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/Order/SymmDiff.lean | himp_bihimp_eq_inf | [] | [
307,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.to_rightInverse | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.10275\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nhf : AntilipschitzWith K f\ng : β → α\nhg : Function.RightInverse g f\nx y : β\n⊢ edist (g x) (g y) ≤ ↑K * edist x y",
"state_befor... | [
163,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.iInter_compl_mem_nhds | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.8425\nα : Type ?u.8428\nX : Type u_2\nY : Type ?u.8434\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g : ι → Set X\nhf : LocallyFinite f\nhc : ∀ (i : ι), IsClosed (f i)\nx : X\n⊢ IsOpen (⋂ (i : ι) (_ : ¬x ∈ f i), f iᶜ)",
"state_before": "ι : Type u_... | [
149,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.shiftl_to_nat | [
{
"state_after": "case zero\nα : Type ?u.621708\nn : ℕ\n⊢ ↑0 = Nat.shiftl (↑zero) n\n\ncase pos\nα : Type ?u.621708\nn : ℕ\na✝ : PosNum\n⊢ ↑(pos (PosNum.shiftl a✝ n)) = Nat.shiftl (↑(pos a✝)) n",
"state_before": "α : Type ?u.621708\nm : Num\nn : ℕ\n⊢ ↑(shiftl m n) = Nat.shiftl (↑m) n",
"tactic": "cases ... | [
964,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_inj | [] | [
66,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
66,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.IsComplement'.index_eq_card | [] | [
515,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_eq_of_rank_eq | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nn : ℕ\nh : ↑toNat (Module.rank K V) = ↑toNat ↑n\n⊢ finrank K V = n",
"state_before": "K : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCom... | [
68,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ico.nonneg | [] | [
221,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.compExactValue_correctness_of_stream_eq_some_aux_comp | [
{
"state_after": "K : Type u_1\ninst✝¹ : LinearOrderedField K\nv : K\nn : ℕ\ninst✝ : FloorRing K\na b c : K\nfract_a_ne_zero : Int.fract a ≠ 0\n⊢ ↑⌊a⌋ * b + c + b * Int.fract a = b * a + c",
"state_before": "K : Type u_1\ninst✝¹ : LinearOrderedField K\nv : K\nn : ℕ\ninst✝ : FloorRing K\na b c : K\nfract_a_n... | [
85,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.topologicalClosure_coe | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_inter_Ioc | [
{
"state_after": "α : Type u_1\nβ : Type ?u.186303\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioi a₁ ∩ Iic b₁ ∩ (Ioi a₂ ∩ Iic b₂) = Ioi a₁ ∩ Ioi a₂ ∩ (Iic b₁ ∩ Iic b₂)",
"state_before": "α : Type u_1\nβ : Type ?u.186303\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder ... | [
1788,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1787,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_normalizer_comap | [
{
"state_after": "G : Type u_2\nG' : Type ?u.390813\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.390822\ninst✝¹ : AddGroup A\nH K : Subgroup G\nN : Type u_1\ninst✝ : Group N\nf : N →* G\nx : N\n⊢ (∀ (h : G), h ∈ H ↔ ↑f x * h * (↑f x)⁻¹ ∈ H) → ∀ (h : N), ↑f h ∈ H ↔ ↑f (x * h * x⁻¹) ∈ H",
"state_before":... | [
2216,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2212,
1
] |
Mathlib/Algebra/Star/Pointwise.lean | Set.inter_star | [] | [
79,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.eval_maximal₁ | [
{
"state_after": "σ : Type u_1\nf : σ → Option σ\na b : σ\nh : b ∈ eval f a\nc : σ\nx✝ : Reaches₁ f b c\nbc : Reaches₁ f b c := x✝\nleft✝ : Reaches f a b\nb0 : f b = none\n⊢ False",
"state_before": "σ : Type u_1\nf : σ → Option σ\na b : σ\nh : b ∈ eval f a\nc : σ\nx✝ : Reaches₁ f b c\nbc : Reaches₁ f b c :=... | [
858,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.sub_left | [] | [
143,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | isPrimePow_iff_card_support_factorization_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2961\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n : ℕ\n⊢ IsPrimePow n ↔ Finset.card (Nat.factorization n).support = 1",
"tactic": "simp_rw [isPrimePow_iff_factorization_eq_single, Finsupp.card_support_eq_one', exists_prop,\n pos_iff_ne_zero]"
... | [
64,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csSup_mem | [
{
"state_after": "case h.e'_4\ns : Set ℤ\nh1 : Set.Nonempty s\nh2 : BddAbove s\n⊢ sSup s = ↑(greatestOfBdd (choose h2) (_ : choose h2 ∈ upperBounds s) h1)",
"state_before": "s : Set ℤ\nh1 : Set.Nonempty s\nh2 : BddAbove s\n⊢ sSup s ∈ s",
"tactic": "convert (greatestOfBdd _ (Classical.choose_spec h2) h1)... | [
101,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.colLen_anti | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\nj1 j2 : ℕ\nhj : j1 ≤ j2\n⊢ colLen μ j2 ≤ colLen μ j1",
"tactic": "convert μ.transpose.rowLen_anti j1 j2 hj using 1 <;> simp"
}
] | [
397,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.Functor.pentagon | [
{
"state_after": "no goals",
"state_before": "A : Type u₁\ninst✝⁴ : Category A\nB : Type u₂\ninst✝³ : Category B\nC : Type u₃\ninst✝² : Category C\nD : Type u₄\ninst✝¹ : Category D\nE : Type u₅\ninst✝ : Category E\nF : A ⥤ B\nG : B ⥤ C\nH : C ⥤ D\nK : D ⥤ E\n⊢ whiskerRight (associator F G H).hom K ≫ (associ... | [
292,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Prod/TProd.lean | List.TProd.snd_mk | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.map_map | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | irreducible_pow_sup_of_ge | [
{
"state_after": "R : Type ?u.924933\nA : Type ?u.924936\nK : Type ?u.924939\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\nT : Type u_1\ninst✝² : CommRing T\ninst✝¹ : IsDomain T\ninst✝ : IsDedekindDomain T\nI J : Ideal T\nhI : I ≠ ⊥\nhJ : Irreducible J\nn : ℕ\nhn : multiplici... | [
961,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_smul_eq | [
{
"state_after": "case intro\nR : Type u_1\nR₂ : Type ?u.149702\nK : Type ?u.149705\nM : Type u_2\nM₂ : Type ?u.149711\nV : Type ?u.149714\nS : Type ?u.149717\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddComm... | [
453,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_diff_sphere | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.37806\nι : Type ?u.37809\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ closedBall x ε \\ sphere x ε = ball x ε",
"tactic": "rw [← ball_union_sphere, Set.union_diff_cancel_right sphere_disjoint_ball.s... | [
565,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.inr_fst' | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nb : BinaryBicone X Y\nh : BinaryBicone.IsBilimit b\n⊢ IsPullback 0 b.inr 0 b.fst",
"state_before": "C : Type u₁\ninst✝² : Category C\... | [
598,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Order/CompleteLattice.lean | Antitone.map_sSup_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nβ₂ : Type ?u.85499\nγ : Type ?u.85502\nι : Sort ?u.85505\nι' : Sort ?u.85508\nκ : ι → Sort ?u.85513\nκ' : ι' → Sort ?u.85518\ninst✝¹ : CompleteLattice α\nf✝ g s✝ t : ι → α\na b : α\ninst✝ : CompleteLattice β\ns : Set α\nf : α → β\nhf : Antitone f\n⊢ f (⨆ (a : α) (_ ... | [
1027,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/ModelTheory/Basic.lean | Equiv.toFun_inducedStructureEquiv | [] | [
1048,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_true | [] | [
1444,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_refl_restr' | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.48613\nδ : Type ?u.48616\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set β\n⊢ e.source ∩ ↑e ⁻¹' s = e.source ∩ (e.source ∩ ↑e ⁻¹' s)",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.48613\nδ : Type ?u.48616\ne : LocalEquiv α β\ne' : Local... | [
768,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp_contDiffWithinAt | [] | [
729,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | existsUnique_zsmul_near_of_pos' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : Archimedean α\na : α\nha : 0 < a\ng : α\n⊢ ∃! k, 0 ≤ g - k • a ∧ g - k • a < a",
"tactic": "simpa only [sub_nonneg, add_zsmul, one_zsmul, sub_lt_iff_lt_add'] using\n existsUnique_zsmul_near_of_pos ... | [
82,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_sq | [] | [
101,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.mem_uIcc' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.200961\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ a ∈ [[b, c]] ↔ b ≤ a ∧ a ≤ c ∨ c ≤ a ∧ a ≤ b",
"tactic": "simp [uIcc_eq_union]"
}
] | [
1009,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.inf | [] | [
3001,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2999,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr_nhdsWithin | [] | [
107,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.of_pseudoEMetricSpace | [
{
"state_after": "α : Type ?u.57133\nβ : Type ?u.57136\ninst✝³ : MeasurableSpace α\ninst✝² : TopologicalSpace α\nμ✝ : Measure α\np q : Set α → Prop\nU✝ s : Set α\nε r✝ : ℝ≥0∞\nX : Type u_1\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : MeasurableSpace X\nμ : Measure X\nU : Set X\nhU : IsOpen U\nr : ℝ≥0∞\nhr : r < ↑↑μ ... | [
448,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.disjoint_def | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.30416\nA : Type ?u.30419\ninst✝¹ : MulOneClass M\ns : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS p₁ p₂ : Submonoid M\n⊢ Disjoint p₁ p₂ ↔ ∀ {x : M}, x ∈ p₁ → x ∈ p₂ → x = 1",
"tactic": "simp_rw [disjoint_iff_inf_le, SetLike.le_def, ... | [
564,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : AddGroup α\ninst✝² : LinearOrder α\ninst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\na b c : α\ninst✝ : CovariantClass α α (swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ -a < b ∧ a < b ↔ -b < a ∧ a < b",
"t... | [
200,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.nonUnitalAlgHom_ext | [] | [
674,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_neg_cancel_right | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a + b + -b = a",
"tactic": "rw [Int.add_assoc, Int.add_right_neg, Int.add_zero]"
}
] | [
324,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
323,
11
] |
Mathlib/Algebra/Order/SMul.lean | bddBelow_smul_iff_of_pos | [] | [
291,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_charFn | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iff_tendstoLocallyUniformly_comp_coe | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\n⊢ (∀ (x : { a // a ∈ s }), Tendsto ((fun y => (f y.snd, F y.fst y.snd)) ∘ Prod.map id Subtype.val) (p ×ˢ �... | [
634,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/SetTheory/Cardinal/SchroederBernstein.lean | Function.Embedding.schroeder_bernstein | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nf : α → β\ng : β → α\nhf : Injective f\nhg : Injective g\nhβ : IsEmpty β\n⊢ ∃ h, Bijective h\n\ncase inr\nα : Type u\nβ : Type v\nf : α → β\ng : β → α\nhf : Injective f\nhg : Injective g\nhβ : Nonempty β\n⊢ ∃ h, Bijective h",
"state_before": "α : Type u\nβ... | [
78,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_concat | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\n⊢ reverse\n (match p x with\n | true => x :: takeWhile p (reverse l)\n | false => []) =\n if p x = true then reverse (takeWhile p (reverse l)) ++ [x] else []",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn... | [
203,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.inv_map_iSup | [] | [
520,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.id_apply | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.eq_of_le_of_finrank_eq | [] | [
710,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec2_eq | [
{
"state_after": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nb₀ b₁ : α\n⊢ ![b₀, b₁] = ![b₀, b₁]",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\na₀ a₁ b₀ b₁ : α\nh₀ : a₀ = b₀\nh₁ : a₁ = b₁\n⊢ ![a₀, a₁] = ![b₀, b₁]",
"tactic": "su... | [
461,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.isEmpty_of_colorable_zero | [
{
"state_after": "case false\nV : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nh : Colorable G 0\n⊢ V → False",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\nh : Colorable G 0\n⊢ IsEmpty V",
"tactic": "constructor"
},
{
"state_after": "case false\nV : ... | [
155,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/LinearAlgebra/Matrix/Polynomial.lean | Polynomial.coeff_det_X_add_C_card | [
{
"state_after": "n : Type u_1\nα : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : CommRing α\nA B : Matrix n n α\n⊢ ∑ b : Equiv.Perm n, coeff (↑sign b • ∏ i : n, (X • Matrix.map A ↑C + Matrix.map B ↑C) (↑b i) i) (Fintype.card n) =\n ∑ σ : Equiv.Perm n, ↑sign σ • ∏ i : n, A (↑σ i) i",
"sta... | [
97,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.is_greatest' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nm : ℕ\nh : Finite a b\nhm : Part.get (multiplicity a b) h < m\n⊢ multiplicity a b < ↑m",
"tactic": "rwa [← PartENat.coe_lt_coe, PartENat.natCast_get] at hm"
}
] | [
122,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/Convex/Integral.lean | ConcaveOn.average_mem_hypograph | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.731861\nm0 : MeasurableSpace α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nμ : MeasureTheory.Measur... | [
131,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_natAbs_of_zero_le | [
{
"state_after": "a : Int\nh : 0 ≤ a\nn : Nat\ne : a = ↑n\n⊢ a = ↑(natAbs a)",
"state_before": "a : Int\nh : 0 ≤ a\n⊢ a = ↑(natAbs a)",
"tactic": "let ⟨n, e⟩ := eq_ofNat_of_zero_le h"
},
{
"state_after": "a : Int\nh : 0 ≤ a\nn : Nat\ne : a = ↑n\n⊢ ↑n = ↑(natAbs ↑n)",
"state_before": "a : Int... | [
730,
14
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
728,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Pi.summable | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.799420\nγ : Type ?u.799423\nδ : Type ?u.799426\nι : Type u_3\nπ : α → Type u_2\ninst✝¹ : (x : α) → AddCommMonoid (π x)\ninst✝ : (x : α) → TopologicalSpace (π x)\nf : ι → (x : α) → π x\n⊢ Summable f ↔ ∀ (x : α), Summable fun i => f i x",... | [
1318,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.source_inter_preimage_inv_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.33320\nδ : Type ?u.33323\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set α\nx : α\nhx : x ∈ e.source\n⊢ x ∈ ↑e ⁻¹' (↑(LocalEquiv.symm e) ⁻¹' s) ↔ x ∈ s",
"tactic": "simp only [mem_preimage, e.left_inv hx]"
}
] | [
516,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.subtype_Iio_eq | [] | [
1350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/Topology/ContinuousOn.lean | tendsto_nhdsWithin_congr | [] | [
446,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.toContinuousMap_apply | [] | [
142,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_apply | [] | [
1031,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
11
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_le_norm | [] | [
1116,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_mem_pointwise_smul_iff | [] | [
340,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Computability/Partrec.lean | Computable.sum_inl | [] | [
338,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_star | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝² : Star R\ninst✝¹ : AddMonoid A\ninst✝ : StarAddMonoid A\nr : R\n⊢ snd (inl (star r)) = snd (star (inl r))",
"tactic": "simp only [snd_star, star_zero, snd_inl]"
}
] | [
538,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.CompClosure.of | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝ : Category C\nr : HomRel C\na b : C\nm₁ m₂ : a ⟶ b\nh : r m₁ m₂\n⊢ CompClosure r m₁ m₂",
"tactic": "simpa using CompClosure.intro (𝟙 _) m₁ m₂ (𝟙 _) h"
}
] | [
71,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.le_of_eq_of_le | [] | [
749,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.quotientInfEquivQuotientProd_fst | [] | [
519,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_unique | [] | [
642,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_cons | [] | [
87,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/Order/Ring/Canonical.lean | mul_add_mul_lt_mul_add_mul | [
{
"state_after": "case intro\nα : Type u\nβ : Type ?u.10176\ninst✝¹ : StrictOrderedSemiring α\na c d : α\ninst✝ : ExistsAddOfLE α\nhcd : c < d\nb : α\nhab : a < a + b\n⊢ a * d + (a + b) * c < a * c + (a + b) * d",
"state_before": "α : Type u\nβ : Type ?u.10176\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\... | [
74,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_submatrix_equiv | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.398160\nm : Type u\nn : Type u'\nα : Type v\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\ninst✝² : CommRing α\nA✝ B : Matrix n n α\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nA : Matrix m m α\ne₁ e₂ : n ≃ m\n⊢ IsUnit (submatrix A ↑e₁ ↑e₂) ↔ IsUnit A",... | [
675,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_assoc' | [] | [
767,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_typein | [
{
"state_after": "α : Type ?u.341106\nβ : Type ?u.341109\nγ : Type ?u.341112\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nh : (lsub fun i => typein (fun x x_1 => x < x_1) i) < o\n⊢ False",
"state_before": "α : Type ?u.341106\nβ : Type ?u.341109\nγ : Type ?u.341112\nr : α → α → Prop\ns... | [
1724,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1718,
1
] |
Mathlib/Algebra/AddTorsor.lean | vadd_right_cancel | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nP : Type u_1\ninst✝ : AddGroup G\nT : AddTorsor G P\ng1 g2 : G\np : P\nh : g1 +ᵥ p = g2 +ᵥ p\n⊢ g1 = g2",
"tactic": "rw [← vadd_vsub g1 p, h, vadd_vsub]"
}
] | [
103,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | one_lt_pow | [
{
"state_after": "β : Type ?u.223542\nA : Type ?u.223545\nG : Type ?u.223548\nM : Type ?u.223551\nR : Type u_1\ninst✝ : OrderedSemiring R\na x y : R\nn✝ m : ℕ\nha : 1 < a\nn : ℕ\nx✝ : n + 1 ≠ 0\n⊢ 1 < a * a ^ n",
"state_before": "β : Type ?u.223542\nA : Type ?u.223545\nG : Type ?u.223548\nM : Type ?u.223551... | [
475,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Std/Data/Option/Lemmas.lean | Option.join_eq_none | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\no : Option (Option α✝)\nval✝ : α✝\n⊢ join (some (some val✝)) = none ↔ some (some val✝) = none ∨ some (some val✝) = some none",
"tactic": "simp"
}
] | [
117,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
116,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendsto_prod_top_iff | [
{
"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\nc : β\n⊢ Tendsto (↿F) (p ×ˢ ⊤) (𝓝 c) ↔ TendstoUniformlyOnFilter F (fun x => c) p ⊤",
"state_before": "α : Type u\nβ : Type v\nγ : ... | [
343,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_insert | [
{
"state_after": "α : Type u_1\nβ : Type ?u.114651\nE : Type ?u.114654\nF : Type ?u.114657\nG : Type ?u.114660\nE' : Type u_2\nF' : Type u_3\nG' : Type ?u.114669\nE'' : Type ?u.114672\nF'' : Type ?u.114675\nG'' : Type ?u.114678\nR : Type ?u.114681\nR' : Type ?u.114684\n𝕜 : Type ?u.114687\n𝕜' : Type ?u.114690\... | [
680,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.GradesBy.decompose_single | [] | [
212,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.mem_sections | [
{
"state_after": "case empty\nα : Type u_1\n⊢ ∀ {a : Multiset α}, a ∈ Sections 0 ↔ Rel (fun s a => a ∈ s) 0 a\n\ncase cons\nα : Type u_1\na✝¹ : Multiset α\ns✝ : Multiset (Multiset α)\na✝ : ∀ {a : Multiset α}, a ∈ Sections s✝ ↔ Rel (fun s a => a ∈ s) s✝ a\n⊢ ∀ {a : Multiset α}, a ∈ Sections (a✝¹ ::ₘ s✝) ↔ Rel (f... | [
66,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.stepAux_move | [
{
"state_after": "Γ : Type u_3\ninst✝² : Inhabited Γ\nΛ : Type u_2\ninst✝¹ : Inhabited Λ\nσ : Type u_1\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nd : Dir\nq : Stmt Bool Λ' σ\nv : σ\nT : Tape Bool\nthis : ∀ (i : ℕ), stepAux ((Stmt.move d^[i]) q) v T = stepAux q v ((Tape.move d... | [
1707,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1700,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.lt_base_pow_length_digits' | [
{
"state_after": "case h.e'_3\nn b m : ℕ\n⊢ m = ofDigits (b + 2) (digits (b + 2) m)",
"state_before": "n b m : ℕ\n⊢ m < (b + 2) ^ List.length (digits (b + 2) m)",
"tactic": "convert @ofDigits_lt_base_pow_length' b (digits (b + 2) m) fun _ => digits_lt_base'"
},
{
"state_after": "no goals",
"... | [
418,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Tactic/Positivity/Basic.lean | Mathlib.Meta.Positivity.mul_ne_zero_of_pos_of_ne_zero | [] | [
126,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
9
] |
Mathlib/Data/Finset/Basic.lean | Finset.toList_insert | [] | [
3414,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3412,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.IsConnected.of_constant_of_preserves_morphisms | [
{
"state_after": "case as\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : Nonempty J\nh : ∀ {α : Type u₁} (F : J → α), (∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → F j₁ = F j₂) → ∀ (j j' : J), F j = F j'\nx✝ : Type u₁\nF : J ⥤ Discrete x✝\nj₁✝ j₂✝ : J\nf : j₁✝ ⟶ j₂✝\n⊢ (F.obj j₁✝).as = (F.obj j₂✝).a... | [
144,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.isIso_arrow_iff_eq_top | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX Y✝ Z : C\nD : Type u₂\ninst✝ : Category D\nY : C\nP : Subobject Y\n⊢ IsIso (arrow P) ↔ P = ⊤",
"tactic": "rw [isIso_iff_mk_eq_top, mk_arrow]"
}
] | [
268,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.count_map_roots | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b✝ : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝² : CommRing A\ninst✝¹ : CommRing B\ninst✝ : IsDomain A\np : A[X]\nf : A →+* B\nhmap : map f p ≠ 0\nb : B\n⊢ Multiset.prod\n (Multiset.map (fun a => X - ↑C a) (Multiset.replicate (Multiset.count b (Multi... | [
1170,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousLinearMap.compContinuousMultilinearMap_coe | [
{
"state_after": "case h\nR : Type u\nι : Type v\nn : ℕ\nM : Fin (Nat.succ n) → Type w\nM₁ : ι → Type w₁\nM₁' : ι → Type w₁'\nM₂ : Type w₂\nM₃ : Type w₃\nM₄ : Type w₄\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝¹⁶ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝¹⁵ : (i : ι) → AddC... | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.one_one | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_le_of_one_le | [] | [
661,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.filter_lt_lt_eq_Ioo | [
{
"state_after": "case a\nι : Type ?u.35376\nα : Type u_1\ninst✝³ : Preorder α\ninst✝² : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\ninst✝¹ : Fintype α\ninst✝ : DecidablePred fun j => a < j ∧ j < b\na✝ : α\n⊢ a✝ ∈ filter (fun j => a < j ∧ j < b) univ ↔ a✝ ∈ Ioo a b",
"state_before": "ι : Type ?u.35376\nα... | [
369,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.of_results_bind | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns✝ : Computation α\nf : α → Computation β\nb : β\ns : Computation α\ne : α\nh : Results (bind (pure e) f) b Nat.zero\n⊢ ∃ a m n, Results (pure e) a m ∧ Results (f a) b n ∧ Nat.zero = n + m\n\nα : Type u\nβ : Type v\nγ : Type w\ns✝ : Computation α\nf : α → Co... | [
845,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_strictMono | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.155987\nβ : Type ?u.155990\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx✝ : 1 ≠ 0\n⊢ StrictMono fun x => x ^ 1",
"tactic": "simpa only [pow_one] using strictMono_id"
}
] | [
986,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.prod_map | [] | [
1157,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Ideal.Quotient.torsionBy_eq_span_singleton | [
{
"state_after": "case h\nR✝ : Type ?u.707004\nM : Type ?u.707007\nR : Type w\ninst✝ : CommRing R\na b : R\nha : a ∈ R⁰\nx : R ⧸ Submodule.span R {a * b}\n⊢ x ∈ torsionBy R (R ⧸ Submodule.span R {a * b}) a ↔ x ∈ Submodule.span R {↑(mk (Submodule.span R {a * b})) b}",
"state_before": "R✝ : Type ?u.707004\nM ... | [
824,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Expr.eq_of_toNormPoly_eq | [
{
"state_after": "ctx : Context\ne e' : Expr\nh✝ : (toNormPoly e == toPoly e') = true\nh : Poly.denote ctx (toNormPoly e) = Poly.denote ctx (toPoly e')\n⊢ denote ctx e = denote ctx e'",
"state_before": "ctx : Context\ne e' : Expr\nh : (toNormPoly e == toPoly e') = true\n⊢ denote ctx e = denote ctx e'",
... | [
723,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
720,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.Semiconj.mapsTo_fixedPoints | [] | [
160,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_iff_singleton | [] | [
2362,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2361,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | isBounded_le_atBot | [] | [
69,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.isCountablyGenerated_principal | [] | [
1177,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
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