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/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.lift_index_left_left | [
{
"state_after": "case a\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : ¬f ≈ 0\nv2 v3 : ℕ\n⊢ stationaryPoint hf ≤ max (stationaryPoint hf) (max v2 v3)\n\ncase a\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : ¬f ≈ 0\nv2 v3 : ℕ\n⊢ stationaryPoint hf ≤ stationaryPoint hf",
"state_before": "... | [
183,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/RingTheory/Adjoin/Tower.lean | exists_subalgebra_of_fg | [
{
"state_after": "case intro\nR : Type u\nS : Type v\nA : Type w\nB : Type u₁\nC : Type u_1\ninst✝⁶ : CommSemiring A\ninst✝⁵ : CommSemiring B\ninst✝⁴ : Semiring C\ninst✝³ : Algebra A B\ninst✝² : Algebra B C\ninst✝¹ : Algebra A C\ninst✝ : IsScalarTower A B C\nhBC : FG ⊤\nx : Finset C\nhx : Algebra.adjoin A ↑x = ... | [
147,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_biUnion_finset₀ | [
{
"state_after": "α : Type u_2\nβ : Type ?u.12040\nγ : Type ?u.12043\nδ : Type ?u.12046\nι : Type u_1\nR : Type ?u.12052\nR' : Type ?u.12055\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : Finset ι\nf : ι → Set α\nhd : Set.Pairwise (↑s) (AEDisjoint μ on f)\nhm : ∀ (b : ι), b ∈ s → NullMeasu... | [
187,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.toList_injective | [
{
"state_after": "no goals",
"state_before": "V : Type u\ninst✝¹ : Quiver V\na✝ b c✝ d : V\ninst✝ : ∀ (a b : V), Subsingleton (a ⟶ b)\na c : V\np : Path a c\nf : c ⟶ a\nh : toList nil = toList (cons p f)\n⊢ nil = cons p f",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": ... | [
195,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_def_module | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_univ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : TopologicalSpace α\nβ : Type u_2\ninst✝ : Preorder β\nf g : α → β\nx : α\ns t : Set α\ny z : β\n⊢ UpperSemicontinuousOn f univ ↔ UpperSemicontinuous f",
"tactic": "simp [UpperSemicontinuousOn, UpperSemicontinuous, upperSemicontinuousWi... | [
695,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_lt_of_neg_lt | [
{
"state_after": "a b : Int\nh✝ : -a < b\nh : -b < - -a\n⊢ -b < a",
"state_before": "a b : Int\nh : -a < b\n⊢ -b < a",
"tactic": "have h := Int.neg_lt_neg h"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : -a < b\nh : -b < - -a\n⊢ -b < a",
"tactic": "rwa [Int.neg_neg] at... | [
916,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
914,
11
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.nfpBFamily_lt_ord_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.163687\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nho : card o < c\nhc' : c ≠ ℵ₀\nhf : ∀ (i : Ordinal) (hi : i < o) (b : Ordinal), b < ord c → f i hi b < ord c\na : Ordinal\n⊢ lift (c... | [
1148,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.tail_update_zero | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\ni : Fin n\ny : α (succ i)\nz : α 0\nj : Fin n\n⊢ tail (update q 0 z) j = tail q j",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α 0\nq : (i : Fin (n + 1)) → α i\np : (... | [
223,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_singleton | [] | [
935,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.not_surjective_Type | [
{
"state_after": "α✝ : Sort ?u.9302\nβ : Sort ?u.9305\nγ : Sort ?u.9308\nf✝ : α✝ → β\nα : Type u\nf : α → Type (max u v)\nhf : Surjective f\n⊢ False",
"state_before": "α✝ : Sort ?u.9302\nβ : Sort ?u.9305\nγ : Sort ?u.9308\nf✝ : α✝ → β\nα : Type u\nf : α → Type (max u v)\n⊢ ¬Surjective f",
"tactic": "int... | [
303,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.eq_div_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.57889\nG : Type ?u.57892\nα : Type u_1\nM : Type ?u.57898\nN : Type ?u.57901\ninst✝ : DivisionMonoid α\na b c : α\nh : IsUnit c\n⊢ a = b / c ↔ a * c = b",
"tactic": "rw [div_eq_mul_inv, h.eq_mul_inv_iff_mul_eq]"
}
] | [
418,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
11
] |
Mathlib/Data/Finset/Lattice.lean | Finset.exists_min_image | [] | [
1703,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_injective | [] | [
176,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.eq_image_iff_symm_image_eq | [] | [
84,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.coeff_eval_eq_eval_coeff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.1195723\na a' a₁ a₂ : R\ne : ℕ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\ns' : Fin n → R\nf : (MvPolynomial (Fin n) R)[X]\ni : ℕ\n⊢ Polynomial.coeff (Polynomial.map (eval s') f) i = ↑(eval s') (Poly... | [
418,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | norm_zsmul | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.4110\nβ : Type u_2\nγ : Type ?u.4116\nι : Type ?u.4119\ninst✝³ : NormedField α✝\ninst✝² : SeminormedAddCommGroup β\nα : Type u_1\ninst✝¹ : NormedField α\ninst✝ : NormedSpace α β\nn : ℤ\nx : β\n⊢ ‖n • x‖ = ‖↑n‖ * ‖x‖",
"tactic": "rw [← norm_smul,... | [
70,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.IsComplete.realize_sentence_iff | [
{
"state_after": "case inl\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nh : IsComplete T\nφ : Sentence L\nM : Type u_1\ninst✝² : Structure L M\ninst✝¹ : M ⊨ T\ninst✝ : Nonempty M\nhφ : T ⊨ᵇ φ\n⊢ M ⊨ φ ↔ T ⊨ᵇ φ\n\ncase inr\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nh : IsComplete T\nφ : Sentence L\nM : T... | [
385,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_pos | [] | [
747,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
11
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.coe_zero | [] | [
569,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.24533\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.24545\ninst✝³ : Top α\ninst✝² : Top β\ninst✝¹ : Top γ\ninst✝ : Top δ\ng : TopHom β γ\nf₁ f₂ : TopHom α β\nhg : Injective ↑g\nh : comp g f₁ = comp g f₂\na : α\n⊢ ↑g (↑f₁ a) = ↑g (↑f₂ a)",
... | [
294,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_len | [
{
"state_after": "case h\nn✝¹ b n✝ : ℕ\nhb : 1 < b\nhn✝ : n✝ ≠ 0\nn : ℕ\nIH : ∀ (m : ℕ), m < n → m ≠ 0 → List.length (digits b m) = log b m + 1\nhn : n ≠ 0\n⊢ List.length (digits b n) = log b n + 1",
"state_before": "n✝ b n : ℕ\nhb : 1 < b\nhn : n ≠ 0\n⊢ List.length (digits b n) = log b n + 1",
"tactic"... | [
343,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.symm_trans | [] | [
142,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.range_coe | [] | [
220,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.ccosh | [] | [
201,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.Int.natAbs | [
{
"state_after": "case inl\nα : Type ?u.1342344\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na : ℕ\nb : ℤ\nh : b = ↑(_root_.Int.natAbs b)\n⊢ multiplicity a (_root_.Int.natAbs b) = multiplicity ↑a ↑(_root_.Int.natAbs b)\n\ncase inr\nα : Type ?u.1342344\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x... | [
434,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.coe_flipₗᵢ | [] | [
880,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_countable' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1727935\nγ : Type ?u.1727938\nδ : Type ?u.1727941\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : Countable α\ninst✝ : MeasurableSingletonClass α\nf : α → ℝ≥0∞\n⊢ (∑' (i : α), ∫⁻ (a : α), f a ∂↑↑μ {i} • dirac i) = ∑' (a : α), f a * ↑↑μ {a}",
"state_before": "α :... | [
1448,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/GroupTheory/Solvable.lean | solvable_of_ker_le_range | [
{
"state_after": "case mk.intro\nG : Type u_3\nG'✝ : Type ?u.45008\ninst✝³ : Group G\ninst✝² : Group G'✝\nf✝ : G →* G'✝\nG' : Type u_1\nG'' : Type u_2\ninst✝¹ : Group G'\ninst✝ : Group G''\nf : G' →* G\ng : G →* G''\nhfg : MonoidHom.ker g ≤ MonoidHom.range f\nhG' : IsSolvable G'\nhG'' : IsSolvable G''\nn : ℕ\nh... | [
150,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_zero | [
{
"state_after": "no goals",
"state_before": "𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝⁵ : Field 𝕂\ninst✝⁴ : Ring 𝔸\ninst✝³ : Algebra 𝕂 𝔸\ninst✝² : TopologicalSpace 𝔸\ninst✝¹ : TopologicalRing 𝔸\ninst✝ : T2Space 𝔸\n⊢ exp 𝕂 0 = 1",
"tactic": "simp_rw [exp_eq_tsum, ← expSeries_apply_eq, expSeries_apply_... | [
125,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.isLocalMax | [] | [
151,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | Nat.cast_bit0 | [] | [
176,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Order/SymmDiff.lean | Disjoint.symmDiff_left | [
{
"state_after": "ι : Type ?u.76942\nα : Type u_1\nβ : Type ?u.76948\nπ : ι → Type ?u.76953\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\nha : Disjoint a c\nhb : Disjoint b c\n⊢ Disjoint ((a ⊔ b) \\ (a ⊓ b)) c",
"state_before": "ι : Type ?u.76942\nα : Type u_1\nβ : Type ?u.76948\nπ : ι → Type ?u.76953\... | [
559,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
11
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.sInf_toAddSubmonoid | [] | [
688,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.mk_smul | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/Max.lean | isBot_ofDual_iff | [] | [
253,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.toWord_mk | [] | [
1308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.cylinder_eq_cylinder_of_le_firstDiff | [
{
"state_after": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nhn : n ≤ firstDiff x y\n⊢ x ∈ cylinder y n",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nhn : n ≤ firstDiff x y\n⊢ cylinder x n = cylinder y n",
"tactic": "rw [← mem_cylinder_iff_eq]"
},
{
"state_after": "E : ℕ → ... | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsLimit.nat_lt | [] | [
297,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalk_hom_ext | [
{
"state_after": "case mk\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y✝ Z : TopCat\nF : Presheaf C X\nx : ↑X\nY : C\nf₁ f₂ : stalk F x ⟶ Y\nih :\n ∀ (U : Opens ↑X) (hxU : x ∈ U), germ F { val := x, property := hxU } ≫ f₁ = germ F { val := x, property := hxU } ≫ f₂\nU : OpenNhds x\n⊢ colimit.ι (... | [
123,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | nonPrincipals_def | [] | [
479,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_add | [] | [
1711,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1710,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_principal_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.317533\nι : Sort x\nf : α → β\ns : Set α\nt : Set β\n⊢ Tendsto f (𝓟 s) (𝓟 t) ↔ ∀ (a : α), a ∈ s → f a ∈ t",
"tactic": "simp only [tendsto_principal, eventually_principal]"
}
] | [
3048,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3046,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.pointwise_smul_le_iff₀ | [] | [
471,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.mul_mem | [] | [
260,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
11
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.exists_orthogonal_basis | [
{
"state_after": "case zero\nS : Type ?u.672109\nR : Type ?u.672112\nR₁ : Type ?u.672115\nM : Type ?u.672118\ninst✝⁹ : Ring R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nV✝ : Type u\nK : Type v\ninst✝⁶ : Field K\ninst✝⁵ : AddCommGroup V✝\ninst✝⁴ : Module K V✝\ninst✝³ : FiniteDimensional K V✝\nhK : Invertible... | [
1127,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.223062\nβ : Type ?u.223065\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx✝ : ℝ≥0∞\n⊢ (x✝ ^ 0)⁻¹ = x✝⁻¹ ^ 0",
"tactic": "simp only [pow_zero, inv_one]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.223062\nβ : Type ?u.223065\na b c d :... | [
1378,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_mono' | [] | [
410,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.mul_inv_cancel | [
{
"state_after": "a b c : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\na0 : n /. ↑d ≠ 0\nn0 : n ≠ 0\n⊢ n /. ↑d * (n /. ↑d)⁻¹ = 1",
"state_before": "a b c : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\na0 : n /. ↑d ≠ 0\n⊢ n /. ↑d * (n /. ↑d)⁻¹ = 1",
"tactic": "have n0 : n ≠ 0 := mt (by rintro rfl; simp) a0"
},
{
"state_after": "n... | [
293,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
11
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_re_le | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | z.re ≤ a} = {z | z.re = a}",
"tactic": "simpa only [frontier_Iic] using frontier_preimage_re (Iic a)"
}
] | [
138,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/CompleteLattice.lean | ofDual_sInf | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_zero | [
{
"state_after": "no goals",
"state_before": "case some\nval✝ : ℝ≥0\n⊢ (if val✝ = 0 ∧ 0 < 0 then ⊤ else ↑(NNReal.rpow val✝ 0)) = 1",
"tactic": "simp [lt_irrefl]"
}
] | [
307,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec2_dotProduct | [] | [
496,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/Hom/Aut.lean | MulAut.mul_def | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | LinearMap.toMatrix_id_eq_basis_toMatrix | [
{
"state_after": "ι : Type u_1\nι' : Type u_2\nκ : Type ?u.583643\nκ' : Type ?u.583646\nR : Type u_3\nM : Type u_4\ninst✝¹² : CommSemiring R\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : Module R M\nR₂ : Type ?u.583839\nM₂ : Type ?u.583842\ninst✝⁹ : CommRing R₂\ninst✝⁸ : AddCommGroup M₂\ninst✝⁷ : Module R₂ M₂\ne : Basi... | [
230,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Iic | [
{
"state_after": "case h\nF : Type ?u.77511\nι : Type ?u.77514\nα : Type ?u.77517\nβ : Type ?u.77520\nK : Type u_1\ninst✝ : LinearOrderedField K\na x : ℚ\n⊢ x ∈ Rat.cast ⁻¹' Iic ↑a ↔ x ∈ Iic a",
"state_before": "F : Type ?u.77511\nι : Type ?u.77514\nα : Type ?u.77517\nβ : Type ?u.77520\nK : Type u_1\ninst✝ ... | [
401,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableWithinAt.const_cpow | [] | [
134,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concat_inj | [
{
"state_after": "case nil.nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v v' w : V\nh' h : Adj G v' w\nhe : concat nil h = concat nil h'\n⊢ ∃ hv, Walk.copy nil (_ : v' = v') hv = nil\n\ncase nil.cons\nV : Type u\nV' : Type v\nV'' : Type w\nG : Simp... | [
510,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_pwFilter | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.51574\nR S T : α → α → Prop\na : α\nl✝ : List α\ninst✝ : DecidableRel R\nx : α\nl : List α\nh : ∀ (y : α), y ∈ pwFilter R l → R x y\n⊢ Pairwise R (pwFilter R (x :: l))\n\ncase neg\nα : Type u_1\nβ : Type ?u.51574\nR S T : α → α → Prop\na : α\nl✝ : List α\nin... | [
412,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.Tendsto.inv_inv | [] | [
898,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
11
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.insert | [] | [
284,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
11
] |
Std/Data/Nat/Lemmas.lean | Nat.div_eq_of_lt_le | [
{
"state_after": "k n m : Nat\nlo : 0 ≤ m\nhi : m < 0\nhn : n = 0\n⊢ False",
"state_before": "k n m : Nat\nlo : k * n ≤ m\nhi : m < succ k * n\nhn : n = 0\n⊢ False",
"tactic": "rw [hn, Nat.mul_zero] at hi lo"
},
{
"state_after": "no goals",
"state_before": "k n m : Nat\nlo : 0 ≤ m\nhi : m < ... | [
606,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
601,
11
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.zero_max | [] | [
114,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.indicatorConstLp_coeFn_nmem | [] | [
745,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Topology/ContinuousFunction/Weierstrass.lean | polynomialFunctions_closure_eq_top' | [
{
"state_after": "⊢ ⊤ ≤ Subalgebra.topologicalClosure (polynomialFunctions I)",
"state_before": "⊢ Subalgebra.topologicalClosure (polynomialFunctions I) = ⊤",
"tactic": "apply eq_top_iff.mpr"
},
{
"state_after": "f : C(↑I, ℝ)\n⊢ f ∈ Subalgebra.topologicalClosure (polynomialFunctions I)",
"st... | [
47,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.list_cons | [] | [
1014,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Subset.refl | [] | [
343,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.Factors.finrank_pow_ramificationIdx | [
{
"state_after": "case he\nR : Type u\ninst✝⁵ : CommRing R\nS : Type v\ninst✝⁴ : CommRing S\nf : R →+* S\np : Ideal R\nP✝ : Ideal S\ninst✝³ : IsDomain S\ninst✝² : IsDedekindDomain S\ninst✝¹ : Algebra R S\ninst✝ : IsMaximal p\nP : { x // x ∈ Multiset.toFinset (factors (map (algebraMap R S) p)) }\n⊢ ramificationI... | [
735,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Complex.hasStrictDerivAt_cpow_const | [
{
"state_after": "no goals",
"state_before": "f g : ℂ → ℂ\ns : Set ℂ\nf' g' x c : ℂ\nh : 0 < x.re ∨ x.im ≠ 0\n⊢ HasStrictDerivAt (fun z => z ^ c) (c * x ^ (c - 1)) x",
"tactic": "simpa only [MulZeroClass.mul_zero, add_zero, mul_one] using\n (hasStrictDerivAt_id x).cpow (hasStrictDerivAt_const x c) h"
... | [
168,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.closedComplemented_top | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : Ring R\nM : Type u_2\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nM₂ : Type ?u.2068318\ninst✝² : TopologicalSpace M₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R M₂\nx : { x // x ∈ ⊤ }\n⊢ ↑(↑(codRestrict (Cont... | [
2589,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2588,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.mem_cons_of_mem | [] | [
195,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_prod_same | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.217515\ninst✝¹ : PseudoEMetricSpace α\nx✝ y✝ z✝ : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\ninst✝ : PseudoEMetricSpace β\nx : α\ny : β\nr : ℝ≥0∞\nz : α × β\n⊢ z ∈ ball x r ×ˢ ball y r ↔ z ∈ ball (x, y) r",
"tactic": "simp [Prod.edis... | [
710,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | AntilipschitzWith.le_mul_norm_div | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1214055\n𝕜 : Type ?u.1214058\nα : Type ?u.1214061\nι : Type ?u.1214064\nκ : Type ?u.1214067\nE : Type u_1\nF : Type u_2\nG : Type ?u.1214076\ninst✝² : SeminormedCommGroup E\ninst✝¹ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ninst✝ : ... | [
1911,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1910,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.coe_set_mk | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.Normal.mem_comm_iff | [] | [
1951,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1950,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Int.exists_sq_add_sq_add_one_eq_mul | [
{
"state_after": "case inl\nhp : Fact (Nat.Prime 2)\n⊢ ∃ a b k, 0 < k ∧ k < 2 ∧ a ^ 2 + b ^ 2 + 1 = k * 2\n\ncase inr\np : ℕ\nhp : Fact (Nat.Prime p)\nhodd : Odd p\n⊢ ∃ a b k, 0 < k ∧ k < p ∧ a ^ 2 + b ^ 2 + 1 = k * p",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ∃ a b k, 0 < k ∧ k < p ∧ a ^ 2 + b ^ ... | [
103,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.ι_map | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF : J ⥤ C\ninst✝ : HasColimitsOfShape J C\nG : J ⥤ C\nα : F ⟶ G\nj : J\n⊢ ι F j ≫ colim.map α = α.app j ≫ ι G j",
"tactic": "simp"
}
] | [
1105,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Topology/Category/TopCommRingCat.lean | TopCommRingCat.coe_of | [] | [
74,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.IsInitial.strict_hom_ext | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasStrictInitialObjects C\nI : C\nhI : IsInitial I\nA : C\nf g : A ⟶ I\nthis : IsIso f\n⊢ f = g",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasStrictInitialObjects C\nI : C\nhI : IsInitial I\nA : C\nf g : A ⟶ I\n⊢ f = g",
"tactic... | [
80,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | exists_disjoint_smul_of_isCompact | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : NoncompactSpace G\nK L : Set G\nhK : IsCompact K\nhL : IsCompact L\nA : ¬K * L⁻¹ = univ\n⊢ ∃ g, Disjoint K (g • L)",
"state_before": "α : Type u\nβ : Type v\n... | [
1634,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1624,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.inl_mem_disjSum | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ns : Multiset α\nt : Multiset β\ns₁ s₂ : Multiset α\nt₁ t₂ : Multiset β\na : α\nb : β\nx : α ⊕ β\n⊢ (∃ a_1, a_1 ∈ s ∧ inl a_1 = inl a) ↔ a ∈ s\n\nα : Type u_2\nβ : Type u_1\ns : Multiset α\nt : Multiset β\ns₁ s₂ : Multiset α\nt₁ t₂ : Multiset β\na : α\nb : β\nx : α ⊕... | [
63,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Control/ULift.lean | ULift.seq_up | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | HasDerivAt.inner | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.77069\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : NormedSpace ℝ E\nG : Type ?u.77198\ninst✝¹ : NormedAddComm... | [
124,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_le_iff | [] | [
1103,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/Logic/Basic.lean | ball_cond_comm | [] | [
501,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.isCauSeq_nthHom | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\nr : R\nε : ℚ\nhε : ε > 0\n⊢ ∃ i, ∀ (j : ℕ), j ≥ i → padicN... | [
517,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Analysis/ODE/Gronwall.lean | hasDerivAt_gronwallBound_shift | [
{
"state_after": "case h.e'_7\nE : Type ?u.20531\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.20627\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nδ K ε x a : ℝ\n⊢ K * gronwallBound δ K ε (x - a) + ε = (K * gronwallBound δ K ε (id x - a) + ε) * 1",
"state_before": "E : Typ... | [
79,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Ideal.torsionOf_eq_top_iff | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\nh : torsionOf R M m = ⊤\n⊢ m = 0",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\n⊢ torsionOf R M m = ⊤ ↔ m = 0",
... | [
98,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | le_neg_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.188008\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ a ≤ -a ↔ - -a ≤ -a",
"tactic": "rw [neg_neg]"
}
] | [
1115,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhds_eq_comap_uniformity' | [] | [
737,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.coprime_mul_right_right | [] | [
316,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
315,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_sort | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nm : Poly\n⊢ denote ctx (sort m) = denote ctx m",
"tactic": "simp"
}
] | [
293,
7
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
292,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | charmatrix_apply_natDegree | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁴ : CommRing R\nn G : Type v\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα β : Type v\ninst✝¹ : DecidableEq α\nM : Matrix n n R\ninst✝ : Nontrivial R\ni j : n\n⊢ natDegree (charmatrix M i j) = if i = j then 1 else 0",
"tactic": "by_cases i ... | [
52,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_one' | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.exp_log | [
{
"state_after": "x y : ℝ\nhx : 0 < x\n⊢ abs x = x",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ exp (log x) = x",
"tactic": "rw [exp_log_eq_abs hx.ne']"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ abs x = x",
"tactic": "exact abs_of_pos hx"
}
] | [
64,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Order.lean | continuous_iff_le_induced | [] | [
695,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_nat_atTop_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.688066\nβ : Type ?u.688069\nE : Type ?u.688072\nF : Type ?u.688075\nG : Type ?u.688078\nE' : Type ?u.688081\nF' : Type ?u.688084\nG' : Type ?u.688087\nE'' : Type u_2\nF'' : Type u_1\nG'' : Type ?u.688096\nR : Type ?u.688099\nR' : Type ?u.688102\n𝕜 :... | [
2125,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2123,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bindOnSupport_apply | [] | [
223,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Init/Algebra/Classes.lean | trichotomous_of | [] | [
316,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.singleton_self | [] | [
108,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.