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/MetricSpace/HausdorffDistance.lean | Metric.cthickening_mono | [] | [
1079,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/Data/Set/Accumulate.lean | Set.mem_accumulate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.214\ns : α → Set β\nt : α → Set γ\ninst✝ : LE α\nx : α\nz : β\n⊢ z ∈ Accumulate s x ↔ ∃ y, y ≤ x ∧ z ∈ s y",
"tactic": "simp_rw [accumulate_def, mem_iUnion₂, exists_prop]"
}
] | [
36,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem | [
{
"state_after": "R : Type u_2\ninst✝¹ : CommRing R\nS : Type u_1\ninst✝ : CommRing S\nf : R →+* S\nI J : Ideal S\nr : S\nhr : r ∈ I\np : R[X]\nhp : eval₂ f r (divX p) * r + ↑f (coeff p 0) ∈ I\n⊢ coeff p 0 ∈ comap f I",
"state_before": "R : Type u_2\ninst✝¹ : CommRing R\nS : Type u_1\ninst✝ : CommRing S\nf ... | [
51,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.update_inr_apply_inl | [] | [
319,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.liftPropOn_univ | [
{
"state_after": "no goals",
"state_before": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.12254\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : Top... | [
222,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_finset_prod | [] | [
649,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.proj_symm_apply' | [] | [
155,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_neg | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.exists_pow_neg_lt | [
{
"state_after": "case intro\np : ℕ\nhp : Fact (Nat.Prime p)\nε : ℝ\nhε : 0 < ε\nk : ℕ\nhk : ε⁻¹ < ↑k\n⊢ ∃ k, ↑p ^ (-↑k) < ε",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nε : ℝ\nhε : 0 < ε\n⊢ ∃ k, ↑p ^ (-↑k) < ε",
"tactic": "obtain ⟨k, hk⟩ := exists_nat_gt ε⁻¹"
},
{
"state_after": "case int... | [
348,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.nhdsWithin_extend_target_eq | [] | [
853,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.of.injective_of_degree_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nK : Type w\ninst✝¹ : CommRing R\nf : R[X]\ninst✝ : IsDomain R\nhf : degree f ≠ 0\n⊢ ∀ (a : R), ↑(of f) a = 0 → a = 0",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝¹ : CommRing R\nf : R[X]\ninst✝ : IsDomain R\nhf : degree f ≠ 0\n⊢ Function.Injective ↑(o... | [
269,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/BooleanAlgebra.lean | disjoint_sdiff_self_left | [] | [
213,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.top_boxes | [] | [
168,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_add_C | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\na : R\n⊢ IsCoprime (X + ↑C a) 1",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\na : R\n⊢ Separable (X + ↑C a)",
"tactic": "rw [separable_def, derivative_add, derivative_... | [
70,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/PathConnected.lean | JoinedIn.trans | [
{
"state_after": "case intro\nX : Type u_1\nY : Type ?u.622850\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.622865\nF : Set X\nhxy : JoinedIn F x y\nhyz : JoinedIn F y z\nhx : x ∈ F\nhy : y ∈ F\n⊢ JoinedIn F x z",
"state_before": "X : Type u_1\nY : Type ?u.622850\ninst✝¹ ... | [
891,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.toSup_commutes | [] | [
277,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.mulHom_injective | [] | [
265,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.comap_injective | [] | [
396,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.smul_torsionBy | [] | [
249,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_C | [
{
"state_after": "case h.e'_3\nR : Type u_1\ninst✝ : Semiring R\nr : R\n⊢ ↑C r = ↑C r * T ↑0",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\n⊢ ↑toLaurent (↑Polynomial.C r) = ↑C r",
"tactic": "convert Polynomial.toLaurent_C_mul_T 0 r"
},
{
"state_after": "no goals",
"state_before"... | [
222,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.trans_symm | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.473556\nE : Type ?u.473559\nF : Type ?u.473562\nG : Type ?u.473565\nE' : Type ?u.473568\nF' : Type ?u.473571\nG' : Type ?u.473574\nE'' : Type ?u.473577\nF'' : Type ?u.473580\nG'' : Type ?u.473583\nR : Type u_2\nR' : Type ?u.473589\n𝕜 : Type u_3\n𝕜' : Type ?u.473595\... | [
1581,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_inv_le_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.32669\nα : Type u_1\nβ : Type ?u.32675\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : 0 < b\n⊢ a * b⁻¹ ≤ c ↔ a ≤ b * c",
"tactic": "rw [mul_comm, inv_mul_le_iff h]"
}
] | [
186,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.ker_int_castRingHom | [
{
"state_after": "case h\nn : ℕ\nx✝ : ℤ\n⊢ x✝ ∈ RingHom.ker (Int.castRingHom (ZMod n)) ↔ x✝ ∈ Ideal.span {↑n}",
"state_before": "n : ℕ\n⊢ RingHom.ker (Int.castRingHom (ZMod n)) = Ideal.span {↑n}",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\nn : ℕ\nx✝ : ℤ\n⊢ x✝ ∈ ... | [
567,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.pointwise_smul_toAddSubmonoid | [] | [
467,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Parity.lean | Even.trans_dvd | [] | [
257,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Analysis/ODE/Gronwall.lean | dist_le_of_trajectories_ODE | [] | [
230,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_bit0 | [
{
"state_after": "case inl\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℤ\nnonneg : 0 ≤ n\n⊢ A ^ bit0 n = A ^ n * A ^ n\n\ncase inr\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nn : ℤ\nnonpos :... | [
248,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_smul | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Algebra/Group/Basic.lean | rightInverse_inv | [] | [
285,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTrivAsLocalEquiv_target | [
{
"state_after": "ι : Type u_3\nB : Type u_1\nF : Type u_2\nX : Type ?u.32284\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nZ : FiberBundleCore ι B F\ni : ι\np : B × F\n⊢ p.fst ∈ baseSet Z i ∧ p.snd ∈ univ ↔ p.fst ∈ baseSet Z i",
"state_before": "ι : Type u_3\nB : Ty... | [
542,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.cos_arctan_pos | [] | [
141,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_attach | [] | [
174,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/Order/Basic.lean | inf_nhds_atTop | [] | [
1540,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.ideal_eq_span_pow_p | [] | [
625,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | EquicontinuousAt.continuousAt | [
{
"state_after": "ι : Type u_1\nκ : Type ?u.28015\nX : Type u_2\nY : Type ?u.28021\nZ : Type ?u.28024\nα : Type u_3\nβ : Type ?u.28030\nγ : Type ?u.28033\n𝓕 : Type ?u.28036\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\n... | [
157,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformGroup.ext | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.165655\nβ : Type ?u.165658\ninst✝³ : UniformSpace α\ninst✝² : Group α\ninst✝¹ : UniformGroup α\nG : Type u_1\ninst✝ : Group G\nu v : UniformSpace G\nhu : UniformGroup G\nhv : UniformGroup G\nh : 𝓝 1 = 𝓝 1\n⊢ 𝓤 G = 𝓤 G",
"tactic": "rw [@unifor... | [
295,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_triangle | [
{
"state_after": "ι : Type ?u.34775\nα : Type u_1\nβ : Type ?u.34781\nπ : ι → Type ?u.34786\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ b ⊔ b \\ c ⊔ (c \\ b ⊔ b \\ a) = a ∆ b ⊔ b ∆ c",
"state_before": "ι : Type ?u.34775\nα : Type u_1\nβ : Type ?u.34781\nπ : ι → Type ?u.34786\ninst✝ : General... | [
219,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.iInf_mul_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nα : Type ?u.15694\ninst✝ : LinearOrderedField α\nr : ℝ\nha : 0 ≤ r\nf : ι → ℝ\n⊢ (⨅ (i : ι), f i) * r = ⨅ (i : ι), f i * r",
"tactic": "simp only [Real.mul_iInf_of_nonneg ha, mul_comm]"
}
] | [
135,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_le_iff_one_le_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ a⁻¹ * a ≤ b * a ↔ 1 ≤ b * a",
"tactic": "rw [inv_mul_self]"
}
] | [
234,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.ofDual | [] | [
480,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.isBigO | [] | [
187,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Commute.iterate_right | [] | [
128,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.map_sup | [
{
"state_after": "case verts\nι : Sort ?u.147638\nV : Type u\nW : Type v\nG✝ : SimpleGraph V\nG₁ G₂ : Subgraph G✝\na b : V\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nH H' : Subgraph G\n⊢ (Subgraph.map f (H ⊔ H')).verts = (Subgraph.map f H ⊔ Subgraph.map f H').verts\n\ncase Adj\nι : Sort ?u.147638\nV :... | [
681,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.ae_sum_iff | [] | [
2068,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2066,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_le_pow | [] | [
451,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.one_le_count_iff_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.358132\nγ : Type ?u.358135\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ 1 ≤ count a s ↔ a ∈ s",
"tactic": "rw [succ_le_iff, count_pos]"
}
] | [
2411,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2410,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_prod' | [] | [
819,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_pi_div_two | [
{
"state_after": "⊢ cos (↑π / 2) = cos ↑(π / 2)",
"state_before": "⊢ cos (↑π / 2) = ↑(Real.cos (π / 2))",
"tactic": "rw [ofReal_cos]"
},
{
"state_after": "no goals",
"state_before": "⊢ cos (↑π / 2) = cos ↑(π / 2)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_befor... | [
1111,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_and_le_add_one_iff | [
{
"state_after": "m n k l : ℕ\n⊢ m = n + 1 → n ≤ m",
"state_before": "m n k l : ℕ\n⊢ n ≤ m ∧ m ≤ n + 1 ↔ m = n ∨ m = n + 1",
"tactic": "rw [le_add_one_iff, and_or_left, ← le_antisymm_iff, eq_comm, and_iff_right_of_imp]"
},
{
"state_after": "n k l : ℕ\n⊢ n ≤ n + 1",
"state_before": "m n k l :... | [
223,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.pre_post | [
{
"state_after": "case w\nJ : Type u₁\ninst✝⁶ : Category J\nK : Type u₂\ninst✝⁵ : Category K\nC : Type u\ninst✝⁴ : Category C\nF✝ : J ⥤ C\nD : Type u'\ninst✝³ : Category D\nE : K ⥤ J\nF : J ⥤ C\nG : C ⥤ D\ninst✝² : HasColimit F\ninst✝¹ : HasColimit (E ⋙ F)\ninst✝ : HasColimit (F ⋙ G)\nh : HasColimit ((E ⋙ F) ⋙ ... | [
1066,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_comm | [
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ ofNat n + ofNat m = ofNat m + ofNat n",
"tactic": "simp [Nat.add_comm]"
},
{
"state_after": "no goals",
"state_before": "a✝¹ a✝ : Nat\n⊢ -[a✝¹+1] + -[a✝+1] = -[a✝+1] + -[a✝¹+1]",
"tactic": "simp [Nat.add_comm]"
}
] | [
222,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
218,
11
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_ofNat | [] | [
44,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_pi_mulSingle' | [] | [
1128,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_some | [] | [
125,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
125,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_nonneg_of_ae | [] | [
1363,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_pos_of_lt | [
{
"state_after": "m n : Nat\nh : m < n\n⊢ 0 + m < n - m + m",
"state_before": "m n : Nat\nh : m < n\n⊢ 0 < n - m",
"tactic": "apply Nat.lt_of_add_lt_add_right (b := m)"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : m < n\n⊢ 0 + m < n - m + m",
"tactic": "rwa [Nat.zero_a... | [
430,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
428,
11
] |
Mathlib/Order/FixedPoints.lean | OrderHom.gfp_gfp | [] | [
182,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ofNat'_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.445696\n⊢ ofNat' 0 = ↑0",
"tactic": "simp"
},
{
"state_after": "α : Type ?u.445696\nb : Bool\nn : ℕ\nIH : Nat.binaryRec 0 (fun b x => bif b then Num.bit1 else Num.bit0) n = ↑n\n⊢ Nat.binaryRec 0 (fun b x => bif b then Num.bit1 else Num.bi... | [
772,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/Erased.lean | Erased.mk_out | [
{
"state_after": "α : Sort u_1\ns : α → Prop\nh : ∃ a, (fun b => a = b) = s\n⊢ { fst := fun b => out { fst := s, snd := h } = b,\n snd := (_ : ∃ a, (fun b => a = b) = fun b => out { fst := s, snd := h } = b) } =\n { fst := s, snd := h }",
"state_before": "α : Sort u_1\ns : α → Prop\nh : ∃ a, (fun b ... | [
68,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_mem_convexHull | [] | [
226,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.m_iUnion | [] | [
111,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.eval_ker | [
{
"state_after": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι✝ : Type w\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : DecidableEq ι✝\nb✝ : Basis ι✝ R M\nι : Type u_1\nb : Basis ι R M\n⊢ ∀ (m : M), ↑(Dual.eval R M) m = 0 → m = 0",
"state_before": "R : Type u\nM : Type v\... | [
470,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.le_of_mem_compression_of_not_mem | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a b : α\nh : a ∈ s ∧ compress u v a ∈ s ∨ ¬a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = a\nha : ¬a ∈ s\n⊢ u ≤ a",
"state_before": "α : Type u_1\ninst✝² ... | [
233,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.self | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : 1 < p\n⊢ padicValRat p ↑p = 1",
"tactic": "simp [hp]"
}
] | [
205,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.smul_single' | [] | [
1594,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1592,
1
] |
Mathlib/Topology/Order/Basic.lean | continuous_min | [] | [
694,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_mono_set_of_one_le' | [] | [
172,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.not_le | [] | [
49,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
48,
19
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lcurry_apply | [] | [
575,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.KernelFork.app_one | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ns : KernelFork f\n⊢ s.π.app one = 0",
"tactic": "simp [Fork.app_one_eq_ι_comp_right]"
}
] | [
96,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.star_dotProduct_star | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.208169\nm : Type u_1\nn : Type ?u.208175\no : Type ?u.208178\nm' : o → Type ?u.208183\nn' : o → Type ?u.208188\nR : Type ?u.208191\nS : Type ?u.208194\nα : Type v\nβ : Type w\nγ : Type ?u.208201\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : NonUn... | [
899,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.eq_of_le_of_finrank_le' | [
{
"state_after": "K : Type u_1\nL : Type u_2\nL' : Type ?u.284724\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Field L'\ninst✝² : Algebra K L\ninst✝¹ : Algebra K L'\nS F E : IntermediateField K L\ninst✝ : FiniteDimensional K L\nh_le : F ≤ E\nh_finrank : finrank { x // x ∈ F } L ≤ finrank { x // x ∈ E } L\n⊢ fi... | [
719,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.coeff_zero_ne_zero | [
{
"state_after": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : IsDomain B\ninst✝ : Algebra A B\nx : B\nhx : IsIntegral A x\nh : coeff (minpoly A x) 0 = 0\n⊢ x = 0",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : IsDomain B\ninst✝ : Algebra... | [
278,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_mem_one | [] | [
358,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/List/NodupEquivFin.lean | List.Sorted.coe_getIso_symm_apply | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.intermediateFieldMap_apply_coe | [] | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictFDerivAt_exp_zero | [] | [
166,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iInf_apply' | [
{
"state_after": "α : Type u_2\nι : Sort u_1\nm : ι → OuterMeasure α\ns : Set α\nhs : Set.Nonempty s\n⊢ (⨅ (t : ℕ → Set α) (_ : s ⊆ iUnion t), ∑' (n : ℕ), ⨅ (μ : OuterMeasure α) (_ : μ ∈ range fun i => m i), ↑μ (t n)) =\n ⨅ (t : ℕ → Set α) (_ : s ⊆ iUnion t), ∑' (n : ℕ), ⨅ (i : ι), ↑(m i) (t n)",
"state_... | [
1202,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_inj | [] | [
184,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factors_left_of_factors_add | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : Preadditive C\nX Y : C\nP : Subobject Y\nf g : X ⟶ Y\nw : Factors P (f + g)\nwg : Factors P g\n⊢ (factorThru P (f + g) w - factorThru P g wg) ≫ MonoOver.arrow (representativ... | [
201,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.im_exp | [
{
"state_after": "no goals",
"state_before": "q : ℍ\n⊢ im (exp ℝ q) = (exp ℝ q.re * (Real.sin ‖im q‖ / ‖im q‖)) • im q",
"tactic": "simp [exp_eq, smul_smul]"
}
] | [
116,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | image_range_orderOf | [
{
"state_after": "case a\nG : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝³ : Group G\ninst✝² : AddGroup A\ninst✝¹ : Fintype G\ninst✝ : DecidableEq G\nx : G\n⊢ x ∈ Finset.image (fun i => x✝ ^ i) (Finset.range (orderOf x✝)) ↔ x ∈ Set.toFinset ↑(zpowers x✝)",
"state_before": "G : Type u\nA : Type v\n... | [
1015,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.add_measure | [] | [
1700,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1697,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | continuous_clm_apply | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁷ : AddCommGroup F'\ninst✝⁶ : Module 𝕜 F'\ninst✝⁵ ... | [
590,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_injective | [] | [
256,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.mem_iff_star_mul_self | [] | [
155,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_measure_zero_of_exponent_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.947882\nF : Type u_2\nG : Type ?u.947888\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : MeasurableSpace α\nf : α → F\n⊢ s... | [
233,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.mergeIdem_nonEmpty | [
{
"state_after": "no goals",
"state_before": "e : List Nat\nh : e ≠ []\n⊢ mergeIdem e ≠ []",
"tactic": "induction e using List.two_step_induction with\n| empty => simp_all\n| single => simp [mergeIdem, mergeIdem.loop]\n| step => simp [mergeIdem, mergeIdem.loop] at *; split <;> simp_all"
},
{
"st... | [
122,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
118,
1
] |
Mathlib/Topology/Order/Basic.lean | map_coe_Ioi_atBot | [] | [
2521,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2520,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.liftRel_inr_inr | [
{
"state_after": "case inr\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type u_2\nr r₁ r₂ : α → γ → Prop\ns s₁ s₂ : β → δ → Prop\na : α\nb : β\nc : γ\nd : δ\nx : α ⊕ β\ny : γ ⊕ δ\na✝ : s b d\n⊢ s b d",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ... | [
417,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | mul_right_bijective_of_finite₀ | [] | [
44,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.strictAntiOn_of_deriv_neg | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.418135\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.418231\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ (x : ℝ), x ∈ interior D → deriv f x < 0... | [
939,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_add_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocDiv hp a (p + b) = toIocDiv hp a b + 1",
"tactic": "rw [add_comm, toIocDiv_add_right]"
}
] | [
330,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Order/Basic.lean | ne_of_not_le | [] | [
364,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.mul_const' | [] | [
1094,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_one_eq_zero | [] | [
144,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.ext | [] | [
163,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumCompl_symm_apply_compl | [
{
"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 ∈ sᶜ\n⊢ ↑(Set.sumCompl s).symm ↑{ val := x, property := hx } = Sum.inr { val := x, property := hx }",
"state_before": "α✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u_... | [
354,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Equalizers.lean | CategoryTheory.Limits.PreservesEqualizer.iso_hom | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.