before": "α : Type u\ns : Set α\n⊢ IsClosed {u | s ∈ u}",
"tactic": "rw [← isOpen_compl_iff]"
},
{
"state_after": "case h.e'_3\nα : Type u\ns : Set α\n⊢ {u | s ∈ u}ᶜ = {u | sᶜ ∈ u}",
"state_before": "α : Type u\ns : Se... | [
65,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Deprecated/Subring.lean | Ring.exists_list_of_mem_closure | [
{
"state_after": "R : Type u\ninst✝¹ : Ring R\ncR : Type u\ninst✝ : CommRing cR\ns : Set R\na : R\nh : a ∈ closure s\nb : R\nih✝ : ∃ L, (∀ (l : List R), l ∈ L → ∀ (x : R), x ∈ l → x ∈ s ∨ x = -1) ∧ List.sum (List.map List.prod L) = b\nL1 : List (List R)\nh1 : ∀ (l : List R), l ∈ L1 → ∀ (x : R), x ∈ l → x ∈ s ∨ ... | [
126,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finite_mulSupport | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDedekindDomain R\nK : Type ?u.12131\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv✝ : HeightOneSpectrum R\nI : Ideal R\nhI : I ≠ 0\nv : HeightOneSpectrum R\nhv : v ∈ {v | maxPowDividing v I ≠ 1}\nh_zero ... | [
86,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Order/Basic.lean | not_lt_of_le | [] | [
359,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_bit0_pos | [] | [
658,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Biprod.ofComponents_fst | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasBinaryBiproducts C\nX₁ X₂ Y₁ Y₂ : C\nf₁₁ : X₁ ⟶ Y₁\nf₁₂ : X₁ ⟶ Y₂\nf₂₁ : X₂ ⟶ Y₁\nf₂₂ : X₂ ⟶ Y₂\n⊢ ofComponents f₁₁ f₁₂ f₂₁ f₂₂ ≫ biprod.fst = biprod.fst ≫ f₁₁ + biprod.snd ≫ f₂₁",
"tactic":... | [
694,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_eq_re_sub_im | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.2851475\ninst✝ : IsROrC K\nz : K\n⊢ ↑(starRingEnd K) (↑(↑re z) + ↑(↑im z) * I) = ↑(↑re z) - ↑(↑im z) * I",
"tactic": "rw [map_add, map_mul, conj_I, conj_ofReal, conj_ofReal, mul_neg, sub_eq_add_neg]"
}
] | [
379,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_of_isIntegral_mul_unit | [] | [
618,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.smul_def | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.union | [] | [
185,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsClosed.Icc_subset_of_forall_mem_nhdsWithin | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁷ : ConditionallyCompleteLinearOrder α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : ConditionallyCompleteLinearOrder β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderTopology β\ninst✝¹ : Nonempty γ\ninst✝ : DenselyOrdered α\na✝ b✝ a b :... | [
390,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_const_smul_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.417786\nι : Type ?u.417789\ninst✝¹¹ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹⁰ : TopologicalSpace β\ninst✝⁹ : TopologicalSpace γ\nf g : α → β\nM : Type ?u.417820\nG : Type u_3\nG₀ : Type ?u.417826\ninst✝⁸... | [
1760,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1758,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1464610\nG : Type ?u.1464613\n𝕜 : Type ?u.1464616\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\... | [
1409,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.universally_respectsIso | [
{
"state_after": "case left\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.81425\ninst✝ : Category D\nP : MorphismProperty C\n⊢ ∀ {X Y Z : C} (e : X ≅ Y) (f : Y ⟶ Z), universally P f → universally P (e.hom ≫ f)\n\ncase right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.81425\ninst✝ : Category D\nP : MorphismPro... | [
579,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/List/Join.lean | List.take_sum_join | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.5739\ni : ℕ\n⊢ take (sum (take i (map length []))) (join []) = join (take i [])\n\ncase cons\nα : Type u_1\nβ : Type ?u.5739\nhead✝ : List α\ntail✝ : List (List α)\ntail_ih✝ : ∀ (i : ℕ), take (sum (take i (map length tail✝))) (join tail✝) = join (take i tail... | [
94,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_refl | [] | [
372,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | biSup_inf_biSup | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\nκ : ι✝ → Sort ?u.5320\ninst✝ : Frame α\ns✝ t✝ : Set α\na b : α\nι : Type u_1\nι' : Type u_2\nf : ι → α\ng : ι' → α\ns : Set ι\nt : Set ι'\n⊢ (⨆ (i : { i // i ∈ s } × { i // i ∈ t }), f ↑i.fst ⊓ g ↑i.snd) = ⨆ (x : { i // i ∈ s ×ˢ t }), f (↑x).fst ⊓ g (↑x).sn... | [
125,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_cond_eq_cond_inter' | [
{
"state_after": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\nhms : MeasurableSet s\nhmt : MeasurableSet t\nhcs : ↑↑μ s ≠ ⊤\nhci : ↑↑μ (s ∩ t) ≠ 0\nhcs' : ↑↑μ s ≠ 0\n⊢ μ[|s][|t] = μ[|s ∩ t]",
"state_before": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω... | [
134,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_def | [] | [
1446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_of_not_le | [] | [
996,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux3_symm_trans_trans | [
{
"state_after": "case h\nα : Type u\nβ : Type v\ninst✝³ : DecidableEq α\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nf : Perm α\ne : α ≃ β\ns✝ : Multiset α\nt✝ : Multiset β\nhs✝ : ∀ (x : α), x ∈ s✝\nht✝ : ∀ (x : β), x ∈ t✝\nt : List β\ns : List α\nhs : ∀ (x : α), x ∈ Quotient.mk (List.isSeto... | [
602,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_coe | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.continuousOn_fderiv_of_open | [] | [
1205,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.unit_le_op_norm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι)... | [
370,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.le_def | [] | [
424,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.bot_N | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Metric.Bounded.exists_pos_norm_le' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.99872\n𝕜 : Type ?u.99875\nα : Type ?u.99878\nι : Type ?u.99881\nκ : Type ?u.99884\nE : Type u_1\nF : Type ?u.99890\nG : Type ?u.99893\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
691,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.map_comap_le | [] | [
225,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.toNNReal_rpow | [
{
"state_after": "case inl\nx : ℝ≥0∞\nz : ℝ\nH : z < 0\n⊢ ENNReal.toNNReal x ^ z = ENNReal.toNNReal (x ^ z)\n\ncase inr.inl\nx : ℝ≥0∞\nz : ℝ\nH : z = 0\n⊢ ENNReal.toNNReal x ^ z = ENNReal.toNNReal (x ^ z)\n\ncase inr.inr\nx : ℝ≥0∞\nz : ℝ\nH : 0 < z\n⊢ ENNReal.toNNReal x ^ z = ENNReal.toNNReal (x ^ z)",
"sta... | [
732,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_inv | [] | [
514,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists'Aux_eq_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nr₁ x✝ : List (List α)\n⊢ sublists'Aux a [] x✝ = x✝ ++ map (cons a) []",
"tactic": "simp [sublists'Aux]"
},
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nr₁✝ r₁ : List (List α)\nl : List α\nih ... | [
75,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Normalized.lean | AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality | [
{
"state_after": "no goals",
"state_before": "A : Type u_2\ninst✝¹ : Category A\ninst✝ : Abelian A\nX✝ X Y : SimplicialObject A\nf : X ⟶ Y\n⊢ AlternatingFaceMapComplex.map f ≫ PInftyToNormalizedMooreComplex Y =\n PInftyToNormalizedMooreComplex X ≫ NormalizedMooreComplex.map f",
"tactic": "aesop_cat"
... | [
87,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_fin | [] | [
302,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasStrictDerivAt_arccos | [] | [
142,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.brange_bfamilyOfFamily' | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.276348\nγ : Type ?u.276351\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nr : ι → ι → Prop\ninst✝ : IsWellOrder ι r\nf : ι → α\na : α\n⊢ a ∈ brange (type r) (bfamilyOfFamily' r f) → a ∈ range f\n\ncase refine'_2\nα : Type u_1\nβ : ... | [
1206,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.res_zero | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.eval₂Hom_rename | [] | [
195,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_top_right | [] | [
330,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_inv_snd | [
{
"state_after": "case mk\nC : Type u\n𝒞 : Category C\ninst✝⁴ : MonoidalCategory C\nC₁ : Type u₁\ninst✝³ : Category C₁\ninst✝² : MonoidalCategory C₁\nC₂ : Type u₂\ninst✝¹ : Category C₂\ninst✝ : MonoidalCategory C₂\nfst✝ : C₁\nsnd✝ : C₂\n⊢ (ρ_ (fst✝, snd✝)).inv.snd = (ρ_ (fst✝, snd✝).snd).inv",
"state_befor... | [
677,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Deprecated/Subgroup.lean | Multiplicative.isNormalSubgroup | [] | [
203,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/List/Basic.lean | List.ext_nthLe | [] | [
1400,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | exists_le_mul_self | [] | [
1945,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1943,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_comp_map | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.reify_one | [] | [
191,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Init/CcLemmas.lean | eq_false_of_not_eq_true | [] | [
111,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.revAtFun_inj | [
{
"state_after": "R : Type ?u.1604\ninst✝ : Semiring R\nf : R[X]\nN a b : ℕ\nhab : revAtFun N a = revAtFun N b\n⊢ a = b",
"state_before": "R : Type ?u.1604\ninst✝ : Semiring R\nf : R[X]\nN : ℕ\n⊢ Function.Injective (revAtFun N)",
"tactic": "intro a b hab"
},
{
"state_after": "no goals",
"sta... | [
55,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Int/CharZero.lean | RingHom.injective_int | [] | [
70,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.sign_bot | [] | [
1113,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_zero | [] | [
381,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | Real.nnnorm_mul_toNNReal | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.381722\nβ : Type ?u.381725\nγ : Type ?u.381728\nι : Type ?u.381731\nx y : ℝ\nhy : 0 ≤ y\n⊢ ‖x‖₊ * toNNReal y = ‖x * y‖₊",
"tactic": "rw [mul_comm, mul_comm x, toNNReal_mul_nnnorm x hy]"
}
] | [
819,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.linearMap_vsub | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV1 : Type u_2\nP1 : Type u_3\nV2 : Type u_4\nP2 : Type u_5\nV3 : Type ?u.43498\nP3 : Type ?u.43501\nV4 : Type ?u.43504\nP4 : Type ?u.43507\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ : Add... | [
140,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.stream_eq_none_of_fr_eq_zero | [
{
"state_after": "case mk\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nb✝ : ℤ\nfr : K\nstream_nth_eq : IntFractPair.stream v n = some { b := b✝, fr := fr }\nnth_fr_eq_zero : { b := b✝, fr := fr }.fr = 0\n⊢ IntFractPair.stream v (n + 1) = none",
"state_before": "K : Type u... | [
74,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | IsConj.normalClosure_eq_top_of | [
{
"state_after": "case intro\nG : Type u_1\nG' : Type ?u.732819\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.732828\ninst✝¹ : AddGroup A\nN✝ : Type ?u.732834\ninst✝ : Group N✝\nN : Subgroup G\nhn : Normal N\ng : G\nhg : g ∈ N\nht : normalClosure {{ val := g, property := hg }} = ⊤\nc : G\nhg' : c * g * c⁻¹ ... | [
3697,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3677,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.pow_iff | [
{
"state_after": "R : Type u_1\nS : Type ?u.17315\nM : Type u_2\na b : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\nn : ℕ\nn0 : 0 < n\n⊢ IsSMulRegular M (a ^ n) → IsSMulRegular M a",
"state_before": "R : Type u_1\nS : Type ?u.17315\nM : Type u_2\na b : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R... | [
166,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.comp_apply | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.exists_large_sphere_aux | [
{
"state_after": "case refine'_1\nα : Type ?u.566246\nβ : Type ?u.566249\nn✝ d✝ k N : ℕ\nx✝ : Fin n✝ → ℕ\nn d : ℕ\nx : Fin n → ℕ\nhx : x ∈ box n d\n⊢ ∑ i : Fin n, x i ^ 2 ∈ range (n * (d - 1) ^ 2 + 1)\n\ncase refine'_2\nα : Type ?u.566246\nβ : Type ?u.566249\nn✝ d✝ k N : ℕ\nx : Fin n✝ → ℕ\nn d : ℕ\n⊢ card (rang... | [
251,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_zero_X | [
{
"state_after": "case hnc\nσ : Type u_2\nR : Type u_1\ninst✝ : Semiring R\ns : σ\n⊢ ¬0 = single s 1",
"state_before": "σ : Type u_2\nR : Type u_1\ninst✝ : Semiring R\ns : σ\n⊢ ↑(coeff R 0) (X s) = 0",
"tactic": "rw [coeff_X, if_neg]"
},
{
"state_after": "case hnc\nσ : Type u_2\nR : Type u_1\nin... | [
420,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.zero_term | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommMonoid α\nx a : α\n⊢ term 0 x a = a",
"tactic": "simp [term, zero_nsmul, one_nsmul]"
}
] | [
153,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.coe_coeHom | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_true | [] | [
680,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.10594\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\ninst✝ : Nontrivial α\n⊢ lcm s f = 0 ↔ 0 ∈ f '' ↑s",
"tactic": "simp only [Multiset.mem_map, lcm_def, Multiset.l... | [
127,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym2_mono | [] | [
113,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_zero_iff_closure_eq_closure | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.50354\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\n⊢ hausdorffEdist s t = 0 ↔ closure s = closure t",
"tactic": "simp only [hausdorffEdist_def, ENNReal.sup_eq_zero, ENNRe... | [
383,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Algebra/Associated.lean | not_prime_zero | [] | [
69,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_comp | [] | [
78,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_max_aux₁ | [
{
"state_after": "E : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℂ E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℂ F\ninst✝ : CompleteSpace F\nf : ℂ → F\nz w : ℂ\nr : ℝ := dist w z\nhd : DiffContOnCl ℂ f (ball z r)\nhz : IsMaxOn (norm ∘ f) (closedBall z r) z\n⊢ ‖f w‖ = ‖f z... | [
140,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_refl | [] | [
63,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nhs : Set.Finite s\nht : Set.Finite t\n⊢ ∀ (a : α × β), a ∈ Finite.toFinset hs ×ˢ Finite.toFinset ht ↔ a ∈ Finite.toFinset (_ : Set.Finite (s ×ˢ t))",
"tactic": "simp"
}
] | [
1071,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_ereal_toReal | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.3040955\nβ : Type ?u.3040958\nγ : Type ?u.3040961\nγ₂ : Type ?u.3040964\nδ : Type ?u.3040967\nι : Sort y\ns t u : Set α\ninst✝ : MeasurableSpace α\n⊢ Measurable fun p => EReal.toReal ↑p",
"tactic": "simpa using measurable_id"
}
] | [
1995,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1994,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousAt_sum | [
{
"state_after": "α : Type u_2\ninst✝⁵ : TopologicalSpace α\nβ : Type ?u.107722\ninst✝⁴ : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Type u_1\nγ : Type u_3\ninst✝³ : LinearOrderedAddCommMonoid γ\ninst✝² : TopologicalSpace γ\ninst✝¹ : OrderTopology γ\ninst✝ : ContinuousAdd γ\nf : ι → α → γ\na : F... | [
530,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.realize_onSentence | [] | [
767,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.