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 |
|---|---|---|---|---|---|---|
Std/Logic.lean | not_or | [] | [
340,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
340,
1
] |
Mathlib/Topology/ExtendFrom.lean | extendFrom_eq | [] | [
56,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.merge_lemma | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.353008\ninst✝ : Preorder α\na b c : ℕ\nh₁ : 3 * a < b + c + 1\nh₂ : b ≤ 3 * c\n⊢ 2 * (a + b) ≤ 9 * c + 5",
"tactic": "linarith"
}
] | [
1459,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_insert | [] | [
1802,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj₂.id_left | [] | [
157,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.smul_ofModule_asModule | [
{
"state_after": "k : Type u_1\nG : Type u_2\nV : Type ?u.428533\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\nρ : Representation k G V\nM : Type u_3\ninst✝¹ : AddCommMonoid M\ninst✝ : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : asModule (ofModule M)\n⊢... | [
239,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.not_fuzzy_of_ge | [] | [
947,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.div2_bit | [
{
"state_after": "no goals",
"state_before": "b : Bool\nn : ℕ\n⊢ div2 (bit b n) = n",
"tactic": "rw [bit_val, div2_val, Nat.add_comm, add_mul_div_left, div_eq_of_lt, Nat.zero_add]\n<;> cases b\n<;> exact by decide"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 0 < 2",
"tactic... | [
316,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_const | [] | [
1253,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.111002\nγ : Type ?u.111005\nι : Sort u_3\nι' : Sort ?u.111011\nκ : ι → Sort ?u.111016\nκ' : ι' → Sort ?u.111021\ninst✝ : CompleteLattice α\nf✝ g✝ s t : ι → α\na b : α\ng : β → α\nf : ι → β\n⊢ (⨆ (b : β) (_ : b ∈ range f),... | [
1384,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.range_sigmaMk | [
{
"state_after": "case h₁\nι : Type u_1\nι' : Type ?u.81\nα : ι → Type u_2\nβ : ι → Type ?u.91\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni✝ j : ι\na : α i✝\ni : ι\n⊢ range (Sigma.mk i) ⊆ Sigma.fst ⁻¹' {i}\n\ncase h₂\nι : Type u_1\nι' : Type ?u.81\nα : ι → Type ... | [
30,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Mathlib/Topology/Constructions.lean | closedEmbedding_inl | [] | [
944,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.star_add_self' | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.310983\nT : Type ?u.310986\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ star a + a = ↑(2 * a.re)",
"tactic": "rw [add_comm, self_add_star']"
}
] | [
655,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Topology/Maps.lean | QuotientMap.isClosed_preimage | [] | [
331,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
11
] |
Mathlib/Order/Filter/Bases.lean | Filter.map_sigma_mk_comap | [
{
"state_after": "α : Type u_3\nβ : Type u_4\nγ : Type ?u.83924\nι : Sort ?u.83927\nι' : Sort ?u.83930\nπ : α → Type u_1\nπ' : β → Type u_2\nf : α → β\nhf : Function.Injective f\ng : (a : α) → π a → π' (f a)\na : α\nl : Filter (π' (f a))\n⊢ HasBasis (comap (Sigma.map f g) (map (Sigma.mk (f a)) l)) (fun s => s ∈... | [
966,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.apply_zpow_apply_eq_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nn : ℤ\nx : α\n⊢ ↑f (↑(f ^ n) x) = ↑(f ^ n) x ↔ ↑f x = x",
"tactic": "rw [← mul_apply, Commute.self_zpow f, mul_apply, apply_eq_iff_eq]"
}
] | [
378,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.preimage_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.224545\nι : Sort ?u.224548\nι' : Sort ?u.224551\nι₂ : Sort ?u.224554\nκ : ι → Sort ?u.224559\nκ₁ : ι → Sort ?u.224564\nκ₂ : ι → Sort ?u.224569\nκ' : ι' → Sort ?u.224574\nf : α → β\ns : Set (Set β)\n⊢ f ⁻¹' ⋃₀ s = ⋃ (t : Se... | [
1727,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomialOneHom_apply | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.image_mem_map | [] | [
1838,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_mul_of_pos_right | [
{
"state_after": "m n k l : ℕ\nh : 0 < n\n⊢ m * 1 ≤ m * n",
"state_before": "m n k l : ℕ\nh : 0 < n\n⊢ m ≤ m * n",
"tactic": "conv =>\n lhs\n rw [← mul_one m]"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nh : 0 < n\n⊢ m * 1 ≤ m * n",
"tactic": "exact mul_le_mul_of_nonn... | [
317,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueSet_mono' | [] | [
270,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Icc_union_Icc | [] | [
1647,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1646,
1
] |
Mathlib/Order/WithBot.lean | WithTop.lt_toDual_iff | [] | [
891,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Data/List/Basic.lean | List.length_attach | [] | [
3153,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3152,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_ne_zero | [] | [
318,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.equalizer_as_kernel | [] | [
235,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.Blunt.anti | [] | [
368,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.mem_norm_comm | [
{
"state_after": "G : Type u_1\nH : Type ?u.22432\nA : Type ?u.22435\na✝ a₁ a₂ b✝ c : G\ninst✝ : Group G\ns : Set G\nhs : IsNormalSubgroup s\na b : G\nhab : a * b ∈ s\nh : a⁻¹ * (a * b) * a⁻¹⁻¹ ∈ s\n⊢ b * a ∈ s",
"state_before": "G : Type u_1\nH : Type ?u.22432\nA : Type ?u.22435\na✝ a₁ a₂ b✝ c : G\ninst✝ :... | [
223,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.verts_toSubgraph | [] | [
2240,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2239,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_cons_of_not_mem' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : DecidableEq α\na : α\nl : List α\nh : ¬a ∈ dedup l\n⊢ ∀ (b : α), b ∈ pwFilter (fun x x_1 => x ≠ x_1) l → a ≠ b",
"tactic": "simpa only [forall_mem_ne] using h"
}
] | [
43,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_eq_lineMap | [] | [
801,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.coe_inj | [] | [
745,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.bicone_ι_π_ne | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasZeroMorphisms C\nF : J → C\nB : Bicone F\nj j' : J\nh : j ≠ j'\n⊢ Bicone.ι B j ≫ Bicone.π B j' = 0",
"tactic": "simpa [h] using B.ι_π j j'"
}
] | [
93,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.mem_rootSet' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\np✝ q : R[X]\ninst✝³ : CommRing T\np : T[X]\nS : Type u_1\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra T S\na : S\n⊢ a ∈ rootSet p S ↔ map (algebraMap T ... | [
939,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.id_apply | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_mono | [] | [
742,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.ker_completion | [
{
"state_after": "G : Type u_1\ninst✝² : SeminormedAddCommGroup G\nH : Type u_2\ninst✝¹ : SeminormedAddCommGroup H\nK : Type ?u.21573\ninst✝ : SeminormedAddCommGroup K\nf : NormedAddGroupHom G H\nC : ℝ\nh : SurjectiveOnWith f (range f) C\n⊢ ↑(ker (completion f)) ≤ closure ↑(range (NormedAddGroupHom.comp toCompl... | [
196,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_congr_set' | [] | [
309,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.add | [] | [
200,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.fin_cons | [] | [
1249,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuous_iInf | [] | [
1058,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_const_smul | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝³ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : α) → Module 𝕜 (E i)\ninst✝ : ∀ (i : α), BoundedSMul 𝕜 (E i)\nhp : p ≠ 0\nf : { x // x ∈ lp E p }\n⊢ ‖0 • f‖ = ‖0‖ * ‖f‖\n\ncase inr\... | [
708,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_imJ | [] | [
152,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_prod_uniformity_snd | [] | [
1607,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_inr | [] | [
919,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.tail_cons | [] | [
262,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_pow_iff | [
{
"state_after": "n k : ℕ\nhn : n ≠ 1\nhk : k ≠ 0\nh : Squarefree (n ^ k)\n⊢ Squarefree n ∧ k = 1",
"state_before": "n k : ℕ\nhn : n ≠ 1\nhk : k ≠ 0\n⊢ Squarefree (n ^ k) ↔ Squarefree n ∧ k = 1",
"tactic": "refine' ⟨fun h => _, by rintro ⟨hn, rfl⟩; simpa⟩"
},
{
"state_after": "case inl\nk : ℕ\nh... | [
95,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 1 < 2",
"tactic": "decide"
}
] | [
171,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.prodCongr_symm | [] | [
474,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_coe_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\n⊢ Finite ↑s ↔ Set.Finite s",
"tactic": "rw [finite_iff_nonempty_fintype, finite_def]"
}
] | [
81,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_adjoinIntegral_self | [] | [
1628,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_ne_zero | [] | [
907,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_mul_nat | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\nhn : n ≠ 0\n⊢ ℵ₀ * ↑n = ℵ₀",
"tactic": "rw [mul_comm, nat_mul_aleph0 hn]"
}
] | [
1648,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1648,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.lt_on_openSegment | [] | [
691,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | continuous_of_le_add_edist | [
{
"state_after": "α : Type u_1\nβ : Type ?u.419875\nγ : Type ?u.419878\ninst✝ : PseudoEMetricSpace α\nf : α → ℝ≥0∞\nC : ℝ≥0∞\nhC : C ≠ ⊤\nh : ∀ (x y : α), f x ≤ f y + C * edist x y\nx : α\nε : ℝ≥0∞\nε0 : ε > 0\n⊢ ∀ᶠ (x_1 : α) in 𝓝 x, f x_1 ∈ Icc (f x - ε) (f x + ε)",
"state_before": "α : Type u_1\nβ : Type... | [
1442,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.Ico_succ_right_eq_insert_Ico | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\nh : a ≤ b\n⊢ Ico a (b + 1) = insert b (Ico a b)",
"tactic": "rw [Ico_succ_right, ← Ico_insert_right h]"
}
] | [
201,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.map_sSup_of_continuousAt' | [] | [
2650,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2646,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.absolutelyContinuous_of_le_smul | [] | [
2409,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2407,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.isPartitionSplit | [] | [
193,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_eq_blsub' | [] | [
1763,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1761,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.isUnit_det_zpow_iff | [
{
"state_after": "case hz\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\n⊢ IsUnit (det (A ^ 0)) ↔ IsUnit (det A) ∨ 0 = 0\n\ncase hp\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nz : ℕ\na✝ : IsUnit (d... | [
136,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_of_coprime_right | [
{
"state_after": "p a b : ℕ\nhab : coprime a b\nhpb : p ∈ factors b\n⊢ ↑(factorization (b * a)) p = ↑(factorization b) p",
"state_before": "p a b : ℕ\nhab : coprime a b\nhpb : p ∈ factors b\n⊢ ↑(factorization (a * b)) p = ↑(factorization b) p",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no g... | [
777,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convex_convexHull | [] | [
61,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Control/ULift.lean | ULift.rec.constant | [] | [
161,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.coe_copy | [] | [
556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.galoisConnection | [] | [
512,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Order/Lattice.lean | toDual_sup | [] | [
968,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.coe_toEquiv | [] | [
1183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.other_invol' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.105892\nγ : Type ?u.105895\ninst✝ : DecidableEq α\na x✝ y✝ : α\nha : a ∈ Quotient.mk (Rel.setoid α) (x✝, y✝)\nhb : Mem.other' ha ∈ Quotient.mk (Rel.setoid α) (x✝, y✝)\n⊢ Mem.other' hb = a",
"state_before": "α : Type u_1\nβ : Type ?u.105892\nγ : Type ?u.105... | [
722,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.colorable_chromaticNumber | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nm : ℕ\nhc : Colorable G m\n⊢ Colorable G (chromaticNumber G)",
"tactic": "classical\ndsimp only [chromaticNumber]\nrw [Nat.sInf_def]\napply Nat.find_spec\nexact colorable_set_nonempty_of_colorable ... | [
270,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Topology/ContinuousOn.lean | mem_of_mem_nhdsWithin | [] | [
173,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/Lie/Matrix.lean | Matrix.reindexLieEquiv_symm | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_neg_eq_set_integral_nonpos | [
{
"state_after": "α : Type u_2\nβ : Type ?u.102789\nE : Type u_1\nF : Type ?u.102795\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\nf✝ g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : LinearOrder E\nf : α → E\nhf : AEStronglyMeasu... | [
419,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.coeNat_ofPrime | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.Integrable.integral_norm_prod_right | [] | [
310,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Order/Atoms.lean | isCoatom_bot | [] | [
493,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_ne_zero | [] | [
334,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasDerivWithinAt_arccos_Ici | [] | [
156,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.127990\nα : Type u_1\nβ : Type ?u.127996\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ ⌊0⌋ = 0",
"tactic": "rw [← cast_zero, floor_intCast]"
}
] | [
706,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.inv_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\ninst✝² : LinearOrderedField α\nβ : Type u_1\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\n⊢ (if h : LimZero (const abv 0) then 0 else inv (const abv 0) h) = const abv 0",
"tactic": "rw [dif_pos] <;> [rfl; exact zero_limZer... | [
237,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_boole | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nR : Type x\nα : Type u_1\ninst✝¹ : MulZeroOneClass α\nP : Prop\ninst✝ : Decidable P\na : α\n⊢ (a * if P then 1 else 0) = if P then a else 0",
"tactic": "simp"
}
] | [
221,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.mul_apply | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix'_id | [
{
"state_after": "case a.h\nR : Type u_1\ninst✝² : CommSemiring R\nk : Type ?u.523416\nl : Type ?u.523419\nm : Type ?u.523422\nn : Type u_2\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\ni✝ x✝ : n\n⊢ ↑toMatrix' id i✝ x✝ = OfNat.ofNat 1 i✝ x✝",
"state_before": "R : Type u_1\ninst✝² : CommSemiring R\nk : Type ?u... | [
364,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/Algebra/Ring/Ideal.lean | Ideal.coe_closure | [] | [
38,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Set/Basic.lean | Set.bex_insert_iff | [
{
"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 : Set α\nP : α → Prop\na : α\ns : Set α\n⊢ (∃ x, x ∈ insert a s ∧ P x) ↔ P a ∨ ∃ x, x ∈ s ∧ P x",
"tactic": "simp [mem_insert_iff, or_and_right, exists_and_left, exists_or]"
}
] | [
1235,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_toOrdinal | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrFilter.neg | [] | [
491,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.support_inf | [
{
"state_after": "case a\nι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyLinearOrderedAddMonoid α\ninst✝ : DecidableEq ι\nf g : ι →₀ α\na✝ : ι\n⊢ a✝ ∈ (f ⊓ g).support ↔ a✝ ∈ f.support ∩ g.support",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyLinearOrderedAddMonoid α\ninst✝ : DecidableE... | [
231,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul | [
{
"state_after": "α : Type u_1\ninst✝² : MetricSpace α\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝ : IsUnifLocDoublingMeasure μ\nK : ℝ\nC : ℝ≥0 := doublingConstant μ\n⊢ ∃ C, ∀ᶠ (ε : ℝ) in 𝓝[Ioi 0] 0, ∀ (x : α) (t : ℝ), t ≤ K → ↑↑μ (closedBall x (t * ε)) ≤ ↑C * ↑↑μ (closedBall x ε)",
"st... | [
106,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.prod_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.153934\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.153955\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\ns : Submonoid M\nt : Submonoid N\n⊢ prod s t = ⊥ ↔ ... | [
1323,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_inj | [] | [
146,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.centralizer_univ | [] | [
552,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | derivWithin_pow' | [] | [
117,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_trim | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.3172842\nG : Type ?u.3172845\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhm : m ≤ m0\nf : α → E\nhf : StronglyMeasurable f\nh0 : p = 0\... | [
995,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.param_pow_mul | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\n⊢ SuperpolynomialDecay l k (k ^ Nat.zero * f)\n\ncase succ\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝¹ : Topologi... | [
123,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_image | [] | [
555,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_empty | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.89881\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ : ℝ\ns : Set α\nx : α\nδ : ℝ\n⊢ thickening δ ∅ = ∅",
"tactic": "simp only [thickening, setOf_false, infEdist_empty, not_top_lt]"
}
] | [
925,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.of_const_mul_right | [] | [
1513,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1511,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.tendsto_of_tendsto_pointwise_of_cauchySeq | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.2884213\nE : Type ?u.2884216\nEₗ : Type ?u.2884219\nF : Type u_4\nFₗ : Type ?u.2884225\nG : Type ?u.2884228\nGₗ : Type ?u.2884231\n𝓕 : Type ?u.2884234\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup F\ninst✝¹¹ ... | [
1575,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
1
] |
Mathlib/Computability/Reduce.lean | manyOneReducible_toNat | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝⁵ : Primcodable α\ninst✝⁴ : Inhabited α\nβ : Type v\ninst✝³ : Primcodable β\ninst✝² : Inhabited β\nγ : Type w\ninst✝¹ : Primcodable γ\ninst✝ : Inhabited γ\np : Set α\n⊢ ∀ (a : α), p a ↔ toNat p (Encodable.encode a)",
"tactic": "simp [toNat, ... | [
347,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
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