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/Algebra/Module/Basic.lean | smul_left_injective | [] | [
728,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.toPoly_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.552582\nF : Type ?u.552585\nK : Type ?u.552588\nP✝ Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nP : Cubic R\n⊢ toPoly P = 0 ↔ P = 0",
"tactic": "rw [← zero, toPoly_injective]"
}
] | [
178,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | LinearMap.uncurryLeft_apply | [] | [
1242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/Topology/Separation.lean | compact_t2_tot_disc_iff_tot_sep | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : T2Space α\ninst✝ : CompactSpace α\nh : TotallyDisconnectedSpace α\nx : α\nx✝¹ : x ∈ univ\ny : α\nx✝ : y ∈ univ\n⊢ x ≠ y → ∃ u v, IsOpen u ∧ IsOpen v ∧ x ∈ u ∧ y ∈ v ∧ univ ⊆ u ∪ v ∧ Disjoint u v",
"state_before": "α : Type u\nβ ... | [
1949,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1939,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.bot_sets_eq | [] | [
519,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_iff | [] | [
93,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_ne_zero_of_right_inverse | [] | [
235,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_injOn_pos | [] | [
219,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.88567\nγ : Type ?u.88570\nι : Sort ?u.88573\nκ : ι → Sort ?u.88578\ninst✝ : LE α\ns t : LowerSet α\na : α\nS : Set (LowerSet α)\n⊢ ↑(compl (sInf S)) = ↑(⨅ (s : LowerSet α) (_ : s ∈ S), compl s)",
"tactic": "simp only [coe_compl, coe... | [
913,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
11
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | nndist_mul_right | [] | [
381,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_inv_of_neg | [] | [
440,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Topology/Algebra/Order/Archimedean.lean | AddSubgroup.dense_or_cyclic | [
{
"state_after": "G : Type u_1\ninst✝³ : LinearOrderedAddCommGroup G\ninst✝² : TopologicalSpace G\ninst✝¹ : OrderTopology G\ninst✝ : Archimedean G\nS : AddSubgroup G\nh : ¬∀ (ε : G), ε > 0 → ∃ g, g ∈ S ∧ g ∈ Ioo 0 ε\n⊢ ∃ a, S = closure {a}",
"state_before": "G : Type u_1\ninst✝³ : LinearOrderedAddCommGroup ... | [
74,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isClosed_sphere | [] | [
1868,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1867,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_div_pow_mul_exp_add_atTop | [
{
"state_after": "α : Type ?u.34915\nx y z : ℝ\nl : Filter α\nb c : ℝ\nn : ℕ\nhb : 0 ≠ b\nH : ∀ (d e : ℝ), 0 < d → Tendsto (fun x => x ^ n / (d * exp x + e)) atTop (𝓝 0)\n⊢ Tendsto (fun x => x ^ n / (b * exp x + c)) atTop (𝓝 0)",
"state_before": "α : Type ?u.34915\nx y z : ℝ\nl : Filter α\nb c : ℝ\nn : ℕ\... | [
274,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/List/Sigma.lean | List.NodupKeys.eq_of_mk_mem | [
{
"state_after": "case refl\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\na : α\nb : β a\nl : List (Sigma β)\nnd : NodupKeys l\nh h' : { fst := a, snd := b } ∈ l\n⊢ b = b",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\na : α\nb b' : β a\nl : List (Sigma β)\nnd : NodupKeys... | [
129,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.ext | [] | [
107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.mabs_inf_div_inf_le_mabs | [
{
"state_after": "case h\nα : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ ?a * abs ((a ⊓ c) / (b ⊓ c)) ≤ abs (a / b)\n\ncase hle\nα : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1... | [
547,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_insert | [] | [
924,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_sqrt_rat_iff | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nH1 : Rat.sqrt q * Rat.sqrt q = q\n⊢ ↑(Rat.sqrt q) = Real.sqrt ↑q",
"tactic": "rw [← H1, cast_mul, sqrt_mul_self (cast_nonneg.2 <| Rat.sqrt_nonneg q), sqrt_eq,\n abs_of_nonneg (Rat.sqrt_nonneg q)]"
},
{
"state_after": "q : ℚ\nH1 : ¬Rat.sqrt q ... | [
141,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_pair | [] | [
1004,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.zero_mem_smul_iff | [
{
"state_after": "F : Type ?u.934836\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.934845\ninst✝⁴ : Zero α\ninst✝³ : Zero β\ninst✝² : SMulWithZero α β\ninst✝¹ : DecidableEq β\ns : Finset α\nt : Finset β\ninst✝ : NoZeroSMulDivisors α β\na : α\n⊢ 0 ∈ ↑s ∧ Set.Nonempty ↑t ∨ 0 ∈ ↑t ∧ Set.Nonempty ↑s ↔ 0 ∈ s ∧ Finset.Non... | [
2129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2126,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augment_X_succ | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.smul | [] | [
988,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.VectorsProdEqOne.one_eq | [
{
"state_after": "α : Type ?u.553591\ninst✝¹ : Fintype α\nG : Type u_1\ninst✝ : Group G\nn : ℕ\n⊢ ∀ (x : Vector G 1), Vector.head x = 1 → x = 1 ::ᵥ Vector.nil",
"state_before": "α : Type ?u.553591\ninst✝¹ : Fintype α\nG : Type u_1\ninst✝ : Group G\nn : ℕ\n⊢ vectorsProdEqOne G 1 = {1 ::ᵥ Vector.nil}",
"t... | [
390,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_snd' | [] | [
1096,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Algebra/Order/Module.lean | inv_smul_le_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.93364\ninst✝³ : LinearOrderedField k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nh : c < 0\n⊢ c⁻¹ • a ≤ b ↔ c • b ≤ a",
"tactic": "rw [← smul_le_smul_iff_of_neg h, smu... | [
167,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.cons_append | [] | [
780,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Topology/Instances/Int.lean | Int.cocompact_eq | [
{
"state_after": "⊢ comap (fun y => ↑(abs y)) atTop = comap (Int.cast ∘ abs) atTop",
"state_before": "⊢ cocompact ℤ = atBot ⊔ atTop",
"tactic": "simp_rw [← comap_dist_right_atTop_eq_cocompact (0 : ℤ), dist_eq', sub_zero,\n ← comap_abs_atTop, ← @Int.comap_cast_atTop ℝ, comap_comap]"
},
{
"state_... | [
78,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_top | [] | [
786,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | MonoidHom.uniformContinuous_of_continuousAt_one | [] | [
411,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Order/RelClasses.lean | ssubset_of_ssubset_of_subset | [] | [
757,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Data/Bundle.lean | Bundle.Pullback.lift_mk | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_submatrix_equiv | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.4512\nm : Type u_3\nn : Type u_1\nA✝ : Matrix n n α\ninst✝¹ : Star α\ninst✝ : Star β\nA : Matrix n n α\ne : m ≃ n\nh : IsHermitian (submatrix A ↑e ↑e)\n⊢ IsHermitian A",
"tactic": "simpa using h.submatrix e.symm"
}
] | [
96,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/List/Zip.lean | List.unzip_eq_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.84326\nδ : Type ?u.84329\nε : Type ?u.84332\na : α\nb : β\nl : List (α × β)\n⊢ unzip ((a, b) :: l) = (map Prod.fst ((a, b) :: l), map Prod.snd ((a, b) :: l))",
"tactic": "simp only [unzip_cons, map_cons, unzip_eq_map l]"... | [
214,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | closure_ae_eq_of_null_frontier | [] | [
424,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_toMul | [] | [
3214,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3214,
9
] |
Mathlib/Data/List/Perm.lean | List.Subperm.trans | [] | [
435,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.ext | [] | [
461,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_map_measure | [
{
"state_after": "case pos\nα : Type u_3\nE : Type u_2\nF : Type ?u.3096236\nG : Type ?u.3096239\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nβ : Type u_1\nmβ : MeasurableSpace β\nf : α → β\ng : β → E\nhg... | [
916,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_single | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.1348706\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\nA : Type u₃\ninst✝³ : Semiring A\ninst✝² : Algebra k A\nB : Type ?u.1348743\ninst✝¹ : Semiring B\ninst✝ : Algebra k B\nF : G →* A\na : G\nb : k\n⊢ ↑(↑(lift k G A) F) (sing... | [
922,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.continuous | [] | [
185,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_eval_dom | [] | [
956,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_X_pow | [
{
"state_after": "case h.e'_2.h.e'_3\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nH : ¬1 = 0\nn : ℕ\n⊢ X ^ n = ↑(monomial n) 1",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nH : ¬1 = 0\nn : ℕ\n⊢ support (X ^ n) = {n}",
"tactic": "convert support_mono... | [
904,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCopairing_apply | [] | [
1221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_eq_zero | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0∞\n⊢ ↑x = 0 ↔ x = 0",
"tactic": "rw [← coe_ennreal_eq_coe_ennreal_iff, coe_ennreal_zero]"
}
] | [
521,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Set/Function.lean | Set.codRestrict_restrict | [] | [
360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Topology/Algebra/UniformConvergence.lean | UniformOnFun.continuousSMul_submodule_of_image_bounded | [] | [
278,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_monomial | [
{
"state_after": "case inl\nR : Type u_1\ninst✝¹ : Semiring R\nφ : PowerSeries R\nn : ℕ\na : R\ninst✝ : Decidable (a = 0)\nh : a = 0\n⊢ order (↑(monomial R n) a) = ⊤\n\ncase inr\nR : Type u_1\ninst✝¹ : Semiring R\nφ : PowerSeries R\nn : ℕ\na : R\ninst✝ : Decidable (a = 0)\nh : ¬a = 0\n⊢ order (↑(monomial R n) a... | [
2401,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2391,
1
] |
Mathlib/Data/List/Range.lean | List.nthLe_finRange | [] | [
222,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotent_center_quotient_ind | [
{
"state_after": "case intro\nG✝ : Type ?u.314742\ninst✝³ : Group G✝\nH : Subgroup G✝\ninst✝² : Normal H\nP : (G : Type u_1) → [inst : Group G] → [inst : Group.IsNilpotent G] → Prop\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : Group.IsNilpotent G\nhbase : ∀ (G : Type u_1) [inst : Group G] [inst_1 : Subsingleton G],... | [
675,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.sup | [] | [
456,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
8
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.sInf_orthogonal | [] | [
187,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_bot | [] | [
870,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.injective | [] | [
1003,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.not_disjoint_coe_iff_nonempty_inter | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J : Box ι\nx y : ι → ℝ\n⊢ ¬Disjoint ↑I ↑J ↔ Set.Nonempty (↑I ∩ ↑J)",
"tactic": "rw [disjoint_coe, Set.not_disjoint_iff_nonempty_inter]"
}
] | [
386,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.subset_one_iff_eq | [] | [
132,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iic_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.120495\nγ : Type ?u.120498\nι : Sort ?u.120501\nκ : ι → Sort ?u.120506\ninst✝ : CompleteLattice α\nS : Set α\nc : α\n⊢ c ∈ Iic (sInf S) ↔ c ∈ ⨅ (a : α) (_ : a ∈ S), Iic a",
"tactic": "simp only [mem_Iic_iff, mem_iInf₂_iff, le_sInf_i... | [
1237,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.mul_aux_left | [
{
"state_after": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx1 x2 y : ℕ × K\nH : R K p x1 x2\nn : ℕ\nx : K\n⊢ R K p ((n, x).fst + y.fst, (↑(frobenius K p)^[y.fst]) (n, x).snd * (↑(frobenius K p)^[(n, x).fst]) y.snd)\n (Nat.succ (n + y.fst), ↑(frobenius K p) ((↑(f... | [
197,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
9
] |
Mathlib/Data/Finset/Basic.lean | Finset.ssubset_singleton_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.36053\nγ : Type ?u.36056\ns✝ : Finset α\na✝ b : α\ns : Finset α\na : α\n⊢ s ⊂ {a} ↔ s = ∅",
"tactic": "rw [← coe_ssubset, coe_singleton, Set.ssubset_singleton_iff, coe_eq_empty]"
}
] | [
798,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Data/Sigma/Basic.lean | PSigma.elim_val | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | LinearIsometryEquiv.piLpCongrLeft_apply | [] | [
742,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | abs_mem_iff | [
{
"state_after": "no goals",
"state_before": "G✝ : Type ?u.2524\nG' : Type ?u.2527\ninst✝⁵ : Group G✝\ninst✝⁴ : Group G'\nA : Type ?u.2536\ninst✝³ : AddGroup A\nS : Type u_1\nG : Type u_2\ninst✝² : InvolutiveNeg G\ninst✝¹ : LinearOrder G\nx✝ : SetLike S G\ninst✝ : NegMemClass S G\nH : S\nx : G\n⊢ abs x ∈ H ... | [
139,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
9
] |
Mathlib/MeasureTheory/PiSystem.lean | IsPiSystem.singleton | [
{
"state_after": "α : Type u_1\nS s : Set α\nh_s : s ∈ {S}\nt : Set α\nh_t : t ∈ {S}\na✝ : Set.Nonempty (s ∩ t)\n⊢ s ∩ t ∈ {S}",
"state_before": "α : Type u_1\nS : Set α\n⊢ IsPiSystem {S}",
"tactic": "intro s h_s t h_t _"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nS s : S... | [
84,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_invOfUnit | [] | [
1922,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.idv | [] | [
359,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_eq_singleton | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.121890\nf : α → β\ns : Multiset α\nb : β\n⊢ map f s = {b} → ∃ a, s = {a} ∧ f a = b\n\ncase mpr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.121890\nf : α → β\ns : Multiset α\nb : β\n⊢ (∃ a, s = {a} ∧ f a = b) → map f s = {b}",
"state_before": "α... | [
1254,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.id_apply | [] | [
1098,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_deleteEdges | [
{
"state_after": "case h\nι : Sort ?u.163733\n𝕜 : Type ?u.163736\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne✝ : Sym2 V\ns : Set (Sym2 V)\ne : Sym2 V\n⊢ e ∈ edgeSet (deleteEdges G s) ↔ e ∈ edgeSet G \\ s",
"state_before": "ι : Sort ?u.163733\n𝕜 : Type ?u.1... | [
1176,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.map_prod_map_const_id_principal_coprod_principal | [
{
"state_after": "α✝ : Type ?u.66772\nβ✝ : Type ?u.66775\nγ : Type ?u.66778\nδ : Type ?u.66781\nι✝ : Sort ?u.66784\nf : Filter α✝\ng : Filter β✝\nα : Type u_1\nβ : Type u_2\nι : Type u_3\na : α\nb : β\ni : ι\n⊢ 𝓟 (Prod.map (fun x => b) id '' ({a}ᶜ ×ˢ {i}ᶜ)ᶜ) = 𝓟 ({b} ×ˢ univ)",
"state_before": "α✝ : Type ... | [
562,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | Isometry.coe_affineIsometryOfStrictConvexSpace | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/GroupTheory/Schreier.lean | Subgroup.closure_mul_image_mul_eq_top | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nR S : Set G\nhR : R ∈ rightTransversals ↑H\nhR1 : 1 ∈ R\nhS : closure S = ⊤\nf : G → ↑R := fun g => toFun hR g\n⊢ ↑(closure ((fun g => g * (↑(toFun hR g))⁻¹) '' (R * S))) * R = ⊤",
"state_before": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G... | [
61,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.count_toMultiset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.53685\nι : Type ?u.53688\ninst✝ : DecidableEq α\nf : α →₀ ℕ\na : α\n⊢ Multiset.count a (sum f fun a n => n • {a}) = sum f fun x n => Multiset.count a (n • {x})",
"state_before": "α : Type u_1\nβ : Type ?u.53685\nι : Type ?u.53688\ninst✝ : DecidableEq α\nf : α →₀ ℕ... | [
131,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/FiniteField.lean | FiniteField.Matrix.charpoly_pow_card | [
{
"state_after": "case inl\nn : Type u_2\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : Fintype K\nM : Matrix n n K\nh✝ : Nonempty n\n⊢ charpoly (M ^ Fintype.card K) = charpoly M\n\ncase inr\nn : Type u_2\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nK : Type u_1\ninst✝¹ : F... | [
46,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_sup | [] | [
2060,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2059,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ cos θ = 0 ↔ θ = ↑(π / 2) ∨ θ = ↑(-π / 2)",
"tactic": "rw [← cos_pi_div_two, ← cos_coe, cos_eq_iff_eq_or_eq_neg, ← coe_neg, ← neg_div]"
}
] | [
428,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.jordan_holder | [
{
"state_after": "case zero\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁✝ s₂✝ : CompositionSeries X\nhb✝ : bot s₁✝ = bot s₂✝\nht✝ : top s₁✝ = top s₂✝\nx✝ : ℕ\nhle✝ : s₁✝.length = x✝\ns₁ s₂ : CompositionSeries X\nhb : bot s₁ = bot s₂\nht : top s₁ = top s₂\nhle : s₁.length = Nat.zero\n⊢ Equi... | [
806,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_gcd_self_left_right | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd (gcd n m) m = gcd n m",
"tactic": "rw [gcd_comm, gcd_gcd_self_right_right]"
}
] | [
168,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
167,
9
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_ne_zero | [] | [
335,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
334,
11
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_prod_of_measurable | [
{
"state_after": "α : Type u_1\nα' : Type ?u.5352968\nβ : Type u_2\nβ' : Type ?u.5352974\nγ : Type ?u.5352977\nE : Type ?u.5352980\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
751,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.dropFun_comp | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/List/Basic.lean | List.get_reverse_aux₁ | [
{
"state_after": "ι : Type ?u.93887\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl r : List α\ni : ℕ\n⊢ ∀ (h1 : i + 1 + length l < length (reverseAux (a :: l) r)) (h2 : i < length r),\n get (reverseAux (a :: l) r) { val := i + 1 + length l, isLt := h1 } = get r { val := i, isLt := ... | [
1425,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
] |
Mathlib/Topology/TietzeExtension.lean | BoundedContinuousFunction.exists_extension_forall_mem_Icc_of_closedEmbedding | [
{
"state_after": "case intro.intro\nX : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : NormalSpace Y\nf : X →ᵇ ℝ\na b : ℝ\ne : X → Y\nhf : ∀ (x : X), ↑f x ∈ Icc a b\nhle : a ≤ b\nhe : ClosedEmbedding e\ng : Y →ᵇ ℝ\nhgf : ‖g‖ = ‖f - const X ((a + b) / 2)‖\nhge : ↑g ∘ e ... | [
192,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | Measurable.measurableEmbedding | [] | [
651,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Order/Minimal.lean | maximals_antichain | [] | [
99,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.pos_of_subset_ne_zero | [] | [
110,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_empty | [] | [
63,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.comp_sub | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y Z : C\nf : X ⟶ Y\ng h : Y ⟶ Z\n⊢ f ≫ (g - h) = f ≫ g - f ≫ h",
"tactic": "rw [sub_def, ← Category.assoc, prod.comp_lift, sub_def]"
}
] | [
432,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Set/Opposite.lean | Set.op_mem_op | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Set α\na : α\n⊢ op a ∈ Set.op s ↔ a ∈ s",
"tactic": "rfl"
}
] | [
43,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_smul_measure_of_ne_zero_of_ne_top | [
{
"state_after": "α : Type u_1\nE : Type ?u.2068541\nF : Type u_2\nG : Type ?u.2068547\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np : ℝ≥0∞\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nf : α → F\nc : ℝ≥0∞\n⊢... | [
623,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
9
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_zero_sub_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoMod hp 0 (a - b) = p - toIocMod hp 0 (b - a)",
"tactic": "rw [← neg_sub, toIcoMod_neg, neg_zero]"
}
] | [
761,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.sub_zero | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na : X ⟶ Y\n⊢ prod.lift a 0 ≫ σ = a",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na : X ⟶ Y\n⊢ a - 0 = a",
"tactic": "rw [sub_def]"
},
{
"state_after": "C :... | [
359,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le | [] | [
396,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.natDegree_eq_zero_of_derivative_eq_zero | [
{
"state_after": "case inl\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroSMulDivisors ℕ R\nh : ↑derivative 0 = 0\n⊢ natDegree 0 = 0\n\ncase inr\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst... | [
284,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.properDivisors_subset_divisors | [] | [
173,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_pow_mul | [
{
"state_after": "case zero\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ X ^ Nat.zero * p = p * X ^ Nat.zero\n\ncase succ\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nih : X ^ n * p = p * X ^ n\n⊢ X ^ Nat.succ n * p = p * X ^ Nat.succ n",
"state_before": "R : Ty... | [
583,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_iff_aemeasurable | [] | [
1453,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1451,
1
] |
Mathlib/Computability/Ackermann.lean | ack_le_ack | [] | [
252,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_pi_const_le | [] | [
493,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.subset | [] | [
113,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.comm_from | [] | [
546,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
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