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/Disjointed.lean | disjointed_eq_inf_compl | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.11805\ninst✝ : CompleteBooleanAlgebra α\nf : ℕ → α\n⊢ disjointed f Nat.zero = f Nat.zero ⊓ ⨅ (i : ℕ) (_ : i < Nat.zero), f iᶜ\n\ncase succ\nα : Type u_1\nβ : Type ?u.11805\ninst✝ : CompleteBooleanAlgebra α\nf : ℕ → α\nn✝ : ℕ\n⊢ disjointed f (Nat.succ n✝) = ... | [
158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.coe_iSup_of_directed | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_2\nM : Type u_1\nA : Type ?u.1446\nB : Type ?u.1449\ninst✝ : Mul M\nS : ι → Subsemigroup M\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : M\n⊢ x ∈ ↑(⨆ (i : ι), S i) ↔ x ∈ ⋃ (i : ι), ↑(S i)",
"tactic": "simp [mem_iSup_of_directed hS]"
}
] | [
63,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.eq_top_iff' | [] | [
772,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
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Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.antidiagonal_succ_succ' | [
{
"state_after": "n : ℕ\n⊢ (0, n + 1 + 1) ::ₘ\n (Nat.succ (n + 1, 0).fst, id (n + 1, 0).snd) ::ₘ\n map (Prod.map Nat.succ id ∘ Prod.map id Nat.succ) (antidiagonal n) =\n (0, n + 2) ::ₘ (n + 2, 0) ::ₘ map (Prod.map Nat.succ Nat.succ) (antidiagonal n)",
"state_before": "n : ℕ\n⊢ antidiagonal (n... | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Algebra/GroupWithZero/Power.lean | zpow_eq_zero | [] | [
173,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/Field/Basic.lean | div_sub_div | [] | [
232,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Order/RelIso/Set.lean | RelIso.range_eq | [] | [
51,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaCurry_add | [
{
"state_after": "case h.h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.605040\nα : ι → Type u_1\nδ : (i : ι) → α i → Type v\ninst✝ : (i : ι) → (j : α i) → AddZeroClass (δ i j)\nf g : Π₀ (i : (i : ι) × α i), δ i.fst i.snd\ni : ι\nj : α i\n⊢ ↑(↑(si... | [
1494,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1490,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.antidiagonalTuple_one | [
{
"state_after": "n : ℕ\n⊢ (List.bind (range n) fun a => map (fun x => Fin.cons a x) (antidiagonalTuple 0 (n - a))) ++\n map (fun x => Fin.cons n x) (antidiagonalTuple 0 0) =\n [![n]]",
"state_before": "n : ℕ\n⊢ antidiagonalTuple 1 n = [![n]]",
"tactic": "simp_rw [antidiagonalTuple, antidiagonal... | [
144,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_node4R | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nP : α → Prop\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ All P (node4R l x m y r) ↔ All P l ∧ P x ∧ All P m ∧ P y ∧ All P r",
"tactic": "cases m <;> simp [node4R, all_node', All, all_node3R, and_assoc]"
}
] | [
514,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.mem_of_promises | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\na : α\np : s ~> a\nh : ∃ a, a ∈ s\n⊢ a ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nh : Terminates s\na : α\np : s ~> a\n⊢ a ∈ s",
"tactic": "cases' h with h"
},
{
"state_after": "c... | [
495,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Monotone.map_limsInf_of_continuousAt | [] | [
401,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nh : IsMatching M\nv w : V\nhv : v ∈ M.verts\nhvw : Adj M v w\n⊢ Quotient.mk (Sym2.Rel.setoid V) (v, Exists.choose (_ : ∃! w, Adj M (↑{ val := v, property := hv }) w)) =\n Quotient.mk (Sym2.Rel.setoid V) (v, w)",
"state_before": "V : Type... | [
70,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.csinh | [] | [
272,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\nt : IsTerminal X\n⊢ (zeroIsoIsTerminal t).inv = 0",
"tactic": "ext"
}
] | [
316,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_top | [] | [
226,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Topology/Constructions.lean | continuous_sInf_dom₂ | [
{
"state_after": "α✝ : Type u\nβ✝ : Type v\nγ✝ : Type ?u.29369\nδ : Type ?u.29372\nε : Type ?u.29375\nζ : Type ?u.29378\ninst✝⁵ : TopologicalSpace α✝\ninst✝⁴ : TopologicalSpace β✝\ninst✝³ : TopologicalSpace γ✝\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\nα : Type ?u.294... | [
470,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Order/SuccPred/Limit.lean | IsMin.isSuccLimit | [] | [
64,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.exists_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nf : CauSeq α abs\na : α\nh : -f < const a\n⊢ Pos (f - const (-a))",
"tactic": "rwa [const_neg, sub_neg_eq_add, add_comm, ← sub_neg_eq_add]"
}
] | [
809,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/RingTheory/Ideal/Prod.lean | Ideal.ideal_prod_prime | [
{
"state_after": "case mp\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ J' : Ideal S\nI : Ideal (R × S)\n⊢ IsPrime I → (∃ p, IsPrime p ∧ I = prod p ⊤) ∨ ∃ p, IsPrime p ∧ I = prod ⊤ p\n\ncase mpr\nR : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ J' : Idea... | [
175,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_subset_iUnion_closedBall_of_lt | [
{
"state_after": "ι : Sort ?u.146791\nα✝ : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α✝\nδ✝ ε : ℝ\ns t : Set α✝\nx✝ : α✝\nα : Type u_1\ninst✝ : PseudoMetricSpace α\nE : Set α\nδ δ' : ℝ\nhδ₀ : 0 < δ'\nhδδ' : δ < δ'\nx : α\nhx : x ∈ thickening δ' E\n⊢ x ∈ ⋃ (x : α) (_ : x ∈ E), closedBall x δ'",
"state_... | [
1400,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1396,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eq_biInf_of_mem_iff_exists_mem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.93784\nι : Sort x\nf✝ g : Filter α\ns t : Set α\nf : ι → Filter α\np : ι → Prop\nl : Filter α\nh : ∀ {s : Set α}, s ∈ l ↔ ∃ i, p i ∧ s ∈ f i\n⊢ l = ⨅ (x : { i // p i }), f ↑x",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.... | [
798,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Bool/Count.lean | List.count_not_add_count | [
{
"state_after": "l : List Bool\nb : Bool\nthis : (fun x => x == b) = fun a => decide ¬(a == !b) = true\n⊢ countp (fun x => x == b) l = countp (fun a => decide ¬(a == !b) = true) l\n\ncase this\nl : List Bool\nb : Bool\n⊢ (fun x => x == b) = fun a => decide ¬(a == !b) = true",
"state_before": "l : List Bool... | [
32,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_neg' | [] | [
268,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | inv_smul_smul₀ | [] | [
196,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.interior_preimage_re | [] | [
73,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.Prime.dvd_mul' | [
{
"state_after": "m n : ℤ\np : ℕ\nhp : Nat.Prime p\nh : ↑p ∣ m * n\n⊢ p ∣ natAbs m ∨ p ∣ natAbs n",
"state_before": "m n : ℤ\np : ℕ\nhp : Nat.Prime p\nh : ↑p ∣ m * n\n⊢ ↑p ∣ m ∨ ↑p ∣ n",
"tactic": "rw [Int.coe_nat_dvd_left, Int.coe_nat_dvd_left]"
},
{
"state_after": "no goals",
"state_before... | [
278,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.natPair | [] | [
1480,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1478,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.symm | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH✝ : IsCoprime x y\na b : R\nH : a * x + b * y = 1\n⊢ b * y + a * x = 1",
"tactic": "rw [add_comm, H]"
}
] | [
49,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_inter_distrib_right | [] | [
1054,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Data/Matrix/Basic.lean | AddMonoidHom.mapMatrix_comp | [] | [
1419,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Order/MinMax.lean | min_lt_max | [] | [
214,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ico_ae_eq_Ioc | [] | [
3360,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3359,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.isOpen_setOf_mem_nhds_and_isMaxOn_norm | [
{
"state_after": "E : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\ns : Set E\nhd : DifferentiableOn ℂ f s\nz : E\nhz : z ∈ {z | s ∈ 𝓝 z ∧ IsMaxOn (norm ∘ f) s z}\n⊢ ∀ᶠ (z : E) in 𝓝 z, IsMaxOn (norm ∘ f) s z",
... | [
229,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isGLB_ciInf | [] | [
504,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isPartition_single | [] | [
314,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Init/Logic.lean | if_simp_congr_prop | [] | [
401,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
src/lean/Init/Prelude.lean | Nat.zero_le | [] | [
1580,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1578,
1
] |
src/lean/Init/Prelude.lean | Nat.not_le_of_not_ble_eq_true | [] | [
1694,
48
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1693,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | Monotone.continuous_of_surjective | [] | [
290,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.cons_equiv_eq_equiv_cons | [
{
"state_after": "case mk.mk\nα✝ : Type ?u.27619\nβ : Type ?u.27622\nn✝ n' m : ℕ\ns : Sym α✝ n✝\na✝ b : α✝\nα : Type u_1\nn : ℕ\na : α\nval✝ : Multiset α\nl : List α\nproperty✝ : ↑Multiset.card (Quot.mk Setoid.r l) = n\n⊢ (a :: ↑symEquivSym' { val := Quot.mk Setoid.r l, property := property✝ }) =\n ↑symEquiv... | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.isIso_iff_bijective | [] | [
382,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.restrictScalars_one_smulRight' | [
{
"state_after": "case h.mk\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nx : E\na b : ℝ\n⊢ ↑(restrictScalars ℝ (smulRight 1 x)) { re := a, im := b } =\n ↑(smulRight reClm x + I • smulRight imClm x) { re := a, im := b }",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup... | [
299,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.kerLiftAlg_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nF : Type w\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\nR₁ : Type u_1\nR₂ : Type ?u.819159\nA : Type u_2\nB : Type u_3\ninst✝⁶ : CommSemiring R₁\ninst✝⁵ : CommSemiring R₂\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : Algebra R₁ A\nins... | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.div_I | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6059054\ninst✝ : IsROrC K\nz : K\n⊢ z / I = -(z * I)",
"tactic": "rw [div_eq_mul_inv, inv_I, mul_neg]"
}
] | [
607,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_map | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\n⊢ Walk.map f' (Walk.map f p) = Walk.map (Hom.comp f' f) p",
"tactic": "induction p with\n| nil =... | [
1483,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.mk0_surjective | [
{
"state_after": "case mk\nR : Type u_1\nK : Type ?u.1490084\nL : Type ?u.1490087\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : DecidableEq L\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : Algebra K L\ninst✝⁴ : FiniteDimensional K L\ninst✝³ : Algebra R L\ninst✝² : IsScalarTo... | [
364,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.nonarchimedean_aux | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nh : padicValRat p q ≤ padicValRat p r\nhnqp : padicNorm p q ≥ 0\nhnrp : padicNorm p r ≥ 0\nhq : q = 0\n⊢ padicNorm p (q + r) ≤ max (padicNorm p q) (padicNorm p r)",
"tactic": "simp [hq, max_eq_right hnrp, le_max_right... | [
202,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
9
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_toSubsemiring | [] | [
61,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/MeasureTheory/Covering/OneDim.lean | Real.tendsto_Icc_vitaliFamily_left | [
{
"state_after": "case refine'_1\nx : ℝ\n⊢ ∀ᶠ (i : ℝ) in 𝓝[Iio x] x, Icc i x ∈ VitaliFamily.setsAt (vitaliFamily volume 1) x\n\ncase refine'_2\nx : ℝ\n⊢ ∀ (ε : ℝ), ε > 0 → ∀ᶠ (i : ℝ) in 𝓝[Iio x] x, Icc i x ⊆ Metric.closedBall x ε",
"state_before": "x : ℝ\n⊢ Tendsto (fun y => Icc y x) (𝓝[Iio x] x) (Vitali... | [
62,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Star/Basic.lean | MulOpposite.unop_star | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Topology/MetricSpace/MetrizableUniformity.lean | UniformSpace.metrizableSpace | [
{
"state_after": "X : Type u_1\ninst✝² : UniformSpace X\ninst✝¹ : IsCountablyGenerated (𝓤 X)\ninst✝ : T0Space X\nthis : MetricSpace X := UniformSpace.metricSpace X\n⊢ TopologicalSpace.MetrizableSpace X",
"state_before": "X : Type u_1\ninst✝² : UniformSpace X\ninst✝¹ : IsCountablyGenerated (𝓤 X)\ninst✝ : T... | [
287,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAtFilter.isBigO_sub_rev | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx✝ : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : F... | [
299,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
8
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.mul_subset_closure | [] | [
71,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_subset_insert | [] | [
1168,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.prod | [] | [
423,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
8
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_pos | [] | [
2072,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2071,
1
] |
Mathlib/CategoryTheory/Bicategory/NaturalTransformation.lean | CategoryTheory.OplaxNatTrans.Modification.whiskerRight_naturality | [
{
"state_after": "no goals",
"state_before": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G : OplaxFunctor B C\nη θ ι : F ⟶ G\nΓ : Modification η θ\na b c : B\na' : C\nf : a ⟶ b\ng : (↑G.toPrelaxFunctor).obj b ⟶ a'\n⊢ (↑F.toPrelaxFunctor).map f ◁ app Γ b ▷ g ≫\n (α_ ((↑F.to... | [
275,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atBot_iff_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.246385\nι' : Type ?u.246388\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.246397\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nh : Tendsto f l atTop\n⊢ Tendsto (fun x => f x * r) l atBot ↔ r < 0",
"tactic": "simp onl... | [
1187,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.toList_nil | [] | [
335,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
335,
9
] |
Mathlib/Data/Int/Order/Basic.lean | Int.ediv_eq_zero_of_lt_abs | [
{
"state_after": "a✝ b✝ : ℤ\nn✝ : ℕ\na b : ℤ\nH1 : 0 ≤ a\nH2✝ : a < abs b\nn : ℕ\nH2 : a < ↑(natAbs -[n+1])\n⊢ a / - -[n+1] = -0",
"state_before": "a✝ b✝ : ℤ\nn✝ : ℕ\na b : ℤ\nH1 : 0 ≤ a\nH2✝ : a < abs b\nn : ℕ\nH2 : a < ↑(natAbs -[n+1])\n⊢ -(a / -[n+1]) = -0",
"tactic": "rw [← Int.ediv_neg]"
},
{
... | [
207,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Algebra/GeomSum.lean | Commute.geom_sum₂_comm | [
{
"state_after": "case zero\nα✝ α : Type u\ninst✝ : Semiring α\nx y : α\nh : Commute x y\n⊢ ∑ i in range Nat.zero, x ^ i * y ^ (Nat.zero - 1 - i) = ∑ i in range Nat.zero, y ^ i * x ^ (Nat.zero - 1 - i)\n\ncase succ\nα✝ α : Type u\ninst✝ : Semiring α\nx y : α\nh : Commute x y\nn✝ : ℕ\n⊢ ∑ i in range (Nat.succ n✝... | [
247,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
11
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.lt_iff_le_and_exists | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\ns1 s2 : AffineSubspace k P\n⊢ s1 < s2 ↔ s1 ≤ s2 ∧ ∃ p, p ∈ s2 ∧ ¬p ∈ s1",
"tactic": "rw [lt_iff_le_not_le, not_le_iff_exists]"
}
] | [
653,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.id_comp | [
{
"state_after": "no goals",
"state_before": "M' : Type ?u.267738\nX : Type ?u.267741\ninst✝²³ : SMul M' X\nY : Type ?u.267748\ninst✝²² : SMul M' Y\nZ : Type ?u.267755\ninst✝²¹ : SMul M' Z\nM : Type u_1\ninst✝²⁰ : Monoid M\nA : Type ?u.267768\ninst✝¹⁹ : AddMonoid A\ninst✝¹⁸ : DistribMulAction M A\nA' : Type... | [
567,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_neg | [] | [
160,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
157,
9
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.prod_prodExtendRight | [
{
"state_after": "case H.mk\nα✝ : Type u\nβ : Type v\ninst✝² : DecidableEq α✝\ninst✝¹ : Fintype α✝\nα : Type u_1\ninst✝ : DecidableEq α\nσ : α → Perm β\nl : List α\nhl : List.Nodup l\nmem_l : ∀ (a : α), a ∈ l\na : α\nb : β\n⊢ ↑(List.prod (List.map (fun a => prodExtendRight a (σ a)) l)) (a, b) = ↑(prodCongrRight... | [
732,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_eq_span_vsub_set_left | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.250908\ns : Set P\np : P\nhp : p ∈ s\n⊢ Submodule.span k (s -ᵥ s) = Submodule.span k ((fun x x_1 => x -ᵥ x_1) p '' s)",
"state_before": "k : Type u_... | [
1035,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_mul | [] | [
248,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Complex/Cardinality.lean | mk_univ_complex | [
{
"state_after": "no goals",
"state_before": "⊢ (#↑Set.univ) = 𝔠",
"tactic": "rw [mk_univ, mk_complex]"
}
] | [
34,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.algebraMap_apply | [
{
"state_after": "F : Type ?u.1519076\nα : Type u\nβ : Type v\nγ : Type w\n𝕜 : Type u_1\ninst✝⁵ : NormedField 𝕜\ninst✝⁴ : TopologicalSpace α\ninst✝³ : SeminormedAddCommGroup β\ninst✝² : NormedSpace 𝕜 β\ninst✝¹ : NormedRing γ\ninst✝ : NormedAlgebra 𝕜 γ\nf g : α →ᵇ γ\nx : α\nc k : 𝕜\na : α\n⊢ ↑(k • 1) a = k ... | [
1385,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/Data/Part.lean | Part.bind_map | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ✝ : Type ?u.31792\nγ : Type u_1\nf : α → β\nx : Part α\ng : β → Part γ\n⊢ (Part.bind x fun x => Part.bind ((some ∘ f) x) g) = Part.bind x fun y => g (f y)",
"state_before": "α : Type u_2\nβ : Type u_3\nγ✝ : Type ?u.31792\nγ : Type u_1\nf : α → β\nx : Part α\ng ... | [
553,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.NeBot.nonempty_of_mem | [] | [
692,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.transferNatTrans_counit | [
{
"state_after": "C : Type u₁\nD : Type u₂\ninst✝³ : Category C\ninst✝² : Category D\nE : Type u₃\nF : Type u₄\ninst✝¹ : Category E\ninst✝ : Category F\nG : C ⥤ E\nH : D ⥤ F\nL₁ : C ⥤ D\nR₁ : D ⥤ C\nL₂ : E ⥤ F\nR₂ : F ⥤ E\nadj₁ : L₁ ⊣ R₁\nadj₂ : L₂ ⊣ R₂\nf : G ⋙ L₂ ⟶ L₁ ⋙ H\nY : D\n⊢ (L₂.map (adj₂.unit.app (G.o... | [
123,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_add | [] | [
904,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_add_le | [
{
"state_after": "α : Type u_1\nE : Type ?u.2937028\nF : Type u_2\nG : Type ?u.2937034\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → F\nx : α\n⊢ (fun x => ↑‖(f + g) x‖₊) x ≤ ((fun x => ↑‖f x‖₊) +... | [
773,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Logic/Denumerable.lean | Denumerable.ofEquiv_ofNat | [
{
"state_after": "α✝ : Type ?u.3562\nβ✝ : Type ?u.3565\ninst✝² : Denumerable α✝\ninst✝¹ : Denumerable β✝\nα : Type u_1\nβ : Type u_2\ninst✝ : Denumerable α\ne : β ≃ α\nn : ℕ\nthis : Denumerable β := ofEquiv α e\n⊢ ofNat β n = ↑e.symm (ofNat α n)",
"state_before": "α✝ : Type ?u.3562\nβ✝ : Type ?u.3565\ninst✝... | [
113,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.coe_inj | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nq r : ℚ\nh : q = r\n⊢ ↑q = ↑r",
"tactic": "rw [h]"
}
] | [
530,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.ennreal_toReal | [] | [
1917,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_upperSemicontinuous_antitone | [] | [
878,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | RingHom.domain_localRing | [
{
"state_after": "R✝ : Type u\nS✝ : Type v\nT : Type w\nK : Type u'\ninst✝⁵ : Semiring R✝\ninst✝⁴ : Semiring S✝\ninst✝³ : Semiring T\nR : Type u_1\nS : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\nH : LocalRing S\nf : R →+* S\ninst✝ : IsLocalRingHom f\nthis : Nontrivial R\n⊢ LocalRing R",
"st... | [
268,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.map_comp | [] | [
1684,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.cinfi_ne_top | [] | [
430,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_iff_eq_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.71269\nβ : Type ?u.71272\nG : Type u_1\ninst✝ : CommGroup G\na b c d : G\n⊢ a / b = c ↔ a = b * c",
"tactic": "rw [div_eq_iff_eq_mul, mul_comm]"
}
] | [
958,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.HasLift.iff_unop | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nA✝ B✝ X✝ Y✝ : C\nf✝ : A✝ ⟶ X✝\ni✝ : A✝ ⟶ B✝\np✝ : X✝ ⟶ Y✝\ng✝ : B✝ ⟶ Y✝\nsq✝ : CommSq f✝ i✝ p✝ g✝\nA B X Y : Cᵒᵖ\nf : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\ng : B ⟶ Y\nsq : CommSq f i p g\n⊢ Nonempty (LiftStruct sq) ↔ Nonempty (LiftStruct (_ : CommSq g.unop p.unop i.uno... | [
217,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_of_chain | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝ b : α\nh✝ : Chain R a✝ l\na : α\nh : Chain R a []\n⊢ destutter' R a [] = [a]\n\ncase cons\nα : Type u_1\nl✝ : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝ b✝ : α\nh✝ : Chain R a✝ l✝\nb : α\nl : List α\nhb ... | [
108,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.sInter_lift_sets | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.8812\nι : Sort ?u.8815\nf f₁ f₂ : Filter α\ng g₁ g₂ : Set α → Filter β\nhg : Monotone g\n⊢ ⋂₀ {s | s ∈ Filter.lift f g} = ⋂ (s : Set α) (_ : s ∈ f), ⋂₀ {t | t ∈ g s}",
"tactic": "simp only [sInter_eq_biInter, mem_setOf... | [
82,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_bit0_atBot | [] | [
682,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
15
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_comp_le_hammingNorm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.26239\nι : Type u_3\nβ : ι → Type u_1\ninst✝⁴ : Fintype ι\ninst✝³ : (i : ι) → DecidableEq (β i)\nγ : ι → Type u_2\ninst✝² : (i : ι) → DecidableEq (γ i)\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → Zero (γ i)\nf : (i : ι) → γ i → β i\nx : (i : ι)... | [
217,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.sublist | [] | [
80,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.177408\nδ : Type ?u.177411\nι : Type ?u.177414\nR : Type ?u.177417\nR' : Type ?u.177420\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν✝ ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nμ... | [
1172,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.eq_of_forall_toMeasure_apply_eq | [
{
"state_after": "case a\nΩ : Type u_1\ninst✝ : MeasurableSpace Ω\nμ ν : FiniteMeasure Ω\nh : ∀ (s : Set Ω), MeasurableSet s → ↑↑↑μ s = ↑↑↑ν s\n⊢ ↑μ = ↑ν",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nμ ν : FiniteMeasure Ω\nh : ∀ (s : Set Ω), MeasurableSet s → ↑↑↑μ s = ↑↑↑ν s\n⊢ μ = ν",
"ta... | [
195,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.st_eq | [
{
"state_after": "x : ℝ*\nr : ℝ\nhxr : IsSt x r\nh : ∃ r, IsSt x r\n⊢ st x = r",
"state_before": "x : ℝ*\nr : ℝ\nhxr : IsSt x r\n⊢ st x = r",
"tactic": "have h : ∃ r, IsSt x r := ⟨r, hxr⟩"
},
{
"state_after": "x : ℝ*\nr : ℝ\nhxr : IsSt x r\nh : ∃ r, IsSt x r\n⊢ choose h = r",
"state_before":... | [
285,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ixx_mem | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u_1\nι : Sort ?u.7054\nι' : Sort ?u.7057\ninst✝ : LinearOrder α\nIxx : α → α → Set α\np : α → α → Prop\nHne : ∀ {a b : α}, Set.Nonempty (Ixx a b) → p a b\nHi : ∀ {a₁ b₁ a₂ b₂ : α}, Ixx a₁ b₁ ∩ Ixx a₂ b₂ = Ixx (max a₁ a₂... | [
162,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Control/Bifunctor.lean | Bifunctor.id_fst | [] | [
81,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.compl_iInter | [] | [
502,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Topology/Constructions.lean | continuous_sum_dom | [] | [
860,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.IsWeightedHomogeneous.weighted_total_degree | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\nσ : Type u_3\ninst✝¹ : AddCommMonoid M\nφ ψ : MvPolynomial σ R\nm n : M\ninst✝ : SemilatticeSup M\nw : σ → M\nhφ : IsWeightedHomogeneous w φ n\nh : φ ≠ 0\n⊢ (sup (support φ) fun s => ↑(↑(weightedDegree' w) s)) = ↑n",
"state_before": "R :... | [
312,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/LocallyFinite.lean | Ici_toDual | [] | [
936,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_emod_mul_of_pos | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH : 0 < a\n⊢ a * b % (a * c) = a * (b % c)",
"tactic": "rw [emod_def, emod_def, mul_ediv_mul_of_pos _ _ H, Int.mul_sub, Int.mul_assoc]"
}
] | [
545,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
543,
9
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.isBridge_iff_adj_and_forall_cycle_not_mem | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nv w : V\n⊢ Adj G v w →\n (¬Reachable (G \\ fromEdgeSet {Quotient.mk (Sym2.Rel.setoid V) (v, w)}) v w ↔\n ∀ ⦃u : V⦄ (p : Walk G u u), Walk.IsCycle p → ¬Quotient.mk (Sym2.Rel.setoid V) (... | [
2531,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2524,
1
] |
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