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/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.isSymmetric_zero | [] | [
89,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_continuous | [] | [
129,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.ne_of_lt_of_lt_nat | [
{
"state_after": "ι : Type ?u.45154\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.45163\nπ : ι → Type ?u.45168\nr : α → α → Prop\ninst✝ : Preorder α\nf : ℕ → α\nhf : Monotone f\nn a : ℕ\nh1 : f n < f a\nh2 : f a < f (n + 1)\n⊢ False",
"state_before": "ι : Type ?u.45154\nα : Type u\nβ : Type v\nγ : Type w... | [
1104,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_empty | [] | [
1311,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_single_subset | [] | [
1169,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | Orthonormal.linearIsometryEquiv_symm_apply_single_one | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.899044\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G ... | [
554,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Topology/Constructions.lean | continuousAt_pi | [] | [
1228,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.le_einfsep_pi_of_le | [
{
"state_after": "α : Type ?u.48758\nβ : Type u_2\ninst✝² : PseudoEMetricSpace α\nx✝ y✝ z : α\ns✝ t : Set α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoEMetricSpace (π b)\ns : (b : β) → Set (π b)\nc : ℝ≥0∞\nh : ∀ (b : β), c ≤ einfsep (s b)\nx : (i : β) → π i\nhx : x ∈ pi univ s\ny : (i : β) →... | [
247,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_left | [] | [
497,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_eq_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nh : 0 ≤ x\n⊢ sqrt x = 0 ↔ x = 0",
"tactic": "simpa using sqrt_inj h le_rfl"
}
] | [
337,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_one_of_mul_eq_self_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\nHpos : a ≠ 0\nH : b * a = a\n⊢ b * a = 1 * a",
"tactic": "rw [Int.one_mul, H]"
}
] | [
1320,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1319,
1
] |
Mathlib/CategoryTheory/Limits/Presheaf.lean | CategoryTheory.coconeOfRepresentable_ι_app | [] | [
344,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_cos | [] | [
230,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_le_iff_le_left | [] | [
139,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_congr' | [] | [
221,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.mem_iff_ofSubtype_apply_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\np : α → Prop\nf✝ : Perm α\ninst✝ : DecidablePred p\na : α\nf : Perm (Subtype p)\nx : α\nh : p x\n⊢ p x ↔ p (↑(↑ofSubtype f) x)",
"tactic": "simpa only [h, true_iff_iff, MonoidHom.coe_mk, ofSubtype_apply_of_mem f h] using (f ⟨x, h⟩).2"... | [
466,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.step_one | [] | [
240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Analysis/MeanInequalities.lean | ENNReal.rpow_sum_le_const_mul_sum_rpow | [
{
"state_after": "case inl\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0∞\np q : ℝ\nhp✝ : 1 ≤ p\nhp : 1 = p\n⊢ (∑ i in s, f i) ^ p ≤ ↑(card s) ^ (p - 1) * ∑ i in s, f i ^ p\n\ncase inr\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0∞\np q : ℝ\nhp✝ : 1 ≤ p\nhp : 1 < p\n⊢ (∑ i in s, f i) ^ p ≤ ↑(card s) ^ (p - 1) * ∑ i in s,... | [
765,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Data/List/Sigma.lean | List.kreplace_of_forall_not | [
{
"state_after": "case mk\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\nl : List (Sigma β)\nH : ∀ (b : β a), ¬{ fst := a, snd := b } ∈ l\na' : α\nb' : β a'\nh : { fst := a', snd := b' } ∈ l\n⊢ (if a = { fst := a', snd := b' }.fst then some { fst := a, snd := b } ... | [
351,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.map_subtype_embedding_Icc | [
{
"state_after": "α : Type u_1\nβ : Type ?u.218518\ninst✝² : Preorder α\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : LocallyFiniteOrder α\na b : Subtype p\nhp : ∀ ⦃a b x : α⦄, a ≤ x → x ≤ b → p a → p b → p x\n⊢ map (Embedding.subtype p) (Finset.subtype p (Icc ↑a ↑b)) = Icc ↑a ↑b",
"state_before": "α : T... | [
1289,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.lt_tsub_of_add_lt_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.40621\ninst✝³ : PartialOrder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\nb c d : α\nhc : AddLECancellable c\nh : b - c + c < b\n⊢ False",
"state_before": "α : Type u_1\nβ : Type ?u.40621\ninst✝³ : PartialOrder α\ninst✝² : AddCommSemigroup... | [
329,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
11
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.bot_prod_bot | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.52443\nσ : Type ?u.52446\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS : Subsemigroup M\n⊢ ↑(prod ⊥ ⊥) = ↑⊥",
"tactic": "simp [coe_prod, Prod.one_eq_mk]"
}
] | [
686,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv | [
{
"state_after": "ι : Type u₁\nk : Type u₂\nV : Type u₃\nP : Type u₄\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : AffineSpace V P\ninst✝⁵ : Ring k\ninst✝⁴ : Module k V\nb : AffineBasis ι k P\nι' : Type u_1\ninst✝³ : Fintype ι'\ninst✝² : Fintype ι\nb₂ : AffineBasis ι k P\ninst✝¹ : DecidableEq ι\ninst✝ : Nontrivial k\np : ... | [
106,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.coe_lowerCentralSeries_ideal_le | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nL' : Type w\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI : LieIdeal R L\n⊢ ↑(lowerCentralSeries R { x // x ∈ ↑I } { x // x ∈ ↑I } Nat.zero) ≤ ↑(lowerCentralSeries R L { x // x ∈ ↑I } Nat.ze... | [
585,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mul_mem | [] | [
239,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Functor.zero_obj | [] | [
357,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_iff_continuous_differentiable | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
1648,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerLeft_twice | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi'_eq_pi | [] | [
394,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot | [
{
"state_after": "case h\nR : Type u_1\nA : Type ?u.937974\nK : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : IsDomain R\ninst✝¹ : IsDedekindDomain R\nv : HeightOneSpectrum R\ninst✝ : Algebra R K\nhK : IsFractionRing R K\nx : K\n⊢ (x ∈\n ⨅ (v : HeightOn... | [
1035,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.inter_ae_eq_empty_of_ae_eq_empty_left | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type ?u.127483\nγ : Type ?u.127486\nδ : Type ?u.127489\nι : Type ?u.127492\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : s =ᵐ[μ] ∅\n⊢ ∅ = ∅ ∩ t",
"state_before": "α : Type u_1\nβ : Type ?u.127483\nγ : Type ?u.127486\nδ : Type ?u.1274... | [
544,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_const | [] | [
524,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Icc_iff_left | [] | [
66,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_inv | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/List/MinMax.lean | List.argmax_eq_none | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder β\ninst✝ : DecidableRel fun x x_1 => x < x_1\nf : α → β\nl : List α\no : Option α\na m : α\n⊢ argmax f l = none ↔ l = []",
"tactic": "simp [argmax]"
}
] | [
162,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym2_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ Finset.sym2 s = ∅ ↔ s = ∅",
"tactic": "rw [Finset.sym2, image_eq_empty, product_eq_empty, or_self_iff]"
}
] | [
76,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ico_bot_coe | [] | [
1164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_lt_of_le | [] | [
895,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.pullback_obj_arrow | [] | [
242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.const.get_map | [
{
"state_after": "case mk\nn m : ℕ\nP : MvPFunctor n\nA : Type u\nα β : TypeVec n\nf : α ⟹ β\nfst✝ : (const n A).A\nsnd✝ : B (const n A) fst✝ ⟹ α\n⊢ get (f <$$> { fst := fst✝, snd := snd✝ }) = get { fst := fst✝, snd := snd✝ }",
"state_before": "n m : ℕ\nP : MvPFunctor n\nA : Type u\nα β : TypeVec n\nf : α ⟹... | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | eq_sum_orthogonalProjection_self_orthogonalComplement | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.946458\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace ... | [
1021,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.isUnitTrinomial_iff' | [
{
"state_after": "p q : ℤ[X]\n⊢ IsUnitTrinomial p ↔ (sum p fun n x => x ^ 2) = 3",
"state_before": "p q : ℤ[X]\n⊢ IsUnitTrinomial p ↔ coeff (p * mirror p) ((natDegree (p * mirror p) + natTrailingDegree (p * mirror p)) / 2) = 3",
"tactic": "rw [natDegree_mul_mirror, natTrailingDegree_mul_mirror, ← mul_ad... | [
214,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_ne_zero_iff | [] | [
262,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Function.Surjective.tsum_eq_tsum_of_hasSum_iff_hasSum | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\nδ : Type ?u.332033\ninst✝⁴ : AddCommMonoid α\ninst✝³ : TopologicalSpace α\ninst✝² : T2Space α\nf✝ g✝ : β → α\na a₁ a₂ : α\nα' : Type u_1\ninst✝¹ : AddCommMonoid α'\ninst✝ : TopologicalSpace α'\ne : α' → α\nhes : Surjective e\nh0 : e 0 = 0\nf : β → α\ng... | [
560,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | ChartedSpace.locallyConnectedSpace | [
{
"state_after": "H : Type u\nH' : Type ?u.45851\nM : Type u_1\nM' : Type ?u.45857\nM'' : Type ?u.45860\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : LocallyConnectedSpace H\ne : M → LocalHomeomorph M H := chartAt H\n⊢ LocallyConnectedSpace M",
"state_before":... | [
626,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_singleton | [] | [
1331,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
] |
Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_matrix'' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nN : Type w\ninst✝⁹ : Ring R\ninst✝⁸ : StrongRankCondition R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : Module.Free R M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module R N\ninst✝² : Module.Free R N\nm n : Type u\ninst✝¹ : Finite m\n... | [
97,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_eq_linear_combination | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type ?u.291809\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.292465\ns₂ : Finset ι₂\ns : Finset ι\np : ι → V\nw : ι → k\nhw : ∑ i in s, w i = 1\n⊢ ↑(a... | [
476,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_monomial_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.5165\nr : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\ns : σ →₀ ℕ\na : R\nha : a ≠ 0\n⊢ degrees (↑(monomial s) a) = ↑toMultiset s",
"tactic": "classical\n refine' le_antisy... | [
110,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.map_get? | [] | [
741,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_range | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na : α\nhs : Set.Finite s\nht : Set.Finite t\ninst✝¹ : DecidableEq α\ninst✝ : Fintype β\nf : β → α\nh : Set.Finite (range f)\na✝ : α\n⊢ a✝ ∈ Finite.toFinset h ↔ a✝ ∈ Finset.image f Finset.univ",
"state_before": "α : Type u... | [
301,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
11
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.nndist_conj_conj | [] | [
336,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integrable_of_lintegral_nnnorm_bounded' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nι : Type u_1\nE : Type u_3\ninst✝³ : MeasurableSpace α\nμ : Measure α\nl : Filter ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NeBot l\ninst✝ : IsCountablyGenerated l\nφ : ι → Set α\nhφ : AECover μ l φ\nf : α → E\nI : ℝ≥0\nhfm : AEStronglyMeasurable ... | [
429,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivWithinAt.cos | [] | [
935,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | le_tsub_iff_le_tsub | [] | [
254,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_dvd | [] | [
783,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_eq_one_iff | [
{
"state_after": "ι : Type ?u.2371612\nα : Type u_1\nβ : Type ?u.2371618\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx y : α\nf : Perm α\n⊢ (∀ (x_1 : α), (if SameCycle f x x_1 then ↑f x_1 else x_1) = x_1) ↔ ↑f x = x",
"state_before": "ι : Type ?u.2371612\nα : Type u_1\nβ : Type ?u.2371618\nin... | [
1054,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.getSection_is_unique | [
{
"state_after": "case a\nC D : Type u\ninst✝³ : Category C\ninst✝² : Category D\nA : Type w\ninst✝¹ : Category A\ninst✝ : HasLimits A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nG : C ⥤ D\nhu : CoverLifting J K G\nℱ : Sheaf J A\nX : A\nU : D\nS : Sieve U\nhS : S ∈ GrothendieckTopology.sieves K U\n... | [
179,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/LinearAlgebra/InvariantBasisNumber.lean | card_le_of_surjective' | [
{
"state_after": "R : Type u\ninst✝³ : Semiring R\ninst✝² : RankCondition R\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nf : (α →₀ R) →ₗ[R] β →₀ R\ni : Surjective ↑f\nP : (β →₀ R) ≃ₗ[R] β → R := Finsupp.linearEquivFunOnFinite R R β\n⊢ Fintype.card β ≤ Fintype.card α",
"state_before": ... | [
154,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_triangle' | [
{
"state_after": "ι : Sort ?u.84126\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nfin : hausdorffEdist u t ≠ ⊤\n⊢ hausdorffDist s u ≤ hausdorffDist s t + hausdorffDist t u",
"state_before": "ι : Sort ?u.84126\nα : Type u\nβ : Type v\ni... | [
852,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.restrictDom_comp_subtype | [
{
"state_after": "case h.a.h\nα : Type u_1\nM : Type u_2\nN : Type ?u.73225\nP : Type ?u.73228\nR : Type u_3\nS : Type ?u.73234\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\ns... | [
259,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_singleton_mul_left_injective | [] | [
596,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.alternatingProd_reverse | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.19288\nα : Type u_1\nM : Type ?u.19294\nN : Type ?u.19297\nP : Type ?u.19300\nM₀ : Type ?u.19303\nG : Type ?u.19306\nR : Type ?u.19309\ninst✝ : CommGroup α\n⊢ alternatingProd (reverse []) = alternatingProd [] ^ (-1) ^ (length [] + 1)",
"tactic": ... | [
120,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.map_id_apply | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nF G H : C ⥤ Type w\nX Y Z : C\nσ : F ⟶ G\nτ : G ⟶ H\na : F.obj X\n⊢ F.map (𝟙 X) a = a",
"tactic": "simp [types_id]"
}
] | [
150,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/LinearAlgebra/Dual.lean | TensorProduct.dualDistribInvOfBasis_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_3\nN : Type u_5\nι : Type u_1\nκ : Type u_4\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : DecidableEq κ\ninst✝⁶ : Fintype ι\ninst✝⁵ : Fintype κ\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Modu... | [
1587,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherian_submodule | [
{
"state_after": "R : Type u_1\nM : Type u_2\nP : Type ?u.632\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid P\ninst✝¹ : Module R M\ninst✝ : Module R P\nN : Submodule R M\nh : ∀ (s : Submodule R M), s ≤ N → Submodule.FG s\ns : Submodule R { x // x ∈ N }\n⊢ Submodule.FG s",
"state_bef... | [
102,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_zero_succ | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_zero_of_isEmpty_leftMoves | [] | [
697,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Data/Polynomial/Inductions.lean | Polynomial.degree_pos_induction_on | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nP : R[X] → Prop\np : R[X]\nh0 : 0 < degree p\nhC : ∀ {a : R}, a ≠ 0 → P (↑C a * X)\nhX : ∀ {p : R[X]}, 0 < degree p → P p → P (p * X)\nhadd : ∀ {p : R[X]} {a : R}, 0 < degree p → P p → P (p + ↑C a)... | [
146,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.forall_image₂_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.16668\nβ : Type u_3\nβ' : Type ?u.16674\nγ : Type u_1\nγ' : Type ?u.16680\nδ : Type ?u.16683\nδ' : Type ?u.16686\nε : Type ?u.16689\nε' : Type ?u.16692\nζ : Type ?u.16695\nζ' : Type ?u.16698\nν : Type ?u.16701\ninst✝⁷ : DecidableEq α'\... | [
104,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.symm_trans_self | [] | [
1274,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_insert_iff | [] | [
900,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.coe_prodComm | [] | [
939,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_int_cast | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Data/List/Basic.lean | List.map_tail | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.135547\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\nl : List α\n⊢ map f (tail l) = tail (map f l)",
"tactic": "cases l <;> rfl"
}
] | [
1828,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_succ_ne_one | [] | [
993,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁵ : Semiring R\ninst✝⁴ : (i : ι) → AddCommGroup (M₁ i)\ninst✝³ : AddCommGroup M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module ... | [
1154,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.arzela_ascoli₂ | [
{
"state_after": "F : Type ?u.855510\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : CompactSpace α\ninst✝ : PseudoMetricSpace β\nf g : α →ᵇ β\nx : α\nC : ℝ\ns : Set β\nhs : IsCompact s\nA : Set (α →ᵇ β)\nclosed : IsClosed A\nin_s : ∀ (f : α →ᵇ β) (x : α), f ∈ A → ↑f x ∈ s\nH : Equico... | [
601,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_congr_iff | [] | [
533,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.dropFun_id | [] | [
771,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_order | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nh : (order φ).Dom\n⊢ ↑(coeff R (Nat.find (_ : ∃ n, ↑(coeff R n) φ ≠ 0))) φ ≠ 0",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nh : (order φ).Dom\n⊢ ↑(coeff R (Part.get (order φ) h)) φ ≠ 0",
"tactic": "simp onl... | [
2258,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2255,
1
] |
Mathlib/Algebra/Ring/Basic.lean | AddMonoidHom.coe_mulLeft | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.deriv_arccos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ -deriv (fun y => arcsin y) x = -(1 / sqrt (1 - x ^ 2))",
"tactic": "simp only [deriv_arcsin]"
}
] | [
180,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_two | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ lift 2 = 2",
"tactic": "simp [←one_add_one_eq_two]"
}
] | [
635,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\n⊢ support 1 = ∅",
"tactic": "rw [support_eq_empty_iff]"
}
] | [
312,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mk_apply | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.coe_subtypeEquivCodomain | [] | [
1362,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.hasDerivAt_cos | [] | [
608,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_sinh | [] | [
657,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_reverse | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np : Poly\n⊢ denote ctx (List.reverse p) = denote ctx p",
"tactic": "simp [List.reverse]"
}
] | [
319,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
318,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.continuousOn_coordChange | [] | [
888,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Order/RelIso/Group.lean | RelIso.mul_apply | [] | [
43,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.isLimit_ext | [] | [
55,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.setOf_forall | [] | [
281,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/Basic.lean | lt_iff_not_le | [] | [
476,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSumFinEquiv_symm_apply_natAdd | [] | [
350,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.of_prim | [] | [
314,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.congr_of_eventuallyEq | [] | [
454,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.sigma | [
{
"state_after": "α : Type u_2\nβ : Type ?u.9365\nγ : Type ?u.9368\nr : α → α → Prop\ns t✝ : Multiset α\na : α\nσ : α → Type u_1\nt : (a : α) → Multiset (σ a)\nl₁ : List α\nf : (a : α) → List (σ a)\nhf : ∀ (a : α), Quotient.mk (isSetoid (σ a)) (f a) = t a\n⊢ Nodup (Quot.mk Setoid.r l₁) → (∀ (a : α), Nodup (t a)... | [
198,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
11
] |
Std/Logic.lean | Decidable.not_imp | [] | [
569,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
568,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.