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/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.ext_iff | [] | [
827,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_eq_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.21180\nγ : Type ?u.21183\na b : α\nas bs : Multiset α\nthis : DecidableEq α\n⊢ a ::ₘ as = b ::ₘ bs ↔ a = b ∧ as = bs ∨ a ≠ b ∧ ∃ cs, as = b ::ₘ cs ∧ bs = a ::ₘ cs",
"state_before": "α : Type u_1\nβ : Type ?u.21180\nγ : Type ?u.21183\na b : α\nas bs : Multiset α\n⊢... | [
313,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Left.mul_lt_mul | [] | [
193,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_pred_left | [] | [
746,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.inl.inj_iff | [] | [
156,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/QuasiSeparated.lean | IsQuasiSeparated.of_subset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.18691\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns t : Set α\nht : IsQuasiSeparated t\nh : s ⊆ t\nU V : Set α\nhU : U ⊆ s\nhU' : IsOpen U\nhU'' : IsCompact U\nhV : V ⊆ s\nhV' : IsOpen V\nhV'' : IsCompact V\n⊢ IsCompact (U ∩ V)",
"state_be... | [
114,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | Pi.exp_apply | [] | [
553,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.step_invRev_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nh : Step (FreeGroup.invRev L₁) (FreeGroup.invRev L₂)\n⊢ Step L₁ L₂",
"tactic": "simpa only [invRev_invRev] using h.invRev"
}
] | [
631,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarAlgHom.map_adjoin | [] | [
755,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.mem_neighborSet | [] | [
222,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.fderivWithin | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.68931\ninst✝¹... | [
115,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.iUnion_inter_closedBall_nat | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.43642\nι : Type ?u.43645\ninst✝ : PseudoMetricSpace α\nx✝ y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ s : Set α\nx : α\n⊢ (⋃ (n : ℕ), s ∩ closedBall x ↑n) = s",
"tactic": "rw [← inter_iUnion, iUnion_closedBall_nat, inter_univ]"
}
] | [
657,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | isComplete_iff_ultrafilter' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\n⊢ (∀ (l : Ultrafilter α), Cauchy ↑l → ↑l ≤ 𝓟 s → ∃ x, x ∈ s ∧ ↑l ≤ 𝓝 x) ↔\n ∀ (l : Ultrafilter α), Cauchy ↑l → s ∈ l → ∃ x, x ∈ s ∧ ↑l ≤ 𝓝 x",
"tactic": "simp only [le_principal_iff, Ultrafilte... | [
335,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Order/Basic.lean | left_nhdsWithin_Ioc_neBot | [] | [
2434,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2433,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iSup_add_iSup_le | [
{
"state_after": "α : Type ?u.138674\nβ : Type ?u.138677\nγ : Type ?u.138680\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Sort u_1\nι' : Sort u_2\ninst✝¹ : Nonempty ι\ninst✝ : Nonempty ι'\nf : ι → ℝ≥0∞\ng : ι' → ℝ≥0∞\na : ℝ≥0∞\nh : ∀ (i : ι) (j : ι'), f i + g j ≤ a\n⊢ (⨆ (b : ι) (b_1 :... | [
599,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.inv_sup | [] | [
186,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.rtendsto_iff_le_rcomap | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nr : Rel α β\nl₁ : Filter α\nl₂ : Filter β\n⊢ (∀ (s : Set β), s ∈ l₂ → Rel.core r s ∈ l₁) ↔ l₁ ≤ rcomap r l₂",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nr : Rel α β\nl₁ : Filter α\nl₂ : Filter β\n⊢ RTendsto r l₁ l₂ ↔ l₁ ≤ rcomap r l₂",
"tac... | [
139,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.toSubgraph_cons_nil_eq_subgraphOfAdj | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\nh : Adj G u v\n⊢ Walk.toSubgraph (cons h nil) = subgraphOfAdj G h",
"tactic": "simp"
}
] | [
2227,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2226,
1
] |
Std/Data/List/Lemmas.lean | List.mem_map_of_mem | [] | [
160,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
160,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add_comm | [
{
"state_after": "case c\nR : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\ny : OreLocalization R S\nr✝ : R\ns✝ : { x // x ∈ S }\n⊢ r✝ /ₒ s✝ + y = y + r✝ /ₒ s✝",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nx y : OreLocalization R S\n⊢ x + y = y ... | [
682,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
11
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt_one_div_of_neg_of_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.178065\nα : Type u_1\nβ : Type ?u.178071\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhb : b < 0\nh : a < b\n⊢ 1 / b < 1 / a",
"tactic": "rwa [div_lt_iff_of_neg' hb, ← div_eq_mul_one_div, div_lt_one_of_neg (h.trans hb)]"
}
] | [
871,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.self_symm_id_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nβ : X ≅ Z\n⊢ α ≪≫ α.symm ≪≫ β = β",
"tactic": "rw [← trans_assoc, self_symm_id, refl_trans]"
}
] | [
218,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_lt_ceil_of_lt | [] | [
1228,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_le_chainHeight_TFAE | [
{
"state_after": "case tfae_1_iff_3\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LT α\ninst✝ : LT β\ns✝ t✝ : Set α\nl : List α\na : α\ns : Set α\nt : Set β\n⊢ chainHeight s ≤ chainHeight t ↔ ∀ (l : List α), l ∈ subchain s → ∃ l', l' ∈ subchain t ∧ length l ≤ length l'\n\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LT α\ninst... | [
198,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Topology/Basic.lean | clusterPt_iff | [] | [
1095,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.range_fst | [] | [
955,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Compatibility.lean | AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eq | [
{
"state_after": "case w.w.h\nA : Type u_1\nA' : Type u_5\nB : Type u_4\nB' : Type u_6\ninst✝³ : Category A\ninst✝² : Category A'\ninst✝¹ : Category B\ninst✝ : Category B'\neA : A ≌ A'\neB : B ≌ B'\ne' : A' ≌ B'\nF : A ⥤ B'\nhF : eA.functor ⋙ e'.functor ≅ F\nG : B ⥤ A\nhG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.func... | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_inv | [] | [
1802,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1800,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_div' | [] | [
543,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.coe_toOrderEmbedding | [] | [
228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.not_isUnit | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nq : ℤ[X]\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nu v w : ℤˣ\n⊢ ¬IsUnit (trinomial k m n ↑u ↑v ↑w)",
"state_before": "p q : ℤ[X]\nhp : IsUnitTrinomial p\n⊢ ¬IsUnit p",
"tactic": "obtain ⟨k, m, n, hkm, hmn, u, v, w, rfl⟩ := hp"
},
{... | [
146,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_mul_right_of_neg | [] | [
1147,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.inf_left_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : BoundedOrder α\na b x y z : α\nh : IsCompl y z\n⊢ x ⊓ y = ⊥ ↔ x ≤ z",
"tactic": "rw [← le_bot_iff, ← h.le_sup_right_iff_inf_left_le, bot_sup_eq]"
}
] | [
522,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.isCompact | [] | [
473,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
11
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.trans_sbtw_left | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.288204\nP : Type u_3\nP' : Type ?u.288210\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : NoZeroSMulDivisors R V\nw x y z : ... | [
485,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/CategoryTheory/Subobject/WellPowered.lean | CategoryTheory.essentiallySmall_monoOver_iff_small_subobject | [] | [
61,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.RedRed.of_red | [] | [
141,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
139,
11
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_neg | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.19834\nι : Type ?u.19837\nα : Type u_1\nβ : Type ?u.19843\ninst✝ : DivisionRing α\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : Nat.coprime (Int.natAbs n) d\n⊢ ↑(-mk' n d) = -↑(mk' n d)",
"tactic": "simpa only [cast_def] using\n show (↑(-n) / d : α) = -(n / d) ... | [
127,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.erase_image_subset_image_erase | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.90806\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt : Finset β\na✝ : α\nb c : β\ninst✝ : DecidableEq α\nf : α → β\ns : Finset α\na : α\n⊢ ∀ ⦃x : β⦄, x ≠ f a → ∀ (x_1 : α), x_1 ∈ s → f x_1 = x → ∃ a_4, (a_4 ≠ a ∧ a_4 ∈ s) ∧ f a_4 = x",
"stat... | [
513,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_u_l_eq_l | [] | [
209,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_zero | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mkHom_f_succ_succ | [
{
"state_after": "ι : Type ?u.344304\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nP Q : CochainComplex V ℕ\nzero : HomologicalComplex.X P 0 ⟶ HomologicalComplex.X Q 0\none : HomologicalComplex.X P 1 ⟶ HomologicalComplex.X Q 1\none_zero_comm : zero ≫ HomologicalComplex.d Q 0 1 = HomologicalCompl... | [
1114,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_congr | [
{
"state_after": "α✝ : Type ?u.79050\nβ : Type u_2\nγ : Type ?u.79056\nι : Type ?u.79059\ninst✝¹ : ConditionallyCompleteLattice α✝\nα : Type u_1\ninst✝ : ConditionallyCompleteLattice β\nf : Filter α\nu v : α → β\nh : ∀ᶠ (a : α) in f, u a = v a\n⊢ sInf {a | ∀ᶠ (n : α) in f, u n ≤ a} = limsup v f",
"state_bef... | [
575,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Std/Data/List/Lemmas.lean | List.mem_filterMap | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\nf : α → Option β\nb : β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : b ∈ filterMap f tail✝ ↔ ∃ a, a ∈ tail✝ ∧ f a = some b\n⊢ (b ∈\n match f head✝ with\n | none => filterMap f tail✝\n | some b => b :: filterMap f tail✝) ↔\n f head✝ = some b ∨ ... | [
1209,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1207,
9
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsWf.insert | [] | [
483,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_insert_insert_insert_left_of_mem_affineSpan_pair | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.331367\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ p₅ : P\nh₁ : p₁ ∈ affineSpan k {p₄, p₅}\nh₂ : p₂ ∈ affineSpan k {p₄, p₅}\nh₃ : p₃ ∈ affineSpan k {p₄, p₅}\n⊢ {p₁, p₂, p₃, p₄... | [
590,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.coe_list_prod | [] | [
114,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/MetricSpace/CauSeqFilter.lean | CauchySeq.isCauSeq | [
{
"state_after": "case intro\nβ : Type v\ninst✝ : NormedField β\nf : ℕ → β\nhf : CauchySeq f\nhf1 : NeBot (map f atTop)\nhf2 : ∀ (s : Set (β × β)), s ∈ uniformity β → ∃ t, t ∈ map f atTop ∧ t ×ˢ t ⊆ s\n⊢ IsCauSeq norm f",
"state_before": "β : Type v\ninst✝ : NormedField β\nf : ℕ → β\nhf : CauchySeq f\n⊢ IsC... | [
66,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finsum_mul | [] | [
1198,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Data/List/Zip.lean | List.lt_length_right_of_zip | [] | [
110,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_false | [] | [
316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_eq_top | [] | [
672,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_pos_of_nonneg | [] | [
223,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.inv_mul_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c u : αˣ\na : α\nb : αˣ\n⊢ a * ↑b⁻¹ * ↑b = a",
"tactic": "rw [mul_assoc, inv_mul, mul_one]"
}
] | [
303,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.init_update_last | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni : Fin n\ny : α (↑castSucc i)\nz : α (last n)\nj : Fin n\n⊢ init (update q (last n) z) j = init q j",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last ... | [
559,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.sclosure_preimage_le | [] | [
924,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.coe_toNatLinearEquiv | [] | [
806,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | NormedSpace.noncompactSpace | [] | [
446,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
11
] |
Mathlib/Topology/Separation.lean | exists_open_between_and_isCompact_closure | [
{
"state_after": "case intro.intro.intro\nα : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\nγ : Type ?u.141701\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : LocallyCompactSpace α\ninst✝ : T2Space α\nK U : Set α\nhK : IsCompact K\nhU : IsOpen U\nhKU : K ⊆ U\nV : Set α\nhV : IsCompact V\n... | [
1429,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_div_cancel_left_of_imp | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.10733\nM₀ : Type ?u.10736\nG₀ : Type u_1\nM₀' : Type ?u.10742\nG₀' : Type ?u.10745\nF : Type ?u.10748\nF' : Type ?u.10751\ninst✝¹ : MonoidWithZero M₀\ninst✝ : CommGroupWithZero G₀\na✝ b✝ c d a b : G₀\nh : a = 0 → b = 0\n⊢ a * b / a = b",
"tactic"... | [
164,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.forget_obj | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Computability/Halting.lean | ComputablePred.halting_problem | [] | [
240,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulReflectLT_iff_mulPosReflectLT | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : CommSemigroup α\ninst✝¹ : Zero α\ninst✝ : Preorder α\n⊢ PosMulReflectLT α ↔ MulPosReflectLT α",
"tactic": "simp only [PosMulReflectLT, MulPosReflectLT, mul_comm]"
}
] | [
1035,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.comp_id | [] | [
468,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mk_sub_mk | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_mul_self_real | [
{
"state_after": "𝕜 : Type ?u.2403269\nE : Type ?u.2403272\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\nh : ‖x + y‖ * ‖x + y‖ = ‖x‖ * ‖x‖ + 2 * ↑re (inner x y) + ‖... | [
1060,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Data/List/Count.lean | List.count_filter | [
{
"state_after": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\np : α → Bool\na : α\nh : p a = true\n⊢ countp (fun a_1 => decide ((a_1 == a) = true ∧ p a_1 = true)) l = countp (fun x => x == a) l",
"state_before": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\np : α → Bool\na : α\nh : p a = true\n⊢ co... | [
318,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.dirac_apply' | [] | [
1982,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1981,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_le | [] | [
474,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.mul | [] | [
146,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/Valuation/ExtendToLocalization.lean | Valuation.extendToLocalization_apply_map_apply | [] | [
56,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTriv_source | [] | [
704,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isTrail_def | [] | [
869,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.id_comp | [] | [
767,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
src/lean/Init/Core.lean | Quotient.ind₂ | [
{
"state_after": "case a\na b c d : Prop\nα : Sort uA\nβ : Sort uB\nφ : Sort uC\ns₁ : Setoid α\ns₂ : Setoid β\nmotive : Quotient s₁ → Quotient s₂ → Prop\nh : ∀ (a : α) (b : β), motive (Quotient.mk s₁ a) (Quotient.mk s₂ b)\nq₂ : Quotient s₂\na✝ : α\n⊢ motive (Quotient.mk s₁ a✝) q₂",
"state_before": "a b c d ... | [
1452,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1444,
11
] |
Mathlib/Combinatorics/Colex.lean | Colex.empty_toColex_lt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nA : Finset α\nhA : Finset.Nonempty A\n⊢ ∃ k, (∀ {x : α}, k < x → (x ∈ ∅ ↔ x ∈ A)) ∧ ¬k ∈ ∅ ∧ k ∈ A",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA : Finset α\nhA : Finset.Nonempty A\n⊢ toColex ∅ < toColex A",
"tactic": "rw [Colex.lt_def]"
... | [
343,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_of_left_mem | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.114846\nP : Type u_3\nP' : Type ?u.114852\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y : P\n... | [
256,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | DifferentiableWithinAt.hasDerivWithinAt | [] | [
429,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | dslope_eventuallyEq_slope_punctured_nhds | [] | [
67,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.iff_card | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fintype G\nhG : card G ≠ 0\n⊢ IsPGroup p G ↔ ∃ n, card G = p ^ n",
"state_before": "p : ℕ\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fintype G\n⊢ IsPGroup p G ↔ ∃ n, card G = p ^ n",
... | [
70,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_le_toReal | [
{
"state_after": "case intro\nα : Type ?u.795291\nβ : Type ?u.795294\nb c d : ℝ≥0∞\nr p q : ℝ≥0\nhb : b ≠ ⊤\na : ℝ≥0\n⊢ ENNReal.toReal ↑a ≤ ENNReal.toReal b ↔ ↑a ≤ b",
"state_before": "α : Type ?u.795291\nβ : Type ?u.795294\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ ⊤\nhb : b ≠ ⊤\n⊢ ENNReal.toReal a ≤ ENNReal.t... | [
1987,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1984,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.subsumes_self | [] | [
89,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.finite_coproduct_eq_finset_sup | [
{
"state_after": "α : Type u\nJ : Type w\ninst✝⁴ : SmallCategory J\ninst✝³ : FinCategory J\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\nι : Type u\ninst✝ : Fintype ι\nf : ι → α\n⊢ (∐ f) = ?m.37163\n\nα : Type u\nJ : Type w\ninst✝⁴ : SmallCategory J\ninst✝³ : FinCategory J\ninst✝² : SemilatticeSup α\ninst✝¹ ... | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.comp_monotoneOn_right | [] | [
364,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/List/Nodup.lean | List.inj_on_of_nodup_map | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na b : α\nf : α → β\nl : List α\nd✝ : Nodup (map f l)\nd : Nodup (map f [])\n⊢ ∀ ⦃x : α⦄, x ∈ [] → ∀ ⦃y : α⦄, y ∈ [] → f x = f y → x = y\n\ncase cons\nα : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na b : α\nf :... | [
259,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.mem_mk | [] | [
116,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.Paths.lift_unique | [
{
"state_after": "V : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category C\nΦ : Paths V ⥤ C\n⊢ Φ = lift (of ⋙q Φ.toPrefunctor)",
"state_before": "V : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category C\nφ : V ⥤q C\nΦ : Paths V ⥤ C\nhΦ : of ⋙q Φ.toPrefunctor = φ\n⊢ Φ = lift φ",
"tactic":... | [
122,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.lof_eq_of | [] | [
75,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Disjoint.lean | eq_bot_of_top_isCompl | [] | [
642,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.comap_eq | [
{
"state_after": "case a\nα : Type u\nβ : Type u_1\nγ : Type ?u.419491\nδ : Type ?u.419494\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : UniformSpace δ\nh : α ≃ᵤ β\n⊢ uniformity α = uniformity α",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.419491\nδ : Type ?... | [
247,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHom_refl | [] | [
630,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_pow_lt_one_div_pow_of_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.123201\nα : Type u_1\nβ : Type ?u.123207\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm✝ n✝ : ℤ\na1 : 1 < a\nm n : ℕ\nmn : m < n\n⊢ 1 / a ^ n < 1 / a ^ m",
"tactic": "refine' (one_div_lt_one_div _ _).mpr (pow_lt_pow a1 mn) <;> exact pow_pos ... | [
624,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Nat/Cast/Field.lean | Nat.cast_div_div_div_cancel_right | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : DivisionSemiring α\ninst✝ : CharZero α\nm n : ℕ\nhn : 0 ∣ n\nhm : 0 ∣ m\n⊢ ↑(m / 0) / ↑(n / 0) = ↑m / ↑n\n\ncase inr\nα : Type u_1\ninst✝¹ : DivisionSemiring α\ninst✝ : CharZero α\nm n d : ℕ\nhn : d ∣ n\nhm : d ∣ m\nhd : d ≠ 0\n⊢ ↑(m / d) / ↑(n / d) = ↑m / ↑n",... | [
47,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/Chain.lean | chainClosure_maxChain | [] | [
211,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_zero | [] | [
80,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.eval₂_reflect_mul_pow | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝² : Semiring R\nf✝ : R[X]\nS : Type u_2\ninst✝¹ : CommSemiring S\ni : R →+* S\nx : S\ninst✝ : Invertible x\nN : ℕ\nf : R[X]\nhf : natDegree f ≤ N\n⊢ (fun f => eval₂ i (⅟x) (reflect N f) * x ^ N = eval₂ i x f) 0\n\ncase refine'_2\nR : Type u_1\ninst✝² : Semiri... | [
231,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_eq_self_of_subset_left | [] | [
809,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.ι_biproductComparison' | [] | [
253,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | isOpenMap_smul | [] | [
250,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq_mk'_iff_mul_eq | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.784401\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx : M\ny : { x // x ∈ S }\nz : N\nH : z = mk' f x y\n⊢ z * ↑(toMap f) ↑y = ↑(toMap f) x",
"tactic": ... | [
754,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
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