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/Topology/LocalExtr.lean | IsLocalMinOn.inter | [] | [
121,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt.of_nat | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\n⊢ padicValInt p ↑n = padicValNat p n",
"tactic": "simp [padicValInt]"
}
] | [
134,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.smul_isBigO | [
{
"state_after": "case refine'_2\nα : Type u_1\nβ : Type ?u.578538\nE : Type ?u.578541\nF : Type ?u.578544\nG : Type ?u.578547\nE' : Type u_4\nF' : Type u_5\nG' : Type ?u.578556\nE'' : Type ?u.578559\nF'' : Type ?u.578562\nG'' : Type ?u.578565\nR : Type ?u.578568\nR' : Type ?u.578571\n𝕜 : Type u_2\n𝕜' : Type ... | [
1771,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.isIso_right_of_isIso_biprod_map | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝ : IsIso (biprod.map f g)\n⊢ IsIso ((biprod.braiding X W).hom ≫ biprod.map f g ≫ (biprod.braiding Y Z).hom)",
"state_before": "C : Type u\ninst✝³ : Category... | [
1909,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1904,
1
] |
Mathlib/Data/List/Count.lean | List.count_le_length | [] | [
210,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_zero | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingEquiv.fst_comp_coe_prod_comm | [] | [
297,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulMemClass.mul_def | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.noMaxOrder_iff | [
{
"state_after": "case intro.inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.15170\nδ : Type ?u.15173\ninst✝¹ : LT α\ninst✝ : LT β\nx✝ : NoMaxOrder (α ⊕ β)\na b : α\nh : inl a < inl b\n⊢ ∃ b, a < b\n\ncase intro.inr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.15170\nδ : Type ?u.15173\ninst✝¹ : LT α\ninst✝ : LT β\nx✝ ... | [
253,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Order/BoundedOrder.lean | not_isTop_iff_ne_top | [] | [
148,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem | [] | [
210,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.copy_eq | [] | [
149,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_mono | [] | [
209,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_mono_nnnorm_ae | [] | [
385,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_le_inv | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.46241\nα : Type u_1\nβ : Type ?u.46247\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ a⁻¹ ≤ b⁻¹ ↔ b ≤ a",
"tactic": "rw [← one_div, div_le_iff ha, ← div_eq_inv_mul, le_div_iff hb, one_mul]"
}
] | [
259,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.equicontinuousAt_iff_right | [
{
"state_after": "ι : Type u_3\nκ✝ : Type ?u.122958\nX : Type u_4\nY : Type ?u.122964\nZ : Type ?u.122967\nα : Type u_2\nβ : Type ?u.122973\nγ : Type ?u.122976\n𝓕 : Type ?u.122979\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSp... | [
289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bodd_bit0 | [] | [
174,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_le_map_iff' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.588384\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.588393\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nH K : Subgroup G\n⊢ map f H ≤ map f K ↔ H ⊔ ker f ≤ K ⊔ ker f",
"tactic": "simp only [map_le_map_if... | [
3084,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3082,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | le_or_lt_of_mul_le_mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4712\ninst✝³ : LinearOrder α\ninst✝² : Mul α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na₁ a₂ b₁ b₂ : α\n⊢ a₂ < a₁ ∧ b₂ ≤ b₁ → a₂ * b₂ < a₁ * b₁",
"state_be... | [
97,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.eq_of_comp_arrow_eq | [] | [
253,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/Convex/Basic.lean | MonotoneOn.convex_lt | [] | [
347,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.card_functions_sum_skolem₁_le | [
{
"state_after": "L : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ : Structure L M\n⊢ (#(n : ℕ) × BoundedFormula L Empty (n + 1)) ≤ max ℵ₀ (card L)",
"state_before": "L : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ : Structure L M\n⊢ (#(n : ℕ) × Functions (Language.sum L (skolem₁ L)) n) ≤ max ℵ₀ (c... | [
76,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_eq_self | [] | [
495,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Std/Logic.lean | apply_dite | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort u_2\nf : α → β\nP : Prop\ninst✝ : Decidable P\nx : P → α\ny : ¬P → α\n⊢ f (dite P x y) = if h : P then f (x h) else f (y h)",
"tactic": "by_cases h : P <;> simp [h]"
}
] | [
694,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
692,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_le_of_le_bot | [
{
"state_after": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈ Ico n m\n⊢ l ≤ k",
"state_before": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈ Ico n m\n⊢ decide (l ≤ k) = true",
"tactic": "rw [decide_eq_true_eq]"
},
{
"state_after": "no goals",
"state_before": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈... | [
191,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.exists_eq_add_of_le | [] | [
286,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.associated_iff | [
{
"state_after": "a b : ℤ\n⊢ natAbs a = natAbs b ↔ a = b ∨ a = -b",
"state_before": "a b : ℤ\n⊢ Associated a b ↔ a = b ∨ a = -b",
"tactic": "rw [Int.associated_iff_natAbs]"
},
{
"state_after": "no goals",
"state_before": "a b : ℤ\n⊢ natAbs a = natAbs b ↔ a = b ∨ a = -b",
"tactic": "exact... | [
381,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_nonneg | [] | [
203,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.isometry | [] | [
243,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
11
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp_zero | [] | [
217,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.div_le_div_left | [] | [
786,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_of_eq_one_of_eq_zero | [
{
"state_after": "k : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.299390\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\ni : ι\nhis : i ∈ s\nhwi : w i = 1\nhw0 : ∀ (i2 : ι), i2 ∈ s → i2 ≠ i → w i2 = 0\nh... | [
492,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntitoneOn.antivaryOn | [] | [
352,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
11
] |
Mathlib/Data/List/Join.lean | List.drop_take_succ_join_eq_nthLe | [
{
"state_after": "α : Type u_1\nβ : Type ?u.11187\nL : List (List α)\ni : ℕ\nhi : i < length L\nthis : take i (map length L) = take i (map length (take (i + 1) L))\n⊢ drop (sum (take i (map length L))) (take (sum (take (i + 1) (map length L))) (join L)) = nthLe L i hi",
"state_before": "α : Type u_1\nβ : Ty... | [
155,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.min_radius_le_radius_add | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.262305\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np✝ : FormalMultilinea... | [
349,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivWithinAt.eventually_ne | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.457298\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.457393\... | [
439,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/Basic.lean | closure_eq_interior_union_frontier | [] | [
784,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticOn.add | [] | [
596,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.w_apply' | [] | [
328,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.exists_seq_monotone_tendsto | [
{
"state_after": "case pos\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : LinearOrder α\ninst✝³ : LinearOrder β\ninst✝² : OrderTopology α\ninst✝¹ : OrderTopology β\nt : Set α\nx : α\ninst✝ : IsCountablyGenerated (𝓝 x)\nhtx : IsLUB t x\nht : Set.Nonempty ... | [
2126,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2120,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.const_comp | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_symm_eq_iff | [
{
"state_after": "case mp\nR : Type u_1\nR₁ : Type ?u.2284641\nR₂ : Type u_2\nR₃ : Type ?u.2284647\nR₄ : Type ?u.2284650\nS : Type ?u.2284653\nK✝ : Type ?u.2284656\nK₂ : Type ?u.2284659\nM : Type u_3\nM' : Type ?u.2284665\nM₁ : Type ?u.2284668\nM₂ : Type u_4\nM₃ : Type ?u.2284674\nM₄ : Type ?u.2284677\nN : Type... | [
2526,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2518,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_mul_iff | [] | [
350,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.exists_comap_eq_of_injective | [] | [
183,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_smul | [] | [
266,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | isOpenMap_barycentric_coord | [] | [
43,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_pi | [
{
"state_after": "no goals",
"state_before": "α : Sort u_2\nβ : Sort ?u.2205\nγ : Sort ?u.2208\nπ : α → Sort u_1\n⊢ IsEmpty ((a : α) → π a) ↔ ∃ a, IsEmpty (π a)",
"tactic": "simp only [← not_nonempty_iff, Classical.nonempty_pi, not_forall]"
}
] | [
151,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_ssubset_edgeFinset | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.108522\n𝕜 : Type ?u.108525\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\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑(edgeSet G)\ninst✝¹ : Fintype ↑(edgeSet G₁)\ninst✝ : Fintype ↑(edgeSet G₂)\n... | [
911,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Analysis/NormedSpace/WeakDual.lean | NormedSpace.Dual.toWeakDual_eq_iff | [] | [
131,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Logic/Basic.lean | or_of_or_of_imp_left | [] | [
338,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_one | [] | [
196,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
196,
9
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.IsPrimitive.content_eq_one | [] | [
243,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_ne_zero | [
{
"state_after": "x y : ℝ\nh : ↑(Complex.exp ↑x).re = ↑0\n⊢ Complex.exp ↑x = 0",
"state_before": "x y : ℝ\nh : exp x = 0\n⊢ Complex.exp ↑x = 0",
"tactic": "rw [exp, ← ofReal_inj] at h"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : ↑(Complex.exp ↑x).re = ↑0\n⊢ Complex.exp ↑x =... | [
1165,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
8
] |
Mathlib/Order/Hom/Lattice.lean | map_symm_diff' | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nι : Type ?u.39178\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.39187\nδ : Type ?u.39190\ninst✝² : BooleanAlgebra α\ninst✝¹ : BooleanAlgebra β\ninst✝ : BoundedLatticeHomClass F α β\nf : F\na b : α\n⊢ ↑f (a ∆ b) = ↑f a ∆ ↑f b",
"tactic": "rw [symmDif... | [
299,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.comp | [
{
"state_after": "α : Type u_3\nβ : Type ?u.51964\nι✝ : Type ?u.51967\nι'✝ : Type ?u.51970\ninst✝ : CompleteLattice α\ns : Set α\nhs : SetIndependent s\nt✝ : ι✝ → α\nht✝ : Independent t✝\nι : Sort u_1\nι' : Sort u_2\nt : ι → α\nf : ι' → ι\nht : Independent t\nhf : Injective f\ni✝ i : ι'\n⊢ (⨆ (_ : i ≠ i✝), (t ∘... | [
295,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | IntermediateField.splits_of_splits | [
{
"state_after": "F✝ : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\np : K[X]\nF : IntermediateField K L\nh : Splits (algebraMap K L) p\nhF : ∀ (x : L), x ∈ roots (Polynomial.map (algebraMap K L) p) → x ∈ F\n⊢ Splits (algebraMap K { x // x ∈ F }) p",
"state_before"... | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.subsingleton_of_einfsep_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.49562\ninst✝ : PseudoMetricSpace α\ns : Set α\nhs : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → x ≠ y → edist x y = ⊤\n⊢ Set.Subsingleton s",
"state_before": "α : Type u_1\nβ : Type ?u.49562\ninst✝ : PseudoMetricSpace α\ns : Set α\nhs : einfsep s = ⊤\n⊢ Set.Subsingleton... | [
258,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_inj | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nH : m = n\n⊢ -[m+1] = -[n+1]",
"tactic": "simp [H]"
}
] | [
72,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
72,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.monic_map_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Field R\np✝ q : R[X]\ninst✝ : DivisionRing k\nf : R →+* k\np : R[X]\n⊢ Monic (map f p) ↔ Monic p",
"tactic": "rw [Monic, leadingCoeff_map, ← f.map_one, Function.Injective.eq_iff f.injec... | [
294,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_congr | [
{
"state_after": "α : Type u_1\nβ : Type ?u.61096\nE : Type u_2\nF : Type u_3\nG : Type ?u.61105\nE' : Type ?u.61108\nF' : Type ?u.61111\nG' : Type ?u.61114\nE'' : Type ?u.61117\nF'' : Type ?u.61120\nG'' : Type ?u.61123\nR : Type ?u.61126\nR' : Type ?u.61129\n𝕜 : Type ?u.61132\n𝕜' : Type ?u.61135\ninst✝¹² : N... | [
350,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image_iUnion₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.196148\nι : Sort u_3\nι' : Sort ?u.196154\nι₂ : Sort ?u.196157\nκ : ι → Sort u_4\nκ₁ : ι → Sort ?u.196167\nκ₂ : ι → Sort ?u.196172\nκ' : ι' → Sort ?u.196177\nf : α → β\ns : (i : ι) → κ i → Set α\n⊢ (f '' ⋃ (i : ι) (j : κ i... | [
1662,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/Order/Minimal.lean | minimals_singleton | [] | [
73,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_proj_dvd | [
{
"state_after": "case pos\nn p : ℕ\nhp : Prime p\n⊢ p ^ ↑(factorization n) p ∣ n\n\ncase neg\nn p : ℕ\nhp : ¬Prime p\n⊢ p ^ ↑(factorization n) p ∣ n",
"state_before": "n p : ℕ\n⊢ p ^ ↑(factorization n) p ∣ n",
"tactic": "by_cases hp : p.Prime"
},
{
"state_after": "case pos\nn p : ℕ\nhp : Prime ... | [
375,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.iSup_induction | [
{
"state_after": "ι : Sort u_2\nM : Type u_1\nA : Type ?u.9348\nB : Type ?u.9351\ninst✝ : Mul M\nS : ι → Subsemigroup M\nC : M → Prop\nx₁ : M\nhx₁ : x₁ ∈ closure (⋃ (i : ι), ↑(S i))\nhp : ∀ (i : ι) (x₂ : M), x₂ ∈ S i → C x₂\nhmul : ∀ (x y : M), C x → C y → C (x * y)\n⊢ C x₁",
"state_before": "ι : Sort u_2\n... | [
129,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.IntegralClosure.comap_ne_bot | [] | [
357,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_nonpos_left | [] | [
626,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coe_fst' | [] | [
364,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.exists_eq_cons_of_succ | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.30706\nn n' m : ℕ\ns✝ : Sym α n\na✝ b : α\ns : Sym α (Nat.succ n)\na : α\nha : a ∈ s\n⊢ ∃ a s', s = a ::ₛ s'",
"state_before": "α : Type u_1\nβ : Type ?u.30706\nn n' m : ℕ\ns✝ : Sym α n\na b : α\ns : Sym α (Nat.succ n)\n⊢ ∃ a s', s = a ::ₛ s'",
"ta... | [
304,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.top_eraseTop | [
{
"state_after": "case h\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\n⊢ ↑{ val := ↑(Fin.last (eraseTop s).length), isLt := (_ : ↑(Fin.last (eraseTop s).length) < s.length + 1) } =\n ↑{ val := s.length - 1, isLt := (_ : s.length - 1 < s.length + 1) }",
"state_be... | [
402,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.zero | [] | [
209,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.pow_log_le_add_one | [
{
"state_after": "no goals",
"state_before": "b : ℕ\n⊢ b ^ log b 0 ≤ 0 + 1",
"tactic": "rw [log_zero_right, pow_zero]"
}
] | [
181,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Std/Data/List/Lemmas.lean | List.ne_nil_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\nh : a ∈ l\n⊢ l ≠ []",
"tactic": "cases h <;> intro."
}
] | [
84,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
84,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.pure_apply_self | [] | [
61,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_inv_eq_one | [] | [
344,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
11
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_le_of_forall_le' | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : Nonempty α\nf : { x // x ∈ lp E ⊤ }\nC : ℝ\nhCf : ∀ (i : α), ‖↑f i‖ ≤ C\n⊢ C ∈ upperBounds (Set.range fun i => ‖↑f i‖)",
"state_before": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i... | [
580,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Logic/Basic.lean | not_forall_not | [] | [
696,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_preserving_pi_empty | [] | [
839,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_coe | [] | [
76,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.rel_head? | [
{
"state_after": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na b x : α\nl : List α\ny : α\nh : Chain' R (x :: y :: List.tail l)\nhy : y ∈ head? l\n⊢ R x y",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na b x : α\nl : List α\nh : Chain' R (x :: l)\ny : α... | [
273,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_strictMono | [] | [
69,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_ite_univ_left | [] | [
2209,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2207,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.prod_const' | [] | [
1054,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.conj_smul_le_of_le | [
{
"state_after": "case intro.intro\nα : Type ?u.101125\nG : Type u_1\nA : Type ?u.101131\nS : Type ?u.101134\ninst✝³ : Group G\ninst✝² : AddGroup A\ns : Set G\ninst✝¹ : Monoid α\ninst✝ : MulDistribMulAction α G\nP H : Subgroup G\nhP : P ≤ H\nh : { x // x ∈ H }\ng : G\nhg : g ∈ ↑P\n⊢ ↑(↑(MulDistribMulAction.toMo... | [
320,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_lt_succ | [] | [
107,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
106,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_inv | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\ns s' : { x // x ∈ S }\n⊢ ↑s /ₒ s' * (↑s' /ₒ s) = 1",
"tactic": "simp [oreDiv_mul_char (s : R) s' s' s 1 1 (by simp)]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_... | [
330,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
11
] |
Mathlib/Topology/Constructions.lean | Filter.Eventually.prod_mk_nhds | [] | [
485,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.prod_mk | [] | [
678,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Std/Data/List/Lemmas.lean | List.get?_of_mem | [] | [
523,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
522,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_X_pow_sub_C | [
{
"state_after": "case intro\nR✝ : Type u\nS : Type v\na✝ b : R✝\nm n : ℕ\nι : Type y\ninst✝¹ : Ring R✝\np : R✝[X]\nR : Type u\ninst✝ : Ring R\na : R\nk : ℕ\nh : Nat.succ k ≠ 0\n⊢ Monic (X ^ Nat.succ k - ↑C a)",
"state_before": "R✝ : Type u\nS : Type v\na✝ b : R✝\nm n✝ : ℕ\nι : Type y\ninst✝¹ : Ring R✝\np :... | [
389,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Hom.id_apply | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.comp_coe | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.272750\nβ : Type ?u.272753\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a / ⊤ = 0",
"tactic": "rw [div_eq_mul_inv, inv_top, mul_zero]"
}
] | [
1537,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1537,
9
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_le_left | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 ≤ y\n⊢ sqrt x ≤ y ↔ x ≤ y ^ 2",
"tactic": "rw [sqrt, ← Real.le_toNNReal_iff_coe_le hy, NNReal.sqrt_le_iff, sq, ← Real.toNNReal_mul hy,\n Real.toNNReal_le_toNNReal_iff (mul_self_nonneg y), sq]"
}
] | [
286,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_map_rev | [] | [
1303,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_int_cast | [
{
"state_after": "case mk.refl\nR : Type u_1\ninst✝ : Ring R\nm : ℕ\n⊢ IsNat (↑↑m) m",
"state_before": "R : Type u_1\ninst✝ : Ring R\nn : ℤ\nm : ℕ\n⊢ IsNat n m → IsNat (↑n) m",
"tactic": "rintro ⟨⟨⟩⟩"
},
{
"state_after": "no goals",
"state_before": "case mk.refl\nR : Type u_1\ninst✝ : Ring R... | [
84,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Deprecated/Submonoid.lean | Monoid.closure_singleton | [] | [
344,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Ring R\np q r : R[X]\nS : Type u_1\ninst✝ : Ring S\nf : R →+* S\nx : S\n⊢ eval₂ f x (-p) = -eval₂ f x p",
"tactic": "rw [eq_neg_iff_add_eq_zero, ← eval₂_add, add_left_neg, eval₂_zero... | [
1251,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen | [
{
"state_after": "case refine'_1\nJ : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\nX Y : C\ninst✝ : HasInitial C\nc : BinaryCofan X Y\nh : IsVanKampenColimit c\n⊢ mapPair (initial.to X) (𝟙 Y) ≫ c.ι =\n (BinaryCofan.mk (initial.to Y) (𝟙 Y)).ι ≫ (Functor.const (Discrete WalkingPair)).map (B... | [
267,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Order/SemiconjSup.lean | Function.Semiconj.symm_adjoint | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4510\ninst✝¹ : PartialOrder α\ninst✝ : Preorder β\nfa : α ≃o α\nfb : β ↪o β\ng : α → β\nh : Semiconj g ↑fa ↑fb\ng' : β → α\nhg' : IsOrderRightAdjoint g g'\ny : β\n⊢ IsLUB {x | g x ≤ ↑fb y} (↑fa (g' y))",
"state_before": "α : Type u_1\nβ : Type u_2\nγ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Zip.lean | List.zip_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type u_3\nε : Type ?u.21794\nf : α → γ\ng : β → δ\nl₁ : List α\n⊢ zip (map f l₁) (map g []) = map (Prod.map f g) (zip l₁ [])",
"tactic": "simp only [map, zip_nil_right]"
},
{
"state_after": "α : Type u\nβ :... | [
127,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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