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/List/Basic.lean | List.modifyLast.go_append_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.316975\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\na : α\ntl : List α\nr : Array α\n⊢ go f (tl ++ [a]) r = Array.toListAppend r (go f (tl ++ [a]) #[])",
"tactic": "cases tl with\n| nil =>\n simp only [nil_append, ... | [
3044,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3034,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurable_fderiv | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst... | [
420,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Topology/Order/Basic.lean | eventually_nhdsWithin_pos_mem_Ioo | [] | [
2886,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2885,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_add | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.zero_divOf | [] | [
77,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.pow_mem | [] | [
719,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
11
] |
Mathlib/Data/Finset/Image.lean | Finset.map_empty | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPushforward_union | [] | [
691,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.smul | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : IsUpperSet s\ny x : α\nhx : x ∈ s\nhxy : (fun x => a • x) x ≤ y\n⊢ y ∈ a • s",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : IsUpperSet s\n⊢ IsUpperSet (a • s)",
"... | [
50,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ici_le_Ioi | [] | [
1118,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.enum_eq_zip | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.isInternal_submodule_iff_independent_and_iSup_eq_top | [] | [
411,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.exists_elementarySubstructure_card_eq | [
{
"state_after": "case intro\nL : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ : Structure L M\ns : Set M\nκ : Cardinal\nh1 : ℵ₀ ≤ κ\nh2 : lift (#↑s) ≤ lift κ\nh3 : lift (card L) ≤ lift κ\nh4 : lift κ ≤ lift (#M)\ns' : Set (ULift M)\nhs' : (#↑s') = lift κ\n⊢ ∃ S, s ⊆ ↑S ∧ lift (#{ x // x ∈ S }) = lift κ",
... | [
163,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ ¬s ⊆ t ↔ ∃ a, a ∈ s ∧ ¬a ∈ t",
"tactic": "simp only [subset_def, not_forall, exists_prop]"
}
] | [
393,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Order/Directed.lean | DirectedOn.mono' | [] | [
86,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_subset_left | [] | [
65,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.continuous_cos | [] | [
332,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhdset_of_mem_uniformity | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.79531\ninst✝ : UniformSpace α\nd s : Set (α × α)\nhd : d ∈ 𝓤 α\ncl_d : Set (α × α) := {p | ∃ x y, (p.fst, x) ∈ d ∧ (x, y) ∈ s ∧ (y, p.snd) ∈ d}\n⊢ ∃ t, IsOpen t ∧ s ⊆ t ∧ t ⊆ {p | ∃ x y, (p.fst, x) ∈ d ∧ (x, y) ∈ s ∧ (y, p.snd) ∈... | [
909,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Real.toNNReal_eq_nnnorm_of_nonneg | [
{
"state_after": "𝓕 : Type ?u.1109488\n𝕜 : Type ?u.1109491\nα : Type ?u.1109494\nι : Type ?u.1109497\nκ : Type ?u.1109500\nE : Type ?u.1109503\nF : Type ?u.1109506\nG : Type ?u.1109509\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nhr : 0 ≤ r\n⊢ { val := r, p... | [
1765,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1762,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.map_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\ndec : DecidableEq α\na b : α\ng : β → γ\nf : α → β\nR S : RegularExpression α\n⊢ map g (map f (R + S)) = map (g ∘ f) (R + S)",
"tactic": "simp only [map, Function.comp_apply, map_map]"
},
{
"state_after": "no... | [
442,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.sub_mem_iff_left | [
{
"state_after": "no goals",
"state_before": "G : Type u''\nS : Type u'\nR : Type u\nM : Type v\nι : Type w\ninst✝¹ : Ring R\ninst✝ : AddCommGroup M\nmodule_M : Module R M\np p' : Submodule R M\nr : R\nx y : M\nhy : y ∈ p\n⊢ x - y ∈ p ↔ x ∈ p",
"tactic": "rw [sub_eq_add_neg, p.add_mem_iff_left (p.neg_me... | [
583,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_lt_succ_iff_of_not_isMax | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : SuccOrder α\na b : α\nha : ¬IsMax a\nhb : ¬IsMax b\n⊢ succ a < succ b ↔ a < b",
"tactic": "rw [lt_succ_iff_of_not_isMax hb, succ_le_iff_of_not_isMax ha]"
}
] | [
262,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_zero | [
{
"state_after": "no goals",
"state_before": "⊢ EReal.abs 0 = 0",
"tactic": "rw [abs_eq_zero_iff]"
}
] | [
1078,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.strictAntiOn_logb_of_base_lt_one | [] | [
319,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_mulVec | [
{
"state_after": "case h\nl : Type u_1\nm : Type u_2\nn : Type u_4\no : Type u_5\np : Type ?u.43962\nq : Type ?u.43965\nm' : o → Type ?u.43970\nn' : o → Type ?u.43975\np' : o → Type ?u.43980\nR : Type ?u.43983\nS : Type ?u.43986\nα : Type u_3\nβ : Type ?u.43992\ninst✝² : Fintype l\ninst✝¹ : Fintype m\ninst✝ : N... | [
266,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.comp_proof | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q R : Karoubi C\ng : Hom Q R\nf : Hom P Q\n⊢ f.f ≫ g.f = P.p ≫ (f.f ≫ g.f) ≫ R.p",
"tactic": "rw [assoc, comp_p, ← assoc, p_comp]"
}
] | [
101,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Ioc_mem_nhds' | [] | [
1509,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_iff_infinitesimal_inv_pos | [
{
"state_after": "no goals",
"state_before": "x : ℝ*\nhip : InfinitePos x\nr : ℝ\nhr : 0 < r\n⊢ (↑r)⁻¹ < x",
"tactic": "convert hip r⁻¹"
}
] | [
746,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_le_pred | [] | [
646,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Int/GCD.lean | Int.dvd_lcm_left | [
{
"state_after": "i j : ℤ\n⊢ i ∣ ↑(Nat.lcm (natAbs i) (natAbs j))",
"state_before": "i j : ℤ\n⊢ i ∣ ↑(lcm i j)",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "i j : ℤ\n⊢ natAbs i ∣ Nat.lcm (natAbs i) (natAbs j)",
"state_before": "i j : ℤ\n⊢ i ∣ ↑(Nat.lcm (natAbs i) (natAbs j))",
"tactic"... | [
486,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/RingTheory/FiniteType.lean | AddMonoidAlgebra.finiteType_iff_group_fg | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type ?u.314374\ninst✝³ : AddCommMonoid M\nG : Type u_1\ninst✝² : AddCommGroup G\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\n⊢ FiniteType R (AddMonoidAlgebra R G) ↔ AddGroup.FG G",
"tactic": "simpa [AddGroup.fg_iff_addMonoid_fg] using finite... | [
483,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.size_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nas : List α\n⊢ size { data := as } = List.length as",
"tactic": "simp [size]"
}
] | [
26,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
26,
9
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_sub | [] | [
955,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_le_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.75667\nα : Type u_1\nβ : Type ?u.75673\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhb : 0 < b\n⊢ a / b ≤ 1 ↔ a ≤ b",
"tactic": "rw [div_le_iff hb, one_mul]"
}
] | [
427,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.dist_right_le_of_mem_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.195195\nι : Type ?u.195198\ninst✝ : PseudoMetricSpace α\nx y z : ℝ\nh : y ∈ uIcc x z\n⊢ dist y z ≤ dist x z",
"tactic": "simpa only [dist_comm _ z] using abs_sub_right_of_mem_uIcc h"
}
] | [
1371,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.mul_X_pow_comp | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp (p * X ^ Nat.zero) r = comp p r * r ^ Nat.zero\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nk : ℕ\nih : com... | [
610,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_add_def | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/List/Prime.lean | Prime.dvd_prod_iff | [
{
"state_after": "case mp\nM : Type u_1\ninst✝ : CommMonoidWithZero M\np : M\nL : List M\npp : Prime p\n⊢ p ∣ prod L → ∃ a, a ∈ L ∧ p ∣ a\n\ncase mpr\nM : Type u_1\ninst✝ : CommMonoidWithZero M\np : M\nL : List M\npp : Prime p\n⊢ (∃ a, a ∈ L ∧ p ∣ a) → p ∣ prod L",
"state_before": "M : Type u_1\ninst✝ : Com... | [
41,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_mkFinConsOfLe | [] | [
1330,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.unbounded_of_tendsto_atBot | [] | [
1703,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_Iio | [] | [
1185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.ofArrows_bind | [
{
"state_after": "case h\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y✝ Z✝ : C\nf : Y✝ ⟶ X\nι : Type u_1\nZ : ι → C\ng : (i : ι) → Z i ⟶ X\nj : ⦃Y : C⦄ → (f : Y ⟶ X) → ofArrows Z g f → Type u_2\nW : ⦃Y : C⦄ → (f : Y ⟶ X) → (H : ofArrows Z g f) → j f H → C\nk : ⦃Y : C⦄ → (f :... | [
171,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/List/Lemmas.lean | List.Pairwise.chain | [
{
"state_after": "α✝ : Type u_1\nR : α✝ → α✝ → Prop\na : α✝\nl : List α✝\np : Pairwise R (a :: l)\nr : ∀ (a' : α✝), a' ∈ l → R a a'\np' : Pairwise R l\n⊢ Chain R a l",
"state_before": "α✝ : Type u_1\nR : α✝ → α✝ → Prop\na : α✝\nl : List α✝\np : Pairwise R (a :: l)\n⊢ Chain R a l",
"tactic": "let ⟨r, p'⟩... | [
1805,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1799,
11
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_smul_of_tower | [] | [
139,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | BoundedContinuousFunction.norm_mkOfCompact | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientEquivAlgOfEq_mk | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.constantsOn_constants | [] | [
399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_multiset_prod_X_sub_C | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\ns : Multiset R\n⊢ (Multiset.bind s fun a => roots (X - ↑C a)) = s\n\ncase a\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\ns : Mul... | [
747,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.604744\na : R\nn : ℕ\n⊢ leadingCoeff (↑C a * X ^ n) = a",
"tactic": "rw [C_mul_X_pow_eq_monomial, leadingCoeff_monomial]"
}
] | [
803,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.mul_of_commute | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.482\nN : Type ?u.485\nS : Type u_1\nM₀ : Type ?u.491\nM₁ : Type ?u.494\nR : Type ?u.497\nG : Type ?u.500\nG₀ : Type ?u.503\ninst✝⁷ : Mul M\ninst✝⁶ : Monoid N\ninst✝⁵ : Semigroup S\ninst✝⁴ : MulZeroClass M₀\ninst✝³ : MulOneClass M₁\ninst✝² : NonAssocR... | [
57,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/List/Count.lean | List.count_cons | [
{
"state_after": "α : Type u_1\nl✝ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\n⊢ (count a l + if a = b then 1 else 0) = if a = b then succ (count a l) else count a l",
"state_before": "α : Type u_1\nl✝ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\n⊢ count a (b :: l) = if a = b then succ (c... | [
187,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Computability/Language.lean | Language.join_mem_kstar | [] | [
129,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.intCoe_apply | [] | [
184,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | Complex.contDiffAt_log | [] | [
69,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.commute_int_add | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℤ\n⊢ Function.Commute ↑f fun x => ↑n + x",
"tactic": "simpa only [add_comm _ (n : ℝ)] using f.commute_add_int n"
}
] | [
353,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_le_map₂ | [] | [
103,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.flip | [] | [
85,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.const_smul | [] | [
78,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
8
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.mapFun.add | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_2\nS : Type u_1\nT : Type ?u.80564\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.80579\nβ : Type ?u.80582\nf : R →+* S\nx y : 𝕎 R\n⊢ mapFun (↑f) (x + y) = mapFun (↑f) x + mapFun (↑f) y",
... | [
115,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Topology/Algebra/Order/Filter.lean | Filter.Tendsto.nhds_atBot | [] | [
43,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.codRestrict_apply | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | HasSum.mul | [] | [
169,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.map_inv_map_hom_apply | [] | [
171,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.hausdorffEdist_coe | [
{
"state_after": "V : Type u_1\ninst✝¹ : SeminormedAddCommGroup V\ninst✝ : NormedSpace ℝ V\nK L : ConvexBody V\n⊢ EMetric.hausdorffEdist ↑K ↑L = ENNReal.ofReal (dist K L)",
"state_before": "V : Type u_1\ninst✝¹ : SeminormedAddCommGroup V\ninst✝ : NormedSpace ℝ V\nK L : ConvexBody V\n⊢ EMetric.hausdorffEdist... | [
194,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.MonoidalOpposite.mop_unmop | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_toReal | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ Real.tan (toReal θ) = tan θ",
"tactic": "conv_rhs => rw [← coe_toReal θ, tan_coe]"
}
] | [
815,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.pow_toProd | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_pow | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.surjective | [] | [
1283,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
11
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Icc_eq_zero_of_lt | [] | [
83,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.prod_rightr | [] | [
967,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | powersHom_symm_apply | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/List/Basic.lean | List.find?_mem | [
{
"state_after": "case nil\nι : Type ?u.339715\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\na : α\nH✝ : find? p l = some a\nH : find? p [] = some a\n⊢ a ∈ []\n\ncase cons\nι : Type ?u.339715\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bo... | [
3265,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3258,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_neg | [] | [
474,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.ext | [] | [
374,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.injective | [
{
"state_after": "ι : Type u'\nι' : Type ?u.231997\nR : Type u_1\nK : Type ?u.232003\nM : Type u_2\nM' : Type ?u.232009\nM'' : Type ?u.232012\nV : Type u\nV' : Type ?u.232017\nv : ι → M\ninst✝⁷ : Ring R\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : AddCommGroup M''\ninst✝³ : Module R M\ninst✝² : ... | [
494,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.eq_rnDeriv | [
{
"state_after": "α : Type u_1\nβ : Type ?u.641648\nm : MeasurableSpace α\nμ ν : Measure α\ns t✝ t : SignedMeasure α\nf : α → ℝ\nhfi : Integrable f\nhtμ : t ⟂ᵥ toENNRealVectorMeasure μ\nhadd : s = t + withDensityᵥ μ f\nf' : α → ℝ := AEStronglyMeasurable.mk f (_ : AEStronglyMeasurable f μ)\n⊢ f =ᶠ[ae μ] rnDeriv ... | [
1143,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.natDegree_expand | [
{
"state_after": "case inl\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nf : R[X]\nhp : p = 0\n⊢ natDegree (↑(expand R p) f) = natDegree f * p\n\ncase inr\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nf : R[X]\nhp : p > 0\n⊢ natDegr... | [
173,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.is_weak_closed_closedBall | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.3424525\nE : Type ?u.3424528\nEₗ : Type ?u.3424531\nF : Type u_4\nFₗ : Type ?u.3424537\nG : Type ?u.3424540\nGₗ : Type ?u.3424543\n𝓕 : Type ?u.3424546\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup F\ninst✝¹¹ : NormedAddCommGroup G\n... | [
1654,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1646,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsSymm.isRefl | [] | [
908,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.isPrenex_toPrenexImpRight | [
{
"state_after": "case of_isQF\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.127743\nP : Type ?u.127746\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.127774\nn l : ℕ\nφ✝² ψ✝ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv : α... | [
820,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.eval_rename_prod_mk | [] | [
225,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.reClm_coe | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.add | [] | [
1216,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1214,
1
] |
Mathlib/Topology/Constructions.lean | continuous_sigmaMk | [] | [
1445,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_algebraMap | [] | [
1612,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1611,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.X_pow_sub_one_splits | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝ : Field K\nζ : K\nn : ℕ\nh : IsPrimitiveRoot ζ n\n⊢ Splits (RingHom.id K) (X ^ n - ↑C 1)",
"tactic": "rw [splits_iff_card_roots, ← nthRoots, IsPrimitiveRoot.card_nthRoots h, natDegree_X_pow_sub_C]"
}
] | [
165,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.choice_isFunc | [] | [
1816,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeQuotientEquivQuotientSubtype_mk | [] | [
1495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_lt_of_lt | [
{
"state_after": "a b c : Cardinal\nhc : ℵ₀ ≤ c\nh1 : a < c\nh2 : b < c\nh : ℵ₀ ≤ max a b\n⊢ max a b < c",
"state_before": "a b c : Cardinal\nhc : ℵ₀ ≤ c\nh1 : a < c\nh2 : b < c\nh : ℵ₀ ≤ max a b\n⊢ max a b * max a b < c",
"tactic": "rw [mul_eq_self h]"
},
{
"state_after": "no goals",
"state... | [
603,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.zero_smul | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.924314\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.924323\ninst✝³ : Zero α\ninst✝² : Zero β\ninst✝¹ : SMulWithZero α β\ninst✝ : DecidableEq β\ns : Finset α\nt : Finset β\nht : Finset.Nonempty t\n⊢ 0 ⊆ 0 • t",
"tactic": "simpa [mem_smul] using ht"
... | [
2108,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2107,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_ite_empty_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t✝ t₁ t₂ u : Set α\np : Prop\ninst✝ : Decidable p\nt : Set α\nx : α\n⊢ (∃ h, x ∈ t) ↔ p ∧ x ∈ t",
"tactic": "simp"
}
] | [
2221,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2219,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_lt_iff | [] | [
189,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.submoduleImage_apply_ofLe | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1593776\nR₂ : Type ?u.1593779\nR₃ : Type ?u.1593782\nR₄ : Type ?u.1593785\nS : Type ?u.1593788\nK : Type ?u.1593791\nK₂ : Type ?u.1593794\nM : Type u_3\nM'✝ : Type ?u.1593800\nM₁ : Type ?u.1593803\nM₂ : Type ?u.1593806\nM₃ : Type ?u.15... | [
1758,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1755,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_pow | [] | [
301,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_le_neg | [] | [
94,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_nsmul | [] | [
714,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Algebra/Field/Defs.lean | Rat.smul_def | [] | [
151,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_ne_zero_iff_squarefree | [
{
"state_after": "case mp\nR : Type ?u.580497\nn : ℕ\nh : ↑μ n ≠ 0\n⊢ Squarefree n\n\ncase mpr\nR : Type ?u.580497\nn : ℕ\nh : Squarefree n\n⊢ ↑μ n ≠ 0",
"state_before": "R : Type ?u.580497\nn : ℕ\n⊢ ↑μ n ≠ 0 ↔ Squarefree n",
"tactic": "constructor <;> intro h"
},
{
"state_after": "case mp\nR : ... | [
971,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.421151\nγ : Type ?u.421154\ninst✝ : DecidableEq α\ns : Multiset α\nb : α\n⊢ filter (Eq b) s = replicate (count b s) b",
"tactic": "simp_rw [← filter_eq', eq_comm]"
}
] | [
2578,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2577,
1
] |
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