file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Calculus/Deriv/Inv.lean | Differentiable.div | [] | [
229,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/PathConnected.lean | Path.extend_extends | [] | [
268,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_gt_eq | [] | [
32,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_closure_one_iff_norm | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.463871\n𝕜 : Type ?u.463874\nα : Type ?u.463877\nι : Type ?u.463880\nκ : Type ?u.463883\nE : Type u_1\nF : Type ?u.463889\nG : Type ?u.463892\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁... | [
1129,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_map_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.28728\nι : Sort ?u.28731\ns : Set α\nt : Set β\nf✝ : Filter α\ng : Filter β\nf : α → β\nF : Filter α\nG : Filter γ\n⊢ map f F ×ˢ G = map (Prod.map f id) (F ×ˢ G)",
"tactic": "rw [← prod_map_map_eq', map_i... | [
357,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Algebra/IsPrimePow.lean | isPrimePow_nat_iff | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.81638\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n : ℕ\n⊢ IsPrimePow n ↔ ∃ p k, Nat.Prime p ∧ 0 < k ∧ p ^ k = n",
"tactic": "simp only [isPrimePow_def, Nat.prime_iff]"
}
] | [
80,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.eq_empty_of_isEmpty | [] | [
639,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.eq_formalMultilinearSeries_of_eventually | [] | [
1023,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Combinatorics/SimpleGraph/Acyclic.lean | SimpleGraph.isTree_iff_existsUnique_path | [
{
"state_after": "V : Type u\nG : SimpleGraph V\n⊢ (Connected G ∧ ∀ ⦃v w : V⦄ (p q : Path G v w), p = q) ↔ Nonempty V ∧ ∀ (v w : V), ∃! p, Walk.IsPath p",
"state_before": "V : Type u\nG : SimpleGraph V\n⊢ IsTree G ↔ Nonempty V ∧ ∀ (v w : V), ∃! p, Walk.IsPath p",
"tactic": "rw [IsTree_iff, isAcyclic_iff... | [
152,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | PiToModule.fromEnd_apply | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toOpen_comp_comap | [] | [
1218,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.mono_right | [] | [
198,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.finsetEquivSet_symm_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.136843\nγ : Type ?u.136846\ninst✝¹ : Fintype α\ns : Set α\ninst✝ : Fintype ↑s\n⊢ Set.toFinset s = Set.toFinset s",
"state_before": "α : Type u_1\nβ : Type ?u.136843\nγ : Type ?u.136846\ninst✝¹ : Fintype α\ns : Set α\ninst✝ : Fintype ↑s\n⊢ ↑finsetEquivSet.symm s = ... | [
1055,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Logic/Unique.lean | Unique.default_eq | [] | [
150,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Subsingleton.intersecting | [] | [
99,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
11
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.mem_inv_pointwise_smul_iff₀ | [] | [
541,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.range_finsuppTotal | [
{
"state_after": "case h\nι : Type u_3\nM : Type u_1\ninst✝² : AddCommGroup M\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Module R M\nI : Ideal R\nv : ι → M\nhv : Submodule.span R (Set.range v) = ⊤\nx✝ : M\n⊢ x✝ ∈ LinearMap.range (finsuppTotal ι M I v) ↔ x✝ ∈ I • Submodule.span R (Set.range v)",
"state_befo... | [
1924,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1912,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.subtypeRestr_source | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.115242\nδ : Type ?u.115245\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : TopologicalSpace δ\ne : LocalHomeomorph α β\ns : Opens α\ninst✝ : Nonempty { x // x ∈ s }\n⊢ (subt... | [
1379,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.inseparable_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.226694\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ Inseparable x y ↔ edist x y = 0",
"tactic": "simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']"
}
] | [
735,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.two_le_card_support_of_ne_one | [] | [
605,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.coe_zero | [] | [
355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.Infinitesimal.eq_zero | [] | [
688,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_bind | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.5024\nβ✝ : Type ?u.5027\nγ✝ : Type ?u.5030\nδ : Type ?u.5033\np : α✝ → Prop\nf✝ : (a : α✝) → p a → β✝\nx✝ : Option α✝\nα β γ : Type u_1\nf : β → γ\nx : Option α\ng : α → Option β\n⊢ Option.map f (x >>= g) = do\n let a ← x\n Option.map f (g a)"... | [
150,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_le_of_forall_add_lt | [
{
"state_after": "a b c : Ordinal\nhb : 0 < b\nh : ∀ (d : Ordinal), d < b → a + d < c\nH : a + (c - a) = c\n⊢ a + b ≤ c",
"state_before": "a b c : Ordinal\nhb : 0 < b\nh : ∀ (d : Ordinal), d < b → a + d < c\n⊢ a + b ≤ c",
"tactic": "have H : a + (c - a) = c :=\n Ordinal.add_sub_cancel_of_le\n (by\n ... | [
2505,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2495,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.append_copy_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' v' w' : V\np : Walk G u' v'\nq : Walk G v' w'\n⊢ append (Walk.copy p (_ : u' = u') (_ : v' = v')) (Walk.copy q (_ : v' = v') (_ : w' = w')) =\n Walk.copy (append p q) (_ : u' = u') (_ : ... | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Init/Algebra/Order.lean | le_imp_le_of_lt_imp_lt | [] | [
418,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/Algebra/Field.lean | IsPreconnected.eq_or_eq_neg_of_sq_eq | [
{
"state_after": "K : Type ?u.21895\ninst✝⁷ : DivisionRing K\ninst✝⁶ : TopologicalSpace K\nα : Type u_2\n𝕜 : Type u_1\nf g : α → 𝕜\nS : Set α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : T1Space 𝕜\ninst✝² : Field 𝕜\ninst✝¹ : HasContinuousInv₀ 𝕜\ninst✝ : ContinuousMul 𝕜\nhS : IsPrec... | [
151,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prod_pow_prime_padicValNat | [
{
"state_after": "n : ℕ\nhn : n ≠ 0\nm : ℕ\npr : n < m\n⊢ ∏ p in Finset.filter Prime (Finset.range m), p ^ padicValNat p n = Finsupp.prod (factorization n) fun x x_1 => x ^ x_1",
"state_before": "n : ℕ\nhn : n ≠ 0\nm : ℕ\npr : n < m\n⊢ ∏ p in Finset.filter Prime (Finset.range m), p ^ padicValNat p n = n",
... | [
939,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Combinatorics/Hindman.lean | Hindman.FP.finset_prod | [
{
"state_after": "M : Type u_1\ninst✝ : CommMonoid M\na : Stream' M\ns : Finset ℕ\nhs : Finset.Nonempty s\n⊢ (Finset.prod s fun i => Stream'.nth a i) ∈ FP (Stream'.drop (Finset.min' s hs) a)",
"state_before": "M : Type u_1\ninst✝ : CommMonoid M\na : Stream' M\ns : Finset ℕ\nhs : Finset.Nonempty s\n⊢ (Finset... | [
302,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.is_basis | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7918\nσ : Type ?u.7921\nτ : Type ?u.7924\nT : TopologicalSpace α\nF : Realizer α\nthis : TopologicalSpace.IsTopologicalBasis (range F.F.f)\n⊢ TopologicalSpace.IsTopologicalBasis (range F.F.f)",
"state_before": "α : Type u_1\nβ : Type ?u.7918\nσ : Type ?u.7921\nτ :... | [
132,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
11
] |
Mathlib/Data/Nat/Pow.lean | Nat.one_lt_two_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nh₀ : 0 < n\n⊢ 1 < 2",
"tactic": "decide"
}
] | [
97,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasLimitOfIso | [
{
"state_after": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F G : J ⥤ C\ninst✝ : HasLimit F\nα : F ≅ G\ns : Cone G\nj : J\n⊢ ((Cones.postcompose α.inv).obj s).π.app j ≫ α.hom.app j = s.π.app j",
"state_before": "J : Type u₁\ninst✝³ : Category J\n... | [
330,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.RightInverse.leftInverse_of_surjective | [] | [
381,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/RingTheory/SimpleModule.lean | isSimpleModule_iff_isAtom | [
{
"state_after": "R : Type u_1\ninst✝⁴ : Ring R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nm : Submodule R M\nN : Type ?u.14646\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\n⊢ IsSimpleModule R { x // x ∈ m } ↔ IsSimpleOrder ↑(Set.Iic m)",
"state_before": "R : Type u_1\ninst✝⁴ : Ring R\nM :... | [
74,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_pow | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_const_le | [] | [
118,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.isBoundedUnder_le_atBot | [] | [
74,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finiteDimensional_of_rank_eq_nat | [
{
"state_after": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nn : ℕ\nh : Module.rank K V = ↑n\n⊢ ↑n < ℵ₀",
"state_before": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nn : ℕ\nh : Module.rank K V = ↑n\n⊢ Finit... | [
640,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.ne_zero_of_mem_rootSet | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\np✝ q : R[X]\ninst✝³ : CommRing T\np : T[X]\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra T S\na : S\nh : a ∈ rootSet p S\nhf : p = 0\n⊢ False",
"tacti... | [
962,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.reflectsEpimorphisms.iso_iff | [] | [
175,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Quot.lean | surjective_quotient_mk | [] | [
349,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.smul_apply | [] | [
838,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.listTransvecCol_mul_last_row | [
{
"state_after": "no goals",
"state_before": "n : Type ?u.155183\np : Type ?u.155186\nR : Type u₂\n𝕜 : Type u_1\ninst✝³ : Field 𝕜\ninst✝² : DecidableEq n\ninst✝¹ : DecidableEq p\ninst✝ : CommRing R\nr : ℕ\nM : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\ni : Fin r ⊕ Unit\n⊢ (List.prod (listTransvecCol M) ⬝ M)... | [
375,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_eq_trim | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10446\nγ : Type ?u.10449\nδ : Type ?u.10452\nι : Type ?u.10455\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t s : Set α\n⊢ ↑↑μ s = ↑(OuterMeasure.trim ↑μ) s",
"tactic": "rw [μ.trimmed]"
}
] | [
155,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.right_inl | [] | [
125,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_congr | [] | [
977,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mem_iff_mem | [] | [
317,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mkSpanSingleton'_apply | [
{
"state_after": "R : Type u_2\ninst✝⁶ : Ring R\nE : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.69603\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nx : E\ny : F\nH : ∀ (c : R), c • x = 0 → c • y = 0\nc : R\nh : c • x ∈ (mkSpanS... | [
163,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.bowtie | [
{
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432,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
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Mathlib/Data/Set/Prod.lean | Set.prod_sub_preimage_iff | [
{
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] | [
329,
83
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328,
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Mathlib/Order/Lattice.lean | Monotone.map_inf | [] | [
1127,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_erase | [
{
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639,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.normalize_monic | [
{
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] | [
461,
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461,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.monotone_approx | [] | [
846,
45
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Mathlib/Data/Multiset/Bind.lean | Multiset.card_join | [
{
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},
{
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77,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_map | [
{
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_le_false | [] | [
753,
39
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751,
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Mathlib/Data/Set/Image.lean | Function.Injective.preimage_surjective | [
{
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Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_neg_of_ne_half | [
{
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1025,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
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Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_eq_same | [] | [
242,
29
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241,
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.of_constant_on_preconnected_clopens | [] | [
236,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_neg_iff | [
{
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},
{
"state_after": "no goals",
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191,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.prod_rightl | [] | [
958,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.Subtype.volume_univ | [
{
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1457,
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1452,
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Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_add_const_Ioc | [] | [
102,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.memberSubfamily_memberSubfamily | [
{
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119,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_congr_mono | [
{
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1808,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1806,
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Mathlib/Data/Int/Parity.lean | Int.even_add_one | [
{
"state_after": "no goals",
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] | [
136,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
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Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.SeparationQuotient.uniformContinuous_map | [] | [
401,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.foldlM_eq_foldlM_toList | [
{
"state_after": "no goals",
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}
] | [
354,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
352,
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Mathlib/Topology/MetricSpace/Baire.lean | dense_sUnion_interior_of_closed | [] | [
342,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_div_iff_right | [
{
"state_after": "no goals",
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}
] | [
716,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_add | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹ : Ring R\nm : ℕ\ninst✝ : CharP R m\nh : m ∣ Nat.zero\na b : ZMod Nat.zero\n⊢ ↑(a + b) = ↑a + ↑b\n\ncase succ\nR : Type u_1\ninst✝¹ : Ring R\nm : ℕ\ninst✝ : CharP R m\nn✝ : ℕ\nh : m ∣ Nat.succ n✝\na b : ZMod (Nat.succ n✝)\n⊢ ↑(a + b) = ↑a + ↑b",
"state_before... | [
308,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.induction_on | [
{
"state_after": "case refine'_1\nk : Type u₁\nG : Type u₂\nR : Type ?u.2138330\ninst✝¹ : Semiring k\ninst✝ : AddMonoid G\np : AddMonoidAlgebra k G → Prop\nf : AddMonoidAlgebra k G\nhM : ∀ (g : G), p (↑(of k G) (↑Multiplicative.ofAdd g))\nhadd : ∀ (f g : AddMonoidAlgebra k G), p f → p g → p (f + g)\nhsmul : ∀ (... | [
1679,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
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Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_disjoint | [] | [
164,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Ioc | [] | [
570,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_X | [] | [
523,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Data/Matrix/Basic.lean | IsLeftRegular.matrix | [] | [
390,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Atoms.lean | OrderIso.isSimpleOrder | [] | [
823,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_add_edgeDensity_compl | [
{
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393,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
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Mathlib/Topology/Bases.lean | TopologicalSpace.isOpen_iUnion_countable | [
{
"state_after": "α : Type u\nt : TopologicalSpace α\ninst✝ : SecondCountableTopology α\nι : Type u_1\ns : ι → Set α\nH : ∀ (i : ι), IsOpen (s i)\nB : Set (Set α) := {b | b ∈ countableBasis α ∧ ∃ i, b ⊆ s i}\n⊢ ∃ T, Set.Countable T ∧ (⋃ (i : ι) (_ : i ∈ T), s i) = ⋃ (i : ι), s i",
"state_before": "α : Type ... | [
731,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
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Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousWithinAt_const | [] | [
716,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
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] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_three_mul | [
{
"state_after": "x y : ℝ\n⊢ ↑(cos (3 * x)) = ↑(4 * cos x ^ 3 - 3 * cos x)",
"state_before": "x y : ℝ\n⊢ cos (3 * x) = 4 * cos x ^ 3 - 3 * cos x",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cos (3 * x)) = ↑(4 * cos x ^ 3 - 3 * cos x)",
"ta... | [
1333,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
8
] |
Mathlib/Algebra/Star/Module.lean | IsSelfAdjoint.selfAdjointPart_apply | [] | [
147,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.ball_infDist_subset_compl | [] | [
542,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.closure_neg | [
{
"state_after": "case a\nα : Type ?u.12121\nR : Type u_2\nM : Type u_1\ninst✝² : Semiring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ns : Set M\n⊢ span R (-s) ≤ -span R s\n\ncase a\nα : Type ?u.12121\nR : Type u_2\nM : Type u_1\ninst✝² : Semiring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ns : Set M\n⊢... | [
113,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.card_support_ne_one | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : f = 1\n⊢ card (support f) ≠ 1\n\ncase neg\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : ¬f = 1\n⊢ card (support f) ≠ 1",
"state_before": "α : Type u_1\ninst✝¹ : Decidabl... | [
595,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/List/Basic.lean | List.foldrRecOn_cons | [] | [
2585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2580,
1
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Mathlib/Analysis/Calculus/Series.lean | tendstoUniformlyOn_tsum_nat | [] | [
62,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_diagonal | [] | [
148,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.exists_inv | [
{
"state_after": "case mk\nR : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na✝¹ b : R\nS : Type v\nx y : R\nI : Ideal R\nhI : IsMaximal I\na✝ : R ⧸ I\na : R\nh : Quot.mk Setoid.r a ≠ 0\n⊢ ∃ b, Quot.mk Setoid.r a * b = 1",
"state_before": "R : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nx y :... | [
210,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_lt_of_lt | [] | [
639,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_comp_apply | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1251098\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1251104\ninst✝¹² : Semiring R''\nM : Type u_3\nN : Type u_2\nP : Type u_5\nQ : Type u_4\nS : Type ?u.1251122\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ ... | [
1081,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.image_of_comp | [
{
"state_after": "ι✝ : Type ?u.747618\nι'✝ : Type ?u.747621\nR : Type u_3\nK : Type ?u.747627\nA : Type u_4\nA' : Type ?u.747633\nA'' : Type ?u.747636\nV : Type u\nV' : Type ?u.747641\nx : ι✝ → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra R A\ninst✝¹... | [
319,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_mul_right' | [] | [
72,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/PFun.lean | PFun.toSubtype_apply | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.embedding_comp_inv | [
{
"state_after": "n : ℕ\nc : Composition n\nj : Fin n\n⊢ ↑(↑(embedding c (index c j)) (invEmbedding c j)) = ↑j",
"state_before": "n : ℕ\nc : Composition n\nj : Fin n\n⊢ ↑(embedding c (index c j)) (invEmbedding c j) = j",
"tactic": "rw [Fin.ext_iff]"
},
{
"state_after": "no goals",
"state_bef... | [
375,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_pair_le_left | [] | [
159,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.next_reverse_eq_prev | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns : Cycle α\nhs : Nodup s\nx : α\nhx : x ∈ s\n⊢ next (reverse s) (_ : Nodup (reverse s)) x (_ : x ∈ reverse s) = prev s hs x hx",
"tactic": "simp [← prev_reverse_eq_next]"
}
] | [
861,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | sigmaFinsuppEquivDfinsupp_single | [
{
"state_after": "case mk\nι : Type u_1\nR : Type ?u.70785\nM : Type ?u.70788\nη : ι → Type u_3\nN : Type u_2\ninst✝² : Semiring R\ninst✝¹ : DecidableEq ι\ninst✝ : Zero N\nn : N\ni : ι\na : η i\n⊢ ↑sigmaFinsuppEquivDfinsupp (single { fst := i, snd := a } n) =\n Dfinsupp.single { fst := i, snd := a }.fst (sin... | [
336,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
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