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/Data/Set/Intervals/Basic.lean | Set.not_mem_Iio | [] | [
1056,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nhp : Prime p\nh : Finite p a ∧ Finite p b\n⊢ multiplicity p (a * b) = multiplicity p a + multiplicity p b",
"tactic": "rw [← PartENat.natCast_get (finite... | [
585,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.IsRoot.eq_zero | [] | [
494,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Group/WithOne/Basic.lean | MulEquiv.withOneCongr_refl | [] | [
152,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.dist_le_of_fixedPoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : MetricSpace α\nK : ℝ≥0\nf : α → α\nhf : ContractingWith K f\nx y : α\nhy : IsFixedPt f y\n⊢ dist x y ≤ dist x (f x) / (1 - ↑K)",
"tactic": "simpa only [hy.eq, dist_self, add_zero] using hf.dist_inequality x y"
}
] | [
285,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/List/Basic.lean | List.surjective_tail | [] | [
872,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.mul_re | [] | [
128,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.comp_assoc | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.re_neg | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.toOrderMonoidWithZeroHom_eq_coe | [] | [
216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.AeMeasurable.ae_eq_of_forall_set_lintegral_eq | [
{
"state_after": "α : Type u_1\nE : Type ?u.137396\nm m0 : MeasurableSpace α\nμ : Measure α\ns✝ t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\nhg : AEMeasurable g\nhfi : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\nhgi : (∫⁻ (x : α), g x ... | [
572,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.mem_rangeIcc_apply_iff | [] | [
86,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_leftInverse | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf✝ f : R →+* S₁\ng : S₁ →+* R\nhf : LeftInverse ↑f ↑g\nX : MvPolynomial σ S₁\n⊢... | [
1310,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1308,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.norm_def' | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_iff_eq_bot | [] | [
875,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Data/Set/List.lean | Set.range_list_get? | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1563\nl : List α\n⊢ range (get? l) = insert none (range (some ∘ fun k => nthLe l ↑k (_ : ↑k < length l)))",
"state_before": "α : Type u_1\nβ : Type ?u.1563\nl : List α\n⊢ range (get? l) = insert none (some '' {x | x ∈ l})",
"tactic": "rw [← range_list_nthLe, ←... | [
53,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.exists_dense_seq | [
{
"state_after": "case intro.intro\nα : Type u\nt : TopologicalSpace α\ninst✝¹ : SeparableSpace α\ninst✝ : Nonempty α\ns : Set α\nhs : Set.Countable s\ns_dense : Dense s\n⊢ ∃ u, DenseRange u",
"state_before": "α : Type u\nt : TopologicalSpace α\ninst✝¹ : SeparableSpace α\ninst✝ : Nonempty α\n⊢ ∃ u, DenseRan... | [
325,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.smul_graph | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.518983\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\nM : Type u_4\ninst✝² : Monoid M\ninst✝¹ : DistribMulAction M F\ninst✝... | [
779,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compLeft_apply | [] | [
598,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_mul_limit_aux | [
{
"state_after": "a b c : Ordinal\nba : b + a = a\nl : IsLimit c\nIH : ∀ (c' : Ordinal), c' < c → (a + b) * succ c' = a * succ c' + b\nc' : Ordinal\nh : c' < c\n⊢ (a + b) * succ c' ≤ a * c",
"state_before": "a b c : Ordinal\nba : b + a = a\nl : IsLimit c\nIH : ∀ (c' : Ordinal), c' < c → (a + b) * succ c' = ... | [
2477,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2466,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_reaches | [
{
"state_after": "case inl\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂ → Prop\nH : Respects f₁ f₂ tr\na₂ : σ₂\nb₁ : σ₁\naa : tr b₁ a₂\nab : Reaches f₁ b₁ b₁\n⊢ ∃ b₂, tr b₁ b₂ ∧ Reaches f₂ a₂ b₂\n\ncase inr\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Op... | [
903,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.natDegree_primPart | [
{
"state_after": "case pos\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nh : ↑C (content p) = 0\n⊢ natDegree (primPart p) = natDegree p\n\ncase neg\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\nh : ¬↑C (conte... | [
288,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.transferNatTransSelf_symm_of_iso | [
{
"state_after": "C : Type u₁\nD : Type u₂\ninst✝² : Category C\ninst✝¹ : Category D\nL₁ L₂ L₃ : C ⥤ D\nR₁ R₂ R₃ : D ⥤ C\nadj₁ : L₁ ⊣ R₁\nadj₂ : L₂ ⊣ R₂\nadj₃ : L₃ ⊣ R₃\nf : R₁ ⟶ R₂\ninst✝ : IsIso (↑(transferNatTransSelf adj₁ adj₂).symm f)\n⊢ IsIso (↑(transferNatTransSelf adj₁ adj₂) (↑(transferNatTransSelf adj₁... | [
275,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_smul_deriv' | [] | [
1421,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.squashSeq_nth_of_not_terminated | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nn : ℕ\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\ngp_n gp_succ_n : Pair K\ns_nth_eq : Stream'.Seq.get? s n = some gp_n\ns_succ_nth_eq : Stream'.Seq.get? s (n + 1) = some gp_succ_n\n⊢ Stream'.Seq.get? (squa... | [
120,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/Basic.lean | Pi.compl_def | [] | [
772,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.totallyBounded_Icc | [
{
"state_after": "no goals",
"state_before": "a b : ℚ\n⊢ TotallyBounded (Icc a b)",
"tactic": "simpa only [preimage_cast_Icc] using\n totallyBounded_preimage Rat.uniformEmbedding_coe_real (totallyBounded_Icc (a : ℝ) b)"
}
] | [
124,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
8
] |
Mathlib/Topology/SubsetProperties.lean | IsClopen.diff | [] | [
1577,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
] |
Mathlib/Data/Set/Basic.lean | Set.setOf_app_iff | [] | [
285,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_prod | [
{
"state_after": "case h\nα : Type u_1\nS : Finset α\ng : α → ℕ\nhS : ∀ (x : α), x ∈ S → g x ≠ 0\np : ℕ\n⊢ ↑(factorization (Finset.prod S g)) p = ↑(∑ x in S, factorization (g x)) p",
"state_before": "α : Type u_1\nS : Finset α\ng : α → ℕ\nhS : ∀ (x : α), x ∈ S → g x ≠ 0\n⊢ factorization (Finset.prod S g) = ... | [
255,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.prodExtendRight_apply_ne | [] | [
836,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Iio_of_Iic | [] | [
196,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.imp_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4602\nR S T : α → α → Prop\na : α\nl✝ l : List α\n⊢ ∀ {a b : α}, a ∈ l → b ∈ l → (R a b ↔ a ∈ l → b ∈ l → R a b)",
"tactic": "simp (config := { contextual := true }) only [forall_prop_of_true, iff_self_iff,\nforall₂_true_iff]"
}
] | [
120,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Logic/Basic.lean | xor_iff_not_iff | [] | [
479,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.seqLeft | [] | [
160,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
157,
11
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_mul_normalize | [
{
"state_after": "case mk'\nn₁ n₂ : Int\nd₁ d₂ : Nat\nz₁ : d₁ ≠ 0\nz₂ : d₂ ≠ 0\nnum✝ : Int\nden✝ : Nat\nden_nz✝ : den✝ ≠ 0\nreduced✝ : Nat.coprime (Int.natAbs num✝) den✝\ne₁ : normalize n₁ d₁ = mk' num✝ den✝\n⊢ mk' num✝ den✝ * normalize n₂ d₂ = normalize (n₁ * n₂) (d₁ * d₂)",
"state_before": "n₁ n₂ : Int\nd... | [
272,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
265,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.toCone_π_app_left | [] | [
1003,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mono | [] | [
1305,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.succ_lt_of_not_succ | [] | [
208,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Control/EquivFunctor.lean | EquivFunctor.mapEquiv_symm_apply | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/StoneCech.lean | continuous_stoneCechExtend | [] | [
284,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_of_le_one_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝³ : MulOneClass α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : MulPosMono α\nhb : 0 ≤ b\nh : a ≤ 1\n⊢ a * b ≤ b",
"tactic": "simpa only [one_mul] using mul_le_mul_of_nonneg_right h hb"
}
] | [
670,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.setBlack | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nt : RBNode α\n⊢ Ordered cmp\n (match t with\n | nil => nil\n | node c l v r => node black l v r) ↔\n Ordered cmp t",
"state_before": "α : Type u_1\ncmp : α → α → Ordering\nt : RBNode α\n⊢ Ordered cmp (setBlack t) ↔ Ordered cmp t",
... | [
80,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
79,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.bot_eq_top_of_rank_adjoin_eq_one | [
{
"state_after": "case h\nF : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L : IntermediateField F E\nh : ∀ (x : E), Module.rank F { x_1 // x_1 ∈ F⟮x⟯ } = 1\ny : E\n⊢ y ∈ ⊥ ↔ y ∈ ⊤",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹... | [
753,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_mod_dom | [] | [
788,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.eq_homEquiv_apply | [
{
"state_after": "case refl\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nA : C\nB : D\nf : F.obj A ⟶ B\n⊢ ↑(homEquiv adj A B).symm (↑(homEquiv adj A B) f) = f",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝... | [
232,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_mul | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ natAbs (a * b) = natAbs a * natAbs b",
"tactic": "cases a <;> cases b <;>\n simp only [← Int.mul_def, Int.mul, natAbs_negOfNat] <;> simp only [natAbs]"
}
] | [
173,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
171,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono | [] | [
324,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Order/Grade.lean | grade_lt_grade_iff | [] | [
185,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.sum_disj_union_boxes | [] | [
665,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.card_support_eq_three | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nq : ℤ[X]\nk m n : ℕ\nhkm : k < m\nhmn : m < n\nu v w : ℤˣ\n⊢ card (support (trinomial k m n ↑u ↑v ↑w)) = 3",
"state_before": "p q : ℤ[X]\nhp : IsUnitTrinomial p\n⊢ card (support p) = 3",
"tactic": "obtain ⟨k, m, n, hkm, hmn, u, v, w... | [
151,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMaxOn.hasFDerivWithinAt_eq_zero | [
{
"state_after": "no goals",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMaxOn f s a\nhf : HasFDerivWithinAt f f' s a\ny : E\nhy : y ∈ posTangentConeAt s a\nhy' : -y ∈ posTangentConeAt s a\n⊢ 0 ≤ ↑f' y",
"ta... | [
142,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_isLimit | [] | [
523,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_lt_succ_iff | [] | [
894,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_coe_iff | [] | [
85,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Data/Int/Bitwise.lean | Int.bit_val | [
{
"state_after": "case false\nn : ℤ\n⊢ bit false n = 2 * n + bif false then 1 else 0\n\ncase true\nn : ℤ\n⊢ bit true n = 2 * n + bif true then 1 else 0",
"state_before": "b : Bool\nn : ℤ\n⊢ bit b n = 2 * n + bif b then 1 else 0",
"tactic": "cases b"
},
{
"state_after": "case true\nn : ℤ\n⊢ bit t... | [
135,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.isIso_of_hom_comp_eq_id | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\ng : X ⟶ Y\ninst✝ : IsIso g\nf : Y ⟶ X\nh : g ≫ f = 𝟙 X\n⊢ IsIso (inv g)",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\ng : X ⟶ Y\ninst✝ : IsIso g\nf : Y ⟶ X\nh : g ≫ f = 𝟙 X\n⊢ IsIso f",
"tactic": "rw [(hom_comp_eq_id _).mp ... | [
499,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_mul | [] | [
508,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
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Mathlib/Data/List/Nodup.lean | List.nodup_singleton | [] | [
64,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Rat.comap_cast_atBot | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9070\nR : Type u_1\ninst✝¹ : LinearOrderedField R\ninst✝ : Archimedean R\nr : R\nn : ℕ\nhn : -r ≤ ↑n\n⊢ ↑(-↑n) ≤ r",
"tactic": "simpa [neg_le]"
}
] | [
85,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
9
] |
Std/Logic.lean | Exists.nonempty | [] | [
435,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
435,
1
] |
Mathlib/Order/Lattice.lean | Subtype.mk_inf_mk | [] | [
1397,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_iterate_eq_div_gcd | [] | [
471,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_id | [] | [
770,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Tactic/Lift.lean | Subtype.exists_pi_extension | [
{
"state_after": "ι : Sort u_1\nα : ι → Sort u_2\nne : ∀ (i : ι), Nonempty (α i)\np : ι → Prop\nf : (i : Subtype p) → α i.val\nthis : DecidablePred p\n⊢ ∃ g, (fun i => g i.val) = f",
"state_before": "ι : Sort u_1\nα : ι → Sort u_2\nne : ∀ (i : ι), Nonempty (α i)\np : ι → Prop\nf : (i : Subtype p) → α i.val\... | [
45,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | extremePoints_subset | [] | [
152,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.exists_mem_not_mem_of_ncard_lt_ncard | [] | [
537,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.code_is_ok | [
{
"state_after": "case zero'\nk : Cont\nv : List ℕ\n⊢ eval step ((fun k v => Cfg.ret k (0 :: v)) k v) = do\n let v ← Code.eval Code.zero' v\n eval step (Cfg.ret k v)\n\ncase succ\nk : Cont\nv : List ℕ\n⊢ eval step ((fun k v => Cfg.ret k [Nat.succ (List.headI v)]) k v) = do\n let v ← Code.eval Code.succ... | [
718,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_five | [
{
"state_after": "α : Type ?u.22461\nβ : Type u_1\ninst✝ : CommMonoid β\nf : Fin 5 → β\n⊢ f (↑castSucc 0) * f (↑castSucc 1) * f (↑castSucc 2) * f (↑castSucc 3) * f (last 4) = f 0 * f 1 * f 2 * f 3 * f 4",
"state_before": "α : Type ?u.22461\nβ : Type u_1\ninst✝ : CommMonoid β\nf : Fin 5 → β\n⊢ ∏ i : Fin 5, f... | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.BinaryCofan.isVanKampen_mk | [
{
"state_after": "J : Type v'\ninst✝¹ : Category J\nC : Type u\ninst✝ : Category C\nX✝ Y✝ X Y : C\nc : BinaryCofan X Y\ncofans : (X Y : C) → BinaryCofan X Y\ncolimits : (X Y : C) → IsColimit (cofans X Y)\ncones : {X Y Z : C} → (f : X ⟶ Z) → (g : Y ⟶ Z) → PullbackCone f g\nlimits : {X Y Z : C} → (f : X ⟶ Z) → (g... | [
230,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/PathConnected.lean | Continuous.path_trans | [
{
"state_after": "X : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.347696\nγ : Path x y\nf : Y → Path x y\ng : Y → Path y z\nhf : Continuous f\nhg : Continuous g\n⊢ Continuous fun t => trans (f t) (g t)",
"state_before": "X : Type u_1\nY : Type u_2\... | [
533,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_pow_atTop | [] | [
1057,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.fuzzy_congr_right | [] | [
971,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.tendstoLocallyUniformly_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.31390\ninst✝¹ : PseudoEMetricSpace α\nι : Type u_1\ninst✝ : TopologicalSpace β\nF : ι → β → α\nf : β → α\np : Filter ι\n⊢ TendstoLocallyUniformly F f p ↔\n ∀ (ε : ℝ≥0∞), ε > 0 → ∀ (x : β), ∃ t, t ∈ 𝓝 x ∧ ∀ᶠ (n : ι) in p, ∀... | [
366,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.coe_quotEquivOfEqBot_symm | [] | [
636,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.mul_inv_of_unit | [
{
"state_after": "case intro\nn : ℕ\nu : (ZMod n)ˣ\n⊢ ↑u * (↑u)⁻¹ = 1",
"state_before": "n : ℕ\na : ZMod n\nh : IsUnit a\n⊢ a * a⁻¹ = 1",
"tactic": "rcases h with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nn : ℕ\nu : (ZMod n)ˣ\n⊢ ↑u * (↑u)⁻¹ = 1",
"tactic": "r... | [
720,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_source'' | [] | [
830,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_ofEquivFun | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.687118\nR : Type u_2\nR₂ : Type ?u.687124\nK : Type ?u.687127\nM : Type u_3\nM' : Type ?u.687133\nM'' : Type ?u.687136\nV : Type u\nV' : Type ?u.687141\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCo... | [
971,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_self | [] | [
1061,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.id_def | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.norm_fract_le | [
{
"state_after": "no goals",
"state_before": "E : Type u_2\nι : Type u_3\nK : Type u_1\ninst✝⁵ : NormedLinearOrderedField K\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\nb : Basis ι K E\ninst✝² : FloorRing K\ninst✝¹ : Fintype ι\ninst✝ : HasSolidNorm K\nm : E\n⊢ ‖fract b m‖ ≤ ∑ i : ι, ‖↑b i‖",
... | [
181,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRelO.imp | [] | [
463,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.coe_nonneg | [
{
"state_after": "n : ℕ\n⊢ ↑0 ≤ ↑n",
"state_before": "n : ℕ\n⊢ 0 ≤ ↑n",
"tactic": "rw [← WithBot.coe_zero]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑0 ≤ ↑n",
"tactic": "exact WithBot.coe_le_coe.mpr (Nat.zero_le n)"
}
] | [
59,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.fst_dual | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tanh_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ tanh (-x) = -tanh x",
"tactic": "simp [tanh, neg_div]"
}
] | [
701,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_top | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\n⊢ Prepartition.iUnion ⊤ = ↑I",
"tactic": "simp [Prepartition.iUnion]"
}
] | [
234,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_neg_const_mul_pow_atTop | [] | [
1241,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_injective_of_injective | [] | [
396,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.hasBasis_ball | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.189437\n𝕝 : Type ?u.189440\n𝕝₂ : Type ?u.189443\nE : Type u_2\nF : Type ?u.189449\nG : Type ?u.189452\nι : Type u_3\nι' : Type ?u.189458\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ : TopologicalSpace E\np : ... | [
319,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.unique | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\ncmp : α → α → Ordering\nx y : α\ninst✝ : TransCmp cmp\ne : cmp x y = Ordering.eq\nht : Ordered cmp nil\nhx : x ∈ nil\nhy : y ∈ nil\n⊢ x = y",
"tactic": "cases hx"
},
{
"state_after": "case node\nα : Type u_1\ncmp : α → α → Ord... | [
206,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
190,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.nondegenerate_toBilin'_iff | [] | [
560,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodCongr_refl_right | [
{
"state_after": "case H.mk\nα₁ : Type u_3\nβ₁ : Type u_1\nβ₂ : Type u_2\ne✝ : α₁ → β₁ ≃ β₂\ne : β₁ ≃ β₂\na : β₁\nb : α₁\n⊢ ↑(prodCongr e (Equiv.refl α₁)) (a, b) = ↑(prodCongrLeft fun x => e) (a, b)",
"state_before": "α₁ : Type u_3\nβ₁ : Type u_1\nβ₂ : Type u_2\ne✝ : α₁ → β₁ ≃ β₂\ne : β₁ ≃ β₂\n⊢ prodCongr e... | [
715,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | exists_mem_nhds_ball_subset_of_mem_nhds | [] | [
807,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.205169\nι : Type ?u.205172\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.205184\ninst✝⁷ : Lattice α\ninst✝⁶ : Lattice β\ninst✝⁵ : Lattice γ\ninst✝⁴ : Lattice δ\ninst✝³ : BoundedOrder α\ninst✝² : BoundedOrder β\ninst✝¹ : BoundedOrder γ\ninst✝... | [
1356,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/Data/List/Lattice.lean | List.mem_of_mem_inter_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nh : a ∈ l₁ ∩ l₂\n⊢ a ∈ l₂",
"tactic": "simpa using of_mem_filter h"
}
] | [
159,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/List/Lemmas.lean | List.not_mem_append | [] | [
141,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
140,
1
] |
Mathlib/Topology/Algebra/Semigroup.lean | exists_idempotent_of_compact_t2_of_continuous_mul_left | [
{
"state_after": "M : Type u_1\ninst✝⁴ : Nonempty M\ninst✝³ : Semigroup M\ninst✝² : TopologicalSpace M\ninst✝¹ : CompactSpace M\ninst✝ : T2Space M\ncontinuous_mul_left : ∀ (r : M), Continuous fun x => x * r\nS : Set (Set M) := {N | IsClosed N ∧ Set.Nonempty N ∧ ∀ (m : M), m ∈ N → ∀ (m' : M), m' ∈ N → m * m' ∈ N... | [
78,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.comap | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.65846\nι : Sort u_2\nι' : Sort ?u.65852\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt✝ : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nf : β → α\nhl : HasBasis l p s\nt : Set β\n⊢ (∃ i, p i ∧ s i ⊆ {y | ∀ ⦃x : β⦄, f x = y → x ∈ t}) ↔ ∃ i, p ... | [
800,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_singleton | [] | [
1273,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.exists_ne_one_of_prod_ne_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.430162\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoid β\nh : ∏ x in s, f x ≠ 1\n⊢ ∃ a, a ∈ s ∧ f a ≠ 1",
"tactic": "classical\n rw [← prod_filter_ne_one] at h\n rcases nonempty_of_prod_ne_one h w... | [
1206,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
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