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/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext_iff | [] | [
470,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_iff_measurable | [] | [
259,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/PrimeIdeal.lean | Order.Ideal.PrimePair.I_isPrime | [
{
"state_after": "P : Type u_1\ninst✝ : Preorder P\nIF : PrimePair P\nsrc✝ : IsProper IF.I := I_isProper IF\n⊢ IsPFilter ↑IF.F",
"state_before": "P : Type u_1\ninst✝ : Preorder P\nIF : PrimePair P\nsrc✝ : IsProper IF.I := I_isProper IF\n⊢ IsPFilter (↑IF.Iᶜ)",
"tactic": "rw [IF.compl_I_eq_F]"
},
{
... | [
116,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelHomClass.acc | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.9632\nδ : Type ?u.9635\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nu : δ → δ → Prop\nF : Type u_1\ninst✝ : RelHomClass F r s\nf : F\na : α\nb : β\nh : ↑f a = b\n⊢ Acc s b → Acc r a",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type ?u... | [
95,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_pow_strictAnti | [] | [
632,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | isometry_inv | [] | [
139,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Category/Preorder.lean | CategoryTheory.Functor.monotone | [] | [
158,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_eq_localization_mk | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np q : K[X]\nhq : q ≠ 0\n⊢ RatFunc.mk p q = { toFractionRing := Localization.mk p { val := q, property := (_ : q ∈ K[X]⁰) } }",
"tactic": "rw [mk_def_of_ne, Localization.mk_eq_mk'] <;> exact hq"
}
] | [
230,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Structure.relMap_apply₁ | [] | [
444,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableOn.prod | [] | [
111,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_eq_linear_proj | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.822903\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nx : E\nthis : IsCompl K Kᗮ\n⊢ ↑(orthogon... | [
850,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_neg_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.135719\nE : Type ?u.135722\nF : Type u_3\nG : Type ?u.135728\nE' : Type u_2\nF' : Type ?u.135734\nG' : Type ?u.135737\nE'' : Type ?u.135740\nF'' : Type ?u.135743\nG'' : Type ?u.135746\nR : Type ?u.135749\nR' : Type ?u.135752\n𝕜 : Type ?u.135755\n𝕜' : Type ?u.135758\... | [
913,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Std/Data/Char.lean | String.csize_eq | [
{
"state_after": "c : Char\n⊢ UInt32.toNat\n (if c.val ≤ UInt32.ofNatCore 127 Char.utf8Size.proof_1 then UInt32.ofNatCore 1 Char.utf8Size.proof_2\n else\n if c.val ≤ UInt32.ofNatCore 2047 Char.utf8Size.proof_3 then UInt32.ofNatCore 2 Char.utf8Size.proof_4\n else\n if c... | [
15,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
11,
9
] |
Mathlib/Analysis/Normed/Field/Basic.lean | norm_div | [] | [
566,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.pow_mem | [] | [
417,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
11
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_sub | [
{
"state_after": "R✝ : Type u\na✝ b✝ : R✝\nm n : ℕ\ninst✝¹ : Semiring R✝\np q : R✝[X]\nR : Type u\ninst✝ : Ring R\na b : AddMonoidAlgebra R ℕ\n⊢ { toFinsupp := a } + -{ toFinsupp := b } = { toFinsupp := a } - { toFinsupp := b }",
"state_before": "R✝ : Type u\na✝ b✝ : R✝\nm n : ℕ\ninst✝¹ : Semiring R✝\np q :... | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Computability/Halting.lean | Partrec.cond | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.259014\nγ : Type ?u.259017\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nc : α → Bool\nf g : α →. σ\nhc : Computable c\nhf : Partrec f\nhg : Partrec g\ncf : Code\nef : eval... | [
125,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.pi_map_π_apply | [] | [
64,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.320195\nγ : Type ?u.320198\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Finset α\na : α\n⊢ a ∈ filter q (filter p s) ↔ a ∈ filter (fun a => p a ∧ q a) s",
"tactic": "simp only [mem_filter, and_assoc, Bool.... | [
2678,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2676,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.add_smul | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.270732\nβ : Type ?u.270735\ninst✝⁴ : LinearOrderedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nh_conv : Convex 𝕜 s\np q : 𝕜\nhp ... | [
553,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_iSup_of_mem | [] | [
416,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_prod_map_diagonal | [] | [
390,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.fundamentalInterior_subset | [] | [
576,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.isConjugateExponent_iff | [
{
"state_after": "no goals",
"state_before": "p q : ℝ\nh : 1 < p\nH : q = p / (p - 1)\n⊢ 1 / p + 1 / q = 1",
"tactic": "field_simp [H, ne_of_gt (lt_trans zero_lt_one h)]"
}
] | [
123,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_def | [] | [
56,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
56,
9
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.deriv_eq_zero | [] | [
489,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.add_le_pair | [
{
"state_after": "m n : ℕ\n⊢ max m n ≤ max m n * max m n",
"state_before": "m n : ℕ\n⊢ m + n ≤ max m n ^ 2 + min m n",
"tactic": "rw [sq, ← min_add_max, add_comm, add_le_add_iff_right]"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ max m n ≤ max m n * max m n",
"tactic": "e... | [
175,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.tendsto_nhds_bot_iff_real | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.16686\ninst✝ : TopologicalSpace α✝\nα : Type u_1\nm : α → EReal\nf : Filter α\n⊢ (∀ (i : ℝ), True → ∀ᶠ (x : α) in f, m x ∈ Iio ↑i) ↔ ∀ (x : ℝ), ∀ᶠ (a : α) in f, m a < ↑x",
"tactic": "simp only [true_implies, mem_Iio]"
}
] | [
173,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.length_pure | [] | [
553,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_tsum_compl_atTop_zero | [
{
"state_after": "case intro\nα✝ : Type ?u.262957\nβ : Type ?u.262960\nγ : Type ?u.262963\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α✝ → ℝ≥0∞\nα : Type u_1\nf : α → ℝ≥0\nhf : (∑' (x : α), (fun i => ↑(f i)) x) ≠ ⊤\n⊢ Tendsto (fun s => ∑' (b : { x // ¬x ∈ s }), (fun i => ↑(f i)) ↑b)... | [
970,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.totallyBounded_range | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : ℕ → α\nhs : CauchySeq s\na : Set (α × α)\nha : a ∈ 𝓤 α\n⊢ ∃ t, t ⊆ range s ∧ Set.Finite t ∧ range s ⊆ ⋃ (y : α) (_ : y ∈ t), {x | (x, y) ∈ a}",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : ℕ → α\nhs : CauchySeq s\... | [
618,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_val_nd | [] | [
1561,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
1
] |
Mathlib/Topology/Connected.lean | ConnectedComponents.surjective_coe | [] | [
1465,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1464,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.lift'_mk | [] | [
605,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Algebra/Quandle.lean | Quandle.dihedralAct.inv | [
{
"state_after": "Q : Type ?u.78946\ninst✝ : Quandle Q\nn : ℕ\na b : ZMod n\n⊢ dihedralAct n a (dihedralAct n a b) = b",
"state_before": "Q : Type ?u.78946\ninst✝ : Quandle Q\nn : ℕ\na : ZMod n\n⊢ Function.Involutive (dihedralAct n a)",
"tactic": "intro b"
},
{
"state_after": "Q : Type ?u.78946\... | [
494,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPullback.iso_hom | [] | [
282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Int/Div.lean | Int.eq_mul_div_of_mul_eq_mul_of_dvd_left | [
{
"state_after": "case intro\na b c d : ℤ\nhb : b ≠ 0\nh : b * a = c * d\nk : ℤ\nhk : c = b * k\n⊢ a = c / b * d",
"state_before": "a b c d : ℤ\nhb : b ≠ 0\nhbc : b ∣ c\nh : b * a = c * d\n⊢ a = c / b * d",
"tactic": "cases' hbc with k hk"
},
{
"state_after": "case intro\na b d : ℤ\nhb : b ≠ 0\n... | [
30,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_one | [
{
"state_after": "a : Ordinal\n⊢ a ^ 0 * a = a",
"state_before": "a : Ordinal\n⊢ a ^ 1 = a",
"tactic": "rw [← succ_zero, opow_succ]"
},
{
"state_after": "no goals",
"state_before": "a : Ordinal\n⊢ a ^ 0 * a = a",
"tactic": "simp only [opow_zero, one_mul]"
}
] | [
81,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_source | [] | [
584,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.to_subbox_aux | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝¹ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny✝ y' : F\nc c₁ c... | [
534,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.constant | [] | [
1572,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : IsSplitMono f\n⊢ 𝟙 X = 0 ↔ f = 0",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ ... | [
222,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Logic/Equiv/List.lean | Denumerable.lower_raise | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.44179\nβ : Type ?u.44182\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\nm : ℕ\nl : List ℕ\nn : ℕ\n⊢ lower (raise (m :: l) n) n = m :: l",
"tactic": "rw [raise, lower, add_tsub_cancel_right, lower_raise l]"
}
] | [
306,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_union_left | [
{
"state_after": "α : Type u_1\nα' : Type ?u.34144\nβ : Type u_3\nβ' : Type ?u.34150\nγ : Type u_2\nγ' : Type ?u.34156\nδ : Type ?u.34159\nδ' : Type ?u.34162\nε : Type ?u.34165\nε' : Type ?u.34168\nζ : Type ?u.34171\nζ' : Type ?u.34174\nν : Type ?u.34177\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
173,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_eq_of_ne | [] | [
248,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.neg_def | [] | [
165,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Computability/Ackermann.lean | add_add_one_le_ack | [] | [
192,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.continuous_of_continuous_uncurry | [] | [
354,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Complex.abs_cpow_real | [
{
"state_after": "no goals",
"state_before": "x : ℂ\ny : ℝ\n⊢ ↑abs (x ^ ↑y) = ↑abs x ^ y",
"tactic": "rcases eq_or_ne x 0 with (rfl | hx) <;> [rcases eq_or_ne y 0 with (rfl | hy); skip] <;>\n simp [*, abs_cpow_of_ne_zero]"
}
] | [
286,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.isBoundedBilinearMap | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_3\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace �... | [
355,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_apply_symm | [
{
"state_after": "α : Type u_2\nα' : Type ?u.4457703\nβ : Type u_1\nβ' : Type ?u.4457709\nγ : Type ?u.4457712\nE : Type ?u.4457715\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
524,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.mul_to_int | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.929509\na : ZNum\n⊢ ↑(0 * a) = ↑0 * ↑a",
"tactic": "cases a <;> exact (MulZeroClass.zero_mul _).symm"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.929509\nb : ZNum\n⊢ ↑(b * 0) = ↑b * ↑0",
"tactic": "cases b <;> exa... | [
1351,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.center_toSubsemigroup | [] | [
486,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iUnion | [] | [
659,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.rightDistributor_inv | [
{
"state_after": "case w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX : C\nf : J → C\nj✝ : J\n⊢ biproduct.ι (fun j => f j ⊗ X) j✝ ≫ (rightDistributor X f).inv =\n biprodu... | [
202,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_above | [
{
"state_after": "no goals",
"state_before": "m✝ n : ℕ\ni : Fin (n + 1)\nm : Fin n\nh : i ≤ ↑Fin.castSucc m\n⊢ ↑(finSuccEquiv' i) (Fin.succ m) = some m",
"tactic": "rw [← Fin.succAbove_above _ _ h, finSuccEquiv'_succAbove]"
}
] | [
158,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.isBigO | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace �... | [
371,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
11
] |
Mathlib/CategoryTheory/Balanced.lean | CategoryTheory.balanced_opposite | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Balanced C\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nfmono : Mono f\nfepi : Epi f\n⊢ IsIso f.unop.op",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Balanced C\nX✝ Y✝ : Cᵒᵖ\nf : X✝ ⟶ Y✝\nfmono : Mono f\nfepi : Epi f\n⊢ IsIso f",
"tactic": "rw [← Qu... | [
57,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mapsTo_iInter_iInter | [] | [
1465,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.comp_apply | [] | [
842,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubgroup_fixedPoints_gc | [] | [
132,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.map_mk_nhds | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.60142\nZ : Type ?u.60145\nα : Type ?u.60148\nι : Type ?u.60151\nπ : ι → Type ?u.60156\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X... | [
487,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.card_Ioo_eq_card_Icc_sub_two | [
{
"state_after": "ι : Type ?u.112982\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ c a b : α\n⊢ card (Icc a b) - 1 - 1 = card (Icc a b) - 2",
"state_before": "ι : Type ?u.112982\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ c a b : α\n⊢ card (Ioo a... | [
666,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Submodule.biSup_eq_range_dfinsupp_lsum | [
{
"state_after": "case a\nι : Type u_1\nR : Type u_2\nS✝ : Type ?u.366938\nM : ι → Type ?u.366943\nN : Type u_3\ndec_ι : DecidableEq ι\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\np : ι → Prop\ninst✝ : DecidablePred p\nS : ι → Submodule R N\n⊢ (⨆ (i : ι) (_ : p i), S i) ≤\n LinearMap.... | [
352,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Polynomial/Monomial.lean | Polynomial.ringHom_ext' | [] | [
90,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | cycleType_finRotate_of_le | [
{
"state_after": "case intro\nm : ℕ\nh : 2 ≤ 2 + m\n⊢ cycleType (finRotate (2 + m)) = {2 + m}",
"state_before": "n : ℕ\nh : 2 ≤ n\n⊢ cycleType (finRotate n) = {n}",
"tactic": "obtain ⟨m, rfl⟩ := exists_add_of_le h"
},
{
"state_after": "no goals",
"state_before": "case intro\nm : ℕ\nh : 2 ≤ 2... | [
150,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/ContinuousOn.lean | tendsto_nhdsWithin_mono_left | [] | [
368,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.isCompl_orthogonal_of_completeSpace | [] | [
794,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Topology/Inseparable.lean | Specializes.map | [] | [
193,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Std/Data/String/Lemmas.lean | String.extract.go₁_cons_addChar | [
{
"state_after": "c : Char\ncs : List Char\nb e : Pos\n⊢ go₁ cs (0 + c) (b + c) (e + c) = go₁ cs 0 b e",
"state_before": "c : Char\ncs : List Char\nb e : Pos\n⊢ go₁ (c :: cs) 0 (b + c) (e + c) = go₁ cs 0 b e",
"tactic": "simp [go₁, Pos.ext_iff, Nat.ne_of_lt add_csize_pos]"
},
{
"state_after": "n... | [
420,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
417,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.isometry | [] | [
441,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
11
] |
Mathlib/Data/Nat/Choose/Sum.lean | Nat.sum_range_choose_halfway | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.146799\nm i : ℕ\nhi : i ∈ range (m + 1)\n⊢ i ≤ 2 * m + 1",
"tactic": "linarith [mem_range.1 hi]"
},
{
"state_after": "no goals",
"state_before": "R : Type ?u.146799\nm : ℕ\nthis : ∑ i in range (m + 1), choose (2 * m + 1) (2 * m + 1 - ... | [
119,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Fintype/Fin.lean | Fin.card_filter_univ_eq_vector_get_eq_count | [
{
"state_after": "case h_nil\nα : Type u_1\nβ : Type ?u.19015\nn : ℕ\ninst✝ : DecidableEq α\na : α\n⊢ Finset.card (filter (fun i => a = Vector.get Vector.nil i) univ) = List.count a (Vector.toList Vector.nil)\n\ncase h_cons\nα : Type u_1\nβ : Type ?u.19015\nn✝ : ℕ\ninst✝ : DecidableEq α\na : α\nn : ℕ\nx : α\nxs... | [
92,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.upper_mem_Icc | [] | [
211,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.measurableSet_mulSupport | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.68690\nι : Type ?u.68693\ninst✝³ : Countable ι\nf g : α → β\nm : MeasurableSpace α\ninst✝² : One β\ninst✝¹ : TopologicalSpace β\ninst✝ : MetrizableSpace β\nhf : StronglyMeasurable f\nthis✝¹ : MeasurableSpace β := borel β\nthis✝ : BorelSpace β\n⊢ Measurab... | [
379,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
8
] |
Mathlib/Algebra/Order/Ring/Defs.lean | one_lt_bit1 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.137611\ninst✝ : LinearOrderedSemiring α\na b c d : α\n⊢ 1 < bit1 a ↔ 0 < a",
"tactic": "rw [bit1, lt_add_iff_pos_left, bit0, ← two_mul, zero_lt_mul_left (zero_lt_two : 0 < (2 : α))]"
}
] | [
915,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.div_div_div_comm | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : DivisionMonoid G\na b c d : G\nhbc : Commute b c\nhbd : Commute b⁻¹ d\nhcd : Commute c⁻¹ d\n⊢ a / b / (c / d) = a / c / (b / d)",
"tactic": "simp_rw [div_eq_mul_inv, mul_inv_rev, inv_inv, hbd.symm.eq, hcd.symm.eq,\n hbc.inv_inv.mul_mul... | [
344,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
11
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictDerivAt.map_nhds_eq | [] | [
712,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Nat.cast_multiset_sum | [] | [
2201,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2199,
1
] |
Mathlib/Topology/Separation.lean | locally_compact_of_compact_nhds | [] | [
1394,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffAt.norm_sq | [] | [
172,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
8
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_subset | [] | [
1470,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Topology/Order/Basic.lean | Continuous.bddBelow_range_of_hasCompactMulSupport | [] | [
837,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.Equivalent.snoc | [
{
"state_after": "case refine'_1\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nx₁ x₂ : X\nhsat₁ : IsMaximal (top s₁) x₁\nhsat₂ : IsMaximal (top s₂) x₂\nhequiv : Equivalent s₁ s₂\nhtop : Iso (top s₁, x₁) (top s₂, x₂)\ne : Fin (Nat.succ s₁.length) ≃ Fin (Nat.succ s₂.... | [
676,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.measurableSet_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.227504\nι : Type ?u.227507\ninst✝⁴ : Countable ι\nf✝ g✝ : α → β\nm : MeasurableSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : Preorder β\ninst✝¹ : OrderClosedTopology β\ninst✝ : PseudoMetrizableSpace β\nf g : α → β\nhf : StronglyMeasurable f\nhg : Strong... | [
884,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_asSubtype | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.51072\nδ : Type ?u.51075\nε : Type ?u.51078\nι : Type ?u.51081\nf✝ f : α →. β\ns : Set β\nx : ↑(Dom f)\n⊢ x ∈ asSubtype f ⁻¹' s ↔ x ∈ Subtype.val ⁻¹' preimage f s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.51072\nδ : Type ?u.5... | [
534,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.monotone_span | [] | [
173,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Order/SymmDiff.lean | sup_bihimp_bihimp | [] | [
327,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.lift_ord | [
{
"state_after": "case refine'_1\nα : Type ?u.229284\nβ : Type ?u.229287\nγ : Type ?u.229290\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nc : Cardinal\na : Ordinal\nha : a < Ordinal.lift (ord c)\n⊢ a < ord (lift c)\n\ncase refine'_2\nα : Type ?u.229284\nβ : Type ?u.229287\nγ : Type ?u.229290\nr : α → ... | [
1444,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_eq_one_iff | [
{
"state_after": "case refine'_1\nF : Type ?u.80713\nα : Type u_1\nβ : Type ?u.80719\nγ : Type ?u.80722\ninst✝ : DivisionMonoid α\ns t : Set α\nh : s * t = 1\n⊢ ∃ a b, s = {a} ∧ t = {b} ∧ a * b = 1\n\ncase refine'_2\nF : Type ?u.80713\nα : Type u_1\nβ : Type ?u.80719\nγ : Type ?u.80722\ninst✝ : DivisionMonoid α... | [
1050,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
11
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_lt_iff_lt_rpow_of_base_lt_one | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\n⊢ logb b x < y ↔ b ^ y < x",
"tactic": "rw [← rpow_lt_rpow_left_iff_of_base_lt_one b_pos b_lt_one, rpow_logb b_pos (b_ne_one b_lt_one) hx]"
}
] | [
277,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.eval_zero | [
{
"state_after": "case a.h\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ x₂ x₃ : X\np₀ p₁ : Path x₀ x₁\nF : Homotopy p₀ p₁\nt : ↑I\n⊢ ↑(eval F 0) t = ↑p₀ t",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ x₂ x... | [
89,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/Directed.lean | directed_comp | [] | [
95,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/List/Basic.lean | List.getI_eq_get | [] | [
4472,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4471,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_left_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.70104\nα : Type u_1\nβ : Type ?u.70110\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ a ⇨ b ⇨ c = b ⇨ a ⇨ c",
"tactic": "simp_rw [himp_himp, inf_comm]"
}
] | [
397,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_singleton | [] | [
2350,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2349,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_iInf_le | [] | [
2485,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2484,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_le_count_cons | [] | [
2371,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2370,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_of_isClosed_subset | [] | [
134,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.Pairwise.insert_of_not_mem | [] | [
173,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
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