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/Algebra/Order/Compact.lean | ContinuousOn.image_uIcc_eq_Icc | [] | [
431,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_div_div_cancel_right' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.61046\nβ : Type ?u.61049\nG : Type u_1\ninst✝ : Group G\na✝ b✝ c✝ d a b c : G\n⊢ a / c / (b / c) = a / b",
"tactic": "rw [← inv_div c b, div_inv_eq_mul, div_mul_div_cancel']"
}
] | [
810,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.mul | [] | [
381,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | ContinuousWithinAt.cexp | [] | [
102,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_bit1_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r P Q : R[X]\nn : ℕ\n⊢ coeff (bit1 P * Q) n = 2 * coeff (P * Q) n + coeff Q n",
"tactic": "simp [bit1, add_mul, coeff_bit0_mul]"
}
] | [
359,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_sub | [] | [
465,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.subseq_tendsto_of_neBot | [
{
"state_after": "case intro\nι : Type ?u.373995\nι' : Type ?u.373998\nα : Type u_1\nβ : Type ?u.374004\nγ : Type ?u.374007\nf : Filter α\ninst✝ : IsCountablyGenerated f\nu : ℕ → α\nhx : NeBot (f ⊓ map u atTop)\nB : ℕ → Set α\nh : HasAntitoneBasis f B\n⊢ ∃ θ, StrictMono θ ∧ Tendsto (u ∘ θ) atTop f",
"state_... | [
1926,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_pos_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.323773\nβ : Type ?u.323776\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 0 < a / b ↔ a ≠ 0 ∧ b ≠ ⊤",
"tactic": "simp [pos_iff_ne_zero, not_or]"
}
] | [
1741,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
9
] |
Mathlib/Data/Semiquot.lean | Semiquot.IsPure.min | [
{
"state_after": "α : Type u_1\nβ : Type ?u.16645\ns t : Semiquot α\nh : IsPure t\nst : s ≤ t\n⊢ pure (get t h) ≤ pure (get s (_ : IsPure s))",
"state_before": "α : Type u_1\nβ : Type ?u.16645\ns t : Semiquot α\nh : IsPure t\nst : s ≤ t\n⊢ t ≤ s",
"tactic": "rw [eq_pure h, eq_pure (h.mono st)]"
},
{... | [
248,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.continuous_coe_iff | [] | [
76,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Control/ULift.lean | ULift.map_up | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.clm_comp | [] | [
79,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.memberSubfamily_union_nonMemberSubfamily | [
{
"state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜✝ ℬ : Finset (Finset α)\ns✝ : Finset α\na✝ a : α\n𝒜 : Finset (Finset α)\ns : Finset α\n⊢ s ∈ memberSubfamily a 𝒜 ∪ nonMemberSubfamily a 𝒜 ↔ s ∈ image (fun s => erase s a) 𝒜",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜✝ ℬ : Fi... | [
113,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Term.constantsVarsEquivLeft_symm_apply | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Finmap.lean | Finmap.erase_toFinmap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : AList β\n⊢ erase a ⟦s⟧ = ⟦AList.erase a s⟧",
"tactic": "simp [erase]"
}
] | [
424,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.congr_fun | [] | [
312,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | QuotientGroup.measurable_from_quotient | [] | [
517,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
8
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.isEmpty_congr | [] | [
1064,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_le_of_map_le_add_int | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : ↑f x ≤ x + ↑m\nn : ℕ\n⊢ (↑f^[n]) x ≤ x + ↑n * ↑m",
"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using\n (f.commute_add_int m).iterate_le_of_map_le f.monotone (monotone_id.add_const (m : ℝ)) h n"
}
] | [
574,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.mem_inf | [] | [
240,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.realize_term_substructure | [] | [
354,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.image_mem_nhdsWithin | [] | [
314,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.trivializationAt_proj_fst | [] | [
296,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.mem_coe | [] | [
1781,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1780,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | hasDerivWithinAt_zpow | [] | [
74,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_mk | [] | [
331,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
9
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.completeSpace | [] | [
570,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
11
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_subset_iff | [] | [
76,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_ball_iff_norm''' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.93030\n𝕜 : Type ?u.93033\nα : Type ?u.93036\nι : Type ?u.93039\nκ : Type ?u.93042\nE : Type u_1\nF : Type ?u.93048\nG : Type ?u.93051\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
623,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitIsoLimitCurryCompLim_hom_π_π | [
{
"state_after": "no goals",
"state_before": "J K : Type v\ninst✝⁵ : SmallCategory J\ninst✝⁴ : SmallCategory K\nC : Type u\ninst✝³ : Category C\nF : J ⥤ K ⥤ C\nG : J × K ⥤ C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimit G\ninst✝ : HasLimit (curry.obj G ⋙ lim)\nj : J\nk : K\n⊢ (limitIsoLimitCurryCompLim ... | [
282,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.range_restrictDom | [] | [
264,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.filter_product_card | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.63122\ns✝ s' : Finset α\nt✝ t' : Finset β\na : α\nb : β\ns : Finset α\nt : Finset β\np : α → Prop\nq : β → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\n⊢ card (filter (fun x => p x.fst = q x.snd) (s ×ˢ t)) =\n card (filter (fun x => p x.fs... | [
178,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Sum/Interval.lean | Sum.Ico_inr_inr | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittMul_zero | [
{
"state_after": "case a\np : ℕ\nR : Type ?u.66399\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(map (Int.castRingHom ℚ)) (wittMul p 0) = ↑(map (Int.castRingHom ℚ)) (X (0, 0) * X (1, 0))",
"state_before": "p : ℕ\nR : Type ?u.66399\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ wittMul p 0 = X (0, 0) * ... | [
283,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Init/Classical.lean | Classical.cases_on | [] | [
29,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Prime.exists_mem_multiset_map_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.11639\nδ : Type ?u.11642\ninst✝ : CommMonoidWithZero α\np : α\nhp : Prime p\ns : Multiset β\nf : β → α\nh : p ∣ Multiset.prod (Multiset.map f s)\n⊢ ∃ a, a ∈ s ∧ p ∣ f a",
"tactic": "simpa only [exists_prop, Multiset.me... | [
47,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.perm_inv_on_of_perm_on_finite | [] | [
94,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | eq_of_abs_sub_nonpos | [] | [
371,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.fineSubfamilyOn_of_frequently | [
{
"state_after": "α : Type u_1\ninst✝ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv✝ v : VitaliFamily μ\nf : α → Set (Set α)\ns : Set α\nh : ∀ (x : α), x ∈ s → ∃ᶠ (a : Set α) in filterAt v x, a ∈ f x\nx : α\nhx : x ∈ s\nε : ℝ\nεpos : ε > 0\n⊢ ∃ a, a ∈ setsAt v x ∩ f x ∧ a ⊆ closedBall ... | [
297,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.51575\nγ : Type ?u.51578\nι : Sort ?u.51581\ninst✝² : ConditionallyCompleteLattice α\ns t : Set α\na b : α\ninst✝¹ : NoMinOrder α\ninst✝ : DenselyOrdered α\nw : α\nhw : w < a\n⊢ ∃ a_1, a_1 ∈ Iio a ∧ w < a_1",
"tactic": "simpa [and_c... | [
766,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le_add_of_sub_le | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nh : a - b ≤ c\n⊢ a ≤ c + b",
"tactic": "match le.dest h, Nat.le_total a b with\n| _, Or.inl hle =>\n exact Nat.le_trans hle (Nat.le_add_left ..)\n| ⟨d, hd⟩, Or.inr hge =>\n apply @le.intro _ _ d\n rw [Nat.add_comm, ← Nat.add_sub_assoc hge] at... | [
621,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
613,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.neg | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.251943\nι : Type ?u.251946\ninst✝³ : Countable ι\nm0 : MeasurableSpace α\nμ : Measure α\nf g : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : AddGroup β\ninst✝ : TopologicalAddGroup β\nhf : FinStronglyMeasurable f μ\nn : ℕ\n⊢ ↑↑μ (support ↑((fun n => -FinS... | [
1084,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
11
] |
Std/Data/Int/Lemmas.lean | Int.le_max_left | [
{
"state_after": "a b : Int\n⊢ a ≤ if a ≤ b then b else a",
"state_before": "a b : Int\n⊢ a ≤ max a b",
"tactic": "rw [Int.max_def]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a ≤ if a ≤ b then b else a",
"tactic": "split <;> simp [*]"
}
] | [
714,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
714,
11
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.uniformEquicontinuous_iff_left | [
{
"state_after": "ι : Type u_3\nκ✝ : Type ?u.125171\nX : Type ?u.125174\nY : Type ?u.125177\nZ : Type ?u.125180\nα : Type u_4\nβ : Type u_2\nγ : Type ?u.125189\n𝓕 : Type ?u.125192\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSp... | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_vadd_affineCombination | [
{
"state_after": "no goals",
"state_before": "k : Type u_4\nV : Type u_2\nP : Type u_1\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_3\ns : Finset ι\nι₂ : Type ?u.258239\ns₂ : Finset ι₂\nw₁ w₂ : ι → k\np : ι → P\n⊢ ↑(weightedVSub s p) w₁ +ᵥ ↑(affineCombinatio... | [
432,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Int.cast_finsupp_prod | [] | [
407,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean | CategoryTheory.Idempotents.karoubiUniversal_functor_eq | [] | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_above | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\np : Fin (n + 1)\ni : Fin n\nh : p ≤ ↑castSucc i\n⊢ ↑(succAbove p) i = succ i",
"tactic": "simp [succAbove, h.not_lt]"
}
] | [
2072,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2071,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_eq_bot_iff_le_centralizer | [
{
"state_after": "G : Type u_1\nG' : Type ?u.55266\nF : Type ?u.55269\ninst✝² : Group G\ninst✝¹ : Group G'\ninst✝ : MonoidHomClass F G G'\nf : F\ng₁ g₂ g₃ g : G\nH₁ H₂ H₃ K₁ K₂ : Subgroup G\n⊢ (∀ (g₁ : G), g₁ ∈ H₁ → ∀ (g₂ : G), g₂ ∈ H₂ → ⁅g₁, g₂⁆ ∈ ⊥) ↔ H₁ ≤ centralizer H₂",
"state_before": "G : Type u_1\nG... | [
105,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.smul_mem_skewAdjoint | [] | [
542,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_subset_iff' | [] | [
83,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Order/InitialSeg.lean | PrincipalSeg.coe_coe_fn' | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.π_comp_cokernelIsoOfEq_hom | [
{
"state_after": "case refl\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nX Y : C\nf✝ : X ⟶ Y\ninst✝² : HasCokernel f✝\nf : X ⟶ Y\ninst✝¹ inst✝ : HasCokernel f\n⊢ cokernel.π f ≫ (cokernelIsoOfEq (_ : f = f)).hom = cokernel.π f",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : Has... | [
829,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.glueDist_comm | [] | [
98,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
9
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_thirds | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.317751\nβ : Type ?u.317754\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ a / 3 + a / 3 + a / 3 = a",
"tactic": "rw [div_eq_mul_inv, ← mul_add, ← mul_add, inv_three_add_inv_three, mul_one]"
}
] | [
1735,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1734,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.range_enumOrd | [
{
"state_after": "S : Set Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\n⊢ (∀ (a : Ordinal), enumOrd S a ∈ S) ∧ ∀ (b : Ordinal), b ∈ S → ∃ a, enumOrd S a = b",
"state_before": "S : Set Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\n⊢ range (enumOrd S) = S",
"tactic": "rw [range_eq_iff]"
},
{
... | [
2274,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2272,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.injective_respectsIso | [] | [
662,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_mono | [] | [
845,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.coe_copy | [] | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_ne_zero | [] | [
297,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Order/Hom/Lattice.lean | IsCompl.map | [] | [
278,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.continuous'_coe | [] | [
279,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Finmap.lean | Finmap.union_empty | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ : Finmap β\ns₁ : AList β\n⊢ ⟦s₁⟧ ∪ ⟦∅⟧ = ⟦s₁⟧",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ : Finmap β\ns₁ : AList β\n⊢ ⟦s₁⟧ ∪ ∅ = ⟦s₁⟧",
"tactic": "rw [← empty_toFinmap]"
},
{
"state_after": "no... | [
633,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sub_ae_eq_zero | [
{
"state_after": "case refine'_1\nα : Type u_2\nβ✝ : Type ?u.585371\nγ : Type ?u.585374\nδ : Type ?u.585377\nι : Type ?u.585380\nR : Type ?u.585383\nR' : Type ?u.585386\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β✝\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nβ : Type u... | [
2894,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2891,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_zero | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousAt.inv | [] | [
249,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.Integrable.smul | [] | [
1260,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essInf_measure_zero | [] | [
156,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_mul_self_assoc | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.5121\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA : Matrix n n α\nB : Matrix n m α\ninst✝ : Invertible A\n⊢ ⅟A ⬝ (A ⬝ B) = B",
"tactic": "rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, M... | [
82,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/Order/Basic.lean | Subtype.coe_lt_coe | [] | [
1150,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_of_nonneg | [] | [
216,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.le_pointwise_smul_iff₀ | [] | [
338,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.trace_eq | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.29224\nm : Type ?u.29227\nn : Type u_2\nR : Type ?u.29233\nα : Type u_1\ninst✝⁴ : DecidableEq l\ninst✝³ : DecidableEq m\ninst✝² : DecidableEq n\ninst✝¹ : Semiring α\ni j : n\nc : α\ni' j' : n\ninst✝ : Fintype n\n⊢ trace (stdBasisMatrix i i c) = c",
... | [
173,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/Basic.lean | lt_iff_lt_of_le_iff_le | [] | [
516,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumCompl_symm_apply | [
{
"state_after": "case mk\nα✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u_1\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\nx : α\nhx : x ∈ s\n⊢ ↑(Set.sumCompl s).symm ↑{ val := x, property := hx } = Sum.inl { val := x, property := hx }",
"state_before": "α✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u_1... | [
348,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_bit0 | [] | [
625,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.trans_assoc | [] | [
590,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_succ_of_lt | [] | [
374,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
374,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | norm_mk_nonneg | [] | [
178,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.degree_eq_zero_of_isUnit | [] | [
221,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.WalkingParallelPairHom.assoc | [
{
"state_after": "no goals",
"state_before": "X Y Z W : WalkingParallelPair\nf : WalkingParallelPairHom X Y\ng : WalkingParallelPairHom Y Z\nh : WalkingParallelPairHom Z W\n⊢ comp (comp f g) h = comp f (comp g h)",
"tactic": "cases f <;> cases g <;> cases h <;> rfl"
}
] | [
109,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\n⊢ Collinear ℝ {p₁, p₂, p₃} ↔ p₁ = p₂ ∨ p₃ = p₂ ∨ sin (∠ p₁ p₂ p₃) = 0",
"tactic": "rw [sin_eq_zero_i... | [
515,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_1\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.94059\ns₂ : Finset ι₂\nw : ι → k\np₁ p₂ : ι → P\nb : P\n⊢ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = ↑(wei... | [
191,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.mul_isClassified | [
{
"state_after": "case intro.intro.intro.intro.inl.intro\nz k l m n : ℤ\nco : Int.gcd m n = 1\nh : PythagoreanTriple (l * (m ^ 2 - n ^ 2)) (l * (2 * m * n)) z\n⊢ IsClassified (_ : PythagoreanTriple (k * (l * (m ^ 2 - n ^ 2))) (k * (l * (2 * m * n))) (k * z))\n\ncase intro.intro.intro.intro.inr.intro\nz k l m n ... | [
130,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.le_comap_map | [] | [
617,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.mono_right | [] | [
261,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.cons_sigma | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.69645\nγ : Type ?u.69648\nδ : Type ?u.69651\nσ : α → Type u_2\na : α\ns : Multiset α\nt : (a : α) → Multiset (σ a)\n⊢ Multiset.sigma (a ::ₘ s) t = map (Sigma.mk a) (t a) + Multiset.sigma s t",
"tactic": "simp [Multiset.sigma]"
}
] | [
328,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_sub | [
{
"state_after": "α : Type u_1\nβ : Type ?u.237039\nγ : Type ?u.237042\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidableEq α\nt : Multiset α\n⊢ ∀ (s : Multiset α), filter p (s - t) = filter p s - filter p t",
"state_before": "α : Type u_1\nβ : Type ?u.237039\nγ : Type ?u.237042\np : α → Prop\ninst✝... | [
2054,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2039,
1
] |
Mathlib/Order/Max.lean | Prod.isMin_iff | [] | [
456,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Computability/DFA.lean | DFA.evalFrom_append_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ : Type v\nM : DFA α σ\ns : σ\nx : List α\na : α\n⊢ evalFrom M s (x ++ [a]) = step M (evalFrom M s x) a",
"tactic": "simp only [evalFrom, List.foldl_append, List.foldl_cons, List.foldl_nil]"
}
] | [
69,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_sub_of_ne_zero | [
{
"state_after": "F : Type ?u.21767\nι : Type ?u.21770\nα : Type u_1\nβ : Type ?u.21776\ninst✝ : DivisionRing α\nm n : ℚ\nm0 : ↑m.den ≠ 0\nn0 : ↑n.den ≠ 0\nthis : ↑(-n).den ≠ 0\n⊢ ↑(m - n) = ↑m - ↑n",
"state_before": "F : Type ?u.21767\nι : Type ?u.21770\nα : Type u_1\nβ : Type ?u.21776\ninst✝ : DivisionRin... | [
134,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | piiUnionInter_singleton_left | [
{
"state_after": "case h\nα : Type u_1\nι : Type u_2\ns : ι → Set α\nS : Set ι\ns' : Set α\n⊢ s' ∈ piiUnionInter (fun i => {s i}) S ↔ s' ∈ {s' | ∃ t x, s' = ⋂ (i : ι) (_ : i ∈ t), s i}",
"state_before": "α : Type u_1\nι : Type u_2\ns : ι → Set α\nS : Set ι\n⊢ piiUnionInter (fun i => {s i}) S = {s' | ∃ t x, ... | [
409,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.mk_coord_apply_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nι' : Type ?u.836112\nR : Type u_1\nR₂ : Type ?u.836118\nK : Type ?u.836121\nM : Type u_2\nM' : Type ?u.836127\nM'' : Type ?u.836130\nV : Type u\nV' : Type ?u.836135\nv : ι → M\ninst✝⁸ : Ring R\ninst✝⁷ : CommRing R₂\ninst✝⁶ : AddCommGroup M\ninst✝⁵ ... | [
1153,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_nat_mem | [] | [
153,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
11
] |
Mathlib/Computability/Partrec.lean | Computable.ofNat | [] | [
411,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
11
] |
Mathlib/Data/Set/Image.lean | Set.range_inl_inter_range_inr | [] | [
904,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.lift'_add | [
{
"state_after": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type ?u.459206\nM'' : Type u_3\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\ninst✝¹ : Module R M'\ninst✝ : Module R M''\nf : M →ₗ[R] M'\ng✝ g : M →ₗ[R] M''\nh : ∀ (x ... | [
625,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_add_tsum_ite' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.347788\nδ : Type ?u.347791\ninst✝³ : AddCommMonoid α\ninst✝² : TopologicalSpace α\ninst✝¹ : T2Space α\nf✝ g : β → α\na a₁ a₂ : α\ninst✝ : ContinuousAdd α\nf : β → α\nb : β\nhf : Summable (update f b 0)\nn : β\n⊢ f n = (if ... | [
663,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonpos_of_mul_nonneg_left | [] | [
939,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.liftOn_mk | [] | [
366,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
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