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 |
|---|---|---|---|---|---|---|
Std/Data/Nat/Lemmas.lean | Nat.div_div_eq_div_mul | [
{
"state_after": "case inr\nm n k : Nat\nkpos : k > 0\n⊢ m / n / k = m / (n * k)",
"state_before": "m n k : Nat\n⊢ m / n / k = m / (n * k)",
"tactic": "cases eq_zero_or_pos k with\n| inl k0 => rw [k0, Nat.mul_zero, Nat.div_zero, Nat.div_zero] | inr kpos => ?_"
},
{
"state_after": "case inr.inr\n... | [
636,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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11
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Mathlib/Order/Disjoint.lean | symmetric_codisjoint | [] | [
241,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_centralizer | [] | [
852,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.congr | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nF' : ι → α → β\nhf : TendstoUniformlyOnFilter F f p p'\nhff' : ∀ᶠ (n : ι × α) in p ×ˢ p', F n.fst n.snd = F' n.fst n.snd\nu : Set (β × ... | [
212,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.restrict | [] | [
281,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
11
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Mathlib/Topology/LocalAtTarget.lean | isClosed_iff_coe_preimage_of_iSup_eq_top | [
{
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"tactic": "simpa using i... | [
105,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/RingTheory/AdjoinRoot.lean | PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk | [
{
"state_after": "no goals",
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922,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
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Mathlib/Order/Bounds/Basic.lean | IsLUB.insert | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\na✝ b✝ : α\ninst✝ : SemilatticeSup γ\na b : γ\ns : Set γ\nhs : IsLUB s b\n⊢ IsLUB ({a} ∪ s) (a ⊔ b)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\... | [
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946,
1
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Mathlib/Topology/Constructions.lean | IsOpen.openEmbedding_subtype_val | [] | [
1024,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
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Mathlib/Data/List/Chain.lean | List.chain'_pair | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na b x y : α\n⊢ Chain' R [x, y] ↔ R x y",
"tactic": "simp only [chain'_singleton, chain'_cons, and_true_iff]"
}
] | [
335,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Data/Fin/Basic.lean | Fin.succ_last | [] | [
1239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.ker.incl_comp_lift | [
{
"state_after": "case H\nV : Type ?u.485294\nW : Type ?u.485297\nV₁ : Type u_1\nV₂ : Type u_3\nV₃ : Type u_2\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : SeminormedAddCommGroup W\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf : NormedAddGroupHom V₁... | [
761,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_mul | [] | [
202,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_zsmul_sub_self | [
{
"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⊢ toIcoDiv hp a b • p - b = -toIcoMod hp a b",
"tactic": "rw [toIcoMod, neg_sub]"
}
] | [
126,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Order/Hom/Bounded.lean | BotHom.ext | [] | [
401,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.pos_smul_left | [] | [
161,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.comp_apply | [] | [
339,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.pos_of_mem_rowLens | [
{
"state_after": "μ : YoungDiagram\nx : ℕ\nhx : ∃ a, a ∈ List.range (colLen μ 0) ∧ rowLen μ a = x\n⊢ 0 < x",
"state_before": "μ : YoungDiagram\nx : ℕ\nhx : x ∈ rowLens μ\n⊢ 0 < x",
"tactic": "rw [rowLens, List.mem_map] at hx"
},
{
"state_after": "case intro.intro\nμ : YoungDiagram\ni : ℕ\nhi : i... | [
436,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp_zero_of_radius_pos | [] | [
154,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.edist_le_of_le | [] | [
201,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_mul_eq_of_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.50703\nβ : Type ?u.50706\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : b = a * c\n⊢ a⁻¹ * b = c",
"tactic": "simp [h]"
}
] | [
638,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Topology/Maps.lean | ClosedEmbedding.closure_image_eq | [] | [
700,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinite_iff_exist_lt_gt | [] | [
615,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
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] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.repr_floor_apply | [
{
"state_after": "no goals",
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... | [
82,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.finsupp_sum_apply | [] | [
1130,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
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] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.abs_det_adjustToOrientation | [
{
"state_after": "no goals",
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146,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
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] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.id_apply | [] | [
438,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
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] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.union | [] | [
183,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.isUniformOfEmpty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\n𝕜 : Type u_2\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\nhP : P.parts = ∅\n⊢ IsUniform P G ε",
"tactic": "simp [IsUniform, hP, nonUniforms]"
... | [
256,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Mathlib/Data/Multiset/Fold.lean | Multiset.fold_eq_foldr | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.localizationToStalk_stalkSpecializes | [
{
"state_after": "case h\nR✝ : Type u\ninst✝¹ : CommRing R✝\nR : Type u_1\ninst✝ : CommRing R\nx y : PrimeSpectrum R\nh : x ⤳ y\n⊢ RingHom.comp (localizationToStalk R y ≫ stalkSpecializes (Sheaf.presheaf (structureSheaf R)) h)\n (algebraMap R (Localization.AtPrime y.asIdeal)) =\n RingHom.comp (CommRingC... | [
1036,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.erase_neg | [] | [
1157,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | deriv_cos | [] | [
820,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
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Mathlib/Analysis/Calculus/FDeriv/Comp.lean | fderiv.comp_fderivWithin | [] | [
178,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_le | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedField α\nx y : α\n⊢ const x ≤ const y ↔ x < y ∨ x = y",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nx y : α\n⊢ const x ≤ const y ↔ x ≤ y",
"tactic": "rw [le_iff_lt_or_eq]"
},
{
"state_after": "no goals",
"state_before": "α... | [
788,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/RingTheory/Localization/Ideal.lean | IsLocalization.surjective_quotientMap_of_maximal_of_localization | [
{
"state_after": "R : Type u_2\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝³ : CommRing S\ninst✝² : Algebra R S\ninst✝¹ : IsLocalization M S\nI : Ideal S\ninst✝ : Ideal.IsPrime I\nJ : Ideal R\nH : J ≤ Ideal.comap (algebraMap R S) I\nhI : Ideal.IsMaximal (Ideal.comap (algebraMap R S) I)\ns : S ⧸ I\... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/Order/SuccPred/Basic.lean | Pred.rec_top | [] | [
1513,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
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] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_card_le | [
{
"state_after": "L : Language\nT✝ : Theory L\nα : Type w\nn : ℕ\nT' T : Theory L\ns : Set α\nM : Type w'\ninst✝² : Nonempty M\ninst✝¹ : Structure L M\ninst✝ : M ⊨ T\nh : lift (#↑s) ≤ lift (#M)\nthis : Inhabited M\n⊢ IsSatisfiable (LHom.onTheory (lhomWithConstants L α) T ∪ distinctConstantsTheory L s)",
"st... | [
157,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Topology/Sheaves/Sheaf.lean | TopCat.Presheaf.isSheaf_of_iso | [] | [
107,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | smul_ball_one | [
{
"state_after": "no goals",
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"tactic": "rw [smul_ball, smul_eq_mul, mul_one]"
}
] | [
152,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_eq_mkRat | [
{
"state_after": "no goals",
"state_before": "num : Int\nden : Nat\nden_nz : den ≠ 0\n⊢ normalize num den = mkRat num den",
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}
] | [
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23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
82,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.repeat_succ | [
{
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"state_before"... | [
404,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_nhds | [] | [
1104,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
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Mathlib/Data/Finset/Basic.lean | Finset.mem_of_mem_filter | [] | [
2664,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2663,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_map | [
{
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"tactic": "induction p <;> simp [*]"
}
... | [
1511,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1511,
1
] |
Std/Logic.lean | ne_self_iff_false | [] | [
84,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
84,
1
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Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.inversion_self | [
{
"state_after": "no goals",
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"tactic": "simp [inversion]"
}
] | [
51,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM_ReaderT_eq | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nρ α✝ : Type u_1\np : α✝ → Prop\nx : ReaderT ρ m α✝\ninst✝ : Monad m\na : ReaderT ρ m { a // p a }\n⊢ Subtype.val <$> a = x ↔ ∀ (x_1 : ρ), Subtype.val <$> a x_1 = x x_1",
"tactic": "exact ⟨fun eq _ => eq ▸ rfl, funext⟩"
}
] | [
197,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
195,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprodComparison_inl | [] | [
1345,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1344,
1
] |
Mathlib/Analysis/Convex/Contractible.lean | Convex.contractibleSpace | [] | [
48,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
11
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.trans_isLittleO | [] | [
122,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_adj | [] | [
619,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_symm_map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_3\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_2\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.574326\ninst✝¹ : CommRing... | [
797,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.independent_empty | [] | [
272,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_neg | [] | [
897,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderiv.fst | [] | [
220,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_one_div_cancel | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.54504\nG : Type ?u.54507\nα : Type u_1\nM : Type ?u.54513\nN : Type ?u.54516\ninst✝ : DivisionMonoid α\na b c : α\nh : IsUnit a\n⊢ a * (1 / a) = 1",
"tactic": "simp [h]"
}
] | [
379,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
11
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_tail | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ (fun o => Option.rec nil Prod.snd o) <$> destruct s >>= destruct = do\n let x ← destruct s\n match x with\n | none => Computation.pure none\n | some (fst, s) => destruct s",
"state_before": "α : Type u\nβ : Type v\nγ : Type ... | [
807,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.NormDigits.digits_one | [
{
"state_after": "n✝ b n : ℕ\nn0 : 0 < n\nnb : n < b\nb2 : 1 < b\n⊢ digits b n = [n] ∧ 1 < b ∧ 0 < n",
"state_before": "n✝ b n : ℕ\nn0 : 0 < n\nnb : n < b\n⊢ digits b n = [n] ∧ 1 < b ∧ 0 < n",
"tactic": "have b2 : 1 < b :=\n lt_iff_add_one_le.mpr (le_trans (add_le_add_right (lt_iff_add_one_le.mp n0) 1)... | [
647,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Order/Atoms.lean | IsCoatom.le_iff | [] | [
163,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_lt_coe_nat | [] | [
850,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | LinearMap.map_mul_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : A →ₗ[R] B\na : A\nr : R\n⊢ ↑f (a * ↑(algebraMap R A) r) = ↑f a * ↑(algebraMap R B) r",
"tactic": "rw [... | [
704,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_ne_of_natTrailingDegree_ne | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nthis : ↑n = ↑n\n⊢ natTrailingDegree p ≠ n → trailingDegree p ≠ ↑n",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ natTrailingDegree p ≠ n → trailingD... | [
183,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.inf | [] | [
630,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.zero | [] | [
61,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Inner.lean | MeasureTheory.AEStronglyMeasurable.im | [] | [
51,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.MemBaseSet.unionComplToSubordinate | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂✝ : TaggedPrepartition I\nl l₁ l₂ : IntegrationParams\nhπ₁ : MemBaseSet l I c r₁ π₁\nhle : ∀ (x : ι → ℝ), x ∈ ↑Box.Icc I → r₂ x ≤ r₁ x\nπ₂ : Prepartition I\nhU ... | [
395,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_bypass_le | [
{
"state_after": "no goals",
"state_before": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v u✝ : V\n⊢ length (bypass nil) ≤ length nil",
"tactic": "rfl"
},
{
"state_after": "case cons\nV : Type u\nV' : T... | [
1389,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Set.UniformEquicontinuous.uniformContinuous_of_mem | [] | [
184,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
11
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.comp_antitone_on_left | [] | [
192,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Finsupp.LinearEquiv.finsuppUnique_symm_apply | [
{
"state_after": "case h\nR : Type u_3\nR₁ : Type ?u.31136\nR₂ : Type ?u.31139\nR₃ : Type ?u.31142\nR₄ : Type ?u.31145\nS : Type ?u.31148\nK : Type ?u.31151\nK₂ : Type ?u.31154\nM : Type u_2\nM' : Type ?u.31160\nM₁ : Type ?u.31163\nM₂ : Type ?u.31166\nM₃ : Type ?u.31169\nM₄ : Type ?u.31172\nN : Type ?u.31175\nN... | [
148,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_eq_zero | [] | [
111,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.span_single_image | [
{
"state_after": "α : Type u_2\nM : Type u_1\nN : Type ?u.43675\nP : Type ?u.43678\nR : Type u_3\nS : Type ?u.43684\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 : Set M\na ... | [
180,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
src/lean/Init/SizeOf.lean | Bool.sizeOf_eq_one | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ sizeOf b = 1",
"tactic": "cases b <;> rfl"
}
] | [
86,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
86,
9
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_length | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.29967\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\n⊢ Cycle.length (periodicOrbit f x) = minimalPeriod f x",
"tactic": "rw [periodicOrbit, Cycle.length_coe, List.length_map, List.length_range]"
}
] | [
502,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.add_one_le_exp_of_nonneg | [
{
"state_after": "case inl\nx y : ℝ\nhx : 0 ≤ 0\n⊢ 0 + 1 ≤ exp 0\n\ncase inr\nx✝ y x : ℝ\nhx : 0 ≤ x\nh : 0 < x\n⊢ x + 1 ≤ exp x",
"state_before": "x✝ y x : ℝ\nhx : 0 ≤ x\n⊢ x + 1 ≤ exp x",
"tactic": "rcases eq_or_lt_of_le hx with (rfl | h)"
},
{
"state_after": "no goals",
"state_before": "c... | [
1489,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1486,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.interior_nonempty | [] | [
337,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.centralBinom_zero | [] | [
54,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.mk'_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_3\nB : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : Algebra R B\ninst✝¹ : Algebra A B\ninst✝ : IsIntegralClosure A R B\nh : optParam (IsIntegral R 1) (_ : IsIntegral R 1)\n⊢ ↑(algebraMap A B) (mk' A 1... | [
873,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_of_add_lt_add_left | [
{
"state_after": "no goals",
"state_before": "k n m : Nat\nh : k + n < k + m\nheq : n = m\n⊢ k + m < k + m",
"tactic": "rwa [heq] at h"
}
] | [
75,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
73,
11
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β\na : α\ns : Stream' α\nx✝ : a ∈ s\nn : ℕ\nh : (fun b => a = b) (nth s n)\n⊢ (fun b => f a = b) (nth (map f s) n)",
"tactic": "rw [nth_map, h]"
}
] | [
188,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.inclusion_top_functor | [
{
"state_after": "case refine'_1\nX : TopCat\n⊢ ∀ (X_1 : Opens ↑((toTopCat X).obj ⊤)),\n (IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion ⊤)))).obj X_1 =\n (map (inclusionTopIso X).inv).obj X_1\n\ncase refine'_2\nX : TopCat\n⊢ ∀ (X_1 Y : Opens ↑((toTopCat X).obj ⊤)) (f : X_1 ⟶ Y),\n ... | [
362,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_image | [] | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.left_mem_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3745\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ a ∈ Ico a b ↔ a < b",
"tactic": "simp [le_refl]"
}
] | [
190,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.prod_map' | [
{
"state_after": "case mk\n𝕜 : Type u_2\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type uG\nin... | [
1628,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1625,
1
] |
Mathlib/ModelTheory/Definability.lean | Set.definable_finset_sup | [
{
"state_after": "no goals",
"state_before": "M : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.14150\nB : Set M\ns✝ : Set (α → M)\nι : Type u_1\nf : ι → Set (α → M)\nhf : ∀ (i : ι), Definable A L (f i)\ns : Finset ι\n⊢ Definable A L (Finset.sup s f)",
"tactic": "class... | [
125,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | mem_pregroupoid_of_eq_on_source | [
{
"state_after": "H : Type u\nH' : Type ?u.33053\nM : Type ?u.33056\nM' : Type ?u.33059\nM'' : Type ?u.33062\ninst✝ : TopologicalSpace H\nPG : Pregroupoid H\ne e' : LocalHomeomorph H H\nhe' : e ≈ e'\nhe : Pregroupoid.property PG (↑e) e.source\n⊢ Pregroupoid.property PG (↑e') e.source",
"state_before": "H : ... | [
362,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/Parity.lean | odd_neg_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.103565\nα : Type u_1\nβ : Type ?u.103571\nR : Type ?u.103574\ninst✝ : Ring α\na b : α\nn : ℕ\n⊢ Odd (-1)",
"tactic": "simp"
}
] | [
440,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.invFun_monomial | [] | [
151,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Combinatorics/Catalan.lean | gosper_catalan_sub_eq_central_binom_div | [
{
"state_after": "n : ℕ\nthis : ↑n + 1 ≠ 0\n⊢ gosperCatalan (n + 1) (n + 1) - gosperCatalan (n + 1) 0 = ↑(Nat.centralBinom (n + 1)) / (↑n + 2)",
"state_before": "n : ℕ\n⊢ gosperCatalan (n + 1) (n + 1) - gosperCatalan (n + 1) 0 = ↑(Nat.centralBinom (n + 1)) / (↑n + 2)",
"tactic": "have : (n : ℚ) + 1 ≠ 0 ... | [
118,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
9
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_add | [
{
"state_after": "case ofFinsupp\nR : Type u\na b✝ : R\nm n : ℕ\ninst✝ : Semiring R\np q b : R[X]\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ ({ toFinsupp := toFinsupp✝ } + b).toFinsupp = { toFinsupp := toFinsupp✝ }.toFinsupp + b.toFinsupp",
"state_before": "R : Type u\na✝ b✝ : R\nm n : ℕ\ninst✝ : Semiring R\np q... | [
215,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_jacobi | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L N\ninst... | [
217,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.id_comp | [] | [
347,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Topology/CompactOpen.lean | QuotientMap.continuous_lift_prod_left | [
{
"state_after": "X₀ : Type u_1\nX : Type u_2\nY : Type u_3\nZ : Type u_4\ninst✝⁴ : TopologicalSpace X₀\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : LocallyCompactSpace Y\nf : X₀ → X\nhf : QuotientMap f\ng : X × Y → Z\nhg : Continuous fun p => g (f p.fst, p.snd... | [
489,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.one_le_prod_of_one_le | [
{
"state_after": "case nil\nι : Type ?u.105808\nα : Type ?u.105811\nM : Type u_1\nN : Type ?u.105817\nP : Type ?u.105820\nM₀ : Type ?u.105823\nG : Type ?u.105826\nR : Type ?u.105829\ninst✝⁴ : Monoid M\ninst✝³ : Monoid N\ninst✝² : Monoid P\nl✝ l₁ l₂ : List M\na : M\ninst✝¹ : Preorder M\ninst✝ : CovariantClass M ... | [
371,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/List/MinMax.lean | List.maximum_nil | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.toFun_eq_coe | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_max | [] | [
307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_tsum_of_ne_zero_bij | [] | [
580,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | ball_mul | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ ball x δ * s = x • thickening δ s",
"tactic": "rw [mul_comm, mul_ball]"
}
] | [
243,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
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