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/Part.lean | Part.bind_of_mem | [
{
"state_after": "no goals",
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"tactic": "rw [eq_some_iff.2 h, bind_some]"
}
] | [
525,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
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Mathlib/GroupTheory/GroupAction/Group.lean | MulAction.bijective₀ | [] | [
225,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
11
] |
Mathlib/Order/WellFoundedSet.lean | Set.wellFoundedOn_iff_no_descending_seq | [
{
"state_after": "ι : Type ?u.6720\nα : Type u_1\nβ : Type ?u.6726\nr r' : α → α → Prop\ninst✝ : IsStrictOrder α r\ns t : Set α\n⊢ Nonempty ((fun x x_1 => x > x_1) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s) ↔ ∃ x, ∀ (n : ℕ), ↑x n ∈ s",
"state_before": "ι : Type ?u.6720\nα : Type u_1\nβ : Type ?u.6726\nr r' : α → ... | [
158,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.neg_val | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ (n - val a) % n = if a = 0 then 0 else n - val a",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ val (-a) = if a = 0 then 0 else n - val a",
"tactic": "rw [neg_val']"
},
{
"state_after": "case pos\nn : ℕ\ninst✝ : NeZero n\na : ZM... | [
895,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Topology/Order/Basic.lean | map_coe_Iio_atTop | [] | [
2526,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2525,
1
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Mathlib/Data/Nat/Interval.lean | Nat.cauchy_induction_two_mul | [] | [
381,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.IsPushout.IsVanKampen.isPullback_of_mono_left | [
{
"state_after": "no goals",
"state_before": "J : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝ : Mono f\nH : IsPushout f g h i\nH' : IsVanKampen H\n⊢ g ≫ 𝟙 Y = 𝟙 W ≫ g",
"tactic": "simp"
},
{
"state_after": "no go... | [
198,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wDest'_wMk | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\na : P.A\nf' : B (drop P) a ⟹ α\nf : PFunctor.B (last P) a → W P α\n⊢ wDest' P (wMk P a f' f) = { fst := a, snd := splitFun f' f }",
"tactic": "rw [wDest', wRec_eq]"
}
] | [
310,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_top | [] | [
1911,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1910,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_top | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.37057\nα : Type u_1\nβ : Type ?u.37063\nπ : ι → Type ?u.37068\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ a ⇔ ⊤ = a",
"tactic": "rw [bihimp, himp_top, top_himp, inf_top_eq]"
}
] | [
250,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_X_of_ne | [
{
"state_after": "no goals",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\ni j : σ\nh : j ≠ i\n⊢ ↑(pderiv i) (X j) = 0",
"tactic": "classical simp [h]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : ... | [
107,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.lift_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.66514\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\n⊢ lift q 0 = 0",
"tactic": "simp [lift]"
}
] | [
118,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.Quotient.smul_coe | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_le_of_forall_dist_le | [] | [
2624,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2622,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_partition | [
{
"state_after": "ι : Type ?u.787616\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\nR : Setoid α\ninst✝ : DecidableRel Setoid.r\nx : α\n_hx : x ∈ s\n⊢ ∏ y in filter (fun x_1 => Quotient.mk R x_1 = Quotient.mk'' x) s, f y =\n ∏ x in filter (fun c' => Quotie... | [
1591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1588,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_def | [] | [
1198,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1198,
1
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Mathlib/FieldTheory/Separable.lean | Polynomial.unique_separable_of_irreducible | [
{
"state_after": "F : Type u\ninst✝¹ : Field F\nK : Type v\ninst✝ : Field K\np : ℕ\nHF : CharP F p\nf : F[X]\nhf : Irreducible f\nhp : 0 < p\nn₁ n₂ : ℕ\n⊢ ∀ (g₁ : F[X]),\n Separable g₁ →\n ↑(expand F (p ^ n₁)) g₁ = f → ∀ (g₂ : F[X]), Separable g₂ → ↑(expand F (p ^ n₂)) g₂ = f → n₁ = n₂ ∧ g₁ = g₂",
"... | [
396,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Analysis/Convex/Side.lean | Wbtw.wOppSide₁₃ | [
{
"state_after": "case intro.intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.208118\nP : Type u_3\nP' : Type ?u.208124\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : Affin... | [
406,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_mono | [] | [
114,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_one_sub_nth_order' | [
{
"state_after": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nn : ℕ\nt : R\nht : ‖t‖ < 1\nthis : Summable fun n => t ^ n\n⊢ (∑ i in range n, t ^ i + t ^ n * ∑' (i : ℕ), t ^ i) = ∑ i in range n, t ^ i + t ^ n * ↑(Units.oneSub t ht)⁻¹",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ni... | [
138,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_mul_left | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\n⊢ gcd (m * n) (m * k) = m * gcd n k",
"tactic": "induction n, k using gcd.induction with\n| H0 k => simp\n| H1 n k _ IH => rwa [← mul_mod_mul_left, ← gcd_rec, ← gcd_rec] at IH"
},
{
"state_after": "no goals",
"state_before": "case H0... | [
86,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
83,
1
] |
Mathlib/Order/Basic.lean | Preorder.toLE_injective | [
{
"state_after": "case refl\nι : Type ?u.11187\nα✝ : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.11198\nr : α✝ → α✝ → Prop\nα : Type u_1\nA B : Preorder α\nle✝ A_lt : α → α → Prop\nle_refl✝¹ : ∀ (a : α), a ≤ a\nle_trans✝¹ : ∀ (a b c : α), a ≤ b → b ≤ c → a ≤ c\nA_iff : ∀ (a b : α), a < b ↔ a ≤ b ∧ ¬b ≤ a\nB... | [
608,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.isRoot_map_iff | [] | [
1210,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.of_append_right | [] | [
215,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_int_mul_pi_sub | [] | [
1055,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lcongr_single | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.541821\nM : Type u_4\nN : Type u_5\nP : Type ?u.541830\nR : Type u_3\nS : Type ?u.541836\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P... | [
901,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Limit.map_π_apply | [] | [
203,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_algebraMap | [] | [
82,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.one_le_two_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 0 < 2",
"tactic": "decide"
}
] | [
69,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PullbackCone.op_inl | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nc : PullbackCone f g\n⊢ PushoutCocone.inl (op c) = (fst c).op",
"tactic": "aesop_cat"
}
] | [
541,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.ext_ring_iff | [] | [
493,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.vars_bind₁ | [
{
"state_after": "case calc_1\nσ : Type u_3\nτ : Type u_1\nR : Type u_2\nS : Type ?u.1324347\nT : Type ?u.1324350\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\ninst✝ : DecidableEq τ\nf : σ → MvPolynomial τ R\nφ : MvPolynomial σ R\n⊢ (Finset.biUnion (suppo... | [
389,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Part.lean | Part.map_bind | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ✝ : Type ?u.32518\nγ : Type u_1\nf : α → Part β\nx : Part α\ng : β → γ\n⊢ (Part.bind x fun x => Part.bind (f x) (some ∘ g)) = Part.bind x fun y => map g (f y)",
"state_before": "α : Type u_3\nβ : Type u_2\nγ✝ : Type ?u.32518\nγ : Type u_1\nf : α → Part β\nx : P... | [
559,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_pos_of_pos | [] | [
144,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_mul_comp_perm_lt_sum_mul_iff | [] | [
473,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Set/Function.lean | Function.invFunOn_mem | [] | [
1219,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Data/Fintype/Card.lean | Infinite.exists_not_mem_finset | [] | [
1001,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.toEquiv_mulRight | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atTop_curry | [
{
"state_after": "ι : Type ?u.304213\nι' : Type ?u.304216\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.304225\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\np : α × β → Prop\nhp : ∀ᶠ (x : α × β) in atTop ×ˢ atTop, p x\n⊢ ∀ᶠ (k : α) in atTop, ∀ᶠ (l : β) in atTop, p (k, l)",
"state_before": "ι : Type ?u.30... | [
1491,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1488,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.sup_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.116167\nι : Sort x\nf g : Filter α\ns✝ t✝ s t u : Set α\n⊢ u ∈ 𝓟 s ⊔ 𝓟 t ↔ u ∈ 𝓟 (s ∪ t)",
"tactic": "simp only [union_subset_iff, mem_sup, mem_principal]"
}
] | [
972,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Data/Holor.lean | Holor.slice_eq | [
{
"state_after": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\nx y : Holor α (d :: ds)\nh : slice x = slice y\nt : HolorIndex (d :: ds)\ni : ℕ\nis : List ℕ\nhiis : ↑t = i :: is\n⊢ Forall₂ (fun x x_1 => x < x_1) (↑t) (d :: ds)",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\nx y : Holor α (d :: ds)\... | [
262,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.support_ofFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.124309\nγ : Type ?u.124312\nf : α → ℝ≥0∞\ns : Finset α\nh : ∑ a in s, f a = 1\nh' : ∀ (a : α), ¬a ∈ s → f a = 0\na : α\n⊢ a ∈ support (ofFinset f s h h') ↔ a ∈ ↑s ∩ Function.support f",
"tactic": "simpa [mem_support_iff] using mt (h... | [
170,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.mul_eq_one_iff | [
{
"state_after": "case refine'_1\nF : Type ?u.290745\nα : Type u_1\nβ : Type ?u.290751\nγ : Type ?u.290754\nδ : Type ?u.290757\nε : Type ?u.290760\ninst✝ : DivisionMonoid α\nf g : Filter α\nhfg : f * g = 1\n⊢ ∃ a b, f = pure a ∧ g = pure b ∧ a * b = 1\n\ncase refine'_2\nF : Type ?u.290745\nα : Type u_1\nβ : Typ... | [
754,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
11
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.measure_pos_of_mem_nhds | [] | [
66,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.epsilon_pos | [] | [
186,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_C_le | [
{
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258,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/Algebra/Star/Unitary.lean | unitary.mul_star_self_of_mem | [] | [
66,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Std/Logic.lean | not_and | [] | [
316,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
316,
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Mathlib/Topology/Algebra/Group/Basic.lean | QuotientGroup.continuous_smul₁ | [
{
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"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : Group G\ninst✝¹ : TopologicalSpa... | [
1723,
62
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1721,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.neg_mem | [] | [
363,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
11
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.rightAssocTensor_obj | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Data/PNat/Interval.lean | PNat.map_subtype_embedding_Icc | [] | [
48,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_natDegree_le_one | [] | [
107,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.coeff_le_of_roots_le | [
{
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191,
33
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165,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.countp_add | [
{
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}
] | [
2235,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2234,
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Mathlib/NumberTheory/Multiplicity.lean | Int.two_pow_two_pow_sub_pow_two_pow | [
{
"state_after": "no goals",
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"tactic": "simp only [pow_two_pow_sub_pow_two_pow n, multiplicity.mul Int.prime_two,\n multiplicity.Finset.pro... | [
307,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
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Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_self | [] | [
95,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.smul_closure | [] | [
90,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | RingEquiv.restrictRootsOfUnity_symm | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.continuous_comp | [
{
"state_after": "case intro.intro\nR₁ : Type ?u.179451\nR₂ : Type ?u.179454\nR₃ : Type ?u.179457\ninst✝⁷ : Semiring R₁\ninst✝⁶ : Semiring R₂\ninst✝⁵ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nM₁ : Type u_1\nM₂ : Type u_2\nM₃ : Type u_3\ninst✝⁴ : TopologicalSpace M₁\ninst✝³ : TopologicalSpace M₂\ninst✝² :... | [
270,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ComplexDeriv.lean | Complex.continuousAt_tan | [
{
"state_after": "x : ℂ\nhc : ContinuousAt tan x\nh₀ : cos x = 0\n⊢ False",
"state_before": "x : ℂ\n⊢ ContinuousAt tan x ↔ cos x ≠ 0",
"tactic": "refine' ⟨fun hc h₀ => _, fun h => (hasDerivAt_tan h).continuousAt⟩"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nhc : ContinuousAt tan ... | [
61,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.one_apply | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/CategoryTheory/Limits/Over.lean | CategoryTheory.Over.epi_left_of_epi | [] | [
69,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Data/Set/Basic.lean | Set.diff_compl | [] | [
1963,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1962,
1
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Mathlib/Data/Set/Prod.lean | Set.prod_diff_prod | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.85553\nδ : Type ?u.85556\ns s₁ s₂ :... | [
378,
65
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376,
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.comap_supp | [
{
"state_after": "no goals",
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589,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_sup_eq | [
{
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350,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.supp_subset_range_natDegree_succ | [] | [
207,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.finrank_add_finrank_orthogonal' | [
{
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1120,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
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Mathlib/Algebra/AddTorsor.lean | vsub_right_cancel | [
{
"state_after": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 p : P\nh : p -ᵥ p1 = p -ᵥ p2\n⊢ p -ᵥ p2 +ᵥ p1 = p -ᵥ p2 +ᵥ p2",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 p : P\nh : p -ᵥ p1 = p -ᵥ p2\n⊢ p1 = p2",
"tactic": "refine... | [
230,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_inter_Icc_eq_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.183836\ninst✝ : Lattice α\na b c a₁ a₂ b₁ b₂ : α\nhab : a ≤ b\nhbc : b ≤ c\n⊢ Icc a b ∩ Icc b c = {b}",
"tactic": "rw [Icc_inter_Icc, sup_of_le_right hab, inf_of_le_left hbc, Icc_self]"
}
] | [
1762,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1761,
1
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Mathlib/Data/List/Lattice.lean | List.mem_inter_of_mem_of_mem | [
{
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"tactic": "simpa using h₂"
}
] | [
163,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup'_map | [
{
"state_after": "F : Type ?u.263099\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Type ?u.263111\nκ : Type ?u.263114\ninst✝ : SemilatticeSup α\ns✝ : Finset β\nH : Finset.Nonempty s✝\nf✝ : β → α\ns : Finset γ\nf : γ ↪ β\ng : β → α\nhs : Finset.Nonempty (map f s)\nhs' : optParam (Finset.Nonempty s) (_ : Finset.... | [
887,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_thirty_two | [
{
"state_after": "x : ℝ\n⊢ cos (π / 32) = cos (π / 2 ^ 5)\n\nx : ℝ\n⊢ cos (π / 2 ^ 5) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2",
"state_before": "x : ℝ\n⊢ cos (π / 32) = sqrt (2 + sqrt (2 + sqrt (2 + sqrt 2))) / 2",
"tactic": "trans cos (π / 2 ^ 5)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\... | [
833,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.π'_eq_π | [
{
"state_after": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\n⊢ (kernelSubobjectIso g).hom ≫\n cokernel.π (kernel.lift g f w) ≫\n ((cokernelIsoOfEq (_ : factorThruImage f ≫ imageToKernel' f g w = kernel.lift g f w)).inv ≫\n cokernel.... | [
202,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Data/List/Basic.lean | List.get?_pmap | [
{
"state_after": "case nil\nι : Type ?u.332299\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nh✝ : ∀ (a : α), a ∈ l → p a\nn✝ : ℕ\nh : ∀ (a : α), a ∈ [] → p a\nn : ℕ\n⊢ get? (pmap f [] h) n = Option.pmap f (get? [] n) (_ : ∀ (x : α), x ∈ get? []... | [
3185,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3179,
1
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Mathlib/Data/List/Cycle.lean | Cycle.toFinset_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns : Cycle α\n⊢ ∀ (a : List α), toFinset (Quotient.mk'' a) = ∅ ↔ Quotient.mk'' a = nil",
"tactic": "simp"
}
] | [
820,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
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Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.addHom_ext | [] | [
177,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_sub | [] | [
231,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.le_vsub_iff | [] | [
1157,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.zero_rpow_mul_self | [
{
"state_after": "y : ℝ\n⊢ ((if 0 < y then 0 else if y = 0 then 1 else ⊤) * if 0 < y then 0 else if y = 0 then 1 else ⊤) =\n if 0 < y then 0 else if y = 0 then 1 else ⊤",
"state_before": "y : ℝ\n⊢ 0 ^ y * 0 ^ y = 0 ^ y",
"tactic": "rw [zero_rpow_def]"
},
{
"state_after": "case inl\ny : ℝ\nh✝ ... | [
348,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.sum_map_mul_right | [] | [
133,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_le_sup | [
{
"state_after": "R : Type ?u.72208\nE : Type ?u.72211\nF : Type ?u.72214\nι : Type ?u.72217\nι' : Type ?u.72220\nα : Type ?u.72223\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R ... | [
141,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuous.isClosed_preimage | [] | [
280,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
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Mathlib/Data/Finset/Sort.lean | Finset.sort_sorted | [] | [
42,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.div_smul | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝⁴ : CommRing K\ninst✝³ : IsDomain K\nR : Type u_1\ninst✝² : Monoid R\ninst✝¹ : DistribMulAction R K[X]\ninst✝ : IsScalarTower R K[X] K[X]\nc : R\np q : K[X]\n⊢ ↑(algebraMap K[X] (RatFunc K)) (c • p) / ↑(algebraMap K[X] (RatFunc K)) q =\n c • ... | [
848,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetAux_perm | [] | [
79,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.comp_continuousOn_iff | [] | [
1903,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1901,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_mem_haarProduct | [
{
"state_after": "case mk\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nhU : Set.Nonempty (interior U)\nK : Set G\nhK : IsCompact K\na✝ : { carrier := K, isCompact' := hK } ∈ univ\n⊢ prehaar (↑K₀) U { carrier := K, isCompact' := hK ... | [
369,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_sub | [
{
"state_after": "no goals",
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600,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
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Mathlib/Data/Polynomial/Induction.lean | Polynomial.induction_on' | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type x\nk : Type y\nA : Type z\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np✝ q r : R[X]\nM : R[X] → Prop\np : R[X]\nh_add : ∀ (p q : R[X]), M p → M q → M (p + q)\nh_monomial : ∀ (n : ℕ) (a : R), M (↑(monomial n) a)\nn : ℕ\na : R\n_h : M (↑C a * X ^ n)\n⊢ M... | [
69,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/Topology/Constructions.lean | continuousAt_snd | [] | [
378,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.not_odd_iff | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ¬Odd n ↔ n % 2 = 0",
"tactic": "rw [odd_iff, mod_two_ne_one]"
}
] | [
57,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_vsub_mem_direction | [] | [
366,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_trichotomy | [] | [
672,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
669,
11
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Nat.ofAdd_mul | [] | [
1213,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_gt_31415 | [
{
"state_after": "no goals",
"state_before": "⊢ 3.1415 < π",
"tactic": "pi_lower_bound\n [11482 / 8119, 5401 / 2923, 2348 / 1197, 11367 / 5711, 25705 / 12868, 23235 / 11621]"
}
] | [
183,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | LipschitzWith.completion_map | [] | [
205,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.zero_divMonomial | [] | [
67,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/Lie/TensorProduct.lean | TensorProduct.LieModule.lie_tmul_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹⁸ : CommRing R\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\nQ : Type w₃\ninst✝¹⁷ : LieRing L\ninst✝¹⁶ : LieAlgebra R L\ninst✝¹⁵ : AddCommGroup M\ninst✝¹⁴ : Module R M\ninst✝¹³ : LieRingModule L M\ninst✝¹² : LieModule R L M\ninst✝¹¹ : AddC... | [
90,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
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